Developing and Evaluating New Methods for Assessing Postural Control and Dynamics

 

Industrial and Systems Engineering

Virginia Tech

Hongbo Zhang

Background

• Falls are common and costly– Over 2.3 million older adults suffered nonfatal fall injuries and

662,000 hospitalized in 2010 (CDC, 2012) – The total direct medical costs associated with falls greater than

$19 Billion in 2000 (CDC, 2010)• Multiple factors contribute to falls

– Human physical and mental conditions, work complexity, and environmental factors

• Multi-factorial interventions for fall prevention – Physical strength training – Body flexibility, joint coordination training (e.g. Tai Chi) – Postural controller interventions (e.g. mechanical vibrations)

Existing Methods

• Joint coordination assessment – Frequency-domain coherence analysis (Creath et al., 2005,

Zhang et al., 2007, Saffer et al. 2008)– Uncontrolled manifold (Krishnamoorthy et al., 2005, Hsu et al.,

2012)

• Postural control modeling – Continuous feedback controllers (Peterka, 2000, Mergner et al.,

2003, Peterka and Loughlin, 2004, Qu and Nussbaum, 2007, Kiemel et al., 2008)

• Ankle stiffness assessment – Passive and active ankle stiffness (Kearney et al., 1997, Loram

and Lakie, 2002a, Galiana et al., 2005,Casadio et al., 2005, Roy et al., 2011)

Proposed Methods

• Study 1: Joint coordination assessment – Wavelet (time-frequency domain) coherence analysis

of two-joint coordination – Uncontrolled manifold analysis of whole body

coordination for exploring different control goals

• Study 2: Postural controller modeling – Intermittent sliding mode controller

• Study 3: Ankle stiffness assessment – A new method to calculate passive and active ankle

stiffness

Data Source

• 32 participants (age and gender balanced)

• Localized muscle fatigue (LMF) conducted in muscles at one ankle

• Participants stood as still as possible on a force platform for 3 trials before LMF and 11 trials post-fatigue, each trial lasts 75s with rest interval 1 min

Study 1

Effects of localized muscle fatigue and aging on two-joint and whole-body coordination

during upright stance

Overview• Two-joint coordination

– Ankle-hip coordination, <1 Hz in-phase, >1 Hz anti-phase (Creath, 2005, Zhang et al., 2007)

– Head-trunk coordination, head angular acceleration depending on trunk positions (Keshner, 2003, St-Onge, 2011)

• Whole body coordination– Arm, trunk, knee, and ankle all involved in upright

stance pointing task (Tagliabue, 2009)– COM was treated as the hypothetical coordination

control goal (Hsu, 2012)

• Study objectives– Evaluate two-joint and whole body coordination– Identify control variables involved in whole body coordination– Assess effects of LMF and aging on body coordination

• Study hypotheses– Ankle-knee, ankle-trunk, ankle-head, and whole body

coordination exist during quiet upright stance– Body coordination influenced by aging and ankle LMF– COM, head, and shoulder can all be possible whole body

coordination control goals

Objectives and Hypotheses

Methods

3

4

5

2

7

6

1 Foot Angle

Ankle Angle

Knee Angle

Trunk Angle

Head Angle

Upper Arm Angle

Lower Arm Angle

3

4

5

2

7

6

1 Foot Angle

Ankle Angle

Knee Angle

Trunk Angle

Head Angle

Upper Arm Angle

Lower Arm Angle

Sagittal Plane Frontal Plane

Methods

• Wavelet coherence– Step 1: Perform continuous wavelet transform of

ankle, knee, trunk, and head angle to obtain the wavelets coefficients (Wa, Wk, Wt, Wh) between 2.5 – 4Hz

– Step 2: Calculate cross wavelet transform (CW) of the wavelets (W)

– Step 3: Calculate cross wavelet power (CWP) – Step 4: Calculate wavelet coherence =

s(CWP)/s(WPJ1) s(WPJ2), s: smooth operator, J1, J2 =>{ ankle, knee, trunk, head)}

Methods: Time Interval Ratio

Methods: Phase Ratio

Phase Ratio = In-phase/Anti-phase

Methods

• Uncontrolled manifold (UCM)– Step 1: Determine relevant task variables (COM,

shoulder, and head positions) and joints involved in whole body coordination

– Step 2: Calculate Jacobian matrix, which is the first order derivate of task variables over joint angles

– Step 3: Obtain the basis of null space of the Jacobian matrix

– Step 4: Obtain parallel component of uncontrolled manifold with the projection of joint angle variance on the null space

– Step 5: Obtain perpendicular component by subtracting parallel component from joint angle changes

– Step 6: Obtain uncontrolled manifold ratio equal to parallel component / perpendicular component

Joint Angle Variance

Basis of Null space of the Jacobian matrix

Statistical Analysis• Dependent variables

– Wavelet coherence: phase ratio and time-interval ratio for ankle-knee (AK), ankle-trunk (AT), and ankle head (AH) angles in the sagittal and frontal planes

– UCM: head, shoulder, and COM uncontrolled manifold estimated separately in the AP and ML directions

• Two-way ANOVAs (age, gender) for each dependent variable

• Two-way ANCOVAs (age, gender) on change scores (post-fatigue – pre-fatigue) for each dependent variable, the pre-fatigue variable as a covariate

Results

– AK time-interval ratio SP larger among older vs. young adults 1.05(0.15) and 0.96(0.10) sec

– AT time-interval ratio FP larger among older vs. young adults 1.32(0.14) and1.21(0.11) sec

– AT phase ratio FP larger among females vs. males 1.67(0.69) and 1.21(0.41)

– AH phase ratio FP larger among females vs. males 1.09(0.27) and 0.84(0.24)

• Wavelet coherence: pre-fatigue

Results• UCM: pre-fatigue

– Shoulder UCM AP larger among young vs. older adults 1.15(0.09) and 1.08(0.09)

– Shoulder UCM ML larger among females vs. males 1.13(0.09) and 1.03(0.14)

– COM UCM ML smaller among females vs. males 0.634(0.001) and 0.635(0.0004)

Results

Wavelet Coherence: Post-Fatigue

Age

Tim

e (

sec)

0.0

0.5

1.0

1.5

Young OldPre-LMF Post-LMF Pre-LMF Post-LMF

Young Older

Age Group

Results

• UCM: post-fatigue– COM UCM ML increased, pre-fatigue:

0.633(0.0009), post-fatigue: 0.634(0.0008)– COM UCM AP decreased, pre-fatigue:

0.634(0.0009), post-fatigue: 0.633(0.0009)– Shoulder UCM ML increased, pre-fatigue:

1.07(0.15), post-fatigue: 1.10(0.10)

Discussion

• Two-joint coordination appears Intermittent

• Older adults displayed a larger ankle-knee time-interval ratio in the sagittal plane and a larger ankle-trunk time-interval ratio in the frontal plane

• Females had a larger ankle-trunk phase ratio in the frontal plane and a larger ankle-head phase ratio in the frontal plane

• One joint coordination corresponds to 2 – 3 muscle bursts (Loram and Lakie 2002b)

• Older adults postural control compromised (Qu et al., 2009, Davidson et al., 2011, Nishihori et al., 2011)

• Females tended to display more erect (landing) postures (Decker et al., 2003)

Discussion• Post-fatigue COM UCM increased in the ML direction and

decreased in the AP direction– Directional effects of fatigue

• Post-fatigue time-interval ratio decreased among older adults and increased for young adults – Older adults associated with increase in fatigue-resistant Type I muscles and the

alerted muscular metabolic anaerobic pathways (Chan et al., 2000, Kent-Braun et al., 2002)

• Shoulder and head UCM values >1 in both the AP and ML directions – COM UCM in disagreement with previous results (Hsu et al., 2007, Zhang et al.,

2007)

Increased time-interval ratio ->

reduced coordination

Increased UCM ->Improved coordination

Study 2

Development of an Intermittent Control Model for Evaluating Aging and Muscle Fatigue Effects on Human Upright Stance

Overview• Most of previous research involved using

continuous control modeling (Peterka, 2002, Kuo, 2005, Van Der Kooij & De Vlugt, 2007, Kiemel et al., 2008)

• Both open-loop and closed-loop control needed (Collins and Luca, 1993, Collins et al., 1996)– Only feedback control not sufficient to maintain

upright stance stability (Fitzpatrick et al., 1996, van der Kooij et al., 2001)

– Calf muscles intermittently adjusted 2 -3 times per unidirectional sway (Loram et al. 2005, 2009)

• Study Objectives– Apply sliding mode control to model quiet

upright stance – Identify effects of aging and LMF on the

intermittent postural controller• Study Hypothesis

– Upright stance maintained intermittently

Objectives and Hypothesis

Methods

T+ T-Ankle torque (T) determined by switching function (S) required to meet:Sliding Action

Chattering

Sliding surface

Chattering minimized by sgn function or others functions

Sliding surface S=0

Lyapunov stability condition

• Sliding mode intermittent control– Determine body dynamics– Construct switching function

• Angle and angular velocity errors• Able to meet Lyapunov stability

condition

– Solve estimated ankle torque (EAT)

– Decompose EAT into passive and active ankle torque

Methods

x

y

Th

Statistical Analysis• Dependent variables

– COM angle, angular velocity, and angular acceleration

– Total ankle torque tracking errors– Modeled and experimental ankle torque correlation– Passive and active ankle torques– Passive/active ankle torque ratio

• Two-way ANOVAs (age, gender) for each dependent variable

• Two-way ANCOVAs (age, gender) on change scores (post-fatigue – pre-fatigue) for each dependent variable, the pre-fatigue measure as a covariate

Results: Representative Trial Sliding surface (top-left), first order derivative of sliding surface (top-right), and phase plot of the sliding surface (bottom)

Results: Representative Trial

Modeled and experimental ankle torques

0 10 20 30 40 50 605

10

15

20

25

30

35

40

Ank

le T

orqu

e (N

.m)

Time (sec)

Experimental

Modeled

Results: Representative Trial Passive ankle torque and COM angle

0 10 20 30 40 50 600

20

40

0 10 20 30 40 50 600

2

4

Pa

ssiv

e A

nkl

e T

orq

ue

(N.m

)

CO

M A

ng

le (

deg

ree

)

Passive Ankle Torque

COM Angle

Time (sec)

Results: Representative Trial Active ankle torque and COM angular acceleration

0 10 20 30 40 50 60-5

0

5

0 10 20 30 40 50 60-5

0

5

Act

ive

Ank

le T

orqu

e (N

.m)

CO

M A

ngul

ar A

ccel

erat

ion

(deg

ree/

sec^

2)

Active Ankle Torque

COM Angular Acceleration

Time (sec)

Statistical Results: Pre-Fatigue

• Passive ankle torque larger among young females, followed by (in order) older females, older males, and young males

• Active ankle torque larger in the older group and among males

• Passive/active ankle torque ratio larger in the young group and among females

Statistical Results: Post-Fatigue

• Slightly decreased tracking performance for all measures

• Decreased passive ankle torque contribution to total ankle torque

• Increased active ankle torque contribution to total ankle torque

Discussion

• Acceptable magnitude of tracking errors – COM angle [0.45, 0.7] degree and COM

angular velocity [0.33, 0.53] degree/s • Angle and angular velocity tracking errors about 13

- 25% and 5 – 10% of experimental values– Mean ankle torque tracking error in the range

of 1.45 - 4.48 Nm, overall of 26 - 42 Nm (5 – 10%)

– The tracking performance comparable and slightly smaller than Phasic – Bang Bang controller (Bottaro et al. 2008)

Discussion

• Passive ankle torque accounts for 97% of the entire ankle torque – Active ankle torque accounts for 3% of the entire

ankle torque • These estimates similar but higher than previous

estimates – Passive vs. entire (91 ± 23%) (Loram and Lakie,

2002ª– Passive vs. entire (64 ± 7.8%) (Casadio et al., 2005)

• The estimated differences likely attributed to no mechanical or sensory perturbations involved in our experiment

Discussion

• Older adults displayed greater active ankle torque compared to young adults– Possibly to compensate for the compromised stability

due to aging (Shumway-Cook and Woollacott, 2000, Speers et al., 2002, Qu et al., 2009)

• Males had larger active ankle torques than females– A possible indicator of gender related differences in

fall risks (Hunter, 2009)

Discussion • Larger increase of post-fatigue active ankle torque

among young adults – Possibly due to aging related muscle fiber structure

and metabolic pathway differences (Chan et al., 2000, Ditor and Hicks, 2000, Baudry et al., 2007)

• Smaller post-fatigue active ankle torque changes identified among females – Possibly due to greater oxidative metabolism

capacity, less likelihood to experience central fatigue among females (Hunter, 2004, Paillard, 2012)

Study 3

A New Method to Assess Passive and Active Ankle Stiffness during Quiet Upright Stance

Overview• Passive and active ankle torque measurement

– Used very small mechanical perturbations for measuring passive and active ankle torques (Loram and Lakie, 2002ª, Casadio et al., 2005)

• Effects of aging and ankle LMF on ankle torque – Fatigue induced changes in force capacity (Enoka

and Stuart, 1992)– Aging associated increase in passive joint stiffness

(Silder et al., 2008)

• Study objectives– Quantify passive and active ankle stiffness among

quiet upright stance– Assess effects of aging and LMF on passive and

active ankle stiffness

• Study hypotheses– Upright stance controlled intermittently – LMF and aging alters passive and (or) active ankle

stiffness

Objectives and Hypotheses

Methods

Top-down approach to calculate modeled ankle torque

Experimental ankle torque

Ankle

Fy

Z

COPap

Te = Fz * COPap + Fy * Ha – Mfoot*g*CMfoot-ap

Fz

CMfoot-ap

HaMfoot

Human Body

Ankle

Hip

Neck

ankle

trunk

head

Tm

Top - Down Approach

(A) (B)

Methods

• Determine passive and active ankle torques based on followings

Study 2 showed that active ankle torque is in-phase coherent with ankle angular acceleration

Upright stance controlled through intermittent muscle contractions of 2 – 3 times per second (Loram and Lakie, 2002ab, Loram et al., 2005b,Loram et al., 2011)

0 10 20 30 40 50 60-4

-2

0

2

4

0 10 20 30 40 50 60-4

-2

0

2

4

Ta

(N.m

)

Aa-

ac (

degr

ee/s

ec^2

)

Ta

Aa-ac

Time (sec)

Methods

• Determine passive and active ankle torques– Step 1: Identify passive +

active (P+A) zones using local maxima of absolute values of Aa-ac time series

– Step 2: Calculate the size (duration) of each P+A zone

– Step 3: Locate P zones, which are simply the time windows adjacent to P+A zones

0 0.5 1 1.5 2 2.5-1

-0.5

0

0.5

1

1.5

a

Aa

-ac (d

eg

ree

/se

c^2

)

Time (sec)

P + A Zone

P Zone

Local Maximum of Absolute Value of Aa-ac

Step 1

Step 2 Step 3

200 ms

200 – 400 ms

Methods

• Calculate passive and active ankle stiffness, damping – Perform linear regression between the passive ankle

torque and ankle angle and angular velocity – Perform linear regression between active ankle torque

and ankle angle, ankle angular velocity, ankle angular acceleration, and trunk angle

– The selection of independent variables in the linear regression models determined through an iterative explorative approach

Statistical Analysis

• Dependent variables– Passive ankle torque, stiffness, and damping of the

ankle, – Active ankle torque, stiffness, damping, and moment

inertia of the leg• Two-way ANOVAs (age, gender) for each

dependent variable• Two-way ANCOVAs (age, gender) on change

scores (post-fatigue – pre-fatigue) for each dependent variable, the pre-fatigue variable as a covariate

Results: Representative Trial

• Modeled and experimental ankle torques

0 10 20 30 40 50 60-25

-20

-15

-10

-5

0

5

Time (sec)

An

kle

Tor

que

(N.m

)

Experimental

Modeled

Results: Representative Trial • Passive and passive + active zones on ankle angular

acceleration and ankle torque

0 5 10 15 20 25-4

-2

0

2

4

Time(Second)

An

kle

A-A

C(D

egr

ee/

s2)

0 5 10 15 20 25-30

-20

-10

0

10

Time(Second)

An

kle

Tor

que

(N.m

)

Time (sec)

Ank

le T

orqu

e (N

m)

Ank

le A

-AC

(d

egre

e/se

c^2)

Time (sec)Time Interval:

545ms

Passive + Active (P+A)

Passive (P)

Local Maxima An Assistant Curve to Mark the Identified Local Maximum

Results: Representative Trial

• Relationships between ankle angle and passive ankle torque (left), and ankle angular acceleration and active ankle torque (right)

Results: Representative Trial

• Experimental and predicted passive (left) and active (right) ankle torques

Statistical Results: Pre-Fatigue• Passive ankle stiffness and damping both larger

among older adults and among males • Active ankle stiffness (ankle contribution) larger

among older adults. • Higher values of active ankle torque, stiffness

(both ankle and trunk contributions), damping, and leg inertia among males

Statistical Results: Post-Fatigue

Young

Older

Male

Female

0.81(0.31)

Active Ankle Torque (Nm)

1.33(0.78)

1.34(0.66)

0.82(0.53)

Pre Fatigue Post Fatigue Post - Pre Post - Pre

1.03(0.56)

1.28(0.67)

1.46(0.61)

0.88(0.49)

0.23(0.36)

-0.052(0.18)

0.11(0.44)

0.06(0.11)

Male

Female

Male

Female

0.39 (0.44)

0.053 (0.12)

-0.17 (0.17)

0.068 (0.095)

Discussion• No external mechanical or sensory perturbations

required for calculating passive and active ankle torques

• 540 - 550 ms identified as the active control time interval– 383±55 ms muscle contraction time interval

demonstrated by prior studies (Loram and Lakie, 2002b, Lakie et al., 2003, Loram et al., 2005a, Loram et al., 2011).

Discussion• Passive ankle torque account for 97% of the entire ankle

torque comparable to prior studies (Loram et al. 2005) • An evident linear relationship between ankle angle and

passive ankle torque consistent with the results from Winter et al. (2001)

• An evident linear relationship between active ankle torque and ankle angular acceleration – new finding

• Trunk angle involved in regulating active ankle torque – Trunk movement involved in contributing to the regulation of

active ankle torque – Evidence of ankle-trunk interaction/coordination

Discussion• Greater passive ankle stiffness and damping,

and greater active ankle torque and stiffness among older adults – Possible contributors to older adults increased fall

risks (Hortobágyi and DeVita, 1999,Gajdosik et al., 2004)

• Larger passive ankle stiffness and damping, active ankle torque, stiffness, damping, and leg inertia among males – Consistent with prior studies (Vandervoort et al.,

1992a, Granata et al., 2002, Gajdosik et al., 2006)

Discussion• Overall post-fatigue passive ankle torque

decreased– Suggesting compromised performance related to

passive ankle viscoelastic tissues (Kuitunen et al., 2002)

• A smaller fatigue induced increase in active ankle torque evident among older adults– Different muscle fibers and altered anaerobic

metabolic pathways between two age groups (Chan et al., 2000, Ditor and Hicks, 2000, Baudry et al., 2007, Kent-Braun, 2009)

• General conclusions – Two joint coordination exists and is executed

intermittently; head and shoulder also possible whole body coordination control goals

– Intermittent controller able to track upright stance kinematics and kinetics

– The new passive and active ankle stiffness and damping method able to give comparable results

Overall Research Summary

Overall Research Summary

• Insights for fall prevention– Older adults suffer reduced joint coordination

and increased ankle stiffness– Females display smaller ankle stiffness and

ankle torque– Young male adults tend to suffer more

adverse effects from muscle fatigue

Future Research

• Investigate muscle contraction patterns under different postures– Especially interested in discovering intermittent

muscular control patterns

• Build and validate more complete postural models

• Gain more insights on postural control and fall prevention

Thank You All !!