Post on 08-Sep-2018
Body segment inertial parameters of elite swimmers:
analysis using DXA and estimation of errors from
indirect estimation methods
by
Marcel Mourao Rossi
Bachelor in Sports Training
Submitted as partial requirements for the degree of Master of Science
School of Sport Science, Exercise and Health
The University of Western Australia
August 2012
DEDICATION
This thesis and any other future work or achievement is always dedicated to my parents,
Alberto M. Rossi and Sonia M.O.M. Rossi, the most dedicated, nurturing, encouraging and
supportive human beings I could have ever possibly met in life. Dad, mom, God only knows
how hard this journey has been for us and whether it will pay off after all. It’s not the most
important though, I would go through this another thousand times if necessary, as nothing in
life motivates me more to work as hard as necessary to reach for the stars (amongst which
that sky lantern with my name on that dad launched when I was born may be aloft now) than
knowing that by doing so I’ll be your pride and joy. I know I’ve chosen a road in life that does
not allow me to be with you whenever I want or need, but if after every step forward I make I
can safely picture yourselves alongside me, squeezing my shoulders and saying “Attaboy,
that’s my son!”, I’ll know the step was worthwhile indeed. I love you, endlessly.
“Mas o mundo foi rodando
Nas patas do meu cavalo
E já que um dia montei
Agora sou cavaleiro
(Laço firme e braço forte)
Num reino que não tem rei.”
Geraldo Vandré - Disparada
[iii]
ABSTRACT
The present study proposed a new method to compute body segment inertial parameters
(BSIPs) using DXA. This new approach essentially co-registers the areal density data with
grayscale images, which enables a relationship between the pixel colour intensity and the
mass recorded to be established for the referred area. BSIPs could then be calculated for
various segments. Using this method, BSIP were then measured in elite male swimmers,
elite female swimmers and young adult Caucasian males. The study then compared BSIPs
derived from the proposed technique against five previously used indirect BSIP estimation
methods across all three populations.
Ten elite male swimmers, eight elite female swimmers, and ten young adult Caucasian
males had their whole body mass calculated from the relationship found between pixel
colour intensity and areal density. The calculated masses were compared against the
criterion value obtained from the DXA scanner by percentage root mean square error
(%RMSE). Subjects were also scanned with 3D surface scans to enable mapping of key
anthropometric variables necessary for calculation of BSIPs when using the indirect
estimation methods. The mass, centre of mass (COM) and moment of inertia (MOI) about
the sagittal axis of seven body segments (head, trunk, head combined with trunk, upper arm,
forearm, thigh & shank) were computed from the proposed DXA method for each group.
Differences between participant groups were assessed using the analysis of variance
(ANOVA). When applying the five indirect estimation methods to each of the three referred
populations, errors were assessed, using the BSIPs gathered with DXA as criterion, by
calculating the %RMSE and searching for significant differences in absolute percentage
errors for all BSIPs.
Computing BSIPs using the proposed method yielded %RMSE of less than 1.5%. This
agreed with the accuracy of previous DXA BSIP estimation methods. The results also
revealed significant differences in BSIPs between participant groups. Elite female swimmers
reported significantly lower segment masses than male swimmers and untrained males.
iv
Male swimmers recorded greater inertial parameters of the trunk and upper arms than the
other two groups. Using BSIP computed from DXA as a measurement criterion, the analysis
revealed that none of the indirect methods were able to accurately estimate BSIPs in any of
the participant groups, as large errors were observed for each method. Therefore, caution
should be taken when computing BSIPs for elite swimmers using these indirect methods.
Finally, this work demonstrated that DXA can be used to accurately estimate BSIPs, at least
in the frontal plane. With further development, DXA has the potential to provide a full set of
BSIP in all dimensions.
[v]
TABLE OF CONTENTS
Dedication ................................................................................................................................ 2
Abstract ....................................................................................................................................iii
Table of Contents ..................................................................................................................... v
List of Figures ......................................................................................................................... viii
List of Tables ............................................................................................................................ x
Acknowledgements ................................................................................................................xiv
Chapter 1 ........................................................................................................................... 16
Introduction to the Problem .................................................................................................... 16
1.1 Introduction ................................................................................................................. 16
1.2 Statement of the Problem .......................................................................................... 18
1.3 Significance of the Study ............................................................................................ 19
1.4 Research Hypotheses ................................................................................................ 20
1.5 Delimitations and Limitations ..................................................................................... 20
1.5.1 Delimitations ....................................................................................................... 20
1.5.2 Limitations .......................................................................................................... 20
1.6 Definition of Terms ..................................................................................................... 21
1.7 List of Abbreviations ................................................................................................... 22
Chapter 2 ........................................................................................................................... 23
Literature Review ................................................................................................................... 23
2.1 Introduction ................................................................................................................. 23
2.2 Direct Estimation Methods ......................................................................................... 25
2.3 Indirect Estimation Methods ....................................................................................... 31
2.3.1 The Modified Chandler Method .......................................................................... 32
2.3.2 The Yeadon Method ........................................................................................... 33
2.3.3 The Zatsiorsky Simple Regression Method ....................................................... 34
2.3.4 The Zatsiorsky Multiple Regression Method ...................................................... 34
2.3.5 The Zatsiorsky Geometric Method ..................................................................... 35
[vi]
2.4 The DXA Method ........................................................................................................ 36
2.5 Influence of different methods on dynamic analyses ................................................. 39
2.6 Summary .................................................................................................................... 42
Chapter 3 ........................................................................................................................... 43
Methods and Procedures ....................................................................................................... 43
3.1 Participants ................................................................................................................. 43
3.2 Indirect BSIP estimation methods .............................................................................. 44
3.3 Data acquisition Protocol ........................................................................................... 45
3.3.1 Dual-Energy X-Ray Absorptiometry (DXA) ........................................................ 46
3.3.2 Body laser scan .................................................................................................. 47
3.3.3 Anthropometry .................................................................................................... 49
3.4 Biomechanical model ................................................................................................. 50
3.5 Data Processing ......................................................................................................... 50
3.6 Data Analysis ............................................................................................................. 63
Chapter 4 ........................................................................................................................... 64
Results ................................................................................................................................... 64
Chapter 5 ........................................................................................................................... 77
Discussion .............................................................................................................................. 77
Chapter 6 ........................................................................................................................... 82
Summary Conclusion & Recommendations for Future Studies ............................................. 82
6.1 Summary .................................................................................................................... 82
6.2 Conclusion .................................................................................................................. 84
6.3 Recommendations for Future Studies ....................................................................... 84
REferences............................................................................................................................. 85
Appendix A ......................................................................................................................... 93
Consent Form ........................................................................................................................ 93
Consent Form ....................................................................................................................... 94
Appendix B: ........................................................................................................................ 95
Indirect Estimation Methods ................................................................................................... 95
Cadaveric-based geometric method (modified Yeadon (1990)): ........................................... 96
Cadaveric-based regression equation method (modified Chandler et al. (1975)) ............... 105
Gamma-ray-based simple regression method (Zatsiorsky and Seluyanov, 1983) .............. 107
[vii]
Gamma-ray-based multiple regression method (Zatsiorsky and Seluyanov, 1985) ............ 110
Gamma-ray-based geometric method (Zatsiorsky et al., 1990) .......................................... 115
Appendix C: ..................................................................................................................... 118
Anthropometric measures .................................................................................................... 118
Appendix D: ..................................................................................................................... 127
Biomechanical Model ........................................................................................................... 127
Appendix E ....................................................................................................................... 135
Matlab Codes ....................................................................................................................... 135
Convert_dxa_images.m ....................................................................................................... 136
segment_body.m .................................................................................................................. 140
[viii]
LIST OF FIGURES
Figure 3.1: The GE Lunar DXA scanner ................................................................................ 46
Figure 3.2: The Artec LTM
3D scanner. .................................................................................. 47
Figure 3.3: The 3D scan of the participant after the scanning procedure (before post-
process).................................................................................................................................. 49
Figure 3.4: Screenshot of the enCORE® software when the day pass code is used, showing
the two BMD and TISSUE images derived from the respective matrixes. When the mouse is
placed on a given area (red circle), the mass and the coordinates the local mass element
pointed by the arrow are shown on the bottom of the screen (red ellypses). ........................ 52
Figure 3.5: The relationship between the mass element (red rectangle) and the pixels of the
bitmap image; often the mass element contained pixels from the outside of the body or its
borders were not aligned with the pixels. ............................................................................... 54
Figure 3.6: Grayscale images of the BMD and TISSUE compartment matrices created by
the enCORE® software (right and middle, respectively), and the summation of both images.
Red and blue dots correspond to the locations of the mass elements used for the first and
second matrices, respectively. ............................................................................................... 56
Figure 3.7: Binary images of the BMD, TISSUE and whole body mass created to eliminate
noise outside the region of interest. All black pixels have nil mass value. ............................ 57
Figure 3.8: 2D representation of the I_BMD_mass, I_TISSUE_mass, and I_mass_total
matrices (right, middle and left images, respectively) using a colour scale to show the
density of the mass pixels. ..................................................................................................... 58
Figure 3.9: A 3D representation of the I_mass_total matrix. ................................................ 59
Figure 3.10: Representation of the 25 points used to segment the body using the
segment_whole_body.m function. ......................................................................................... 61
Figure 3.11: Output of the segment_whole_body.m function, containing the segmentation
planes in the whole body (left figure, red dashed line), the clicked points that defined the
geometric figure used as frontier to delimit the segments (red dots), and the segment COM
positions. ................................................................................................................................ 62
[ix]
Figure 4.1: Mean Absolute Percentage Error (MAPE) for segment mass (Kg) of the Chandler
(C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and
Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult
Caucasian males (Normal), Male swimmers and Female swimmers. ................................... 73
Figure 4.2: Mean Absolute Percentage Error (MAPE) for segment centre of mass position in
the longitudinal axis from the distal end point (COM, cm) of the Chandler (C), Yeadon (Y),
Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky
geometric (Z3) estimation methods against DXA, observed for young adult Caucasian males
(Normal), Male swimmers and Female swimmers. ................................................................ 74
Figure 4.3: Mean Absolute Percentage Error (MAPE) for segment principal moment of
inertia about the sagittal axis (Ixx, Kg�cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky
simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3)
estimation methods against DXA, observed for young adult Caucasian males (Normal), Male
swimmers and Female swimmers. ......................................................................................... 75
Figure A1: The stadium-shape section (left) and the stadium frustum (right) (Yeadon, 1990).
............................................................................................................................................... 96
Figure A2: Representation of the solids for the modified Yeadon’s model. ......................... 100
[x]
LIST OF TABLES
Table 3.1. Mean (SD) of the age (years), height (cm) and weight (Kg) of young adult
Caucasian males in the cohort of the present study (DXA, n=10) and in the studies of
Zatsiorsky et al. (1983, 1985, 1990; n=100) .......................................................................... 43
Table 3.2: Glass marble naming and locations ...................................................................... 46
Table 3.3: 3D scan marker naming convention and locations ............................................... 48
Table 4.1: Minimum error (Emin, Kg), Maximum error (Emin, Kg), Mean Absolute Percentage
Error (MAPE, %) and Percent Root Mean Square (%RMSE) for the bone mineral, tissue and
whole body masses calculated from the respective images. ................................................. 64
Table 4.2: Mean (SD) segment masses (kg) of young adult Caucasian males tested in the
present study (DXA, n=10) and the young adult Caucasian males from Zatsiorsky studies
(Zatsiorsky, n=100). ............................................................................................................... 65
Table 4.3: Mean (SD) segment mass (Kg) calculated for adult Caucasian male (n = 10),
male swimmers (n = 10) and female swimmers (n = 8) using the Chandler model (C),
Yeadon model (Y), Zatsiorsky simple regression model (Z1), Zatsiorsky multiple regression
model (Z2), Zatsiorsky geometric model (Z3,) and the proposed estimation protocol using
DXA (DXA). ............................................................................................................................ 66
Table 4.4: Mean (SD) distance of the centre of mass position in the longitudinal axis from the
distal end point (COM, cm) of adult Caucasian male (n = 10), male swimmers (n = 10) and
female swimmers(n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple
regression (Z1), Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA
estimation methods. ............................................................................................................... 67
Table 4.5: Mean (SD) values for segment principal moment of inertia about the sagittal axis
(Ixx, Kg�cm2) of adult Caucasian male (n = 10), male swimmers (n = 10) and female
swimmers (n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression
(Z1), Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation
methods.................................................................................................................................. 68
Table 4.6: Percentage Root Mean Square Error (%RMSE) for segment mass (Kg) of the
Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression
(Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult
Caucasian male (n = 10), male swimmers (n = 10) and female swimmers (n = 8). .............. 70
[xi]
Table 4.7: Percentage Root Mean Square Error (%RMSE) for segment centre of mass
position in the longitudinal axis from the distal end point (COM, cm) of the Chandler (C),
Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and
Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult Caucasian
male (n = 10), male swimmers (n = 10) and female swimmers (n = 8). ................................ 71
Table 4.8: Percentage Root Mean Square Error (%RMSE) for segment principal moment of
inertia about the sagittal axis (Ixx, Kg�cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky
simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3)
estimation methods against DXA, observed for adult Caucasian male (n = 10), male
swimmers (n = 10) and female swimmers (n = 8). ................................................................. 72
Table A1: Labelling of the solids forming each of the 16 segments, with the respective type
of solid used and density (Kg*l-1
) ........................................................................................... 97
Table A2: Labelling of the sections as bottom (b) or top (t) base of the solids, anthropometric
measures used to determine the parameters r and t for each section and the position relative
to the longitudinal axes of the referred segments .................................................................. 98
Table A3: mass (Kg) and principal moments of inertia (Kg*cm2) equations and average
centre of mass position obtained for the modified study of Chandler et al. (1975).............. 106
Table A4: modified predictors for the non-linear equations for segmental moments of inertia
............................................................................................................................................. 107
Table A5: Coefficients of the linear regression equations to determine the inertial parameters
of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is
the body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position
on the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes. ............................................................................................................. 108
Table A6: Coefficients of the linear regression equations to determine the inertial parameters
of the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the
body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on
the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes. ............................................................................................................. 109
Table A7: Coefficients of the linear regression equations to determine the inertial parameters
of the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the
body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on
the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes. ............................................................................................................. 110
[xii]
Table A8: Coefficients of the linear regression equations to determine the inertial parameters
of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3 +
B4X4, where X1, X2, X3 and X4 are the most predictive anthropometric measures for each
segment and Y is segment’s mass (M), centre of mass position on the longitudinal axis
(HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.
............................................................................................................................................. 111
Table A9: Coefficients of the linear regression equations to determine the inertial parameters
of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3,
where X1, X2 and X3 are the most predictive anthropometric measures for each segment and
Y is segment’s mass (M), centre of mass position on the longitudinal axis (HCM), or moments
of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes. ............................. 112
Table A10: Coefficients of the linear regression equations to determine the inertial
parameters of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 +
B3X3, where X1, X2 and X3 are the most predictive anthropometric measures for each
segment and Y is segment’s mass (M), centre of mass position on the longitudinal axis
(HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.
............................................................................................................................................. 113
Table A11: The most predictable anthropometric measures for each segment to be used in
the multiple linear equations for inertial parameters of the head and trunk segments. ....... 114
Table A12: The most predictable anthropometric measures for each segment to be used in
the multiple linear equations for inertial parameters of the head and trunk segments. ....... 114
Table A13: The most predictable anthropometric measures for each segment to be used in
the multiple linear equations for inertial parameters of the head and trunk segments. ....... 114
Table A14: Anthropometric lengths and girths used to create the geometrical model of the
subject and determine the inertial parameters. The coefficient KB is used to multiply the
anthropometric length to obtain the biomechanical length. ................................................. 115
Table A15: Segment mass coefficients (KM), and the moments of inertia coefficients relative
to the sagittal (KX), longitudinal (KY) and transverse (KZ) axes. ........................................... 117
Table A16: Virtual points created ......................................................................................... 128
Table A17: End points of all segments of the biomechanical model ................................... 129
[xiii]
[xiv]
ACKNOWLEDGEMENTS
As the road to complete my thesis has finally come to its end, I cannot help thinking of those
who had a very meaningful role in this journey. Thus, I would like to express my deep
gratitude to all of you, for all the support, guidance, encouragement, friendship, and (why
not?) criticism. Each of you can claim a little piece of this work!!
To my dear family, the first ones ever to believe in me and in my dreams, for all this years by
my side. Here I am, and wouldn’t be without you. Thanks mom, dad, Andrea, Bruce, Mike,
Aunt Ana, Uncle Antonio, grandma, always in my heart.
To all the great Brazilian friends that never let the distance fade our bond away, who always
ensured I could count on them wherever and whenever I needed. So many to be listed, but
not to be forgotten! Miss you a lot guys!!!
To Yes Australia, for the excellent job and assistance throughout all the process to arrive in
Australia and become an UWA student. Thanks Antonio, Thiago and Rodrigo!
To my supervisors, for all valuable feedback provided with expert knowledge and opinions.
Thank you Profs. Amar El-Sallam, Brian Blanksby, Andrew Lyttle and Nat Benjanuvatra,
your expertise and experience were deeply appreciated and helped me improve as an
academic.
To all the participants, who volunteered and handled the data collection with such good
mood and patience. Thank you swimmers, UWA students and cricket lads!
To all the academics, who helped me so much and allowed me to learn a bit from their
expertise in the area. Thank you Profs Ricardo Barros, Cesar Montagner, Jacque Alderson,
Bruce Elliott, Jim Dowling, Tim Ackland, Michael Rosemberg.
To the friends at SSEH who have helped a lot, without you it would simply not happen.
Thanks Koji, Trenton, Laurence, Christian, Fausto, Luqman, Marius, Sathis, Nev, you are
legend!
To the SSEH staff and technicians, always so kind and helpful. Thanks Inga (mother figure
#1), Margareth, Barbara, and Jarrid!
To the Uniswim staff, for all the friendship and empathy!! Thanks Suzette (mother figure #2),
Julia, Michelle, Taku, Susan (mother figure #3), Shan, Julie, Mel, and Daniel for being
alongside on the pool deck!!
[xv]
To Swimming, that tailored the man who I am and still provide me with the values to become
even better, and the courage to pursuit my dreams. Thank you so much, it is more than a
pleasure living for you!
Finally, if you feel you had a meaningful role in this journey but did not see your name listed
here, please do not get mad at me! You know, a bunch of neurons had been burned, and my
memory is not the same after this thesis. I might have forgotten to include your name here,
but not your contribution, so thank you so much _____________, and sorry for my goldfish
memory!!!
[16]
Chapter 1
INTRODUCTION TO THE PROBLEM
1.1 Introduction
Achieving accurate body segment inertial parameters (BSIPs) is important in human motion
analysis. The inertial parameters are segment mass, centre of mass (COM) and principal
moments of inertia (MOI) about the longitudinal, sagittal and transverse axes passing
through the COM; and are needed in inverse dynamic modelling to obtain kinetic information
around joints. Several BSIP estimation methods, classified as either direct (i.e., BSIPs
measured directly from cadavers or using medical imaging technology in living subjects) or
indirect (i.e., BSIPs are estimated based on specific anthropometric values) have been
proposed.
The earlier BSIP estimations in living subjects resulted from modelling direct measurements
of cadavers (Chandler et al., 1975; Clauser, McConville, and Young, 1969; Dempster,
1955). Analysis was limited to only a few cadavers who were elderly Caucasian males.
Hence, extrapolating their results to other populations, especially elite athletes, is restrictive.
Also, factors such as fluid and tissue loss in segmentation, and different properties of living
and deceased tissue, can affect the accuracy of the derived BSIP information (Durkin,
2008).
The development of medical imaging technologies such as gamma-ray scanning (Zatsiorsky
and Seluyanov, 1983; Zatsiorsky, Seluyanov, and Chugunova, 1990), computed
tomography imaging (Ackland, Henson, and Bailey, 1988; Huang and Suarez, 1983), and
magnetic resonance imaging (Cheng et al., 2000; Martin et al., 1989; Mungiole and Martin,
[17]
1990), have enabled direct measurement of BSIPs on living humans. Despite their accuracy,
they are expensive, labour intensive during data processing, not widely accessible and/or
expose subjects to high doses of radiation. Hence, they are not widely used.
Indirect methods estimate BSIPs based on the relationship between anthropometric
variables and the desired inertial parameters. As a subject’s anthropometry can be gathered
quickly, at minimal cost, free of radiation, and without the need of expensive equipment and
facilities, indirect methods are used more than direct estimations. Indirect methods are
classified into regression equations which use anthropometric data to predict the BSIPs
(Chandler et al., 1975; Dempster, 1955; Durkin and Dowling, 2003; Zatsiorsky and
Seluyanov, 1983, 1985); and geometric models which create and use geometric figure
templates for the segments from the anthropometry. Thus, the BSIPs are calculated using
geometric formulae (Durkin and Dowling, 2006; Hanavan Jr, 1964; Yeadon, 1990; Zatsiorsky
et al., 1990). Despite the advantages, the indirect estimations found large errors when
applied to a population having different physical characteristics from those for whom the
methods were devised; and did not provide accurate subject-specific BSIP data (Durkin and
Dowling, 2003). Therefore, it could be expected that indirect estimation methods are
unsuitable for computing BSIPs in elite athletes (e.g., swimmers), due to the different
anatomies of these populations (Olds and Tomkinson, 2009). However, this hypothesis
remains untested.
Dual-energy X-ray absorptiometry (DXA) technology is used mainly to determine bone
mineral density and body composition in vivo (Ellis, 2000; Fuller, Laskey, and Elia, 1992;
Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990). More recently, it has been used to
estimate segment mass, COM position in the frontal plane, and MOI about the sagittal axis
(Durkin, Dowling, and Andrews, 2002; Ganley and Powers, 2004a; Wicke and Dumas,
2008). Using DXA is accurate, non-invasive, costs less, emits lower radiation exposure, and
requires less time for each analysis than the gamma-ray scanning and other imaging
methods (Durkin et al., 2002; Ganley and Powers, 2004b; Wicke and Dumas, 2008).
Therefore, the purpose of this project was to investigate the validity of five currently used
BSIP estimation methods by comparing the resultant BSIPs of three unique participant
[18]
groups to those derived from the newly proposed direct DXA method. The sample groups
were male and female elite swimmers, and 10 healthy, young adult males who were
anthropometrically similar to those examined by Zatsiorsky and colleagues (Zatsiorsky and
Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).
1.2 Statement of the Problem
The aim of this study was to examine the validity of BSIPs calculated from five regularly
used indirect estimation techniques by comparing them against BSIPs gathered using the
propose DXA method in elite swimmers (10 males and 8 females); and a group of 10 healthy
young adult Caucasian males who were selected to match subjects of Zatsiorsky et al.
(Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1985; Zatsiorsky et al., 1990).
More specifically, a series of studies will be conducted to:
• Determine whether the BSIPs from the DXA method devised for this study were as
accurate as other methods reporting DXA findings (Durkin et al., 2002; Ganley and
Powers, 2004a; Wicke and Dumas, 2008);
• Determine whether there were significant differences in BSIPs between elite male
swimmers, elite female swimmers and young adult Caucasian males;
• Examine 5 different indirect BSIP estimation models with similar segmentation
protocols to compare with the new DXA method. They are:
1) The Modified Chandler method: used simple linear relationship between the
whole body weight and the segment masses, the COM position as a fixed
proportion of the segment’s length (Chandler et al., 1975), and the non-linear
equations from Yeadon and Morlock (1989) were used to calculate the MOI
about the sagittal axis (Ixx).
2) The Yeadon method is a geometric method using cylindrical and stadium-
shaped solids to represent body segments (Yeadon, 1990). To calculate BSIPs,
the geometrical representations are assigned a density value based on the
findings of Dempster (Dempster, 1955). Small adaptations to the geometric
figures were made to ensure whenever possible that the body could be
[19]
segmented the same way as in other estimation models. Thus, the number of
anthropometric measurement is minimised.
3) The Zatsiorsky Simple Regression Method (1983) (Z1) only uses the whole
body mass and height as predictors for all BSIPs.
4) The Zatsiorsky Multiple Regression Model (1985) (Z2) uses a set of up to 4
specific anthropometric data for each segment as predictors in linear equations.
5) The Zatsiorsky Geometrical Model (1990) (Z3) assumes each segment as a
circular cylinder and uses a segment-specific, quasi-density value calculated to
minimise the difference between the cylinder and the real segment volumes.
• Compute the errors associated with each of the previously used indirect BSIP
estimation methods when applied to elite male and female swimmers, by means of
root mean square error;
• Determine whether significant differences occur in absolute errors of indirect BSIP
estimation methods; when applied to elite male swimmers, elite female swimmers,
and young adult Caucasian males;
1.3 Significance of the Study
There is a paucity of literature investigating the validity of indirect BSIP estimation methods
drawn from specific populations, especially from elite athletes. Sports analyses demand
great precision, particularly at the elite level where .01 s or miniscule technique alterations
can be the difference between winning and losing. Therefore, they must be highly valid and
accurate when assessing athletes’ performances. A lack of accuracy in determining BSIPs
may jeopardise an analysis and render it useless.
This study introduced a new approach that has the potential for development for extraction
of accurate and subject specific BSIPs. The proposed techniques addressed, in part, some
the limitations associated with the other indirect methods. This study was the first to quantify
errors associated with using indirect BSIP estimation methods for elite athletes. The
outcomes of this study may assist in future development of a full three-dimensional BSIP
measurement technique.
[20]
1.4 Research Hypotheses
• There would be significant differences in the BSIPs between the three groups (elite
male swimmers x elite female swimmers x Caucasian males).
• Errors associated with each of the different indirect estimation methods would vary
with different participant groups, particularly those with different anthropometric
profile to the samples used in their original development. Hence, there would be a
significant participant groups by methods interaction in BSIP estimation errors.
• Errors associated with indirect BSIP methods would be greater in specialised
populations (elite male & female swimmers) than adult Caucasian males.
Currently, the magnitude of such inaccuracies has not been explored for an elite
swimmer population.
1.5 Delimitations and Limitations
1.5.1 Delimitations
• Competitive swimmers participants were limited to athletes who had achieved at
least one qualifying standard for entry into the Australian Championships from
swimming clubs within the Perth metropolitan area of Western Australia (10 males &
8 females).
• The ten young, healthy, adult Caucasian males participants were required to have a
similar anthropometric profile to the cohort used by Zatsiorsky et al. (Zatsiorsky and
Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).
1.5.2 Limitations
• Currently, one cannot definitively determine the validity of the new DXA direct BSIP
estimations, because there are no true criterion measures of the inertial parameters
in vivo (Mungiole and Martin, 1990). Thus, its assessment must be based on
[21]
comparisons with other estimation procedures and the sensitivity of the inertial
parameters to those methods.
• The study did not attempt to validate the new DXA direct estimation method in vitro,
which could provide greater insight regarding its effectiveness. But, this in vitro
approach should be viewed with caution, as errors in the criteria measures were
also reported (Dowling, Durkin, and Andrews, 2006).
1.6 Definition of Terms
• Body segment inertial parameters: measures of the body segment’s resistance to a
change in its linear and angular velocity.
• Principal Moments of Inertia: moments of inertia about the principal axes of the
body.
• Direct body segment inertial parameter estimation methods: methods that enable
each of the inertial parameters to be measured directly.
• Indirect body segment inertial parameter estimation methods: mathematical models
that use other anthropometric measures and their relationship with the inertial
parameters to compute the latter.
• Pixel: the smallest element of a picture represented on the screen.
• Areal density: the mass per unit area of a two-dimensional object.
• Mass element: the rectangular area unit to which a mass value is addressed during
the DXA scan.
• Pixel element: the image pixel with a singular mass value associated after the co-
registration of the areal density matrix data from the DXA scan with the grayscale
image.
[22]
1.7 List of Abbreviations
• DXA: Dual Energy X-Ray Absorptiometry.
• COM: centre of mass.
• MOI: principal moment of inertia.
• Ixx: principal moment of inertia about the sagittal axis.
• Iyy: principal moment of inertia about the longitudinal axis.
• Izz: principal moment of inertia about the transverse axis.
• %RMSE: percentage root mean square error.
• MAPE: mean absolute percentage error.
• ANOVA: analysis of variance.
• SPANOVA: split plot analysis of variance.
[23]
Chapter 2
LITERATURE REVIEW
2.1 Introduction
Biomechanical analyses of human motion use inverse and forward dynamic analyses as
standard tools. Both techniques rely on body segment inertial parameter (BSIP) data such
as the mass, position of the centre of mass (COM) relative to the segment’s length; and the
principal moments of inertia (MOIs) about axes passing through the COM, as input to
calculate the resultant joint forces and moments.
Several techniques were developed to calculate BSIPs. Initially, cadaver specimens were
used to obtain BSIPs directly and, from these, predictive equations were devised and
translated to data from living subjects (Chandler et al., 1975; Clauser et al., 1969; Dempster,
1955). Direct estimation techniques for living subjects also were devised (Drillis and Contini,
1964, 1966), including the use of medical imaging techniques (Durkin et al., 2002; Huang
and Suarez, 1983; Martin et al., 1989; Zatsiorsky, 1983) being the most accurate and
reliable means to obtain subject-specific BSIP data (Durkin, 2008).
As access to the costly instrumentation required for these methods is restrictive, indirect
estimation methods such as calculating BSIPs from subject anthropometry are more
commonly used. Indirect estimation methods extrapolate the relationship between some
anthropometric measures and BSIPs computed from cadavers or living subjects (Durkin and
Dowling, 2003; Zatsiorsky and Seluyanov, 1985); or some modelling techniques are applied
(Durkin and Dowling, 2006; Hanavan Jr, 1964; Zatsiorsky et al., 1990) to the subjects being
analysed. Five of these techniques yield all BSIPs for all body segments and are used
[24]
regularly. Of these five, two were developed from cadaver data (Chandler et al., 1975;
Yeadon, 1990) and three used data collected from living subjects (Zatsiorsky, 1983;
Zatsiorsky and Seluyanov, 1985; Zatsiorsky et al., 1990).
The Modified Chandler Method used simple linear relationship between the whole body
weight and the segment masses, a fixed ratio between the distance from the COM to the
proximal joint relative to the segment’s longitudinal axis (Chandler et al., 1975), and non-
linear equations to compute MOI from measures of segment’s length, width and breadth
(Yeadon and Morlock, 1989).
The Yeadon Method is a geometric method that uses cylindrical and stadium-shaped solids
to represent body segments (Yeadon, 1990). To calculate BSIPs, the geometric
representations were assigned a density value based on the findings of Dempster
(Dempster, 1955). Small adaptations to the geometric figures were made to ensure
whenever possible that the body could be segmented in the same manner as in the other
estimation models. Hence, the number of anthropometric measurements is minimised.
The Zatsiorsky Simple Regression Model (Zatsiorsky and Seluyanov, 1983), the
Zatsiorsky Multiple Regression Model (Zatsiorsky and Seluyanov, 1985) and the Zatsiorsky
Geometrical Model (Zatsiorsky et al., 1990) were developed from measurements collected
from the same 100 adult Caucasian male subjects. The Zatsiorsky Simple Regression
Method (Z1) only uses the whole body mass and height as predictors for all BSIPs.
The Zatsiorsky Multiple Regression Method (Z2) uses a set of specific anthropometric
data (up to 4 measures) for each segment as predictors in linear equations.
The Zatsiorsky Geometrical Method (Z3) assumes each segment as a circular cylinder
and uses a segment-specific quasi-density value, calculated to minimise the difference
between the cylinder and the real segment volumes. A series of kinanthropometric
measures was carried out for all subjects according to the specifications of each study.
However, these techniques might not yield sufficiently accurate results, or be capable of
accounting for morphological differences between subjects. Given the importance of
[25]
accurate BSIP information, the limitations of the previous direct methods must be overcome
so BSIPs of individual subjects can be assessed directly.
2.2 Direct Estimation Methods
Direct BSIPs result from methods enabling direct estimation of the mass, COM position and
MOIs (or the radii of gyration, as the moments of inertia are proportional to the segment’s
mass) of previously defined body segments. They are classified as in vitro (cadaveric) or in
vivo (living subjects), and used to provide individual test scores or to calculate measurement
averages and variations of data drawn from specific populations, which can then be
extrapolated to others in similar populations.
The three most referenced research papers investigating human BSIPs using cadaver
samples were performed at the Wright Paterson USA Air Force Base. The cadavers used by
Dempster (1955) were of eight male war veterans aged 51-83 years old. The limbs were
separated at each of the main joints; and the trunk was divided into neck, shoulder, thorax
and abdomino-pelvis segments. The study provided mass, COM position, volume, density
and MOI about the transverse axis of the segments. The second study was of 13 adult male
cadavers each dissected into 14 segments to provide weight, volume and COM positions
(Clauser et al., 1969). Also, the cadavers were dissected to provide the densities of muscle
(1.08 g/cm3), fat (0.96 g/cm
3), cortical bone (1.8 g/cm
3) and cancellous bone (1.1 g/cm
3)
tissues. Thirdly, Chandler et al. (1975) used six adult male cadavers to obtain mass, COM
position, and the principal MOIs about the three orthogonal axes of the 14 segments (head,
trunk, upper arms, forearms, hands, thighs, shanks & feet).
Direct BSIP estimations from cadavers is the only way to physically separate the body
segments and gather inertial parameters using proper tools such as a balance to measure
mass of a segment. Therefore, in vitro direct BSIP estimations often are used to validate
other estimation procedures, especially in vivo direct methods. Yet, the values obtained,
depend upon the accuracy and reliability of how the measurements were taken; so, results
should be used with caution. For example, Dowling, Durkin and Andrews (2006) studied the
uncertainty/error of the pendulum model used to calculate the moments of inertia of cadaver
[26]
segments, and found them to be subject to errors in the period of oscillation. They also
demonstrated that the uncertainty was reduced to < 3% when the suspension axis was
positioned at a distance from the COM equal to the radius of gyration, rather than at the
proximal site as in previous studies.
Although BSIPs of cadavers can be calculated directly, in vitro methods have limitations to
be considered, such as availability of cadavers, the complexity, cost, time required for the
procedures, and difficulty in obtaining specimens from specific populations. The loss of fluid
and tissue during the segmentation process also should be accounted for as a source of
error. Some procedures have used frozen specimens to avoid this problem, but freezing can
alter the volume of the segment and, subsequently, the calculated moments of inertia
(Durkin, 2008).
Hence, results from a few Caucasian elderly males cannot be extrapolated to other groups
with confidence (Dempster, 1955). Also, pooling data does not account for variations in
segmentation protocols (Durkin, 2008); any differences in tissue properties between living
and dead subjects; or whether the preservation technique influences BSIPs (Pearsall, Reid,
and Livingston, 1996; Pearsall and Reid, 1994). For example, Pearsall et al. (1996) stated
that in-vitro lung tissue density was at least double that of in vivo. This could help to explain
the overestimated trunk mass when cadavers are compared with living subjects. Hence,
extrapolating values from cadaver studies to living subjects, regardless of the approach used
(see indirect BSIP estimation methods), may not be sufficiently accurate.
To overcome the limitations of in vitro methods for estimating BSIP of living subjects, non-
invasive in vivo approaches such as water immersion, photogrammetry, weighing in various
positions, quick release and compound pendulum (Contini, 1972; Drillis and Contini, 1964;
Durkin, 2008; Zatsiorsky et al., 1990) were proposed to enable computation of subject-
specific BSIP data. Water immersion was used originally to measure segment volumes of
either living or cadaver subjects (Clauser et al., 1969; Drillis and Contini, 1964). When
assuming that density is uniform across segments, and its value is known, water immersion
could calculate COM position and MOIs of the segment in vivo (Drillis and Contini, 1964;
Zatsiorsky et al., 1990). However, Drillis and Contini (1966) only used this method to
[27]
estimate BSIPs of the limbs as they were unable to overcome the difficulties in measuring
trunk and head BSIPs with this method. Photogrammetry can obtain volumes of irregularly
shaped segments by using one (mono-photogrammetry) or two cameras (stereo-
photogrammetry). The principle resembles aerial photos of a terrain with applied contour
levels. The volume of each slice (i.e. the portion between successive contour levels) is
calculated with a polar planimeter on the photograph. Thus, the sum of the volume of every
slice equals the volume of the segment (Drillis and Contini, 1964). Then, the same
assumptions used for water immersion regarding the density properties of the segments, are
applied to calculate the BSIP values. Weighing in changing positions is limited in that it
does not allow the calculation of all BSIPs. It only enables one to calculate either the
segment’s COM position when segment’s mass is known, or the segment’s mass when the
segment’s COM position is known (Pataky, Zatsiorsky, and Challis, 2003). The subject lies
on a force plate and moves one segment at a time to adopt a number of positions. For each
position, the centre of pressure displacement is recorded and used to estimate the mass, or
COM position, of the moving segment. According to Pataky, Zatsiorsky and Challis (2003),
it can be assumed that the COM position varies little between individuals. Moreover, when
used in association with either water immersion or photogrammetry (i.e. assuming uniform
density for the segments), it could provide more accurate values of the segment masses for
a single individual without relying on cadaver data (Drillis and Contini, 1964; Pataky et al.,
2003). The quick release method is used exclusively to obtain the MOIs of the segments
(Drillis and Contini, 1964; Zatsiorsky et al., 1990). It is based on Newton’s Law of Rotation
which states that- “the angular acceleration of a body is proportional to the torque applied to
it, and the MOI is the proportionality constant”. Hence, one applies a known force at a given
distance from the segment’s proximal joint, and measures the angular acceleration of the
segment by optical or electrical means to obtain the MOI (Drillis and Contini, 1964).
Calculating MOI in this way does not assume that the density of the segment is uniform;
rather, it assumes no friction at the proximal joint and no antagonistic muscular tension
during the procedure (Zatsiorsky et al., 1990). The compound pendulum method enables
calculation of the MOIs and the COM position of a segment (Drillis and Contini, 1964). Two
approaches can be adopted. Firstly, the segment can be treated as a compound pendulum
[28]
oscillating about its proximal joint in a set of trials that includes oscillation of the segment
alone, or with known weights attached at known positions. The second approach uses a
plaster model of the segment that swings about a fixed point. While both approaches
assume no muscular action or friction at the joints (Zatsiorsky et al., 1990), the first approach
has the advantage of allowing BSIPs to be calculated without assuming that the segment
has a uniform density. On the other hand, the second approach assumes uniform density of
the segment, and overlaps the joint properties and muscle action issues.
Although these in vivo methods provide individual values for BSIPs and are non-invasive,
the non-invasive component requires researchers to make some assumptions that could
jeopardise the accuracy of the results. The most common is assuming uniform density of the
body segment. Ackland, Henson and Bailey (1988) demonstrated marked variations in
cross-section density of the human leg along its length. But, they also found it contributed
less for inaccuracies in MOI measurements than estimations of a segment’s volume. While
assuming uniform density may not significantly influence the BSIP accuracy for the limbs,
this is not so for the trunk segment, where discrepancies were found between the centre of
volume and the centre of mass (Pearsall et al., 1996). When assuming uniform density, the
calculated BSIPs of a living person could be subject to errors from differences in body
composition and mass distribution, between the subject and the specimen used in the in
vitro study; and/or the possible differences between living and dead tissues properties
(Durkin, 2008; Mungiole and Martin, 1990; Pearsall et al., 1996; Pearsall and Reid, 1994).
The quick release and compounding-pendulum segment methods are the only ones not
assuming uniform density. However, their accuracy is compromised due to assuming
frictionless joints and zero muscular tension. Drillis and Contini (1966) combined the five
methods, trying to provide BSIP values for individuals without relying on cadaver data.
However, they noted that the accuracy of results still depends upon the assumptions
associated with each method. Also, to subject research participants through all of these
methods to obtain individual BSIPs is highly time consuming and not practical.
More recently, imaging methods, such as gamma-ray scanning (Zatsiorsky, 1983; Zatsiorsky
and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), computerised tomography (CT)
[29]
(Ackland et al., 1988; Henson, Ackland, and Fox, 1987; Huang and Suarez, 1983; Pearsall
et al., 1996), magnetic resonance imaging (MRI) (Cheng et al., 2000; Martin et al., 1989;
Mungiole and Martin, 1990) have been explored as tools to directly obtain BSIPs.
The first BSIP study using a gamma-ray mass scan was based on the gamma-radiation
beam losing energy when it passes through a material layer (Zatsiorsky and Seluyanov,
1983; Zatsiorsky et al., 1990). The subject lies on a table and is scanned by an emitter
above, and a collimated detector below, the table. The output is the surface density (i.e.
mass per surface unit, expressed as g/cm2). In theory, when the surface density is the sole
output, it only allows an estimation of a segment’s mass, the 2D coordinates of COM (in the
frontal plane) and the MOI around the antero-posterior axis (Durkin et al., 2002; Wicke and
Dumas, 2008). To obtain COM position in the antero-posterior direction, and the MOIs
around the longitudinal and transverse axes, Zatsiorsky and Seluyanov (1983) adopted an
average body density of 1 g/cm3. They integrated this density value with the mass of every
finite surface area unit (pixel, with rectangular shape) to reconstruct the volume (height),
known as parallelpiped, for each pixel. Therefore, the whole body volume was divided into
several parallelepipeds with known dimensions and uniform density (Zatsiorsky et al., 1990).
Using this technique, they collected BSIPs from 100 Caucasian men, mostly college
students. The study provided means and standard deviations for mass; positions of COM
over the longitudinal axis; and the radii of gyration about the three axes for each of the
following segments: feet, shanks, thighs, hands, forearms, upper arms, lower torso, middle
torso, upper torso, and head (with neck). These data formed the basis for several other
studies to develop indirect BSIP estimation models (De Leva, 1996; Zatsiorsky and
Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).
While gamma-ray scanning could provide subject-specific BSIP data, it has some limitations.
Because gamma-rays are ionising radiation, they are biologically hazardous with scanning
exposing subjects to a relatively high dose of radiation (Durkin, 2008; Martin et al., 1989;
Mungiole and Martin, 1990). Secondly, it assumes uniform segment density at 1 g/cm3,
whereas densities have been shown to vary across segments of a subject, and especially
for the trunk where lungs and other internal organs lie (Pearsall et al., 1996; Wicke and
[30]
Dumas, 2010; Wicke, Dumas, and Costigan, 2008; Wicke, Dumas, and Costigan, 2009).
Tissue density is also expected to vary between subjects due to variations in body
composition and proportionality. Hence, this technique could possibly under/overestimate
the segment volume which, in turn, under/overestimate the MOIs. But, gamma ray scanning
could provide direct estimation of BSIPs with sufficient accuracy relatively simply, when
compared with the other non-imaging direct estimation methods. To date, only a few studies
have used this technique, and all come from the same research group (De Leva, 1996;
Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).
To overcome the uniform and arbitrarily-set densities for body segments, other technologies
have been used. Computerised tomography (CT) provides 3D estimations of the internal
structures of the body through a series of X-ray tomograms taken parallel to the transverse
plane, and created by computer processing. Each tomogram enables one to identify bone,
muscle and fat tissues, to each of which an empirical density is assigned to compute the
mass of the tomogram. After obtaining mass density and geometric characteristics of each
tomogram, the inertial parameters of each tomogram, regarding its thickness according to
the CT machine specifications, can be obtained. Data from the tomograms are then
combined to estimate the total segment inertial parameters (Huang and Suarez, 1983;
Pearsall et al., 1996). Therefore, CT scanning is a powerful tool for accurately estimating
density of the body tissues and their distribution throughout the various segments (Ackland
et al., 1988; Huang and Suarez, 1983; Pearsall et al., 1996). Yet, despite some advantages,
CT exposes subjects to higher doses of radiation than gamma ray scanning. Thus, that
could limit its usage to only a few body parts (Erdmann, 1997).
An alternative technology is magnetic resonance imaging (MRI). As with CT, the MRI also
yields a series of tomograms perpendicular to the longitudinal axis of the body to enable
BSIPs to be estimated. However, MRI can provide images with greater resolution than CT
(Martin et al., 1989; Mungiole and Martin, 1990) and, because it uses a large magnetic field
to generate the scanned image, there are no radiation risks. When the body is placed in a
magnetic field, the hydrogen nuclei, which are abundant in all tissues, have a specific
orientation of their magnetic moments (dipole) for a given tissue (Martin et al., 1989). A
[31]
tomogram is then created at the plane where the magnetic field passes, and the brightness
of the image is related to the orientation of the hydrogen magnetic dipole.
Both CT and MRI methods share a similar disadvantage of being labour intensive during the
data processing stage. The procedures used to estimate the inertial parameters of each
slice of the body are demanding as digitisation of every tomogram is required. The time
spent on digitising all tomograms could decrease with future advances in imaging software
that allows recognition of the tissues in the image by shape and pixel intensities (Martin et
al., 1989). Another common disadvantage of CT and MRI is that they do not directly
measure tissue density and, therefore, rely on external input. By doing so, it assumes that
tissue densities are uniform throughout the body. However, these vary across specific sites
of the body, and between subjects. It is known that tissue densities can be influenced by
fitness level, age, gender and somatotype. Moreover, different CT or MRI based research
could yield different values of segmental mass and density distribution, depending on which
tissue density values the researchers used. (e.g. tissue densities obtained from embalmed
cadavers) (Pearsall et al., 1996). Another factor affecting the practicality of using CT and
MRI techniques to obtain subject specific BSIPs, is the cost. The cost of CT and MRI scans,
in combination with the time consuming digitisation procedures, can limit the number of
subjects a research study can undertake. This is evident in the fact that the largest cohort
size using CT or MRI was 12 (Mungiole and Martin, 1990).
In brief, medical-image-based BSIP estimation methods are more accurate than non-
medical direct estimation methods, or by extrapolating in vitro values to living subjects.
However, they can be limited by costs, machine access, onerous data processing, and/or
exposure to high doses of radiation.
2.3 Indirect Estimation Methods
Indirect methods for BSIP estimations are based on the relationship between some
anthropometric variables and the desired inertial parameters. As anthropometric variables
can be gathered quickly, at minimal cost, free of radiation, and without the need of
expensive equipment and facilities, these methods have been more widely used.
[32]
Anthropometry can be used as a predictor in either linear or non-linear equations, where the
criterion is an inertial parameter of a determined segment (e.g. regression equation method).
Also, anthropometry can create a simple geometric representation of the body from which
one then assumes the inertial parameters of the geometric figures are the same of the
segments (geometric methods).
2.3.1 The Modified Chandler Method
Chandler et al. (1975) provided linear equations for determining segment mass and the
three principal MOIs. They used body mass or segmental volume as predictors, and the
COM position as a fixed ratio of the distance from the COM to the proximal joint of the
segment and the length of the segment. The equations were computed from measurements
taken from 6 elderly male cadavers. The protocol segmented the body into 14 segments
(head, trunk, upper arms, forearms, hands, thighs, shanks and feet). This was the first
cadaver study to enable full BSIP calculations of living subjects. However, the authors stated
that the equations “are given for the convenience of the reader, but, again, cannot be
considered to reliably estimate population parameters” (Chandler et al., 1975, p. 66).
Therefore, Yeadon and Morlock (1989) proposed a set of non-linear regression equations for
determining segmental MOIs , using the anthropometry and BSIP data from Chandler et al.
(1975). The authors claimed that it might be inappropriate to establish linear relationships
between dimensionally distinct quantities such as MOI (Kg�cm2) and circumference or length
(cm). Furthermore, the theoretical relationships between the three dimensions of an object
(i.e. height, depth and width) and its inertial properties (i.e. mass and the MOIs ) can be
obtained when the characteristics of density distribution are known, which enables them to
be used as a basis for non-linear equations. To validate the approach, data were compared
from the left and right limbs. That is, the right limb was used to derive the equations and the
left limbs were used for cross-validation. Comparisons with the principal MOIs were
measured with a pendulum model and reported an average standard error of 21% for the
linear equations. The average error was 13% for the non-linear equations. When
extrapolating both equations to living subjects, and using the geometric model as criteria
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(Yeadon, 1990), the average percentage residuals for the linear equation were 286%; and
just 20% for the non-linear equations.
2.3.2 The Yeadon Method
Yeadon (1990) proposed a geometric approach that fractionated the segments into solids of
circular (limbs and head) or stadium-shaped (trunk, hands and feet) cross-sections. Forty
solids were created from 95 anthropometric measures (girths, widths and distances between
each section). Here, the stadium cross-sections (a rectangle with an adjoining semicircle at
each side, so the depth equals the diameter of the semi-circle) match the real cross-
sectional areas more closely than the ellipses used previously (Hanavan Jr, 1964; Hatze,
1980; Jensen, 1978). Then, Dempster’s density values (1955) were used to calculate the
inertial parameters of each solid (uniform density). This enabled calculation of inertial
parameters for 11 segments (head + trunk, upper arms, forearms + hands, thighs, shanks
and feet). Even though the trunk was regarded as a unique segment, adoption of
representing it by five solids plus the different density values according to location in the
trunk from Dempster (1955), enabled the separation of the trunk into sub-segments (e.g.,
thorax, abdomen and pelvis). This procedure was simpler than other geometric methods
proposed by Jensen (1978) and Hatze (1980), and produced a maximum error for the total
mass of 2.3%, which was comparable to the other two methods (Hatze, 1980; Jensen,
1978).
The Yeadon Method (Yeadon, 1990), as with most of the geometric methods, relies on
assuming uniform density of the modelled segment. But, subjects from different populations
have revealed differences in segmental densities, especially when comparing athletes from
different sports, or versus a non-athletic population (Kerr and Stewart, 2009). Therefore, the
average density value obtained from studies with subjects of similar body composition, age,
gender and ethnicity should be chosen to avoid errors when using geometrical models. For
instance, Wicke and Dumas (2010) found an average density value for the lower trunk from
Dempster (1955) was overestimated when applied to their 24 male and 25 female college-
aged participants.
[34]
The geometric models vary with the complexity of the solids adopted as templates for the
limbs. Studies suggest that the more the volume of the solid resembles the actual segment,
the lower are the errors in BSIP calculations. This follows earlier findings that inaccuracies in
volume representation account more for BSIP error than the uniform density assumption
(Ackland et al., 1988; Wicke and Dumas, 2010).
2.3.3 The Zatsiorsky Simple Regression Method
Zatsiorsky and Seluyanov (1983) gathered full BSIPs from 100 young adult Caucasian
males using a gamma-ray scanner and computed individual coefficients for each BSIP in a
set of linear equations that considered whole body weight and height as predictors. The
protocol separated the body into 16 segments (head, upper trunk, middle trunk, lower trunk,
upper arms, forearms, hands, thighs, shanks and feet). Unfortunately, no information was
provided regarding the number of subjects used to devise the equations, or the number of
subjects used in the cross-validation procedure. However, results showed that, when using
only body weight and height as predictors, it is unlikely that the resultant BSIP is accurate.
This is because the formulae provided very low Pearson’s product moment correlation
coefficients, and was especially so for the segmental COM positions (r range 0.25-0.60).
Ratio-based methods use only height or body weight as sole predictors for BSIPs and are
not as accurate as regression equations that use more predictors. This is especially so if
those predictors are restricted to only the segment being analysed because they don’t
account for different proportionalities between subjects (Hatze, 1975). Also, a greater
number of predictors enable the regression equation to better account for variations within
the population from which the equations were derived.
2.3.4 The Zatsiorsky Multiple Regression Method
Multiple regression methods establish linear relationships between a given inertial parameter
and a certain quantity of independent anthropometric variables. Generally, inertial
parameters of a given segment are expected to correlate better with the anthropometry of
that segment, rather than a more global measure such as body weight. Therefore,
Zatsiorsky and Seluyanov (1985) used up to four classes of anthropometric measures (i.e.,
[35]
segment lengths, breadths, girths and diameters) as independent variables from the same
100 young adult Caucasian males analysed with the gamma-ray scanner. These
anthropometric values were derived from the segment of interest. This resulted in stronger
correlations with values gathered via gamma-ray scans than the equation with just body
weight and height as predictors. Moreover, the regression equations derived by Zatsiorsky
and Seluyanov (1985) have achieved the most accurate results when applied to a general
population (de Leva, 1994; Durkin, 2008).
However, the errors can be large when these equations are applied to populations different
from those from which the equations were derived (Durkin and Dowling, 2003). It should be
noted that, if large differences exist within any population, the regression equations also may
yield poor results, and caution is required when estimating BSIPs. The set of predictive
equations also need to acknowledge differences in age, gender, race and morphology.
(Durkin and Dowling, 2003).
2.3.5 The Zatsiorsky Geometric Method
Zatsiorsky et al. (1990) proposed a geometric model for the human body based on living
subject data analysed with a gamma-ray scanner. Each segment was regarded as a cylinder
with a circular base, and the segment’s length and girth were used to calculate the cylinder
volume. To compensate for differences between the actual volume of the segment, and the
volume of its cylindrical representation, a quasi-density value was calculated. Here, the
segment mass was divided by the volume of the representative cylinder, and then
incorporated into the equations.
Zatsiorsky et al. (1990) claimed that this geometric model can estimate the BSIPs of a
population not necessarily matching the anthropometric values found in the cohort from
whom the equations were derived. But, this assumes that the densities of all segments must
remain similar. On the other hand, the authors also noted that results for people with greater
amounts of fat tissue will be less accurate when using their proposed geometric method, and
the same might be true for a population of weightlifters with high muscle mass and low fat
levels, for example.
[36]
2.4 The DXA Method
The dual-energy X-ray absorptiometry (DXA) is the most recent medical-imaging based,
direct BSIP estimation method. It is similar to gamma-ray scanning in that it relies on the
attenuation of radiation beams passing through the body to measure its surface density. The
main difference is that DXA uses two X-ray intensities which allow the measurement of two
compartments separately. These are bone mineral and soft tissue, which includes both fat
mass and lean tissue mass (Ellis, 2000; Laskey, 1996). The mass of these two
compartments is measured at every surface unit (pixel) according to the following formulae
(Laskey, 1996):
��� � ������� � ��� ����� � �� ����� ��������� (Formula 1)
��� � ��� � �� ��������� � ��� ��������� ����� (Formula 2)
Where:
• �� ���� and ��� ����� are the ratios of attenuated and unnattenuated energies of the low and
high X-ray energies, respectively;
• ��� � ���� ������ and ��� � ���� ������ are the ratios of mass attenuation coefficients at the
low and high energies (�� and ���) for soft tissue and bone mineral, respectively.
Initially, DXA was developed to obtain the surface density of the bone minerals at the lumbar
spine, femur and forearm (Ellis, 2000). It was soon discovered that, when the fat-to-lean
tissue ratio is assumed to be constant for a given segment, DXA can estimate the total fat
mass, because the RST calculated is linearly related to the percentage of fat mass in the soft
tissue (Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990). Body composition data
obtained from DXA also has shown to be accurate and reliable (Ellis, 2000; Fuller et al.,
1992; Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990; Ogle et al., 1995; St-Onge et
[37]
al., 2004a; St-Onge et al., 2004b; Wang et al., 2004). As the attenuation coefficients of the
high energy beam are proportional to mass (Durkin et al., 2002), DXA also has been
explored as a potential tool for assessment of human BSIPs during the past decade (Durkin
and Dowling, 2006; Durkin and Dowling, 2003; Durkin et al., 2002; Durkin, Dowling, and
Scholtes, 2005; Ganley and Powers, 2004a, 2004b).
An early study using DXA to estimate BSIPs examined the relationship between the high-
energy attenuation coefficients and mass by scanning a book with known dimensions and
mass (Durkin, Dowling & Andrews, (2002). Then, a mass constant was obtained by
summing the attenuation coefficients and dividing it by the whole mass. The relationship was
validated by scanning 11 male subjects and comparing the whole body mass with the
criterion established. Their custom-built software was developed to increase the areal
resolution of the mass data and enhance the bone image. This enabled specific anatomical
landmarks to be located more accurately. The landmarks were used for segmentation of the
body so that BSIPs in the frontal plane of each segment can be calculated. The mean error
for whole body mass was 1.06% (1.32% SD) which indicated greater accuracy than gamma-
ray scanning (Zatsiorsky et al., 1990). Durkin et al. (2002) also analysed the masses, COM
positions, MOIs about COM, and longitudinal lengths of a plastic cylinder and a human
cadaver leg. To accomplish this, criterion value measures were made with a force plate, by
balancing the object on a knife-edge orthogonal to its length; and using the pendulum
technique and a tape measure, respectively. A geometric formula also was used as the
criterion for the MOI of the cylinder. When the results were compared with those criterion
values, DXA data contained less than 3.2% errors for all inertial parameters except for MOI.
The criterion value for the MOI was derived using the pendulum technique, which was
deemed inaccurate as the values from both criterion measures used for the cylinder did not
match. This was because the objects were suspended from their proximal ends, which is a
distance from the COM greater than the radius of gyration, thereby increasing the errors
(Dowling et al., 2006). Wicke and Dumas (2008) improved accuracy of DXA BSIP
estimations when using a more recent fan-beam DXA scanner that also reduced scanning
time.
[38]
Durkin and Dowling (2003) used DXA to examine the differences in BSIPs of four distinct
human populations (adult males, adult females, elderly males and elderly females). The
forearms, hands, feet, lower legs and thighs of 100 subjects representative of the four
groups were analysed with DXA to obtain the respective mass, COM position and MOI in the
frontal plane. Significant differences were found between the four groups, again indicating
that caution should be taken when applying cadaver-based values to any population.
A series of studies by Ganley and Powers (Ganley and Powers, 2004a, 2004b) also
demonstrated significant differences in BSIPs between DXA and the cadaver-based method
of Dempster (1955), regardless of whether the subjects were adults or children (aged 7-13
years). However, Ganley and Powers used a different approach from Durkin and Dowling
(2003; 2006) and Durkin et al. (Durkin and Dowling, 2006; Durkin and Dowling, 2003; Durkin
et al., 2002; Durkin et al., 2005). Ganley and Powers (2004a, 2004b) used 4 cm-thick
continuous slices as the basic mass data unit rather than smaller mass information units of
0.132 cm x 0.132 cm (Durkin et al., 2002).
Wicke et al. (Wicke and Dumas, 2008, 2010; Wicke et al., 2008; Wicke et al., 2009) also
used DXA to estimate BSIPs. They appear to be the only group to use DXA to explore the
inertial characteristics of the trunk. The trunk is the segment with the greatest variability in
density along its longitudinal axis, and inter-individual differences amongst all body
segments (Wicke et al., 2008). Comparisons between the trunk segmental, inertial
parameters gathered with DXA and other indirect estimation methods showed that the latter
had lower accuracy (errors ranging from 10% to 50%) and consistency (Wicke and Dumas,
2008; Wicke et al., 2009). Wicke and Dumas (2010) assessed the trunk segmental inertial
parameters as functions of the density and volume values. These were calculated by
combining the mass distribution profile gathered with DXA and the volumetric profile
gathered with the photogrammetric method as proposed by Jensen (1978). They found that
the inertial parameters were most sensitive to the variations in volume; and the non-uniform
density model provided more accurate results for the lower trunk, compared to when the
trunk segment was assumed to have uniform density.
[39]
In short, DXA can be a viable alternative to the gamma-ray scanner because it exposes
subjects to lower levels of radiation and appears to provide more accurate results. However,
as the scanning principle is the same for both scanners, the current development only allows
estimation of inertial parameters in the frontal plane. This limitation could be overcome by
combining DXA with other imaging methods or modelling techniques (Durkin et al., 2002).
For instance, Zatsiorsky et al. (1990) used the arbitrary value of 1cm/g3. Others have
identified density values for fat, bone mineral and lean tissue to obtained a more realistic
representation of the human body (Ganley and Powers, 2004a, 2004b). The disadvantages
of the empirical density values have been discussed above. In the studies of Durkin et al.
(Durkin and Dowling, 2006; Durkin et al., 2005), the mass distribution across limb segments
was used to create a volumetric representation from which the other moments of inertia can
be calculated. However, validation of the MOI about the transverse axis could only be
carried out for the lower leg, as the segment also was scanned with its sagittal plane parallel
to the scanning table (Durkin and Dowling, 2006). Finally, volumetric information can be
used along with the DXA output by using the photogrammetric method (Jensen, 1978) or,
more recently and accurately, the 3D body scan (Lee et al., 2009).
2.5 Influence of different methods on dynamic analyses
The sensitivity of joint kinetics to variations in BSIPs is seldom explored in solving inverse
dynamics problems. The BSIP error propagation problem is challenging given the difficulty to
establish the magnitude of the maximum error of any inertial parameter. This is so for any
given segment of any subject; and also due to the dependency of the propagated error in the
joint resultant forces and moments of a given analysed motion (Andrews and Mish, 1996).
Andrews and Mish (1996) tested two different approaches for determining the joint resultant
forces and moments due to variations in BSIPs. They simulated the rotation of a shank-plus-
foot rigid segment around the transverse axis of the knee by using the BSIP values from
Clauser et al. (1969). A BSIP error estimation was assumed of ± 5% and, even with a small
segmental acceleration, the maximum errors in knee moment were up to 12%.
[40]
Desjardins, Plamondon and Gagnon (1998) investigated two inverse dynamic models
(bottom-up and top-down), for estimating the net moment at the L5/S1 joint during lifting. It
was found that in the bottom-up approach, the result was influenced mostly by the external
forces applied (i.e., the ground reaction force). The segmental masses contributed the most
to the sensitivity of the top-down inverse dynamics. Therefore, not only is the bottom-up the
most preferred for the referred analysis, but also it is expected that open-chain activities, or
those where applied external forces cannot be accurately measured, may be more sensitive
to errors in BSIP calculations. Similar findings were observed by Lariviere and Gagnon
(1999).
The influence of the type of movement being analysed and subject characteristics in the
propagation of BSIP errors also can be verified in different velocity gaits. For instance, the
influence of BSIP in walking gait was explored in adults (Ganley and Powers, 2004b; Rao et
al., 2006) and children (Ganley and Powers, 2004a). Ganley and Powers (2004b) compared
the net joint moments in walking gaits of adults when using BSIPs derived from DXA, with
those having used cadaver data. The significant difference between the two sets of BSIPs
had little influence on the calculated moments during the stance phase where the ground
reaction forces exerted greater influence. However, during the swing phase, the inertial
values dominated the moment calculations. Similarly, Rao et al. (2006) found maximal
variation in peak flexion/extension moments at the hip during the swing phase (20%) for a
similar cohort. The BSIP estimation methods provided deviations ranging from 9% to 60%.
Ganley and Powers (2004a) also verified significant differences in BSIP estimation when
using DXA or cadaver values in a population of children ranging from 7 to 13 years old.
Conversely, the influence of different BSIP values on joint moment calculation seems to be
negligible for a group of children.
Sheets, Corazza and Andriacchi (2010) used the abovementioned method when comparing
BSIPs with the regression equations of Dempster (1955) and Clauser et al. (1969); and the
influence of different BSIPs and body mass index values on the hip and knee net moments
during a running swing phase. Given the high linear and angular accelerations of the shanks
during the swing phase, differences in shank inertial parameters had a large influence on
[41]
moment values at the knee which, in turn, also influenced the hip moment as the inverse
dynamics chain progressed upwards. They found that the BSIPs have the largest effect on
kinetic analyses in situations involving subjects with high limb masses or body mass indices;
and movements with high segment accelerations, especially at joints farther along the kinetic
chain.
Kwon (1996) analysed the influence of different sets of BSIPs on the body angular
momentum of airborne movements performed by gymnasts. The estimation methods were
derived from cadaver (Chandler et al., 1975), gamma-ray scanner (Zatsiorsky and
Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) and geometric studies (Hanavan Jr, 1964;
Yeadon, 1990). These were used in the 3D analyses of nine somersaults with full-twist,
horizontal-bar dismounts performed by three collegiate male gymnasts. This was to compute
the whole body angular momentum. The author found that the magnitude of the angular
momentum was affected by the different BSIP estimation methods. However, similar
fluctuations in the angular momentum during airborne movements were observed (i.e., no
estimation method yielded lowest fluctuations in angular momentum during the airborne
manoeuvres, as when in theory the angular momentum is meant to be constant).
In a following study, Kwon (2001) investigated the effect of the BSIP estimation method on
the accuracy of the experimental simulation of complex airborne movements. The
applicability of different methods was assessed along with the sensitivity analysis to identify
the different BSIPs, and segments responsible for inter-method differences in the simulation
accuracy. The same estimation methods were used as in(Kwon, 1996). The accuracy of the
experimental simulation was significantly affected by the different methods, largely being the
mass items, and the trunk and lower limb segments were more responsible for the variability
than other inertial parameters and segments, respectively. More importantly, the estimation
methods which better accounted for differences between subjects enabled the more
accurate simulation. In this study, the geometric models and the cadaver-based stepwise
regression methods were superior to the other methods on the accuracy of more complex
airborne movements.
[42]
Therefore, the extent to which the BSIPs can affect the accuracy of dynamic analyses
depends on the task characteristics. These could include whether it involves rapid
linear/angular movements of the segments, is an open-chain or closed-chain analysis, or the
external forces exert greater or lesser influence than the BSIPs on the kinetic calculations.
Whenever the kinetic analysis of a movement is likely to be affected by the BSIP used, one
must ensure that the estimation method resembles as closely as possible the morphological
characteristics of the segments (i.e., the volume and the mass distribution properties of the
segments) to minimise the errors when estimating the inertial properties. The greater the
ability of the estimation method to yield subject-specific BSIP data, the greater the chances
are of completing accurate dynamic analyses.
2.6 Summary
In summary, several approaches have been proposed above to determine the inertial
properties of human body segments. They can be measured directly (with medical-imaging
technologies the preferred approach) or indirectly through mathematical models devised
from certain specific groups of subjects.
This review has demonstrated that the populations previously assessed and validated using
the most common BSIP estimation methods are representative of only a few groups within
any community. Data for specific populations, by gender and activity levels and type, such
as from elite athletes, is lacking. Therefore, greater clarification is required in several sports
to ascertain the extent to which performance analyses can be affected by inaccurate BSIPs.
A first step towards this clarification is to study some commonly used methods and compare
how DXA rates with those methods for immediate use. Then, the most effective method
could be adopted until a non-medical imaging process is developed which avoids onerous
calculations, high radiation, high cost, is reliable and valid, safe and accessible.
[43]
Chapter 3
METHODS AND PROCEDURES
3.1 Participants
Twenty-eight participants were recruited for this study. Ten experienced competitive male
swimmers (age 26.17 ± 3.96 yrs, height 186.43 ± 8.67 cm, weight 81.16 ± 9.30 kg) and 8
experienced female competitive swimmers (age 21.13 ± 5.85 yrs, height 173.38 ± 6.96 cm,
weight 61.69 ± 5.47 kg) were recruited from swimming clubs in the Perth,Western Australia.
Only swimmers who had qualified for Australian National Championships were selected. In
addition, a group of 10 healthy, young adult Caucasian males were recruited from students
in the School of Sport Science, Exercise and Health at The University of Western Australia.
The latter had similar anthropometric profiles to subjects in the studies by Zatsiorsky et al.
(Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), as seen in Table 3.1.
Table 3.1. Mean (SD) of the age (years), height (cm) and weight (Kg) of young adult Caucasian
males in the cohort of the present study (DXA, n=10) and in the studies of Zatsiorsky et al.
(1983, 1985, 1990; n=100)
Cohort Age Height Weight
DXA (n=10) 22.5 (4.8) 177.2 (8.0) 74.9 (8.7)
Zatsiorsky et al.
(n=100)
23.8 (6.2) 174.1 (6.2) 73.0 (9.1)
Approval was obtained from The University of Western Australia Human Research Ethics
Committee. Information regarding the procedures and possible risks was distributed to all
participants, who completed a written informed consent form prior to testing (Appendix A).
[44]
3.2 Indirect BSIP estimation methods
The BSIPs derived from the proposed DXA method were compared with those gathered
from five different indirect BSIP estimation methods. Two methods were based on data from
cadavers (Chandler et al., 1975; Yeadon, 1990) and the three others were based on data
from living human subjects (Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1985; Zatsiorsky et
al., 1990). These methods were chosen because they are commonly used in biomechanical
analyses, and they provide moments of inertia in all of the orthogonal planes.
Five different indirect BSIP estimation models with similar segmentation protocols were
chosen to be compared with the new DXA method. They are:
1) The Modified Chandler method (C) used simple linear relationships between the whole
body weight and the segment masses, a fixed ratio between the distance from the COM to
the proximal joint relative to the segment’s longitudinal axis (Chandler et al., 1975), and non-
linear equations to compute MOIs from measures of segment lengths, widths and breadths
(Yeadon and Morlock, 1989);
2) The Modified Yeadon method (Y) is a geometric method that uses cylindrical and
stadium-shaped solids to represent body segments. A density value based on the findings of
Dempster (1955) is assigned to each solid to calculate the mass and the MOI of the
segment;
3) Zatsiorsky Simple Regression model (Z1) only uses the whole body mass and height as
predictors for all BSIPs (Zatsiorsky and Seluyanov, 1983);
4) The Zatsiorsky Multiple Regression Model (Z2) uses a set of specific anthropometric data
(up to 4 measures) for each segment as predictors in linear equations (Zatsiorsky and
Seluyanov, 1985);
5) The Zatsiorsky Geometrical Model (Z3) assumes each segment as a circular cylinder and
uses a segment-specific quasi-density value, calculated to minimise the difference between
the cylinder and the real segment volumes (Zatsiorsky et al., 1990).
[45]
In the original work of Chandler et al. (1975), the whole body weight is used as the only
predictor in simple linear equations to calculate the segment masses and MOI. However, as
inaccurate results were expected when computing MOIs from these equations, the non-
linear equations from Yeadon and Morlock (1989) were used, as they were devised using
the same cadavers as Chandler et al. (1975). Small adaptations to the geometric figures of
the original Yeadon (1990) method were made to ensure, whenever possible, that the body
could be segmented in the same manner as in the other estimation models. Thus, the
number of anthropometric measures is minimised. The Zatsiorsky Simple Regression Model
(Zatsiorsky and Seluyanov, 1983), the Zatsiorsky Multiple Regression Model (Zatsiorsky and
Seluyanov, 1985) and the Zatsiorsky Geometrical Model (Zatsiorsky et al., 1990) were
developed from measuring the same 100 adult Caucasian male samples.
Whenever necessary, estimation methods were modified to minimise variations due to
different segmentation protocols; and to facilitate using anthropometric measures derived
from a standardised protocol established by the International Society for Advancement of
Kinanthropometry (ISAK) (Olds and Tomkinson, 2009). A brief explanation of each method
and modifications applied are outlined in Appendix B.
3.3 Data acquisition Protocol
Participants underwent a full body DXA scan and a full body 3D surface scan, at the School
of Sport Science, Exercise and Health (SSEH). For both tests, participants wore Fédération
Internationale de Natation (FINA) approved swimsuits and swimming caps. Participants had
22 spherical markers (20mm diameter) made from glass marbles attached to specific body
landmarks prior to the above scans (Table 3.2). These markers were placed so as to
appear outside the boundary of the body on the DXA output image. Glass was chosen as
the material for markers because its density was vastly different from bone mineral and other
body tissues (approximately 3g/cm3). Therefore, it could be identified easily on the DXA
output image.
[46]
Table 3.2: Glass marble naming and locations
Segment / Joint Label Location
Head L/R FHD Front head marker
Shoulder joint L/R ACR The midpoint on the acromion process lateral ridge
Elbow joint L/R MEL Medial epicondyle of the humerus
L/R LEL Lateral epicondyle of the humerus
Wrist joint L/R AMWR Anterior mid-stylion
L/R PMWR Posterior mid-stylion
Trunk L/R ICP Tubercle of the iliac crest
Knee joint L/R MKN Medial epicondyle of the femur
L/R LKN Lateral epicondyle of the femur
Ankle joint L/R MAN Medial malleolus of the tibia
L/R LAN Lateral malleolus of the tibia
3.3.1 Dual-Energy X-Ray Absorptiometry (DXA)
The DXA scanner was the GE Lunar (Figure 3.1). In brief, the DXA scanner projects two X-
ray beams of different intensities onto the subject’s body. Based on the attenuation of the
energies as they pass through the body, the scanner can evaluate the areal density (i.e.,
mass per area unit at the frontal plane) and the mass associated to each compartment (i.e.,
bone mineral, lean tissue and fat tissue).
Figure 3.1: The GE Lunar DXA scanner
[47]
The subjects assumed a supine lying position with the feet placed at shoulder-width apart,
and the forearms in a neutral position of mid-pronation/supination. Then, the sagittal plane
could be assumed to be parallel to the scan table and the subjects fitting within the 60-cm
wide scanning area. The whole body was scanned once in a process taking around 5
minutes and exposed the subject to a radiation dose of ~0.8 µSv.
3.3.2 Body laser scan
An Artec LTM
3D scanner (Artec, TDSL) was used to create the surface scan of the
participants (Figure 3.2). It consisted of a light projector which emitted a mesh of dots onto
the body surface, and a video camera to capture images of the projected dots (3D frames).
Both the camera and projector were calibrated relative to each other (raster-stereography).
According to the manufacturer, the scanner has a 3D resolution of up to 1.0 mm; 3D point
accuracy of up to 0.2 mm; and a maximal capture rate of 15 frames per second. The Artec
3D Scanner v0.6 software was used to operate the scanner, and capture and process the
scanned data.
Figure 3.2: The Artec L
TM 3D scanner.
[48]
Prior to scanning, 28 additional spherical wooden markers (20 mm diameter) were
strategically placed on the body (Table 3.3). These markers combined with the marble
markers to create the anatomical coordinate system (ACS) for each body segment.
Participants were scanned while standing in the anatomical position, except for the slightly
abducted shoulders and more neutral forearm and hand position having the palms facing
inwards (Figure 3.3). To avoid excessive sway during scanning, subjects looked at a fixed
point on the wall ahead, and rested their fingers on two nearby tripods. The first scanning
phase covered the head, trunk and upper limbs; and the second, the lower limbs.
Table 3.3: 3D scan marker naming convention and locations
Segment / Joint Label Location
Head L/R BHD Back head marker
Shoulder joint L/R Acr1 Acromion triad: posterior marker
L/R Acr2 Acromion triad: central-medial marker
L/R Acr3 Acromion triad: posterior marker
The rigid bar between Acr1 and Acr3 runs parallel with the
lateral ridge of the acromion
Wrist joint L/R MWR Styloid process of the ulna
L/R LWR Styloid process of the radius
Hand L/R Hand1 2nd
carpo-metacarpal joint
L/R Hand2 5th
carpo-metacarpal joint
L/R Hand3 Head of the 3rd
metacarpal
Trunk C7 Spinous process of the 7th
cervical vertebra
IJ Deepest point of the incisura jugularis (suprasternale)
XP Xiphoid process
Nav Navel
L/R ASIS Anterior superior iliac spine
L/R PSIS Posterior superior iliac spine
Foot L/R Foot1 Calcaneus
L/R Foot2 Head of the 1st metatarsal
L/R Foot3 Head of the 5th
metatarsal
[49]
Figure 3.3: The 3D scan of the participant after the scanning procedure (before post-process)
The post-processing was also conducted using the Artec 3D Scanner v0.6 software. The
software enabled finer alignment of the 3D frames, smoothness of the surface, filling the
surface holes, discarding of unwanted objects and the creation of the single polygonal 3D
model of the whole body (i.e., representation of the body surface using a triangulation grid).
Each subject required approximately 5h to create the final 3D scan.
3.3.3 Anthropometry
Heights, lengths, breadths and girths were taken from all subjects’ 3D scans for input into
the equations of the indirect BSIP estimation methods. Anthropometry gathered from 3D
scans was shown to have high validity and reproducibility (Lu and Wang, 2008). When
possible, measures followed the definitions set by the International Society for Advancement
of Kinanthropometry (ISAK); and the Laboratory Standards Assistance Scheme of the
Australian Sports Commission (Olds and Tomkinson, 2009). In some cases, additional
measures were required to comply with a specific BSIP method (i.e., those not listed in the
ISAK protocol). The body landmarks, girths, lengths and breadths, as well as the results of
the concurrent validity tests, are found in Appendix C.
[50]
3.4 Biomechanical model
A 16-segment biomechanical model (head, upper trunk, middle trunk, lower trunk, upper
arms, forearms, hands, thighs, shanks and feet) was devised so all BSIP estimation
methods could be easily fitted to the model. A model of every subject was created using the
3D coordinates of the markers obtained with the Artec 3D Scanner v0.6 software.
The ACS of the upper and lower limb segments were created from the recommendations of
the International Society of Biomechanics (Lu and Wang, 2008; Wu et al., 2005). The ankle,
wrist and shoulder (glenohumeral) joint centres were determined according to the UWA
biomechanical model (Besier et al., 2003; Campbell et al., 2009; Chin et al., 2010). The
elbow and knee joint centres were defined as midway between the medial and the lateral
epicondyles, of the humerus and the femur, respectively. Regression equations proposed
by Harrington et al. (1999) were used for the hip joint centre. A whole trunk coordinate
system was created after de Leva (1996). The long axis of the whole trunk was used as the
long axes of the three sub-segments of the trunk, and also for the head segment. For details
of all anatomical-landmark-based ACS, see Appendix D.
3.5 Data Processing
Previous studies used the linear relationship between the attenuation coefficients of the high
energy beams, and each were recorded in rectangular elements that formed the scan area
matrix, and the mass of a given phantom (Durkin et al., 2002; Wicke and Dumas, 2008).
This was done because the company supplying the scanner and the analysis software
preferred not to provide access to the code enabling calculation of the mass for each
rectangular element (Jim Dowling, personal correspondence). Hence, the raw data was
accessed using an ACSII code de-compiler.
The unique aspect of this study was that mass data were extracted directly from the generic
DXA enCORE® software (version 8.50.093, GE Healthcare, 2004). In order to access raw
data from the DXA generic software, enCORE®, a day-pass licence was required from the
manufacturer. Hence, an agreement was made between The University of Western Australia
and the Healthcare Division of General Electric Company (GEHC) acknowledging that data
[51]
would be used for internal and non-commercial research purposes only. First, contact was
made with the Australia/New Zealand Lunar Product Manager of the GE Healthcare
Systems, who informed the University that an agreement had to be drawn up. Then, contact
was established directly with the Global Research Manager and the Chief Scientist of the
GEHC, with whom the details of the research and details of the licence agreement were
discussed directly.
After approximately four months of interaction with GEHC representatives, the company
kindly supplied a password that would enable the enCORE® software to display two different
data matrices. The first matrix provided mass data for the bone mineral compartment (BMD).
The second provided mass data for the tissue compartment (TISSUE), which consisted of
extracellular fluids and solids, total body water, intracellular solids and fat (St-Onge et al.,
2004a). Each matrix was divided into rectangular elements with dimensions of 0.51 cm x
1.54 cm in the transverse (x) and longitudinal (y) directions, respectively, and referred to as
mass elements. Hence, each element represents a section within the entire scanned area,
and the summation of both matrices provided the whole body mass.
The day-pass licence enabled the enCORE® software to show the coordinates and mass
value of each mass element on the bottom of the screen when the mouse cursor is over an
area of the scan image (Fig 3.4). This worked for both the BMD and the TISSUE images.
However, the enCORE® software (version 8.50.093, GE Healthcare, 2004) did not allow any
of the data matrices to be exported and saved in any other formats for further processing. To
extract mass data manually by moving the mouse cursor from one mass element to the next,
and then record the values externally, was not practical. Therefore, data from the two
matrices were co-registered with their respective grayscale images (8-bits bitmap files,
resolution of 72 DPI) exported by the scanner software (Figure 3.4) using a code written in
Matlab® (Ver. 7.8.0.347). As the images that were created were based on the coefficients of
attenuation measured, it made sense that there should be a linear relationship between the
shade of a given pixel of the image and the areal density of the region represented by the
pixel (i.e., the whiter the shade of the pixel, the greater the amount of mass referred to that
area). Therefore, a Matlab code was created (convert_dxa_images.m, Appendix E) to
[52]
compute the mass distribution of the scanned area using the intensity colour of every pixel in
the grayscale image. As input, this used the BMD and TISSUE images; the dimensions of
the scanning area; the number of mass elements of both matrices and two arrays - one of
which was for the BMD data and another for the TISSUE data, and each containing the
coordinates and the associated mass (in grams) of 15 random mass elements. The following
steps were conducted by the code for both BMD and TISSUE matrices:
Figure 3.4: Screenshot of the enCORE® software when the day pass code is used, showing the
two BMD and TISSUE images derived from the respective matrixes. When the mouse is placed
on a given area (red circle), the mass and the coordinates the local mass element pointed by
the arrow are shown on the bottom of the screen (red ellipses).
1) The grayscale images were scaled to the same size of the scanning area. Each
pixel in the image then represented an area of 0.23 x 0.23 cm. Therefore, this also
enhanced the areal resolution of the mass data.
[53]
2) Then, the image data was co-registered with the raw data such that each mass
element was represented by a group of image pixels in the same area (Figure 3.5).
The colour intensity of each pixel is represented by integer values ranging from 0
(black) to 255 (white) and the relationship between the colour intensity (integer
value) and the mass of the pixel area was assumed to be linear. The summation of
the integer values of all pixels representing the mass element is directly proportional
to the mass of the referred mass element. This relationship is then found using the
following formula:
��� � ��� · ∑ ��, (Formula 1)
Where mel is the mass of a mass element, Ii,j is the gray intensity of a pixel within the
mass element and kel is a constant calculated for each mass element and further
used to calculate the mass value associated with a representative pixel (mass pixel)
by multiplying it by its gray intensity.
[54]
Figure 3.5: The relationship between the mass element (red rectangle) and the pixels of the
bitmap image; often the mass element contained pixels from the outside of the body or its
borders were not aligned with the pixels.
3) It is important to note from Figure 3.5 that the mass elements were not necessarily
represented by integer pixels (i.e., the borders of the pixels and the referred mass
element may not be aligned). Therefore, the relationship between the summation of
the integer values and the mass value of the mass element may be over or under
estimated. To minimise those errors, the step 2) was performed for 15 different
mass elements that had mass pixels computed from the calculated kel constants.
[55]
The mass elements were selected from all segments, and from areas associated to
pixels with varying intensity, trying to cover the greatest range of the colour
spectrum as possible (Figure 3.6). The colour intensity and singular mass of all
those mass pixels, were then used as input and output, respectively, to compute a
final polynomial of degree 1 through a least squares sense:
��, � ( · ��, ) * (Formula 2)
Where mi,j is the mass associated to a pixel in the bitmap image, and α and β are
two real constants.
4) Finally, the two images (BMD and TISSUE) are linearly mapped using Formula (2)
and summed to compute the mass distribution of the whole body in a higher
resolution than the two matrices representing the raw data (Figure 3.6).
5) To eliminate noise from the areas outside the body, binary images for each matrix
were created and used as masks (i.e., the pixels that had a black color in the
referred mask were given a nil mass value). A global threshold was computed such
that all pixels referred to the outside of the body were addressed as black, whereas
the pixels referred to the body mass values were addressed as white (Figure 3.7).
The noise-free matrixes contained all mass pixels for the bone mineral
(I_BMD_mass), tissue compartments (I_TISSUE_mass), and the total body
(I_mass_total=I_BMD_mass + I_TISSUE_mass), to be then used to calculate the
BSIPs (Figures 3.8 and 3.9).
[56]
Figure 3.6: Grayscale images of the BMD and TISSUE compartment matrices created by the enCORE® software (right and middle, respectively), and the
summation of both images. Red and blue dots correspond to the locations of the mass elements used for the first and second matrices, respectively.
[57]
Figure 3.7: Binary images of the BMD, TISSUE and whole body mass created to eliminate noise outside the region of interest. All black pixels have nil mass value.
[58]
Figure 3.8: 2D representation of the I_BMD_mass, I_TISSUE_mass, and I_mass_total matrices (right, middle and left images, respectively) using a colour scale to
show the density of the mass pixels.
[59]
Figure 3.9: A 3D representation of the I_mass_total matrix.
[60]
Validation of the method was carried out by comparing the whole body mass, tissue mass
and bone mineral mass values calculated by the enCORE® software; and those calculated
by summing all pixel masses for the 28 subjects. The minimum (Emin) and maximum (Emax)
errors expressed in kilograms (Kg) were computed using the enCORE® values as criteria.
The mean absolute percentage errors (MAPE) and the percentage root mean square errors
(%RMSE), were calculated as:
-./0 � ∑ 1|�3���|�3 4 5 6��7 (Formula 3)
%�-90 � :∑;�3<���3 =>7 5 100 (Formula 4)
Where MR and MM are the real mass value from the scanner and summing all pixel masses,
and N is the number of subjects.
Another Matlab code (segment_whole_body.m, Appendix E) was created to divide the scan
image into a 16-segment model (head, upper trunk, middle trunk, lower trunk, upper arm,
forearm, hands, thighs, shanks and feet); and calculate the mass (MS, Kg), COM (cm) lying
on the longitudinal axis of the segment (as a distance from the distal end point of the
segment) and the principal MOI about the sagittal axis (Ixx, Kg�cm2, assuming all sagittal
axes were perpendicular to the scanning plane) of each segment. The segmentation
protocol used was the same adopted in the study of Zatsiorsky and Seluyanov (1983). This
function used body landmark coordinates as input to determine the joint centres and
sectioning planes (Figure 3.10). Those coordinates were entered when clicking on the bone
landmarks viewed in the BMD image. Extra clicked points also were used to define vertices
of a geometric figure within which the segment was placed; and, outside which, all the mass
pixels were excluded from the calculations (Figure 3.11). Coordinates of the elbow, wrist,
knee and ankle joint centres were calculated as described previously (Appendix D). The
same points used to define those joint centres also defined the segmentation plane
(perpendicular to the scanning plane). The shoulder and hip joint centres were obtained by
[61]
clicking on the regions of the BMD image that represented the centres of the heads of the
humerus and femur. The segmentation plane of the shoulder was defined by the line linking
the acromion landmark to the armpit. The segmentation plane of the hip was defined by a
line passing over the hip joint centre with an angle of 37º to the longitudinal axis of the trunk
(i.e., line linking the midpoint between the hips and the midpoint between the shoulders).
1 & 2: Left and Right Acromion
3 & 4: Left and Right Armpit
5: C7
6 & 7: Left and Right Shoulder Joint Centre
8 & 12: Left and Right Lateral Epicondyle
9 & 13: Left and Right Medial Epicondyle
10 & 14: Left and Right Posterior Mid Wrist
11 & 15: Left and Right Anterior Mid Wrist
16 & 17: Left and Right Hip Joint Centre
18 & 22: Left and Right Lateral Tibial Condyle
19 & 23: Left and Right Medial Tibial Condyle
20 & 24: Left and Right Lateral Malleolus
21 & 25: Left and Right Medial Malleolus
Figure 3.10: Representation of the 25 points used to segment the body using the
segment_whole_body.m function.
[62]
Figure 3.11: Output of the segment_whole_body.m function, containing the segmentation planes in the whole body (left figure, red dashed line), the clicked points
that defined the geometric figure used as frontier to delimit the segments (red dots), and the segment COM positions.
[63]
The MS, COM and Ixx were computed for each segment using the following equations
(Durkin et al., 2002):
-� � ∑ � (Formula 5)
DE- � F∑ GH��∑ IH�� J (Formula 6)
�KK � ∑ �LM (Formula 7)
Where x and y are the coordinates of the pixel mass, m is the mass value of each pixel
mass, and r is the distance from the pixel mass to the COM of the segment (radius of
gyration).
3.6 Data Analysis
The mean percentage error was calculated between each indirect estimation method and
the DXA/3D surface scan method – the criterion - for each subject group. A 5 X 3 (indirect
estimation method X subject group) mixed-model analysis of variance (SPANOVA, α=0.05)
of the percentage errors was conducted for each segment and for each inertial parameter.
This was followed by a Tukey-HSD post-hoc analysis to determine any differences between
estimation methods, between swimmers and normal Caucasian males, and possible
interaction factors. It was hypothesised that any errors found for the two groups of swimmers
would be significantly greater than those found in the cohort resembling the studies by
Zatsiorsky et al. (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), regardless
of segment or inertial parameters.
[64]
Chapter 4
RESULTS
The errors associated with using the proposed DXA methods are reported in Table 4.1.
While large MAPE and %RMSE could be observed for the bone mineral mass, it had little
influence on total mass prediction But, in contrast, tissue mass was able to be estimated
with marginal errors.
Table 4.1: Minimum error (Emin, Kg), Maximum error (Emin, Kg), Mean Absolute Percentage Error
(MAPE, %) and Percent Root Mean Square (%RMSE) for the bone mineral, tissue and whole
body masses calculated from the respective images.
Compartment Emin (Kg) Emax (Kg) MAPE %RMSE
Bone mineral 0.04 0.60 9.32% 10.55%
Tissue 0.09 1.72 1.09% 1.27%
Total 0.01 2.12 1.18% 1.45%
Table 4.2 shows the means and standard deviations (SD) for segment masses calculated by
using DXA for the 10 young adult males who resembled subjects analysed by Zatsiorsky
and Seluyanov (1983). These results were compared with the segment masses of the
subjects in Zatsiorsky and Seluyanov (Zatsiorsky and Seluyanov, 1983). The ‘Zatsiorsky’
studies (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) presented segment
length as distances between bony landmarks rather than between joint centres. Moreover,
rather than the absolute value of the MOI or the radii of gyrations, they presented the radii
of gyration as percentages of the segmental lengths. Therefore, similar comparisons for
COM and MOI are not provided as the values could not be computed in the same way. A
series of one-sample t-tests was used to determine whether segment masses from of the
[65]
participants were different to those found in the ‘Zatsiorsky’ studies (Zatsiorsky and
Seluyanov, 1983, 1985; Zatsiorsky et al., 1990). Only the head (t = −0.20, p = 0.84) and
forearm (t = 0.51, p = 0.61) segments showed non-significant differences.
Table 4.2: Mean (SD) segment masses (kg) of young adult Caucasian males tested in the
present study (DXA, n=10) and the young adult Caucasian males from Zatsiorsky studies
(Zatsiorsky, n=100).The (*) indicates the segments for which the differences were significant
(p<0.05)
Mass
Segment DXA Zatsiorsky
Head 4.99 (0.50) 5.02 (0.39)
Trunk* 34.08 (2.57) 31.77 (3.24)
Upper arm* 2.30 (0.33) 1.98 (0.32)
Forearm 1.20 (0.16) 1.18 (0.16)
Thigh* 9.69 (1.15) 10.36 (1.57)
Shank* 3.46 (0.44) 3.16 (0.44)
* Significant differences between DXA and Zatsiorsky (p<0.05)
Tables 4.3, 4.4 and 4.5 show the means and SD for mass, COM and Ixx for each of the
estimation methods and subject groups. Despite some variations, comparisons between the
mean values obtained from DXA and the other estimation methods did not reveal them to be
statistically significance (p >.05)
[66]
Table 4.3: Mean (SD) segment mass (Kg) calculated for adult Caucasian male (n = 10), male
swimmers (n = 10) and female swimmers (n = 8) using the Chandler model (C), Yeadon model
(Y), Zatsiorsky simple regression model (Z1), Zatsiorsky multiple regression model (Z2),
Zatsiorsky geometric model (Z3,) and the proposed estimation protocol using DXA (DXA).
Estimation Method
Segment Group C Y Z1 Z2 Z3 DXA
Head Adult male 4.34 4.96 5.13 6.07 5.74 4.99
(0.22) (0.92) (0.23) (0.76) (0.76) (0.50)
Male swimmers 4.54 5.04 5.35 6.37 5.71 5.18
(0.29) (0.65) (0.26) (0.67) (0.68) (0.37)
Female swimmers 3.92 3.79 4.85 5.66 4.91 4.40
(0.16) (0.53) (0.18) (0.35) (0.58) (0.30)
Trunk Adult male 39.72 34.10 33.02 36.05 32.07 34.08
(3.64) (3.29) (2.95) (3.07) (2.61) (2.57)
Male swimmers 43.04 38.91 35.55 37.68 36.52 39.14
(4.89) (4.46) (4.20) (3.72) (3.96) (4.02)
Female swimmers 32.80 27.48 26.71 31.52 26.02 28.45
(2.58) (2.54) (2.03) (2.70) (2.43) (2.09)
Head + Trunk Adult male 44.06 39.06 38.15 42.12 37.81 39.07
(3.86) (4.00) (3.16) (3.46) (3.20) (2.97)
Male swimmers 47.57 43.95 40.91 44.05 42.23 44.32
(5.18) (5.06) (4.44) (3.92) (4.35) (4.34)
Female swimmers 36.72 31.27 31.57 37.18 30.93 32.85
(2.74) (2.94) (2.19) (2.84) (2.65) (2.28)
Upper arm Adult male 2.09 2.41 2.06 2.54 2.25 2.30
(0.14) (0.38) (0.18) (0.29) (0.37) (0.33)
Male swimmers 2.21 2.87 2.23 2.85 2.55 2.61
(0.19) (0.46) (0.25) (0.30) (0.41) (0.42)
Female swimmers 1.84 2.08 1.68 2.27 1.78 1.91
(0.09) (0.22) (0.13) (0.19) (0.20) (0.19)
Forearm Adult male 1.27 1.26 1.21 1.35 1.20 1.20
(0.12) (0.20) (0.09) (0.17) (0.26) (0.16)
Male swimmers 1.37 1.42 1.30 1.48 1.32 1.31
(0.16) (0.26) (0.12) (0.24) (0.25) (0.20)
Female swimmers 1.05 1.04 1.03 1.15 0.92 0.90
(0.08) (0.16) (0.06) (0.16) (0.13) (0.11)
Thigh Adult male 9.70 9.69 10.90 10.34 10.90 9.69
(1.81) (1.22) (1.07) (1.01) (1.36) (1.15)
Male swimmers 10.49 10.23 11.92 10.70 11.06 9.65
(1.96) (1.30) (1.40) (1.15) (1.30) (1.45)
Female swimmers 8.06 8.83 8.94 9.03 9.68 8.11
(1.72) (0.86) (0.77) (0.76) (1.01) (0.63)
Shank Adult male 3.12 4.03 3.30 3.61 3.39 3.46
(0.28) (0.55) (0.33) (0.43) (0.48) (0.44)
Male swimmers 3.37 4.32 3.63 3.81 3.56 3.58
(0.37) (0.62) (0.40) (0.45) (0.61) (0.51)
Female swimmers 2.58 3.31 2.79 3.00 2.60 2.92
(0.19) (0.44) (0.24) (0.36) (0.43) (0.33)
[67]
Table 4.4: Mean (SD) distance of the centre of mass position in the longitudinal axis from the
distal end point (COM, cm) of adult Caucasian male (n = 10), male swimmers (n = 10) and female
swimmers(n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1),
Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation methods.
Estimation Method
Segment Group C Y Z1 Z2 Z3 DXA
Head Adult male 11.91 11.81 11.88 14.77 12.05 11.32
(0.86) (1.20) (1.68) (1.31) (0.87) (0.88)
Male swimmers 13.04 11.94 13.98 15.48 13.19 11.57
(0.72) (0.86) (1.42) (1.80) (0.73) (0.55)
Female swimmers 12.01 11.14 12.12 15.15 12.15 11.69
(0.86) (0.92) (1.80) (0.54) (0.87) (0.31)
Trunk Adult male 35.70 27.29 26.18 28.42 28.36 27.96
(0.92) (0.83) (0.55) (1.32) (0.73) (1.08)
Male swimmers 37.89 30.27 28.47 31.94 30.11 30.81
(1.32) (0.99) (1.21) (1.11) (1.05) (0.89)
Female swimmers 34.47 26.48 24.78 27.16 27.39 27.02
(1.62) (1.13) (1.38) (1.13) (1.29) (0.89)
Head + Trunk Adult male 39.10 32.71 32.12 34.87 34.73 33.74
(0.87) (1.23) (0.65) (1.71) (0.97) (1.27)
Male swimmers 41.44 35.27 34.72 38.55 36.20 36.39
(1.30) (1.15) (1.18) (1.44) (0.97) (0.99)
Female swimmers 38.09 31.44 31.51 33.92 33.91 33.06
(1.63) (1.32) (1.51) (1.15) (1.40) (0.89)
Upper arm Adult male 14.68 15.78 16.19 13.26 12.56 15.28
(0.85) (0.94) (1.59) (0.72) (0.73) (0.82)
Male swimmers 15.76 17.20 17.74 14.10 13.48 16.18
(1.19) (1.20) (1.88) (1.04) (1.02) (1.43)
Female swimmers 14.68 16.02 16.79 13.38 12.56 15.26
(0.73) (0.74) (1.20) (0.64) (0.63) (0.52)
Forearm Adult male 14.93 14.79 11.03 9.97 13.87 15.40
(1.16) (1.29) (1.58) (0.82) (1.08) (1.23)
Male swimmers 15.77 15.49 11.86 10.46 14.65 16.46
(1.32) (1.28) (1.85) (0.92) (1.23) (1.51)
Female swimmers 14.47 14.10 10.22 9.43 13.44 14.86
(0.97) (0.89) (1.33) (0.72) (0.90) (1.01)
Thigh Adult male 26.38 24.06 19.21 22.23 25.74 24.42
(1.92) (1.75) (2.08) (2.38) (1.88) (1.75)
Male swimmers 27.21 24.84 19.23 23.13 26.55 24.80
(2.15) (1.96) (2.59) (2.42) (2.10) (2.20)
Female swimmers 26.19 24.51 19.91 22.39 25.56 23.85
(1.59) (1.61) (1.92) (2.32) (1.55) (1.35)
Shank Adult male 24.36 24.09 25.38 26.34 23.01 24.49
(1.74) (1.75) (2.17) (1.81) (1.65) (1.75)
Male swimmers 25.74 25.50 26.81 27.82 24.32 25.72
(1.91) (2.19) (2.56) (2.12) (1.80) (2.23)
Female swimmers 23.72 23.28 24.32 25.48 22.40 23.66
(1.72) (1.64) (2.24) (1.69) (1.62) (1.56)
[68]
Table 4.5: Mean (SD) values for segment principal moment of inertia about the sagittal axis (Ixx,
Kg����cm2) of adult Caucasian male (n = 10), male swimmers (n = 10) and female swimmers (n = 8)
according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky
multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation methods.
Estimation Method
Segment Group C Y Z1 Z2 Z3 DXA
Head Adult male 248.95 226.92 280.09 400.67 366.98 233.51
(69.14) (71.57) (19.65) (84.37) (84.27) (46.15)
Male swimmers 290.75 230.10 299.95 441.04 372.79 253.81
(61.00) (54.30) (22.06) (93.48) (94.18) (29.45)
Female
swimmers
226.96 141.22 259.11 379.78 309.98 197.83
(25.79) (40.58) (15.72) (33.37) (63.34) (19.44)
Trunk Adult male 16595.16 14500.71 13523.39 16840.92 13142.09 13239.06
(2574.00) (1886.73) (1473.89) (1598.89) (1762.19) (1838.08)
Male swimmers 20323.68 20276.15 16550.85 21742.87 17157.06 17958.63
Female
swimmers
(4132.74) (3149.84) (2460.68) (2860.52) (2750.40) (2773.83)
12013.65 10937.66 9868.27 13467.26 10095.63 10727.80
(2221.96) (1724.73) (1101.34) (1916.16) (1533.64) (1552.61)
Head +
Trunk
Adult male 21522.06 22757.78 22446.33 27679.62 22118.59 21122.58
(2883.82) (3520.69) (2496.32) (3254.45) (2989.02) (2917.95)
Male swimmers 26263.57 29055.61 27355.76 33511.44 27530.55 27197.73
Female
swimmers
(4647.40) (4717.17) (3299.51) (4081.15) (3883.40) (3870.66)
16262.99 16725.16 17968.52 23286.48 17373.26 17510.21
(2454.89) (2783.86) (1660.50) (2839.84) (2225.34) (2253.45)
Upper
arm
Adult male 167.92 194.90 135.71 205.55 133.72 161.64
(42.42) (48.10) (21.56) (28.37) (30.94) (35.41)
Male swimmers 230.29 266.42 157.93 241.06 166.40 207.70
Female
swimmers
(63.78) (75.58) (24.67) (34.00) (49.98) (65.86)
142.30 167.27 109.70 186.09 98.50 125.88
(27.14) (32.75) (16.86) (20.74) (17.29) (18.88)
Forearm Adult male 56.33 67.80 68.42 78.17 63.22 64.25
(17.31) (18.52) (8.77) (18.64) (23.62) (19.20)
Male swimmers 70.52 86.30 77.16 92.46 79.11 75.81
Female
swimmers
(23.18) (28.89) (10.75) (23.84) (27.19) (23.61)
42.22 53.24 54.79 64.25 45.92 44.62
(11.75) (16.11) (6.52) (16.40) (12.25) (12.25)
Thigh Adult male 2072.24 1538.01 2148.83 1617.71 1866.66 1531.03
(592.00) (427.61) (346.60) (302.58) (404.13) (368.93)
Male swimmers 2315.68 1721.38 2500.23 1741.60 1975.19 1552.45
Female
swimmers
(583.40) (445.80) (410.82) (361.78) (417.61) (450.55)
1778.59 1356.51 1666.21 1308.98 1601.63 1177.87
(357.03) (259.67) (263.92) (210.22) (250.00) (185.44)
Shank Adult male 518.60 633.37 418.36 457.95 494.11 449.14
(147.73) (183.73) (80.15) (107.78) (147.19) (122.80)
Male swimmers 619.18 759.39 501.79 527.34 575.65 516.44
Female
swimmers
(165.06) (208.23) (89.44) (103.06) (157.39) (139.82)
395.90 489.37 333.59 375.94 363.23 361.52
(101.27) (124.04) (64.00) (102.64) (112.17) (98.24)
[69]
The ANOVA revealed significant differences in the BSIP data between groups except for the
head COM (F(2,25) = 0.80, p = .46) and thigh COM (F(2,53) = 1.21, p = 0.31). Female
swimmers had significantly lower mass values than the other two groups for all segments
(head: F(2,25) = 8.90; trunk: F(2,25) = 27.03; head plus trunk: F(2,25) = 25.68; upper arm:
F(2,53) = 19.27; forearm: F(2,53) = 28.91; thigh: F(2,53) = 10.41; shank: F(2,53) = 10.87),
forearm Ixx (F(2,53) = 11.64) and thigh Ixx (F(2,53) = 5.78). Male swimmers had
significantly greater values than the other two groups for all parameters of the trunk (mass:
F(2,25) = 27.06; COM: F(2,25) = 39.27; Ixx: F(2,25) = 26.49), head + trunk (mass: F(2,25) =
25.68; COM: F(2,25) = 25.19; Ixx: F(2,25) = 22.13), and upper arm (mass: F(2,53) = 19.27;
COM: F(2,53) = 5.08; Ixx: F(2,53) = 14.14), and the Male swimmers also had significantly
larger forearm COM value (F(2,53) = 7.43), greater head Ixx (F(2,25) = 5.94), shank COM
value (F(2,53) = 5.46) and shank Ixx (F(2,53) = 7.04) than female swimmers.
The %RMSE of mass, COM and Ixx of each indirect estimation method against DXA, for
each group of subjects, are presented in Tables 4.6, 4.7 and 4.8, respectively. Overall, the
Ixx values are the least accurate inertial parameter, while estimation of the COM produced
least amount of errors, when using any indirect estimation methods.
The error assessment of all indirect BSIP methods according to subject group is presented
by plotting the MAPE for the mass (Figure 4.1), COM (Figure 4.2) and Ixx (Figure 4.3)
[70]
Table 4.6: Percentage Root Mean Square Error (%RMSE) for segment mass (Kg) of the Chandler
(C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and
Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult Caucasian male
(n = 10), male swimmers (n = 10) and female swimmers (n = 8).
Estimation Method
Segment Group C Y Z1 Z2 Z3
Head Adult male 13.97 12.99 8.37 23.69 17.44
Male swimmers 12.66 7.83 4.68 25.47 14.50
Female swimmers 11.50 15.50 12.06 30.36 14.76
Trunk Adult male 16.69 4.94 3.87 8.57 6.49
Male swimmers 10.60 3.00 9.99 5.17 7.06
Female swimmers 15.75 4.69 6.72 11.20 9.41
Head + Trunk Adult male 13.04 5.20 3.32 9.46 4.10
Male swimmers 7.99 3.18 8.40 2.80 4.96
Female swimmers 12.20 5.82 4.61 13.31 6.57
Upper arm Adult male 13.47 9.80 13.04 13.58 7.58
Male swimmers 16.88 13.02 15.40 13.87 6.31
Female swimmers 8.20 12.08 13.38 20.27 8.71
Forearm Adult male 11.20 12.93 9.24 16.90 15.79
Male swimmers 9.60 12.40 7.74 15.65 9.24
Female swimmers 19.57 16.95 17.46 28.36 7.27
Thigh Adult male 16.45 4.42 13.53 10.47 13.89
Male swimmers 19.81 7.27 24.92 13.48 16.61
Female swimmers 19.36 10.40 10.97 13.23 20.42
Shank Adult male 12.32 17.01 8.78 6.81 5.65
Male swimmers 7.50 21.13 6.50 8.42 5.60
Female swimmers 13.24 17.82 8.62 10.64 17.24
[71]
Table 4.7: Percentage Root Mean Square Error (%RMSE) for segment centre of mass position in
the longitudinal axis from the distal end point (COM, cm) of the Chandler (C), Yeadon (Y),
Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky
geometric (Z3) estimation methods against DXA, observed for adult Caucasian male (n = 10),
male swimmers (n = 10) and female swimmers (n = 8).
Estimation Method
Segment Group C Y Z1 Z2 Z3
Head Adult male 10.86 11.74 15.73 32.62 11.65
Male swimmers 14.27 8.26 23.71 38.04 15.50
Female swimmers 8.11 9.02 15.31 30.49 8.68
Trunk Adult male 28.06 3.09 7.35 3.45 3.45
Male swimmers 23.10 2.24 8.48 4.42 2.98
Female swimmers 27.74 3.17 8.92 3.04 2.88
Head + Trunk Adult male 16.36 3.88 6.04 4.35 3.93
Male swimmers 14.02 3.20 5.41 6.68 1.98
Female swimmers 15.43 5.53 5.58 3.70 3.87
Upper arm Adult male 5.67 5.89 9.97 13.66 18.11
Male swimmers 3.61 7.28 10.42 12.95 16.72
Female swimmers 5.14 6.17 11.87 12.70 17.92
Forearm Adult male 4.30 5.18 29.26 35.30 10.30
Male swimmers 5.07 6.29 28.85 36.48 11.26
Female swimmers 3.43 5.80 31.83 36.56 9.74
Thigh Adult male 8.52 2.71 21.86 10.34 6.09
Male swimmers 10.16 2.48 23.24 7.85 7.61
Female swimmers 10.02 3.62 17.36 8.49 7.43
Shank Adult male 1.66 2.36 4.38 7.81 6.21
Male swimmers 2.40 1.83 5.74 8.76 5.81
Female swimmers 2.41 2.67 4.44 7.77 5.80
[72]
Table 4.8: Percentage Root Mean Square Error (%RMSE) for segment principal moment of
inertia about the sagittal axis (Ixx, Kg����cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky simple
regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation
methods against DXA, observed for adult Caucasian male (n = 10), male swimmers (n = 10) and
female swimmers (n = 8).
Estimation Method
Segment Group C Y Z1 Z2 Z3
Head Adult male 19.25 24.24 29.84 76.86 59.87
Male swimmers 26.00 18.75 20.48 82.82 57.48
Female swimmers 23.13 32.63 33.96 97.50 63.43
Trunk Adult male 29.33 12.82 6.20 29.07 6.07
Male swimmers 15.24 13.85 11.10 22.63 6.74
Female swimmers 15.98 7.61 9.19 27.19 9.14
Head + Trunk Adult male 8.52 12.78 7.93 32.17 6.63
Male swimmers 7.29 9.23 5.06 24.49 4.30
Female swimmers 9.60 9.49 6.70 33.84 6.03
Upper arm Adult male 14.98 26.91 18.00 33.59 19.57
Male swimmers 18.28 33.55 24.16 30.99 20.43
Female swimmers 18.46 36.61 15.14 50.81 22.51
Forearm Adult male 16.60 13.96 23.75 31.93 20.13
Male swimmers 12.00 17.53 23.05 27.41 13.84
Female swimmers 10.17 22.63 33.80 46.85 12.59
Thigh Adult male 37.23 9.05 45.54 17.91 27.39
Male swimmers 52.30 14.85 72.90 21.23 34.25
Female swimmers 52.33 17.58 42.55 19.81 40.20
Shank Adult male 16.30 41.24 13.40 8.35 12.30
Male swimmers 22.96 49.55 11.89 10.82 16.74
Female swimmers 19.09 40.95 16.25 19.87 25.35
Figure 4.1: Mean Absolute Percentage Error (MAPE) for segment mass (Kg) of the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple
regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult Caucasian males (Normal), Male swimmers and Female
swimmers.
Figure 4.2: Mean Absolute Percentage Error (MAPE) for segment centre of mass position in the longitudinal axis from the distal end point (COM, cm) of the
Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA,
observed for young adult Caucasian males (Normal), Male swimmers and Female swimmers.
Figure 4.3: Mean Absolute Percentage Error (MAPE) for segment principal moment of inertia about the sagittal axis (Ixx, Kg����cm2) of the Chandler (C), Yeadon (Y),
Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult
Caucasian males (Normal), Male swimmers and Female swimmers.
[76]
The SPANOVAs showed significant interactions between the estimation method and subject
groups for all segment masses, except for the head (trunk mass: F(6.99,87.41) = 5.15; head
+ trunk mass: F(7.03,87.91) = 8.42; upper arm mass: F(3.69,97.76) = 3.10; forearm mass:
F(4.71,124.90) = 3.78; thigh mass: F(5.83,154.44) = 8.72; shank mass: F(5.94,157.31) =
4.16). The thigh was the only segment where significant interaction between the estimation
method and subject groups was observed for COM (F(3.17,84.11) = 4.39). Only for the head
and the head + trunk segments no significant interactions occurred between the estimation
method and subject groups for segment Ixx, (trunk Ixx: F(5.72,71.47) = 3.32; upper arm Ixx:
F(4.41,116.98) = 4.43; forearm Ixx: F(5.99,158.76) = 4.25; thigh Ixx: F(5.31,140.63) = 6.92;
shank Ixx: F(5.82,154.33) = 2.19).
The SPANOVAs also showed significant differences (p < 0.05) in absolute errors between
estimation methods for all BSIPs, whereas significant differences between subject groups
were found for trunk mass (F(2,25) = 15.17), head + trunk mass (F(2,25) = 33.50), forearm
mass (F(2,53) = 6.80), thigh mass (F(2,53) = 6.80), head and trunk Ixx (F(2,25) = 3.48),
upper arm Ixx (F(2,53) = 4.58), forearm Ixx (F(2,53) = 4.40) and thigh Ixx (F(2,53) = 7.00).
The Tukey HSD post hoc test indicated significantly greater errors in female swimmers than
the other two groups for trunk mass, head and trunk mass, and forearm mass (p<0.05). The
female swimmers also recorded greater errors than male swimmers for forearm Ixx and
significantly greater errors than normal male subjects for upper arm Ixx (p<0.05). Normal
male subjects revealed significantly lower errors than male and female swimmers for head +
trunk mass, and thigh mass (p<0.05). Normal male subjects also exhibited significantly lower
errors in thigh Ixx than male swimmers, and tended towards demonstrating (p = 0.056) lower
errors than female swimmers. Although significant differences were found between groups
for the head + trunk Ixx, the Tukey HSD did not indicate which pair (s) was (were)
significantly different.
[77]
Chapter 5
DISCUSSION
The primary aim of this study was to validate the proposed method of extracting BSIP data
from DXA scans. The DXA results also were compared with five other regularly used indirect
methods in samples of 10 elite male and 8 elite female swimmers, and 10 normal adult
Caucasian males. The DXA relies on the relationships between the attenuation coefficients
of the high energy beams and the mass of a given phantom to predict the mass of the
scanned object (Durkin et al., 2002). A unique feature of the method developed for this study
is that mass value for each unit area (mass element) could be extracted directly, thanks to
the day-pass licence authorisation from the manufacturer, Healthcare Division of General
Electric Company (GEHC). Their enCORE® software also exports two bitmap images to
graphically illustrate mass distribution within the scanned area. Because the software did
not allow mass element data to be exported into any other formats, it was necessary to
establish the relationship between mass elements and the pixel intensity of the scan images.
The comparison between segment mass calculated from pixel colour-mass relationship and
the mass calculated for the two compartments (BM mass and tissue mass) by the enCORE®
software revealed a similar level of accuracy as previously (Durkin et al., 2002). The lower
accuracy of the bone mineral mass seems to result from inadequate threshold values used
to create the binary images of the bone mineral images. When comparing both the noise
and noise-free images, it seems that some bone information may have been lost. Also, the
edges of a number of flat bones did not line up with the edges of the rectangular mass
elements (Wicke and Dumas, 2008). This could have contributed to the incorrect bone mass
values for the pixels closest to the boundaries of those bones.
[78]
The present study also demonstrated that BSIP profiles of elite swimmers are quite different
from those of untrained Caucasian adults (Tables 4.3, 4.4 and 4.5). Durkin and Dowling
(2003) warned that caution is urged when the population investigated is not reasonably
matched with the population from which the equations were devised. If using the proposed
DXA method as the ‘gold-standard’, the indirect BSIP estimations in the non-athlete group
consistently produced errors (Tables 4.6, 4.7 & 4.8). Figure 4.1 illustrates that none of the 5
indirect estimation methods consistently reported MAPEs less than 5%. This was even
though the characteristics of this group were approximately similar to the Zatsiorsky and
Seluyanov sample (Zatsiorsky and Seluyanov, 1983, 1985) with whom they were compared.
The accuracy of any given indirect estimation method relies on its ability to replicate the
subject-specific body morphology and body composition. Early studies in kinanthropometry
revealed differences in absolute and relative body size, somatotype and body composition,
between elite swimmers and the normal population (Ackland, Elliott, and Bloomfield, 2009).
Carter and Ackland (Carter and Ackland, 1994) also reported variations between genders
and swim events, for different strokes and different distances, even within an elite swimming
population. Therefore, it might be expected that equations using just the whole body mass,
or mass and stature (C and Z1), would showed greater MAPE values or differences in
MAPE between groups. Even the Z2 model, which used the most number of anthropometric
variables as predictors for inertial parameters of a given segment, reported errors > 20% and
varied greatly between groups. The geometric models (Y and Z3) seemed to generate less
error in general, and were more consistent between groups. However, none of the latter
consistently performed better than the others. Even though Y appeared to resemble the
geometric shape of the body better than Z3, using uniform segment densities gathered from
cadavers might have contributed to the errors found. The Z3 method proposed using a
quasi-density value to compensate for differences between the actual segment volume, and
its cylindrical representation. But, this approach was not enough to provide low and
consistent levels of MAPE between the groups for all segments, and especially was more
evident for the lower limbs. For most of the body segments, results of this study reject the
hypothesis that the indirect methods would produce significantly lower errors for the
untrained adult group than the two athlete groups. The hypothesis was based on the
[79]
premise that the indirect method would only be accurate for subjects with similar
anthropometric profile to the population which the method was developed from. The normal
young adults tested in this study closely resembled the population from Zatsiorsky’s
methods (Z1, Z2 and Z3) (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).
However, errors in the BSIPs estimated for this group using Z1, Z2 and Z3 did not produce
consistently less errors than other techniques. Reduced errors were only found for the thigh
and head + trunk segments. Durkin and Dowling (2003) also found similar %RMSE in young
adult males which indicated that not even the apparent anatomical similarities minimised the
errors yielded by those methods.
Analysing the COM of thigh segment revealed a significant interaction between estimation
method and subject group, yet no significant differences were found between groups. Good
consistency can be observed when plotting the MAPE for COM (Figure 4.2), as the three
groups recorded similarly low errors for most COM and estimation methods. Nevertheless,
no estimation method found MAPE to be less than 5% for all COMs and all groups. The Y
method was the only one not showing errors greater than 15% at least once. Also, the
greatest %RMSE for Y was 11.74% (Table 4.7), which was for the head segment of the
untrained subjects. This indicated that the uniform density assumption and the geometrical
solids that were used, enabled fairly accurate results for the COM. The two methods, C and
Z3, used a fixed proportion between COM distance from distal endpoint and segment length.
The first was Chandler which performed poorly for the head, trunk, and sum of head and
trunk. Perhaps this could be partially explained by the different segmentation protocol used
by Chandler et al. (1975). For instance, once elderly cadavers are used, there needs to be
some consideration of the ageing effect over the spine. Over the years, the spine tends to
shorten its longitudinal length due to disc flattening when losing the nucleus pulposus, a jelly
like substance in the middle of the spinal disc. Thus, the resultant, reduced trunk length
might have induced errors when being compared with younger subjects whose spines had
not yet been affected in this way. On the other hand, the Z3 method used adjusted positions
for the COM relative to the joint centres (De Leva, 1996) rather than the anatomical
landmarks. However, rather than using the same cohort as in the studies of Zatsiorsky and
colleagues (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), some
[80]
adjustments were carried out using anthropometric data from other Caucasian ethnic
groups, which certainly added errors to the adjustment. The other two methods (Z1 and Z2)
demonstrated considerably large errors for the head, forearm and thigh COMs, although little
difference between groups were observed.
Not surprisingly, the largest percentage errors (MAPE and %RMSE) were found for Ixx
(Figure 4.3): even though it is not dependent upon the mass and COM values for its
calculation. However, the Ixx is physically related to those two inertial parameters. As
happened with the mass values, significant interactions between the estimation method and
subject group were found for most of segment Ixxs; except for the head, and the head +
trunk segment. The Ixx of all limb segments of female swimmers seemed to be affected
more than in the other two groups. Even though it was hypothesised to occur, it was only
with the thigh segment that there was a trend towards significantly lower percentage errors
for the normal subjects when compared to the two groups of swimmers. But, the %RMSE
was inferior to 10% only for the Y method (Table 4.8). Nevertheless, with %RMSE of up to
50% for each of the estimation methods, regardless of subject group, for at least one
segment (Table 4.8), it is clear that indirect estimation methods should be avoided when
applied to a population of different morphology and body composition.
Despite the accuracy, easy access, low radiation exposure and easier data processing than
required for other medical imaging technologies, calculating BSIPs using DXA is not widely
practised. One limitation is that one might not gain access to the raw data from the scan
because manufacturers need to protect their intellectual property. Another problem is that
had to be resolved was the inability to establish a relationship between the binary files and
channels of data with the mass of the scanned object/subject (Jim Dowling, personal
correspondence). The scan area may not be compatible for elite swimmers or athletes from
other sports who are generally much taller and larger than the normal population. The scan
used in this study was 59.75cm x 197cm; whereas the dimensions were 59.4cm x 192.7cm
in studies that used the Hologic QDR-1000/W model (Hologic Inc., Bedford, MA, USA)
(Durkin and Dowling, 2006; Durkin and Dowling, 2003; Durkin et al., 2002; Durkin et al.,
2005). However, the major limitation of the method is the 2D characteristics of DXA scan,
[81]
which do not enable calculation of the COM position in the sagittal plane, or the principal
moments of inertia about the longitudinal and transverse axes (Durkin et al., 2002; Ganley
and Powers, 2004b; Wicke and Dumas, 2008). Therefore, kinetic analyses in sporting
manoeuvres that are typically three-dimensional (e.g., swimming) cannot rely on data
extracted from DXA without incorporating modelling techniques. Several modelling
technique approaches can be performed, as proposed in previous studies (Durkin and
Dowling, 2006; Durkin et al., 2005; Lee et al., 2009; Wicke et al., 2008; Wicke et al., 2009).
Finally, it can be argued that the influence of errors in BSIP calculations depends on the
nature of the movement being analysed. Factors such as whether the task involves rapid
linear/angular movements of the segments, is an open-chain or closed-chain analysis, or
whether external forces exert greater or lesser influence than the BSIP method used, will
determine the level of accuracy in the joint forces and moments that are calculated.
However, this study demonstrated that using an indirect estimation method can lead to
grossly inaccurate BSIPs. The recent advances in kinematic analysis systems have resulted
in greater validity, reproducibility, and also flexibility with regard to the environment in which
the assessment is required. It seems counter-intuitive to then ignore the potential errors
from using inappropriate BSIP data. However, extracting full body 3D BSIP from DXA
requires further development before it can be readily used.
[82]
Chapter 6
SUMMARY CONCLUSION &
RECOMMENDATIONS FOR FUTURE
STUDIES
6.1 Summary
This study proposed a new method to compute body segment inertial parameters (BSIPs)
via DXA. This was done by co-registering the areal density data with grayscale images,
thereby enabling the relationship between the pixel colour intensity and the mass recorded
for the referred area to be established. BSIPs were then calculated for elite male swimmers,
elite female swimmers and young adult Caucasian males using DXA scans. Thirdly, and
using the DXA method as criterion, the study assessed the errors in BSIP estimations that
could arise when using five different indirect BSIP estimation methods for these three
populations.
Eight elite female swimmers, 10 elite male swimmers, and 10 young adult Caucasian males
had their whole body mass calculated from the relationship found between pixel colour
intensity and areal density. The values were compared against the criterion value obtained
from the DXA scanner when used to calculate body composition by %RMSE. Subjects also
were scanned with 3D surface scans to compute the anthropometry necessary to calculate
the BSIPs when using the indirect estimation methods. The mass, COM and MOI about the
sagittal axis of seven body segments (head, trunk, head + trunk, upper arm, forearm, thigh,
and shank) were computed from the proposed DXA for each group. Differences were
[83]
assessed using analysis of variance (ANOVA). When applying the five indirect estimation
methods to each of the three referred populations, errors were assessed using the BSIPs
gathered with DXA as criterion, by calculating the %RMSE and searching for significant
differences in absolute percentage errors for all BSIPs.
Computing BSIPs using the DXA scanner by establishing the relationship between the areal
density of the full body scan, and the colour intensity of the pixels from the grayscale images
of the scan, resulted in %RMSE errors of less than 1.5%. This agreed with the accuracy of
previous DXA BSIP estimation methods. Using the proposed DXA method, significant
differences in BSIPs were observed when comparing 10 young adult Caucasian males, 10
elite male swimmers, and 8 elite female swimmers. Elite female swimmers reported
significantly lower segment masses than the other two groups. The male swimmers
recorded greater inertial parameters of the trunk and upper arms than the other two groups.
Also, when using DXA as a criterion against the BSIPs computed for the three populations
when using the five indirect estimation methods, the %RMSE and the comparisons between
absolute percentage error of each indirect method for each group revealed that no BSIP
indirect estimation method performed best for all groups, in segments or BSIPs; as large
errors were observed for each method. Therefore, caution should be taken when computing
BSIPs for elite swimmers and the DXA method should be used when accessible.
Using the proposed DXA method, significant differences in BSIP were observed when
comparing 10 young adult Caucasian males, 10 elite male swimmers, and 8 elite female
swimmers. Elite female swimmers have significantly lower segment masses than the other
two groups, whereas male swimmers have greater inertial parameters of the trunk and upper
arms than the other two groups.
When using DXA as a criterion against the BSIP computed for the three populations using
the five indirect estimation methods, the %RMSE and the comparisons between MAPE of
each indirect method for each group revealed that no BSIP indirect estimation method
performed best for all groups, segments or BSIP, as large errors were observed for each
method. Therefore, caution should be taken when computing BSIP for elite swimmers, and
the DXA method should be used when accessible.
[84]
6.2 Conclusion
Based on the results obtained in this study, it can be concluded that:
• The method developed in this study to compute BSIP from DXA was deemed highly
accurate as errors in whole body mass were inferior to 1.5%;
• A population of elite swimmers have significantly different BSIPs when compared
with young adult Caucasian male;
• Elite male swimmers also have significantly different BSIP when compared to elite
female swimmers;
• None of the 5 proposed indirect BSIP estimation methods emerged to be better than
others in providing accurate BSIPs for any of the subject groups. This was true
even for the BSIPs of untrained participants via Z1, Z2 and Z3.
• While it was generally assumed that the indirect estimation methods would produce
least errors when they are used to estimate BSIPs in subjects that are similar to the
samples used to develop the methods, this study found large errors for the non-
swimming group when using the three methods developed by Zatsiorsky et al.
(Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) which indicated
large individual differences within the group;
6.3 Recommendations for Future Studies
It is recommended that future studies should:
• Investigate the BSIP errors yielded by indirect BSIPs when applied to other elite
sportsmen populations, or outliers in physique types (eg. obese, elderly, etc);
• Investigate the influence of inaccurate BSIPs in dynamic analyses of elite athletes;
• Develop methods to compute full BSIP data by combining DXA with modelling or
other imaging techniques;
[85]
REFERENCES
Ackland, T., Henson, P., & Bailey, D. (1988). The uniform density assumption: Its effect
upon the estimation of body segment inertial parameters. International Journal of Sports
Biomechanics, 4, 146-155.
Ackland, T. R., Elliott, B., & Bloomfield, J. (2009). Applied Anatomy and Biomechanics in
Sport: Human Kinetics Publishers.
Andrews, J. G., & Mish, S. P. (1996). Methods for investigating the sensitivity of joint
resultants to body segment parameter variations. Journal of Biomechanics, 29(5), 651-654.
doi: 10.1016/0021-9290(95)00118-2
Besier, T. F., Sturnieks, D. L., Alderson, J. A., & Lloyd, D. G. (2003). Repeatability of gait
data using a functional hip joint centre and a mean helical knee axis. Journal of
Biomechanics, 36(8), 1159-1168.
Campbell, A., Lloyd, D., Alderson, J., & Elliott, B. (2009). MRI development and validation of
two new predictive methods of glenohumeral joint centre location identification and
comparison with established techniques. Journal of Biomechanics, 42(10), 1527.
Carter, J. E. L., & Ackland, T. R. (1994). Kinanthropometry in Aquatic Sports: a Study of
World Class Athletes: Human Kinetics.
Chandler, R. F., Clauser, C. E., McConville, J. T., Reynolds, H. M., & Young, J. W. (1975).
Investigation of inertial properties of the human body. AMRL-TR-70-137. Ohio: Aerospace
Medical Research Laboratory, Wright-Patterson Air Force Base.
[86]
Cheng, C. K., Chen, H. H., Chen, C. S., Lee, C. L., & Chen, C. Y. (2000). Segment inertial
properties of Chinese adults determined from magnetic resonance imaging. Clinical
Biomechanics, 15(8), 559-566. doi: 10.1016/s0268-0033(00)00016-4
Chin, A., Lloyd, D., Alderson, J., Elliott, B., & Mills, P. (2010). A marker-based mean finite
helical axis model to determine elbow rotation axes and kinematics in vivo. Journal of
Applied Biomechanics, 26(3), 305.
Clauser, C. E., McConville, J. T., & Young, J. W. (1969). Weight, volume, and center of
mass of segments of the human body AMRL-TL-69-70 (Vol. AMRL-TL-69-70). Ohio:
Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base.
Contini, R. (1972). Body Segment Parameters, Part II. Artificial Limbs, 16(1), 1-19.
de Leva, P. (1994). Validity and accuracy of four methods for locating the center of mass of
young male and female athletes. Journal of Biomechanics, 27(6), 763-763. doi:
10.1016/0021-9290(94)91235-1
De Leva, P. (1996). Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters.
Journal of Biomechanics, 29(9), 1223-1230.
Dempster, W. T. (1955). Space requirements of the seated operator. WADC Technical
Report 55159(WADC-55-159, AD-087-892), 55-159.
Dowling, J. J., Durkin, J. L., & Andrews, D. M. (2006). The uncertainty of the pendulum
method for the determination of the moment of inertia. Medical Engineering & Physics,
28(8), 837-841.
Drillis, R., & Contini, R. (1964). Body Segment Parameters. Artificial Limbs, 8(1), 44-66.
Drillis, R., & Contini, R. (1966). Body segment parameters. New York: School of Engineering
and Science, New York University.
[87]
Durkin, J., & Dowling, J. (2006). Body Segment Parameter Estimation of the Human Lower
Leg Using an Elliptical Model with Validation from DEXA. Annals of Biomedical Engineering,
34(9), 1483-1493. doi: 10.1007/s10439-006-9088-6
Durkin, J. L. (2008). Measurement and estimation of human body segment parameters. In Y.
Hong & R. Bartlett (Eds.), Routledge Handbook of Biomechanics and Human Movement
Science (pp. 197-213). Abingdon: Routledge.
Durkin, J. L., & Dowling, J. J. (2003). Analysis of Body Segment Parameter Differences
Between Four Human Populations and the Estimation Errors of Four Popular Mathematical
Models. Journal of Biomechanical Engineering, 125(4), 515-522.
Durkin, J. L., Dowling, J. J., & Andrews, D. M. (2002). The measurement of body segment
inertial parameters using dual energy X-ray absorptiometry. Journal of Biomechanics,
35(12), 1575-1580. doi: 10.1016/s0021-9290(02)00227-0
Durkin, J. L., Dowling, J. J., & Scholtes, L. (2005). Using mass distribution information to
model the human thigh for body segment parameter estimation. Journal of Biomechanical
Engineering, 127, 455-464.
Ellis, K. J. (2000). Human body composition: in vivo methods. Physiological Reviews, 80(2),
649-680.
Erdmann, W. S. (1997). Geometric and inertial data of the trunk in adult males. Journal of
Biomechanics, 30(7), 679-688. doi: 10.1016/s0021-9290(97)00013-4
Fuller, N., Laskey, M., & Elia, M. (1992). Assessment of the composition of major body
regions by dual energy X ray absorptiometry (DEXA), with special reference to limb muscle
mass. Clinical Physiology, 12(3), 253-266.
Ganley, K. J., & Powers, C. M. (2004a). Anthropometric parameters in children: a
comparison of values obtained from dual energy x-ray absorptiometry and cadaver-based
estimates. Gait and Posture, 19(2), 133-140.
[88]
Ganley, K. J., & Powers, C. M. (2004b). Determination of lower extremity anthropometric
parameters using dual energy X-ray absorptiometry: the influence on net joint moments
during gait. Clinical Biomechanics, 19(1), 50-56. doi: 10.1016/j.clinbiomech.2003.08.002
Haarbo, J., Gotfredsen, A., Hassager, C., & Christiansen, C. (1991). Validation of body
composition by dual energy X-ray absorptiometry (DEXA). Clinical Physiology, 11(4), 331-
341. doi: 10.1111/j.1475-097X.1991.tb00662.x
Hanavan Jr, E. P. (1964). A mathematical model of the human body AMRL-TR-64-102, AD-
608-463 (Vol. AMRL-TR-64-102, AD-608-463). Ohio: Aerospace Medical Research
Laboratory, Wright-Patterson Air Force Base.
Hatze, H. (1975). A new method for the simultaneous measurement of the moment of
inertia, the damping coefficient and the location of the centre of mass of a body segment in
situ. European Journal of Applied Physiology and Occupational Physiology, 34(1), 217-226.
Hatze, H. (1980). A mathematical model for the computational determination of parameter
values of anthropomorphic segments. Journal of Biomechanics, 13(10), 833-843. doi:
10.1016/0021-9290(80)90171-2
Henson, P., Ackland, T., & Fox, R. (1987). Tissue density measurement using CT scanning.
Australasian Physical & Engineering Sciences in Medicine, 10(3), 162-166.
Huang, H. K., & Suarez, F. R. (1983). Evaluation of cross-sectional geometry and mass
density distributions of humans and laboratory animals using computerized tomography.
Journal of Biomechanics, 16(10), 821-832. doi: 10.1016/0021-9290(83)90006-4
Jensen, R. K. (1978). Estimation of the biomechanical properties of three body types using a
photogrammetric method. Journal of Biomechanics, 11(8-9), 349-358. doi: 10.1016/0021-
9290(78)90069-6
Kerr, D. A., & Stewart, A. D. (2009). Body composition in sports. In T. R. Ackland, B. C.
Elliott & J. Bloomfield (Eds.), Applied Anatomy and Biomechanics in Sport (pp. 67-86).
Champaign, IL: Human Kinetics.
[89]
Kwon, Y. H. (1996). Effects of the method of body segment parameter estimation on
airborne angular momentum. Journal of Applied Biomechanics, 12(4), 413-430.
Kwon, Y. H. (2001). Experimental simulation of an airborne movement: applicability of the
body segment parameter estimation methods. Journal of Applied Biomechanics, 17(3), 232-
240.
Larivière, C., & Gagnon, D. (1999). The L5/S1 joint moment sensitivity to measurement
errors in dynamic 3D multisegment lifting models. Human Movement Science, 18(4), 573-
587. doi: 10.1016/s0167-9457(99)00003-2
Laskey, M. A. (1996). Dual-energy X-ray absorptiometry and body composition. Nutrition,
12(1), 45-51. doi: 10.1016/0899-9007(95)00017-8
Lee, M. K., Le, N. S., Fang, A. C., & Koh, M. T. H. (2009). Measurement of body segment
parameters using dual energy X-ray absorptiometry and three-dimensional geometry: An
application in gait analysis. Journal of Biomechanics, 42(3), 217-222. doi:
10.1016/j.jbiomech.2008.10.036
Lloyd, D. G., Alderson, J., & Elliott, B. C. (2000). An upper limb kinematic model for the
examination of cricket bowling: a case study of Mutiah Muralitharan. / Modele cinematique d
' un membre superieur pour l ' analyse du lancer en cricket: etude du cas de Mutiah
Muralitharan. Journal of Sports Sciences, 18(12), 975-982.
Lu, J. M., & Wang, M. J. J. (2008). Automated anthropometric data collection using 3D
whole body scanners. Expert Systems with Applications, 35, 407-414. doi:
10.1016/j.eswa.2007.07.008
Martin, P. E., Mungiole, M., Marzke, M. W., & Longhill, J. M. (1989). The use of magnetic
resonance imaging for measuring segment inertial properties. Journal of Biomechanics,
22(4), 367-369, 371-376. doi: 10.1016/0021-9290(89)90051-1
[90]
Mazess, R. B., Barden, H. S., Bisek, J. P., & Hanson, J. (1990). Dual-energy x-ray
absorptiometry for total-body and regional bone-mineral and soft-tissue composition. The
American Journal of Clinical Nutrition, 51(6), 1106.
Mungiole, M., & Martin, P. E. (1990). Estimating segment inertial properties: Comparison of
magnetic resonance imaging with existing methods. Journal of Biomechanics, 23(10), 1039-
1046. doi: 10.1016/0021-9290(90)90319-x
Ogle, G. D., Allen, J. R., Humphries, I. R., Lu, P. W., Briody, J. N., Morley, K., Howman-
Giles, R., & Cowell, C. T. (1995). Body-composition assessment by dual-energy x-ray
absorptiometry in subjects aged 4-26 years. The American Journal of Clinical Nutrition,
61(4), 746-753.
Olds, T. S., & Tomkinson, G. R. (2009). Absolute Body Size. In T. R. Ackland, B. C. Elliott &
J. Bloomfield (Eds.), Applied Anatomy and Biomechanics in Sport (pp. 29-46). Champaign,
IL: Human Kinetics.
Pataky, T. C., Zatsiorsky, V. M., & Challis, J. H. (2003). A simple method to determine body
segment masses in vivo: reliability, accuracy and sensitivity analysis. Clinical Biomechanics,
18(4), 364-368.
Pearsall, D., Reid, J., & Livingston, L. (1996). Segmental inertial parameters of the human
trunk as determined from computed tomography. Annals of Biomedical Engineering, 24(2),
198-210. doi: 10.1007/bf02667349
Pearsall, D. J., & Reid, J. G. (1994). The study of human body segment parameters in
biomechanics. An historical review and current status report. Sports Medicine, 18(2), 126.
Rao, G., Amarantini, D., Berton, E., & Favier, D. (2006). Influence of body segments'
parameters estimation models on inverse dynamics solutions during gait. Journal of
Biomechanics, 39(8), 1531-1536. doi: 10.1016/j.jbiomech.2005.04.014
[91]
Sheets, A. L., Corazza, S., & Andriacchi, T. P. (2010). An Automated Image-Based Method
of 3D Subject-Specific Body Segment Parameter Estimation for Kinetic Analyses of Rapid
Movements. Journal of Biomechanical Engineering, 132.
St-Onge, M.-P., Wang, J., Shen, W., Wang, Z., Allison, D. B., Heshka, S., Pierson, R. N., &
Heymsfield, S. B. (2004a). Dual-Energy X-Ray Absorptiometry-Measured Lean Soft Tissue
Mass: Differing Relation to Body Cell Mass Across the Adult Life Span. The Journals of
Gerontology Series A: Biological Sciences and Medical Sciences, 59(8), B796-B800. doi:
10.1093/gerona/59.8.B796
St-Onge, M.-P., Wang, Z., Horlick, M., Wang, J., & Heymsfield, S. B. (2004b). Dual-energy
X-ray absorptiometry lean soft tissue hydration: independent contributions of intra- and
extracellular water. American Journal of Physiology - Endocrinology And Metabolism,
287(5), E842-E847. doi: 10.1152/ajpendo.00361.2003
Thorpe, J., & Steel, S. (1999). Image resolution of the Lunar Expert-XL. Osteoporosis
International, 10(2), 95-101.
Wang, Z., St-Onge, M.-P., Lecumberri, B., Pi-Sunyer, F. X., Heshka, S., Wang, J., Kotler, D.
P., Gallagher, D., Wielopolski, L., Pierson, R. N., & Heymsfield, S. B. (2004). Body cell
mass: model development and validation at the cellular level of body composition. American
Journal of Physiology - Endocrinology And Metabolism, 286(1), E123-E128. doi:
10.1152/ajpendo.00227.2003
Wicke, J., & Dumas, G. A. (2008). Estimating segment inertial parameters using fan-beam
DXA. Journal of Applied Biomechanics, 24(2), 180-184.
Wicke, J., & Dumas, G. A. (2010). Influence of the volume and density functions within
geometric models for estimating trunk inertial parameters. Journal of Applied Biomechanics,
26(1), 26-31.
Wicke, J., Dumas, G. A., & Costigan, P. A. (2008). Trunk density profile estimates from dual
X-ray absorptiometry. Journal of Biomechanics, 41(4), 861-867. doi:
10.1016/j.jbiomech.2007.10.022
[92]
Wicke, J., Dumas, G. A., & Costigan, P. A. (2009). A comparison between a new model and
current models for estimating trunk segment inertial parameters. Journal of Biomechanics,
42(1), 55-60. doi: 10.1016/j.jbiomech.2008.10.003
Wu, G., van der Helm, F. C. T., Veeger, H. E. J., Makhsous, M., Van Roy, P., Anglin, C.,
Nagels, J., Karduna, A. R., McQuade, K., Wang, X., Werner, F. W., & Buchholz, B. (2005).
ISB recommendation on definitions of joint coordinate systems of various joints for the
reporting of human joint motion—Part II: shoulder, elbow, wrist and hand. Journal of
Biomechanics, 38(5), 981-992. doi: 10.1016/j.jbiomech.2004.05.042
Yeadon, M. (1990). The simulation of aerial movement--II. A mathematical inertia model of
the human body. Journal of Biomechanics, 23(1), 67-74.
Yeadon, M. R., & Morlock, M. (1989). The appropriate use of regression equations for the
estimation of segmental inertia parameters. Journal of Biomechanics, 22(6-7), 683-689. doi:
10.1016/0021-9290(89)90018-3
Zatsiorsky, V. (1983). Biomechanical characteristics of the human body. In W. Baumann
(Ed.), Biomechanics and Performance in Sport. Schorndorf: Karl Hofmann Verlag.
Zatsiorsky, V., & Seluyanov, V. (1983). The mass and inertia characteristics of the main
segments of the human body. In H. Matsui & K. Kobayashi (Eds.), Biomechanics VIII-B (pp.
1152-1159). Champaign, IL: Human Kinetics.
Zatsiorsky, V., & Seluyanov, V. (1985). Estimation of the mass and inertia characteristics of
the human body by means of the best predictive regression equations. In D. Winter (Ed.),
Biomechanics IX-B (pp. 233-239). Champaign, IL: Human Kinetics.
Zatsiorsky, V., Seluyanov, V., & Chugunova, L. (1990). In vivo body segment inertial
parameters determination using a gamma-scanner method. In N. Berme & A. Cappozzo
(Eds.), Biomechanics of Human Movement: Applications in Rehabilitation, Sports and
Ergonomics (pp. 187-202). Bertec, Ohio.
[93]
Appendix AAppendix AAppendix AAppendix A
CONSENT FORM
[94]
Consent Form
I (the participant) have read the information provided and any questions I have asked have
been answered to my satisfaction. I agree to participate in this activity, realising that I may
withdraw at any time without reason and without prejudice.
I understand that all identifiable information that I provide is treated as strictly confidential
and will not be released by the investigator in any form that may identify me. The only
exception to this principle of confidentiality is if documents are required by law.
I have been advised as to what data is being collected, the purpose for collecting the data,
and what will be done with the data upon completion of the research.
I agree that research data gathered for the study may be published provided my name or
other identifying information is not used.
____________________________________ __________
Participant Date
____________________________________ __________
Researcher Date
Approval to conduct this research has been provided by The University of Western Australia,
in accordance with its ethics review and approval procedures. Any person considering
participation in this research project, or agreeing to participate, may raise any questions or
issues with the researchers at any time.
In addition, any person not satisfied with the response of researchers may raise ethics
issues or concerns, and may make any complaints about this research project by contacting
the Human Research Ethics Office at The University of Western Australia on (08) 6488 3703
or by emailing to hreo-research@uwa.edu.au.
All research participants are entitles to retain a copy of any Participant Information For
and/or Participant Consent Form relating to this research project.
Sport Science Exercise and Health
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Nedlands, WA 6009
T 08 6488 2437 F 08 6488 1039 E nat.benjanuvatra@uwa.edu.au www.sseh.uwa.edu.au
CRICOS Provider Code: 00126G
[95]
Appendix B:Appendix B:Appendix B:Appendix B:
INDIRECT ESTIMATION METHODS
[96]
This appendix explains each indirect BSIP used to be compared against the new DXA/3D
surface scan method. All models are breathily explained, along with all anthropometric
measures needed and the equations used to obtain the inertial parameters.
Cadaveric-based geometric method (modified Yeadon (1990)):
The method proposed by Yeadon (1990) was slightly modified to minimise the amount of
measures to be taken and to ensure that most of the measures were in accordance with the
ISAK 2001 protocol (Olds and Tomkinson, 2009).
Geometric solids
The modified version contains a total of 19 different solids. They are classified as
hemispheres, circular cylinders, conical frusta, stadium frusta and complex frusta (stadium-
shaped bottom based with circular top base). These solids are created through sections
perpendicular to the longitudinal axis of the segment (the longitudinal axis passes in the
centre of the section), which can be either circular or stadium-shaped (Fig. 1).
Figure A1: The stadium-shape section (left) and the stadium frustum (right) (Yeadon, 1990).
The circular section has a radius r defined by the girth:
π2girth
r =
The stadium section can be classified as a rectangle of width 2t and depth 2r with an
adjacent semi-circle of radius r at each side (fig 1). The parameters t and r can be defined
through the girth, breadth and/or depth as follow:
[97]
( )( ) 242
2 depthbreadthgirthr =
−−
=π
( )( )
( )242
depthbreadthgirthbreadtht
−=
−−
=π
π
The parameters t and r, along with the height of the solid (distance between the top and
bottom sections) and the density provided for each segment by Dempster (1955) are then
used to calculate the inertial properties of each solid. All anthropometry and heights are
measured in cm. Then, these solids combined form a 16-segment model (head, upper trunk,
middle trunk, lower trunk, upper arms, forearms, hands, thighs, shanks, and feet).
Table A1: Labelling of the solids forming each of the 16 segments, with the respective type of
solid used and density (Kg*l-1
)
Segment Solid Type Density
Head H1 Hemisphere 1.11
H2 Conical Frustum 1.11
H3 Circular cylinder 1.11
Upper Trunk T1 Complex frustum 1.04
T2 Stadium Frustum 0.92
T3 Stadium Frustum 0.92
Middle Trunk T4 Stadium Frustum 1.01
Lower Trunk T5 Stadium Frustum 1.01
Upper Arm U1 Conical Frustum 1.07
U2 Conical Frustum 1.07
Forearm F1 Conical Frustum 1.13
F2 Complex frustum 1.13
Hand Ha1 Stadium Frustum 1.16
Ha2 Stadium Frustum 1.16
Thigh Th1 Conical Frustum 1.05
Th2 Conical Frustum 1.05
Th3 Conical Frustum 1.05
Shank S1 Conical Frustum 1.09
S2 Conical Frustum 1.09
Foot Foot Complex frustum 1.10
Head and trunk:
The head segment comprises two solids at the level of the cranium (H1 and H2) and another
for the neck (H3). H1 is the only hemisphere used in the whole model, whereas H2 is an
inverted conical frustum (top base larger than bottom one) and H3 is a circular cylinder.
[98]
The trunk suffered the greatest amount of modifications when compared to the original
model (Yeadon, 1990). The upper trunk is subdivided into T1 (complex frustum), T2 and T3
(stadium frusta). T4 (stadium frustum) represents the middle trunk and T5 represents the
lower trunk. This modified model of the trunk enabled a better representation of the upper
trunk specially for the swimmers and also enabled its segmentation into the three sub-
segments, using the same protocol proposed by Zatsiorsky and Seluyanov (1983).
Table A2: Labelling of the sections as bottom (b) or top (t) base of the solids, anthropometric
measures used to determine the parameters r and t for each section and the position relative
to the longitudinal axes of the referred segments
Section Shape Anthropometry Level
H1(b)=H2(t) Circular Head Girth Glabella
H2(b)=H3(t) Circular Head Girth Chin/neck junction
H3(b)=T1(t) Circular Neck Girth C7
T1(b)=T2(t) Stadium Suprasternale depth
Biacromial breadth
Suprasternale
T2(b)=T3(t) Stadium Chest girth
Transverse chest breadth
Mesosternale
T3(b)=T4(t) Stadium Lower chest girth
Lower chest breadth
Xyphoid process
T4(b)=T5(t) Stadium Waist girth
Waist breadth
Navel
T5(b) Stadium Gluteal girth
Bitrochanterion breadth
Hip joint centre
U1(t) Circular Proximal upper arm girth Shoulder joint centre
U1(b)=U2(t) Circular Arm girth relaxed Mid-distance between shoulder and
elbow joint centres
U2(b)=F1(t) Circular Elbow joint centre girth Elbow joint centre
F1(b)=F2(t) Circular Forearm girth Forearm girth
F2(b)=Ha1(t) Stadium Wrist girth
Wrist breadth
Wrist joint centre
Ha1(b)=Ha2(t) Stadium Hand girth
Hand breadth
Distal point of the third metacarpal
Ha2(b) Stadium Palm girth
Palm breadth
Distal point of the middle finger
Th1(t) Circular Gluteal girth
Bitrochanterion breadth
(same r value as T5(b))
Hip joint centre
Th1(b)=Th2(t) Circular Thigh girth Thigh girth
Th2(b)=Th3(t) Circular Mid-thigh girth Mid-thigh girth
Th3(b)=S1(t) Circular Knee joint centre girth Knee joint centre
S1(b)=S2(t) Circular Calf girth Calf girth
S2(b)=Foot(t) Circular Ankle joint centre girth Ankle joint centre
Foot(b) Stadium Ball of the foot girth
Ball of the foot breadth
Distal point of second toe
[99]
Upper limbs:
The upper arm comprises two conical frusta, U1 and U2. For the forearm, the distal solid
was a conical frustum, whereas the distal solid was a complex frustum, with circular section
at the level of maximum forearm girth and stadium section at the wrist joint centre.
The hand was modified from the original (Yeadon, 1990) as it comprises two frusta, Ha1 and
Ha2. Even though the bottom base for Ha2 was calculated using the anthropometric
measures at the level of the third metacarpal, its location is at the level of the distal point of
the middle finger.
Lower limbs:
The thigh comprises three circular frusta (Th1, Th2, and Th3). The top circular section of
Th1 is calculated using the same anthropometric measures of the bottom stadium section of
T5, as the parameter r for the stadium section is the same for the circular section. The shank
comprises two conical frusta (S1 and S2).
The foot comprises only one complex frustum (Foot), with a distal stadium-shape section
and a proximal circular section. Even though the stadium section is calculated at the level of
the ball of the foot, its level is at the distal point of the distal phalange of the second toe.
[100]
Figure A2: Representation of the solids for the modified Yeadon’s model.
Calculation of each solid’s inertial properties
Five different solids are used: hemisphere, circular cylinder, conical frustum and stadium-
shape frustum and specifically for the distal forearm solids and feet, a frustum with stadium-
shape bottom section and circular top section is also calculated. For all formulas, the
parameters r and t are used along with the height (h) and density (D). The density value is
specific for each segment, obtained from the study of Dempster (1955) and presented in
Table A1. The inertial properties are then defined as mass (M), centre of mass position
along the longitudinal axis (HCM) and the principal moments of inertia about the sagittal (IX),
longitudinal (IY) and transverse (IZ) axes.
Hemisphere:
Only adopted for the H1 (head).
[101]
3
3
2rDM ⋅⋅⋅= π
(Formula A1)
rH CM ⋅=8
3, from the circular face (Formula A2)
2
320
83rMII ZX ⋅⋅==
(Formula A3)
2
5
2rMIY ⋅⋅=
(Formula A4)
Cylinder:
Adopted for the H3 solid (head).
hrDM ⋅⋅⋅=2
π (Formula A )
2
hH CM =
(Formula A6)
22
12
1
4
1hMrMII ZX ⋅⋅+⋅⋅==
(Formula A7)
2
2
1rMIY ⋅⋅=
(Formula A8)
Conical Frustum:
Adopted for H2, U1, U2 (upper arm), F1 (forearm), Th1, Th2, Th3 (thigh), S1 and S2
(shank).
( )2
110
2
03
1rrrrDhM ++= π
(Formula A 9)
( )( )2
110
2
0
2
110
2
0
4
32
rrrr
rrrrhHCM
++
++=
(Formula A10)
[102]
( ) ( )( )2
1
2
010
4
1
4
0
3
10
2
1
2
01
3
0
2
110
2
0
2
20
3632
rrrr
rrrrrrrrrrrrhMII ZX
++
+++++++==
π
(Formula A11)
( )( )2
1
2
010
4
1
4
0
3
10
2
1
2
01
3
0
10
3
rrrr
rrrrrrrrMIY
++
++++=
π (Formula A12)
Stadium Frustum:
Adopted for T2, T3, T4, T5 (trunk), Ha1 and Ha2 (hand). T1 (trunk, F2 (forearm) and Foot
are a special frusta that has a stadium-shape bottom section and a circular top section.
Therefore, in order to calculate their inertial properties, the same formula used for the
stadium frustum is applied, but using the parameter t for the top section as equal to 0.
If a solid is regarded as a series of parallel slices of infinitesimal thickness orthogonal to the
longitudinal (Y) axis, the inertial parameters can be calculated according to the formulas:
∫ ⋅⋅⋅=
1
0
dyAhDM
(Formula A13)
∫ ⋅⋅⋅⋅
=
1
0
2
dyAyM
hDHCM
(Formula A 14)
2
1
0
23
1
0
CMXX HMdyAyhDdyJhDI ⋅−⋅⋅⋅⋅+⋅⋅⋅= ∫∫ (Formula A15)
∫ ⋅⋅⋅=
1
0
dyJhDI YY
(Formula A16)
2
1
0
23
1
0
CMZZ HMdyAyhDdyJhDI ⋅−⋅⋅⋅⋅+⋅⋅⋅= ∫∫
(Formula A17)
[103]
Where JX, JY and JZ are the second moments of area about the xslice, yslice and zslice axes of a
slice (stadium shape), respectively, and thus the integrals ∫ ⋅
1
0
dyJ X , ∫ ⋅
1
0
dyJY , and
∫ ⋅
1
0
dyJ Z are the respective summation of the second moments of area of all slices for each
axis. The theorem of parallel axes is used to calculate (i) the summation of each slice’s
second moment of area about the xsolid and zsolid axes of the solid coordinate system (insert
figure) through the integral ∫1
0
2 Adyy , where y is the normalized distance ( 10 ≤≤ y ) of the
slice from the plane xz and A is the area of the slice in function of the distance, and (ii) the
moment of inertia of the whole solid about the respective xCM and zCM axes passing through
the centre of mass of the solid.
In order to simplify the calculation of all integrals, Yeadon (1990) used the parameters r0 and
t0 for the lower bounding stadium and r1 and t1 for the upper bounding stadium (Fig. 2).
Thus, the parameters a and b are calculated as:
( )0
01
rrr
a−
= (Formula A18)
( )0
01
ttt
b−
= (Formula A19)
The following functions are then defined through the equations:
( ) ( ) bababaF ⋅⋅++⋅+=
3
1
2
11,1
(Formula A20)
( ) ( ) bababaF ⋅⋅++⋅+=
4
1
3
1
2
1,2
(Formula A21)
( ) ( ) bababaF ⋅⋅++⋅+=
5
1
4
1
3
1,3
(Formula A22)
[104]
( ) ( ) ( ) ( ) ( )32
5
13
4
13
2
11,4 abbabbabbabaF ++⋅++⋅++⋅+=
(Formula A23)
( ) ( ) ( ) ( ) ( )2222
5
1
2
14
3
11,5 babaabbabababaF ++⋅+++⋅+++=
(Formula A24)
Therefore, all the previous integrals can be calculated as:
( ) ( )[ ]aaFrbaFtrhDM ,1,14000
⋅⋅+⋅⋅⋅⋅= π
(Formula A25)
( ) ( )[ ]M
aaFrbaFtrhDHCM
,2,242
0002 ⋅⋅+⋅⋅⋅⋅⋅=
π
(Formula A 26)
( ) ( ) ( ) ( )∫ ⋅⋅⋅+⋅⋅+⋅⋅⋅+⋅⋅⋅=
1
0
4
00
3
0
2
0
2
0
3
00,4
4
1,4
3
8,5,4
3
4aaFrabFtrbaFtrbaFtrdJ yX ππ
(Formula A27)
( ) ( ) ( ) ( )aaFrabFtrbaFtrbaFtrdyJY ,42
1,44,5,4
3
4 4
00
3
0
2
0
2
0
3
00
1
0
⋅⋅⋅+⋅⋅+⋅⋅⋅+⋅⋅⋅=∫ ππ
(Formula A28)
( ) ( )aaFrbaFtrdyJ Z ,44
1,4
3
4 4
0
3
00
1
0
⋅⋅⋅+⋅⋅⋅=∫ π
(Formula A29)
( ) ( )aaFrbaFtrAdyy ,3,342
000
1
0
2⋅⋅+⋅⋅⋅=∫ π
(Formula A30)
[105]
Cadaveric-based regression equation method (modified Chandler et al.
(1975))
The cadaver-based method by Chandler et al. (1975) provided simple equations for
segment’s mass and principal moments of inertia using either whole body mass (BW) or
segment’s volume as predictors, along with the average centre of mass position on the
longitudinal axis. Rather than using the BW as predictors to the principal moments of inertia,
the non-linear equations proposed in the study of Yeadon and Morlock (1989) will be
applied, as they were devised from the same cadaveric cohort used in the study of Chandler
et al. (1975).
Apart from the trunk segment (which was not subdivided for this method), the non-linear
equations only used the anatomical length and mean girth ((p1 + p2)/2 when using two girths,
or (p1 + 2p2 + p3)/4 when using three girths) of the segments as predictors. For the trunk, the
anatomical length, mean girth ((p1 + 2p2 + p3)/4) and breadth ((w1 + 2w2 + w3)/4) were used
as predictors (table A2).
In order to suit the method to the biomechanical model used in the study (Appendix D), the
head and trunk centre of mass positions and moments of inertia equations were recalculated
as new coordinate systems were created and different predictors for the moments of inertia
equations were used (table A4).
[106]
Table A3: mass (Kg) and principal moments of inertia (Kg*cm2) equations and average centre of
mass position obtained for the modified study of Chandler et al. (1975).
Segment Mass Centre of Mass Moments of Inertia (10-6
)
Head 0.032BW + 1.906 61.19% IX = IZ = 6M IY +2.19p
2h
3
IY = 1.315p4h
Trunk 0.532BW – 0.706 49.4% IX = dwh[58.66w2 + 92.63h
2]
Iy = dwh[86.67d2 + 58.66w
2]
IZ = dwh[86.67d2 + 92.63h
2]
Right upper arm 0.016BW + 0.809 48.65% IX = IZ = 6M IY + 6.11p
2h
3
IY = 0.979p4h
Right forearm 0.020BW – 0.218 58.76% IX = IZ = 6M IY + 4.98p
2h
3
IY = 0.81p4h
Right hand 0.007BW - 0.030 44.75% IX = IZ = 6M IY + 7.68p
2h
3
IY = 1.309p4h
Left upper arm 0.022BW + 0.485 49.42% IX = IZ = 6M IY + 6.11p
2h
3
IY = 0.979p4h
Left forearm 0.013BW + 0.246 58.41% IX = IZ = 6M IY + 4.98p
2h
3
IY = 0.81p4h
Left hand 0.005BW + 0.076 40.84% IX = IZ = 6M IY + 7.68p
2h
3
IY = 1.309p4h
Right thigh 0.126BW + 1.688 61.19% IX = IZ = 6M IY + 8.12p
2h
3
IY = 1.593p4h
Right shank 0.038BW + 0.179 57.59% IX = IZ = 6M IY + 5.73p
2h
3
IY = 0.853p4h
Right foot 0.008BW + 0.343 43.74% IX = IZ = 6M IY + 3.72p
2h
3
IY = 1.001p4h
Left thigh 0.127BW - 1.511 60.51% IX = IZ = 6M IY + 8.12p
2h
3
IY = 1.593p4h
Left shank 0.044BW – 0.178 58.66% IX = IZ = 6M IY + 5.73p
2h
3
IY = 0.853p4h
Left foot 0.009BW + 0.253 43.92% IX = IZ = 6M IY + 3.72p
2h
3
IY = 1.001p4h
[107]
Table A4: modified predictors for the non-linear equations for segmental moments of inertia
Segment Predictor Definition
head h Stature - C7 height
p Head girth
trunk h C7 height – trochanterion height
p1 Chest girth
w1 Transverse chest breadth
p2 Waist girth
w2 Waist breadth
p3 Gluteal girth
w3 Bitrochanterion breadth
Gamma-ray-based simple regression method (Zatsiorsky and
Seluyanov, 1983)
Zatsiorsky and Seluyanov (1983) presented a set of linear equations using only the whole
body mass and height as predictors for all BSIP. Those equations were devised from a
cohort of 100 male Caucasian men analysed with the gamma-ray scanner.
[108]
Table A5: Coefficients of the linear regression equations to determine the inertial parameters of
the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the
body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the
longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2
Head M 1.296 0.0171 0.0143
HCM 8.357 -0.0025 0.023
IXX -78 1.171 1.519
IYY 61.6 1.72 0.0814
IZZ -112 1.43 1.73
Upper Trunk M 8.2144 0.1862 -0.0584
HCM 3.32 0.0076 0.047
IXX 81.2 36.73 -5.97
IYY 561 36.03 -9.98
IZZ 367 18.3 -5.73
Middle Trunk M 7.181 0.2234 -0.0663
HCM 1.398 0.0058 0.045
IXX 618.5 39.8 -12.87
IYY 1501 43.14 -19.8
IZZ 263 26.7 -8
Lower Trunk M -7.498 0.0976 0.04896
HCM 1.182 0.0018 0.0434
IXX -1568 12 7.741
IYY -775 14.7 1.685
IZZ -934 11.8 3.44
[109]
Table A6: Coefficients of the linear regression equations to determine the inertial parameters of
the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the body
weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the
longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2
Upper Arm M 0.25 0.03012 -0.0027
HCM 1.67 0.03 0.054
IXX -250.7 1.56 1.512
IYY -16.9 0.662 0.035
IZZ -232 1.525 1.343
Forearm M 0.3185 0.01445 -0.00114
HCM 0.192 -0.028 0.093
IXX -64 0.95 0.34
IYY 5.66 0.306 -0.088
IZZ -67.9 0.855 0.376
Hand M -0.1165 0.0036 0.00175
HCM 4.11 0.026 0.033
IXX -19.5 0.17 0.116
IYY -6.26 0.0762 0.0347
IZZ -13.68 0.088 0.092
[110]
Table A7: Coefficients of the linear regression equations to determine the inertial parameters of
the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the body
weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the
longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or
transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2
Thigh M -2.649 0.1463 0.0137
HCM -2.42 0.038 0.135
IXX -3557 31.7 18.61
IYY -13.5 11.3 -2.28
IZZ -3690 32.02 19.24
Shank M -1.592 0.0362 0.0121
HCM -6.05 -0.039 0.142
IXX -1105 4.59 6.63
IYY -70.5 1.134 0.3
IZZ -1152 4.594 6.815
Foot M -0.829 0.0077 0.0073
HCM 3.767 0.065 0.033
IXX -100 0.48 0.626
IYY -15.48 0.144 0.088
IZZ -97.09 0.414 0.614
Gamma-ray-based multiple regression method (Zatsiorsky and
Seluyanov, 1985)
Using the same cohort of the previous study (1983) Zatsiorsky and Seluyanov devised linear
equations with the most predictable anthropometric measures, as they were mostly taken
from the same segment whose inertial parameters were calculated. Total body fat (in Kg)
was also included in some segments’ equations, and was measured using the DXA scan.
Four predictors were used for the head and trunk segments, whereas for all limb segments
only three predictors were used.
[111]
Table A8: Coefficients of the linear regression equations to determine the inertial parameters of
the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3 + B4X4,
where X1, X2, X3 and X4 are the most predictive anthropometric measures for each segment and
Y is segment’s mass (M), centre of mass position on the longitudinal axis (HCM), or moments of
inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2 B3 B4
Head M -7.385 0.146 0.071 0.0356 0.199
HCM 0.21 0.503 0.027 0.043 -0.158
IXX -987 23.74 3.97 3.46 18.58
IYY -721 7.36 6.14 2.28 18.25
IZZ -983 19.9 8.43 3.22 10.2
Upper Trunk M -18.91 0.421 0.199 0.078 0.065
HCM -2.854 0.567 0.0067 0.0321 0.0152
IXX -5175 105.4 45.8 4.01 8.65
IYY -4149 54.8 43.7 8.88 9.63
IZZ -2650 65.6 17.12 5.84 9.8
Middle Trunk M -13.62 0.444 0.195 -0.017 0.0887
HCM -0.742 0.485 0.0007 -0.002 0.001
IXX -3271 76.7 30.3 10.2 18.3
IYY -2657 43 33.3 1.6 20.6
IZZ -2354 65.3 21.5 -2.3 10.57
Lower Trunk M -15.18 0.182 0.243 0.0216 0
HCM 0.205 0.064 0.134 -0.08 0
IXX -2354 22.6 34.37 4.41 0
IYY -2009 20.1 24.9 11.2 0
IZZ -1816 18 23.6 7.29 0
[112]
Table A9: Coefficients of the linear regression equations to determine the inertial parameters of
the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3, where X1, X2 and
X3 are the most predictive anthropometric measures for each segment and Y is segment’s
mass (M), centre of mass position on the longitudinal axis (HCM), or moments of inertia about
the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2 B3
Upper Arm M -2.58 0.0471 0.104 0.0651
HCM -2.004 0.566 0.056 -0.016
IXX -359 10.2 6.4 8.5
IYY -106 0.4 3.8 4.5
IZZ -331 10.3 5.5 5.6
Forearm M -2.04 0.05 -0.0049 0.087
HCM 0.732 0.588 -0.0857 -0.0187
IXX -229 7.12 -0.049 5.066
IYY -39.2 0.56 -0.972 1.996
IZZ -220 7.06 -0.082 4.544
Hand M -0.594 0.941 0.035 0.029
HCM -3.055 0.596 0.264 0.091
IXX -41.05 2.29 1.62 1.27
IYY -14.9 0.596 -0.814 0.818
IZZ -26.6 1.818 -1.083 0.527
[113]
Table A10: Coefficients of the linear regression equations to determine the inertial parameters
of the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3, where X1, X2
and X3 are the most predictive anthropometric measures for each segment and Y is segment’s
mass (M), centre of mass position on the longitudinal axis (HCM), or moments of inertia about
the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.
Inertial
Parameters
Coefficients for the multiple regression
Segment B0 B1 B2 B3
Thigh M -17.819 0.153 0.23 0.367
HCM -3.655 0.478 -0.07 0.088
IXX -6729 87.8 50.3 75.3
IYY -1173 4.06 6 26.8
IZZ -6774 88.4 38.6 78
Shank M -6.017 0.0675 0.0145 0.205
HCM 0.0937 0.396 0.064 -0.041
IXX -1437 28.64 3.202 21.6
IYY -194.8 0.214 -3.64 8.9
IZZ -1489 28.97 6.48 21.5
Foot M -0.6286 0.066 -0.0136 0.0048
HCM -1.267 0.519 0.176 0.061
IXX -91.17 5.25 0.335 0.386
IYY -11.9 0.771 0.047 0.243
IZZ -89.1 4.788 0.477 0.271
[114]
Table A11: The most predictable anthropometric measures for each segment to be used in the
multiple linear equations for inertial parameters of the head and trunk segments.
Segment Variables
Head X1 = head length (stature – C7 height), cm
X2 = head girth, cm
X3 = RSTR>M , where
D1 = head girth, cm
D2 = neck girth, cm
X4 = diameter of the head (head girth/π), cm
Upper Trunk X1 = upper trunk length (C7 height – xyphoid process height), cm
X2 = chest girth, cm
X3 = transverse chest breadth, cm
X4 = fat, Kg
Middle Trunk X1 = length of the middle trunk (xyphoid process height – navel height),
cm
X2 = waist girth, cm
X3 = bitrochanterion breadth, cm
X4 = fat, Kg
Lower Trunk X1 =gluteal girth, cm
X2 =bispinal breadth, cm
X3 = fat, Kg
Table A12: The most predictable anthropometric measures for each segment to be used in the
multiple linear equations for inertial parameters of the head and trunk segments.
Segment Variables
Upper arm X1 = upper arm length*0.73, cm
X2 = arm girth relaxed, cm
X3 = RSTR>M , where
D1 = lower diameter of the upper arm (elbow girth/π), cm
D2 = lower diameter of the forearm (wrist girth/π), cm
Forearm X1 = forearm length, cm
X2 = hand breadth, cm
X3 =RSTR>TRUM , where
D1 = wrist girth, cm
D2 = forearm girth, cm
D3 = elbow girth, cm
Hand X1 = hand length, cm
X2 = hand breadth, cm
X3 = RSTR>M , where
D1 = hand girth, cm
D2 = wrist girth, cm
Table A13: The most predictable anthropometric measures for each segment to be used in the
multiple linear equations for inertial parameters of the head and trunk segments.
[115]
Segment Variables
Thigh X1= thigh length, cm
X2= knee diameter (knee girth/π) , cm
X3 = RSTR>TRUM , where
D1 = knee girth, cm
D2 = mid-thigh girth, cm
D3 = thigh girth, cm
Shank X1= leg length, cm
X2= ankle diameter (ankle girth/π) , cm
X3 = RSTR>TRUM , where
D1 = knee girth, cm
D2 = ankle girth, cm
D3 = calf girth, cm
Foot X1= foot length, cm
X2= foot breadth, cm
X3= fat, Kg
Gamma-ray-based geometric method (Zatsiorsky et al., 1990)
Zatsiorsky, Seluyanov and Chugunova developed the geometrical model from the same
cohort of the foremost gamma-ray study (1983) aiming to provide BSIP to populations of
distinct characteristics of those analysed with the gamma-ray scanner. Each segment is
regarded as a circular cylinder, and therefore its mass is calculated using its girth (G) and
biomechanical length (L, the anthropometric length multiplied by a coefficient KB provided):
π4
2GLK
M D ⋅⋅=
(Formula A31)
Where KD is the quasidensity of the segment, calculated from the average mass of the
segment of the analysed cohort measured with the gamma-ray scanner divided by the
average quasivolume (cylinder volume). The segment mass coefficient (Ki=KD/4π) is then
provided by the authors. A coefficient for correction is also calculated as the ratio between
the summations of all calculated segment masses and the whole body weight to minimize
discrepancies.
Table A14: Anthropometric lengths and girths used to create the geometrical model of the
subject and determine the inertial parameters. The coefficient KB is used to multiply the
[116]
anthropometric length to obtain the biomechanical length.
Segment KB Length Girth
Head 0.76 Head length (stature - C7 height) Head girth
Upper trunk 1.456 Upper trunk length (C7 height - xyphoid process
height)
Chest girth
Middle trunk 1.035 Middle trunk length (xyphoid process height -
navel height)
Waist girth
Lower trunk 2.305 Middle trunk length (xyphoid process height -
midASIS height)
Gluteal girth
Upper arm 0.73 Upper arm length Arm girth relaxed
Forearm 1 Forearm length Forearm girth
Hand 1 Hand length Hand girth
Thigh 1.083 Thigh length Thigh girth
Shank 1 Leg length Calf girth
Foot 1 Foot length Foot girth
Then, the principal moments of inertia are calculated as follows:
2MLKI XX = (Formula A32)
2MCKI YY = (Formula A33)
2MLKI ZZ = (Formula A34)
Where KX, KY, and KZ are the moments of inertia coefficients for the sagittal, longitudinal and
transverse axes, respectively. Given the different orientation of the foot segment, the
squared circumference is used in the equation to determine IX; conversely, the squared
length is used in the equation to determine IY.
[117]
Table A15: Segment mass coefficients (KM), and the moments of inertia coefficients relative to
the sagittal (KX), longitudinal (KY) and transverse (KZ) axes.
Segment Km����10-5
KX����10-2
KY����10-2
KZ����10-2
Head 6.37 8.68 1.25 9.38
Upper Trunk 5.72 21.83 1.35 9.35
Middle Trunk 8.49 20.65 1.43 12.6
Lower Trunk 3.6 10.9 0.76 8.92
Upper Arm 9.67 10.81 2.06 9.71
Forearm 6.26 7.55 1.51 7.03
Hand 5.54 6.65 2.29 4.86
Thigh 6.64 7.18 1.33 7.18
Shank 5.85 8.77 1.44 8.44
Foot 6.14 1.6 7.86 7.14
The study also provided the centre of mass position as the average values of the analysed
cohort. However, the authors used anatomical landmarks rather than the joint centres as
reference for locating the centre of mass and defining segment’s length, and therefore the
adjustments to the centre of mass position proposed by de Leva (1996) were used instead.
The centre of mass position for the head and the upper trunk were adjusted so the projection
of C7 onto the longitudinal axis was used as endpoint between the head and upper trunk.
Therefore, the centre of mass position for the head was 49.98% and for the upper trunk was
49.34%.
[118]
Appendix C:Appendix C:Appendix C:Appendix C:
ANTHROPOMETRIC MEASURES
[119]
Most of the measures are defined according to the ISAK 2001 protocol (Olds and
Tomkinson, 2009). Whenever a measure is not defined by the protocol, its explanation is
given by the study that used it.
All measures except the thigh length were taken from the 3D surface scan of the subject.
The thigh length was obtained from the DXA image, which allowed the visualization of the
throcanter and the lateral epicondyle of the femur. Breadths, girths and lengths were
calculated using the Artec Studio software, whereas the heights were calculated using the
MeshLab, as a Global Coordinate System (GCS) with a sagittal plane at the level of the floor
needed to be created.
For the modified Yeadon methods and the moments of inertia calculated for the modified
Chandler method, anatomical lengths were also used. These lengths are the distance
between two joint centres or end points.
Heights and Lengths:
Stature: the linear distance from the floor level to the subject’s vertex, measured with a
stadiometer. Used in all BSIP estimation methods.
C7 height: the linear distance from the floor level to the subject’s C7 vertebra, measured
with a stadiometer. It is not an ISAK anthropometric measure. Used in the Zatsiorsky
(multiple regression) and Chandler methods.
Suprasternale height: the linear distance from the floor level to the subject’s suprasternale,
measured with a stadiometer. It is not an ISAK anthropometric measure. Used in the
Zatsiorsky (geometrical) method.
Xiphoid process height: the linear distance from the floor level to the subject’s xiphoid
process, measured with a stadiometer. It is not an ISAK anthropometric measure. Used in
the Zatsiorsky (multiple regression and geometrical) methods.
[120]
Navel height: the linear distance from the floor level to the subject’s navel, measured with a
stadiometer. It is not an ISAK anthropometric measure. Used in the Zatsiorsky (multiple
regression and geometrical) methods.
Mid ASIS height: the linear distance from the floor level to the midpoint of the subject’s
anterior superior iliac spine (ASIS), measured with a stadiometer. It is not an ISAK
anthropometric measure. Used in the Zatsiorsky (geometric) method.
Trochanterion height: the linear distance from the floor level to the trochanterion,
measured with a stadiometer while subject maintains an upright stance with feet together.
Used in the Chandler method.
Acromiale – Radiale length (upper arm length): the linear distance from the acromiale to
the radiale, measured with a segmometer. With the right forearm pronated, anchor the end
pointer to the acromiale and move the housing pointer to the radiale. Used in the Zatsiorsky
(multiple regression and geometrical) methods.
Radiale – Stylion length (forearm length): the linear distance from the radiale to the
stylion, to the radiale measured with a segmometer. With the subject standing up, anchor
the end pointer to the radiale and move the housing pointer to the stylion. Used in the
Zatsiorsky (multiple regression and geometrical) methods.
Midstylion – Dactylion length (hand length): the linear distance from the midstylion to the
dactylion, measured with a segmometer. Anchor the end pointer at the midstylion mark and
move the housing pointer to the dactylion. Used in the Zatsiorsky (multiple regression and
geometrical) methods.
Trochanterion – Tibiale laterale length (thigh length): the linear distance from the
trochanter to the tibiale laterale, measured with a segmometer. The subject stands with feet
together and arms folded across the chest. Anchor the end pointer at the trochanter mark
and move the housing pointer to the tibialle laterale. Used in the Zatsiorsky (multiple
regression and geometrical) methods.
[121]
Tibiale mediale-sphyrion tibiale length (leg length): the linear distance from the tibiale
mediale to the sphyrion tibiale, measured with a segmometer. The subject is seated with the
right ankle resting on the left knee. Anchor the end pointer at the tibiale mediale mark and
move the housing pointer to the sphyrion tibiale mark. Used in the Zatsiorsky (multiple
regression and geometrical) methods.
Foot length: the distance from the heel to the distal point of the distal phalang of the second
toe, measured with a calliper. Used in the Zatsiorsky (multiple regression and geometrical)
methods.
Breadths and depths:
Suprasternale depth: the linear distance between the suprasternale and the spinous
process of the vertebra at the horizontal level of the suprasternale, measured with a sliding
calliper. Subject is in a sitting position with hands resting on the thighs. It is not an ISAK
measure. Used in the Yeadon method.
Biacromial breadth: the distance between the most lateral points on the acromion process,
measured with a sliding calliper. Measures are taken behind the subject who holds and
upright stance, with the calliper branches angled at approximately 30o pointing upwards.
Used in the Yeadon method.
Transverse chest breadth: the distance between the most lateral aspects of the torax
when the top of the body of the sliding calliper is positioned at the level of the mesosternale,
and branches angled 30o downwards. Used in the Zatsiorsky (multiple regression) and
Yeadon methods.
Lower chest breadth: the distance between the most lateral aspects of the torax when the
top of the body of the sliding calliper is positioned at the level of the xiphoid process, and
branches angled 30o downwards. It is not an ISAK measure. Used in the Yeadon method.
Waist breadth: the distance between the most lateral aspects of the torax when the top of
the body of the sliding calliper is positioned at the level of the navel. It is not an ISAK
measure. Used in the Yeadon method.
[122]
Bispinal breadth: the distance between the left and right anterior superior iliac spines,
measured with a calliper with branches angled 45o upwards. Subject stands with arms
across the chest. Used in the Zatsiorsky (multiple regression) method.
Bitrochanterion breadth: the distance between the greatest posterior protuberance of the
buttocks, measured with a sliding calliper. It is not an ISAK measure. Used in the Yeadon
method.
Wrist breadth: the distance between the styloid processes of the ulna and the radio,
measured with a segmometer. It is not an ISAK measure. Used in the Yeadon method.
Hand breadth: measured with the calliper perpendicular to the longitudinal axis of the hand
and one branch at the first metacarpal-phalangeal joint (base of the thumb). It is not an ISAK
measure. Used in the Zatsiorsky (multiple regression) and Yeadon methods.
Palm breadth: measured at the level of the second to fourth metacarpal-phalangeal joints
with a sliding calliper. It is not an ISAK measure. Used in the and Yeadon method.
Ball of the foot breadth: measured at the level of the metatarsal-phalangeal joints (I to V)
with a sliding calliper. It is not an ISAK measure. Used in the Zatsiorsky (multiple regression)
and Yeadon methods.
Girths:
Head girth: measured with an anthropometric tape at the level of the glabella. Subject
seated and head in the Frankfort plane. Used in the Zatsiorsky (multiple regression and
geometric), Chandler and Yeadon methods.
Neck girth: measured with an anthropometric tape at the level immediately superior to the
thyroid cartilage. Subject seated and head in the Frankfort plane. Used in the Zatsiorsky
(multiple regression) and Yeadon methods.
Chest girth: measured with an anthropometric tape at the level of the mesosternale.
Subject raises the arms and following lowers them as the measurement is taken. Used in the
Zatsiorsky (multiple regression and geometric) and Yeadon methods.
[123]
Lower chest girth: measured with an anthropometric tape at the level of the xiphoid
process. Subject raises the arms and following lowers them as the measurement is taken. It
is not an ISAK measure. Used in the Yeadon method.
Waist girth: measured with an anthropometric tape at the level of the navel. Subject folds
the arms while measured. Used in the Zatsiorsky (multiple regression and geometric) and
Yeadon methods.
Gluteal girth: measured with an anthropometric tape at the level of the trochanter (greatest
posterior protuberance of the buttocks). Subject stands erect with feet together and gluteal
muscles relaxed. Used in the Zatsiorsky (multiple regression and geometric) and Yeadon
methods.
Proximal upper arm girth: measured at the highest up the upper arm as possible. Subject
adducts the arm without raising the scapula. It is not an ISAK measure. Used in the
Hanavan, Zatsiorsky (multiple regressin) and Yeadon methods.
Arm girth relaxed: measured with an anthropometric tape at the level of the midacromiale-
radiale. The subject assumes a relaxed position with the arm hanging by the side. Used in
the Zatsiorsky (multiple regression and geometric) and Yeadon methods.
Elbow joint centre girth: measured with an anthropometric tape at the level of the knee
joint centre. Subject maintains the elbow fully extended. It is not an ISAK measure. Used in
the Hanavan, Zatsiorsky (multiple regression) and Yeadon methods.
Forearm girth: measured with an anthropometric tape at the maximum girth of the forearm
distal to the humeral epicondyles. Used in the Zatsiorsky (multiple regression and geometric)
and Yeadon methods.
Wrist girth: the minimum writ girth distal to the styloid processes, measured with an
anthropometric tape. Subject maintains the forearm supinated and the hand relaxed. Used in
the Hanavan, Zatsiorsky (multiple regression and geometric) and Yeadon methods.
[124]
Hand girth: measured with an anthropometric tape at the level of the first metacarpal-
phalangeal joint (base of the thumb). Subject maintains fingers extended and together. It is
not an ISAK measure. Used in the Zatsiorsky (multiple regression) and Yeadon methods.
Palm girth: measured with an anthropometric tape at the level of the distal points of the four
last metacarpals. Subject maintains fingers extended and together. It is not an ISAK
measure. Used in the Hanavan and Yeadon methods.
Thigh girth: measured roughly 2 cm below the gluteal fold with an anthropometric tape.
Subject stands erect with the feet slightly apart, the tapes is passed around the leg and slipe
up using a cross-handed technique to a horizontal position. Used in the Hanavan, Zatsiorsky
(multiple regression) and Yeadon methods.
Midthigh girth: measured at the level of the midtrochanterion-tibiale laterale landmark with
an anthropometric tape. Subject stands erect with the feet slightly apart, the tapes is passed
around the leg and slipe up using a cross-handed technique to a horizontal position. Used in
the Zatsiorsky (multiple regression) and Yeadon methods.
Knee joint centre girth: measured at the level of the two epicondyles with an
anthropometric tape. Subject stands erect with the feet slightly apart, the tapes is passed
around the leg and slipe up using a cross-handed technique to a horizontal position. It is not
an ISAK measure. Used in the Hanavan, Zatsiorsky (multiple regression) and Yeadon
methods.
Calf girth: measured at the medial calf skinfold site level with an anthropometric tape.
Subject stands on a box with weight distributed evenly. Used in the Zatsiorsky (multiple
regression) and Yeadon methods.
Ankle girth: the minimum girth of the ankle superior to the sphyrion tibiale. Subject stands
on a box with weight distributed evenly. Used in the Hanavan, Zatsiorsky (multiple
regression) and Yeadon methods.
Ball of foot girth: measured at the level of the metatarsal-phalangeal joints (I to V) with an
anthropometric tape. It is not an ISAK measure. Used in the Yeadon method.
[125]
Landmarks:
Acromiale: the point at the most superior and lateral border of the acromion process when
the subject stands erect with arms relaxed and hanging vertically;
Radiale: the point at the most proximal and lateral border of the head of the radius;
Midacromiale-radiale: the point equidistant from the acromiale and radiale landmarks;
Stylion: the most distal point on the lateral margin of the styloid process of the radius;
Mesosternale: the midpoint of the corpus sterni at the level of the centre of the articulation
of the fourth rib with the sternum;
Iliocristale: the point on the iliac crest where a line drawn from the midaxilla (middle of the
armpit), on the longitudinal axis of the body, meets the ilium;
Iliac crest skinfold site: the site at the centre of the skinfold raised immediately above the
iliocristale;
Iliopsinale: the most inferior or undermost part of the tip of the anterior superior iliac spinale
(ASIS);
Trochanterion: the most superior aspect of the greater trochanter of the femur;
Tibiale laterale: the most superior aspect on the lateral border of the head of the tibia;
Midtrochanterion-tibiale laterale: the point equidistant from the trochanterion and the
tibiale laterale;
Tibiale mediale: the most proximal aspect on the border of the head of the tibia;
Sphyrion tibiale: the most distal tip of the medial malleolus of the tibia;
Akropodion: the most anterior point of the foot, which may be the first or second digit;
Anterior patella: the most anterior and superior margin of the anterior surface of the patella
when the subject is seated and the knee bent at a right angle;
[126]
Dactylon: the tip of the middle (third) finger;
Glabella: midpoint between the brow ridges;
Gluteal fold: the crease at the junction of the gluteal region and the posterior thigh;
Inguinal fold: the crease at the angle of the trunk and the anterior thigh;
Orbitale: the lower bony margin of the eye socket;
Pternion: the most posterior point of the calcaneus;
Tragion: the notch superior to the tragus of the ear;
Vertex: the most superior point on the skull when the head is held in the Frankfort plane
(i.e., when the orbitale and the tragion are horizontally aligned).
[127]
AppendixAppendixAppendixAppendix DDDD::::
BIOMECHANICAL MODEL
[128]
Virtual points
Prior to the creation of the ACSs, some virtual points had to be created using mathematical
procedures and the locations of the markers. Those points can be end points or auxiliary
points conveniently used during the creation of the ACSs.
Table A16: Virtual points created
Segment
/ Joint
Point
Label
Anatomical / extended
name
Location
Head VertexEP Vertex end point Projection of the highest point on the top of
the head onto the straight line defined by
MidHJC and MidSJC
Trunk MidSJC Shoulder midpoint Midpoint between the two SJC
MidHJC Hip midpoint Midpoint between the two HJC
C7EP Cervicale end point Projection of C7 on the straight line defined by
MidHJC and MidSJC
XPEP Xiphoid process end point Projection of XP on the straight line defined
by MidHJC and MidSJC
NavEP Navel end point Projection of Nav on the straight line defined
by MidHJC and MidSJC
AMP Anterior mid-pelvis Midpoint between the two ASIS
PMP Posterior mid-pelvis Midpoint between the two PSIS
Hand L/R IIIEP Third phalange end point The projection of the most distal point of the
hand, on the tip of the third distal phalange,
onto the straight line defined by the ipsi-lateral
EJC and WJC
Foot L/R IIEP Second phalange end
point
The most distal point of the foot, lying on the
tip of the second distal phalange
Shoulder SGCP Shoulder girdle central
point
Midpoint between IJ and C7
L/R AcrLR Acromion triad: lateral
ridge
Midpoint between Acr1 and Acr3
L/R SJC Shoulder joint centre Regression equations (Campbell et al., 2009),
with position relative to the acromion
coordinate system (AcrCS):
x = 96.2 – 0.302 x (IJ – C7mm) – 0.364 x
height (cm) + 0.385 x mass (kg)
y = –66.32 + 0.30 x (IJ – C7mm) – 0.432 x
mass (Kg)
z = 66.468 – 0.531 x (AcrLR – SGCPmm) –
0.364 x height (cm) + 0.385 x mass (Kg)
Elbow L/R EJC Elbow joint centre Midpoint between MEL and LEL
Wrist L/R WJC Wrist joint centre Midpoint between MWR and LWR
Hip L/R HJC Hip joint centre Regression equations (Harrington et al.,
2007), with position relative to the pelvis
coordinate system(PeCS):
x = 9.9 – 0.24 x (AMP –PMPmm)
y = –7.1 + 0.16 x (L ASIS – R ASISmm) –
0.04 x (ASIS – MAN)
z = 7.9 + 0.28 x (AMP – PMPmm) – 0.16 x (L
[129]
ASIS – R ASIS)
Knee L/R KJC Knee joint centre Midpoint between MEL and LEL
Ankle L/R AJC Ankle joint centre Midpoint between MAN and LAN
A proximal and a distal end point is created for each segment to define their anatomical
length and thereby the position of the CM lying on each longitudinal axis (Table A17). The
biomechanical model has six pairs of joint centres (shoulders, elbows, wrists, hips, knees
and ankles joint centres). Given the complexity of the vertebral joints, the end points of the
head and the sub-segments of the trunk are not true joints.
Table A17: End points of all segments of the biomechanical model
Segment Proximal end point Distal end point
Head VertexEP C7EP
Upper trunk C7EP XPEP
Middle trunk XPEP NavEP
Lower trunk NavEP MidHJC
Upper arm SJC EJC
Forearm EJC WJC
Hand WJC IIIEP
Thigh HJC KJC
Shank KJC AJC
foot Foot 1 IIEP
Biomechanical model
The biomechanical model adopted consists of 16 segments (head, upper trunk, middle
trunk, lower trunk, upper arms, forearms, hands, thighs, shanks and feet), to which
anatomical coordinate systems were assigned based on the markers positions and virtual
points created. The model is based on the UWA model (Besier et al., 2003; Campbell et al.,
2009; Chin et al., 2010; Lloyd, Alderson, and Elliott, 2000) with slight modifications so all
BSIP estimation methods can be applied to it.
Head Coordinate System (HCS – HX , H
Y , HZ )
HO : The origin is located at the C7EP;
[130]
The sagittal (H
X ), longitudinal (H
Y ) and transverse (HZ ) axes of the HCS have the same
directions of the respective axes of the trunk coordinate system (TCS) when the anatomical
position is maintained.
Trunk Coordinate System (TCS – TX, TY
, TZ)
The TCS is used to create the coordinate systems of the sub-segments of the trunk (upper
trunk, middle trunk and lower trunk) and head, as all these segments have coordinate
systems with the same orientation in space. Also, it is used for the modified version of
Chandler et al. (1975), as it only uses the whole trunk segment.
TO : The origin is located at the MidHJC;
TY : The line pointing proximally from the DEP to the MidSJC (unit vector
MidHJCMidSJC
MidHJCMidSJCj
−
−=
r)
TX : The line orthogonal to TrY and to the line linking both HJCs (unit vector
LHJCRHJC
LHJCRHJCji
−
−×=
rr)
TZ: The line orthogonal to a plane containing TrX
and TrY (unit vector
jikrrr
×=)
Upper Trunk (UPTC), Middle Trunk (MTCS) and Lower Trunk (LTCS) Coordinate
Systems:
The axes of each sub-segment of the trunk have the same respective directions of the TCS.
UTO : The origin is located at the XPEP;
MTO : The origin is located at the NavEP;
LTO : The origin is located at the MidHJC;
[131]
Upper arm Coordinate System (UCS – UX
, UY
, UZ)
UO : The origin is located at the EJC;
UY : line pointing proximally from the EJC to the SJC (unit vector EJCSJC
EJCSJCj
−
−=
r);
UX : The line orthogonal to UY and to the line linking MEL and LEL (unit vector
RMELRLEL
RMELRLELji
−
−×=
rr) for the right upper arm;
LLELLMEL
LLELLMELji
−
−×=
rr for the left
upper arm);
UZ: The line orthogonal to a plane containing UX
and UY (unit vector jik
rrr×= )
Forearm Coordinate System (FCS – FX
, FY
, FZ)
FO : The origin is located at the WJC;
FY : line pointing proximally from the WJC to the EJC (unit vector WJCEJC
WJCEJCj
−
−=
r);
FX : The line orthogonal to FY and to the line linking MWR and LWR (unit vector
RMWRRLWR
RMWRRLWRji
−
−×=
rr) for the right forearm;
LLWRLMWR
LLWRLMWRji
−
−×=
rr for the left
forearm);
FZ: The line orthogonal to a plane containing FX
and FY (unit vector
jikrrr
×=)
Hand Coordinate System (HaCS – HaX
, HaY
, HaZ)
The HaCS has the same position and orientation of the FCS when the anatomical position is
maintained.
[132]
Thigh Coordinate System (ThCS – ThX
, ThY
, ThZ )
ThO : The origin is located at the KJC;
ThY : The line pointing proximally from the KJC to the HJC (unit vector KJCHJC
KJCHJCj
−
−=
r)
ThX : The line orthogonal to the ThY line and the line linking the MKN and the LKN (unit
vector RMKNRLKN
RMKNRLKNji
−
−×=
rr for the right thigh;
LLKNLMKN
LLKNLMKNji
−
−×=
rr for the left
thigh);
ThZ: The line orthogonal to a plane containing ThX
and ThY (unit vector jik
rrr×= )
Lower leg Coordinate System (LCS – LX
, LY
, LZ)
LO : The origin is located at the AJC;
LY : The line pointing proximally from the AJC to the KJC (unit vector AJCKJC
AJCKJCj
−
−=
r)
LX : The line orthogonal to the LY line and the line linking the MAN and the LAN (unit
vector RMANRLAN
RMANRLANji
−
−×=
rr for the right lower leg;
LLANLMKAN
LLANLMKANji
−
−×=
rr for
the left lower leg);
LZ: The line orthogonal to a plane containing LX
and LY (unit vector
jikrrr
×=)
Foot Coordinate System (FootCS – FootX
, FootY
, FootZ)
FootO : The origin is located at Foot 1 (marker located at the calcaneous)
[133]
To calculate the unit vectors of the anatomical coordinate system, the vectors V1 and V2
had to be defined as follows:
121
FOOTFOOTV −=
132
FOOTFOOTV −=
FootY : The line perpendicular to both V1 and V2 pointing cranially (unit vector
12
12
VV
VVj
×
×=
r
for the right foot;
21
21
VV
VVj
×
×=
rfor the left foot)
FootZ : The line orthogonal to the line linking FOOT1 and IIEP pointing forward and the LY
(unit vector jFOOTIIEP
FOOTIIEPk
rr×
−
−=
1
1
FootX : The line pointing distally from Foot1 to the IIEP (unit vector kjirrr
×= )
Acromion Coordinate System (AcrCS - System AcrX
, AcrY
, AcrZ)
The AcrCS is created uniquely to define the SJC from the regression equations (Campbell et
al., 2009).
AcrO : The origin is located at the AcrLR
AcrX : The line defined by the points Acr1 and Acr3, pointing anteriorly (unit vector
13
13
AcrAcr
AcrAcri
−
−=
r)
AcrY : The line perpendicular to a plane containing Acr1, Acr2 and Acr3 (unit vector
2
2
AcrAcrLR
AcrAcrLRji
−
−×=
rr)
[134]
AcrZ: The line orthogonal to a plane containing LlX
and LlY (unit vector jik
rrr×= )
Pelvis Coordinate System (PeCS – PeX
, PeY
, PeZ)
Similarly to the AcrCS, the PeCS is only created to determine the HJC from the regression
equations used (Thorpe and Steel, 1999).
PeO : The origin is located at the AMP
PeZ : The line linking both ASISs, from left to right (unit vector LASISRASIS
LASISRASISk
−
−=
r);
PeY : defined by the vector resulting from the cross product of the vectors
PMPRASISV −=1
r and PMPLASISV −=
2
r whose common origin is the PMP and the
(unit vector
21
21
VV
VVj rr
rrr
×
×= )
PeX : The line parallel to the line lying in the plane defined by the two ASISs and the PMP,
orthogonal to PeZ , and pointing anteriorly (unit vector kjirrr
×= )
[135]
Appendix EAppendix EAppendix EAppendix E
MATLAB CODES
[136]
Convert_dxa_images.m
function [I_TISSUE_mass,I_BMD_mass,I_mass_total,total_mass,
total_mass_com,total_mass_com_cm,... TISSUE_mass,TISSUE_mass_com,TISSUE_mass_com_cm,... BMD_mass,BMD_mass_com, BMD_mass_com_cm,I_for_part_segementation]
= convert_dxa_images(I1,I2,BMD,TISSUE,DXA_WH)
% Copyright : This code is written by Marcel Rossi
(20676873@student.uwa.edu.au) and Amar El-Sallam
(elsallam@csse.uwa.edu.au) % The University of Western Australia. The code is part
of Marcel's Master degree and % may be used, modified and distributed for research
purposes with % acknowledgment of the authors/publications and
inclusion this copyright information. % % Disclaimer : This code is provided as is without any warranty.
%folder_name = 'D:\Marcel\data\montana'; Wp=DXA_WH(1); W=DXA_WH(2); Hp=DXA_WH(3); H=DXA_WH(4);
dW=W/Wp; dH=H/Hp;
[M,N]= size(I1); mass_scale = H/N*W/M;
rx = N/W*dW; ry = 5*M/H*dH;
Mass1=BMD(1:3:end)*mass_scale; X1=(BMD(2:3:end)+1)*rx; Y1=(BMD(3:3:end)+1)*ry;
X1r=round(X1); Y1r=round(Y1); I1_temp=[];
for n=1:length(X1r) I1_temp = [I1_temp I1(Y1r(n), X1r(n))]; end I1_temp =double(I1_temp);
P1=polyfit(I1_temp,Mass1,1);
level1 = graythresh(I1); BW1 = im2bw(I1,level1/2); %BW1(660:750,110:140)=0; % this is to remove the steel calib cube %I11 = double(I1').*double(BW1');
I11 = double(I1).*double(BW1);
[137]
%I_BMD_mass = polyval(P1,double(I11(:))); %I_BMD_mass = vec2mat(I_BMD_mass,N);
I_BMD_mass = I11*mean(Mass1(:))/mean(I1_temp(:)); clear I11;
Mass2=TISSUE(1:3:end)*mass_scale; X2=(TISSUE(2:3:end)+1)*rx; Y2=(TISSUE(3:3:end)+1)*ry;
X2r=round(X2); Y2r=round(Y2); I2_temp=[]; for n=1:length(X2r) I2_temp = [I2_temp I2(Y2r(n), X2r(n))]; end I2_temp =double(I2_temp);
%P2=polyfit(I2_temp,Mass2,1);
level2 = graythresh(I2); BW2 = im2bw(I2,level2/2); %BW2(660:750,110:140)=0; %I22 = double(I2').*double(BW2'); I22 = double(I2).*double(BW2); %I22=I2; %I_TISSUE_mass = polyval(P2,double(I22(:))); %I_TISSUE_mass = vec2mat(I_TISSUE_mass,N);
I_TISSUE_mass = I22*mean(Mass2(:))/mean(I2_temp(:)); clear I22;
I_total = I1+I2; I_for_part_segementation =I_total;
I_mass_total = I_BMD_mass+I_TISSUE_mass;
[M,N]= size(I_mass_total);
total_mass = sum(I_mass_total(:)); TISSUE_mass = sum(I_TISSUE_mass(:)); BMD_mass = sum(I_BMD_mass(:));
[x,y]=meshgrid(1:M,1:N); x=x(:); y=y(:);
total_mass_com(1)=0; total_mass_com(2)=0; TISSUE_mass_com(1)=0; TISSUE_mass_com(2)=0; BMD_mass_com(1)=0; BMD_mass_com(2)=0;
[138]
for n=1:length(x) total_mass_com(1)= total_mass_com(1)+
I_mass_total(x(n),y(n))*x(n);
total_mass_com(2)=total_mass_com(2)+I_mass_total(x(n),y(n))*y(n);
TISSUE_mass_com(1)=TISSUE_mass_com(1)+I_TISSUE_mass(x(n),y(n))*x(n);
TISSUE_mass_com(2)=TISSUE_mass_com(2)+I_TISSUE_mass(x(n),y(n))*y(n); BMD_mass_com(1)=BMD_mass_com(1)+I_BMD_mass(x(n),y(n))*x(n); BMD_mass_com(2)=BMD_mass_com(2)+I_BMD_mass(x(n),y(n))*y(n); end total_mass_com = total_mass_com/total_mass; TISSUE_mass_com=TISSUE_mass_com/TISSUE_mass; BMD_mass_com=BMD_mass_com/BMD_mass;
total_mass_com_cm(1) = total_mass_com(1)*W/N; total_mass_com_cm(2) = total_mass_com(2)*H/M;
TISSUE_mass_com_cm(1) = TISSUE_mass_com(1)*W/N; TISSUE_mass_com_cm(2) = TISSUE_mass_com(2)*H/M;
BMD_mass_com_cm(1) = BMD_mass_com(1)*W/N; BMD_mass_com_cm(2) = BMD_mass_com(2)*H/M;
%% figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imshow(I1) hold on plot(X1,Y1,'r*') title('BMD Mass in pixels') xlabel('pixel index') ylabel('pixel index')
hold off
subplot(1,3,2) imshow(I2) hold on plot(X2,Y2,'b*') title('TISSUE Mass in pixels') xlabel('pixel index') ylabel('pixel index') hold off axis image
subplot(1,3,3) imshow(I_total) title('TOTAL Mass in pixels') xlabel('pixel index') ylabel('pixel index') axis image %% figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imshow(BW1)
[139]
title('BMD noise removal Mask') xlabel('pixel index') ylabel('pixel index') axis image
subplot(1,3,2) imshow(BW2) %axis(AXIS) title('TISSUE noise removal mask') xlabel('pixel index') ylabel('pixel index') axis image
subplot(1,3,3) imshow(BW1+BW2) title('TOTAL Mass noise removal mask') xlabel('pixel index') ylabel('pixel index') axis image %% Image to Mass figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imagesc(I_BMD_mass) title('BMD True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(BMD_mass_com(2),BMD_mass_com(1),'k+','markersize',10) plot(BMD_mass_com(2),BMD_mass_com(1),'kO','markersize',10) hold off axis image
subplot(1,3,2) imagesc(I_TISSUE_mass) %axis(AXIS) title('TISSUE True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(TISSUE_mass_com(2),TISSUE_mass_com(1),'k+','markersize',10) plot(TISSUE_mass_com(2),TISSUE_mass_com(1),'kO','markersize',10) hold off axis image
subplot(1,3,3) imagesc(I_mass_total) title('TOTAL True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(total_mass_com(2),total_mass_com(1),'k+','markersize',10) plot(total_mass_com(2),total_mass_com(1),'kO','markersize',10) hold off axis image %% figure('units','normalized','outerposition',[0 0 1 1]) [X,Y]=meshgrid(1:N,1:M); X=X*W/N; Y=Y*H/M; mesh(X,Y,I_mass_total)
[140]
title('Total mass represented as depth') %xlabel('cm') %ylabel('cm') zlabel('mass') axis tight
%% return figure('units','normalized','outerposition',[0 0 1 1]) I1t=imresize(I_BMD_mass,W/N); imagesc(I1t)
segment_body.m
function [cropped_part, part_mass, part_com,
part_com_cm,part_com_cm_l, part_com_ratio,Im] =
segment_body_2(I_for_part_segementation,I_mass_total,DXA_WH,x,y,PEP,
DEP)
% Copyright : This code is written by Marcel Rossi
(20676873@student.uwa.edu.au) and Amar El-Sallam
(elsallam@csse.uwa.edu.au) % The University of Western Australia. The code is part
of Marcel's Master degree and % may be used, modified and distributed for research
purposes with % acknowledgment of the authors/publications and
inclusion this copyright information. % % Disclaimer : This code is provided as is without any warranty.
W=DXA_WH(2); H=DXA_WH(4);
[M,N]=size(I_for_part_segementation);
%xo = [PEP(1); DEP(1)]; %yo = [PEP(2), DEP(2)];
cropped_part=I_mass_total;
mask = poly2mask(x,y,M,N); cropped_part(~mask)=0;
part_mass = sum(cropped_part(:));
[x,y]=meshgrid(1:M,1:N); x=x(:); y=y(:);
com(1)=0; com(2)=0;
for n=1:length(x) com(1)= com(1) + cropped_part(x(n),y(n))*x(n); com(2)=com(2) + cropped_part(x(n),y(n))*y(n);
[141]
end
part_com = com/part_mass;
part_com_cm(1) = part_com(1)*W/N; part_com_cm(2) = part_com(2)*H/M;
part_com_cm_t(1) = (part_com(1)-DEP(2))*W/N; part_com_cm_t(2) = (part_com(2)-DEP(1))*H/M;
part_com_cm_l=norm(part_com_cm_t);
[x,y]=find(cropped_part>0);
%figure('units','normalized','outerposition',[0 0 1 1]) %imagesc(I_for_part_segementation) %hold on %plot(y,x,'w*') %axis image %hold off
Im = 0; for n=1:length(x) rsqr = (x(n)*W/N - part_com_cm(1))^2 + (y(n)*H/M -
part_com_cm(2))^2; Im = Im + cropped_part(x(n),y(n))/1000*rsqr; end
V1(1)=part_com(1)-DEP(2); V1(2)=part_com(2)-DEP(1);
V2(1)=PEP(2)-DEP(2); V2(2)=PEP(1)-DEP(1); V2=V2/norm(V2);
V3(1)=PEP(2)-DEP(2); V3(2)=PEP(1)-DEP(1);
part_com_ratio=100*dot(V1,V2)/norm(V3); %%