Subject-specific musculoskeletal modelling in patients before and after

total hip arthroplasty

Mariska Wesselinga, Friedl De Grootea, Christophe Meyerb,c, Kristoff

Cortend, Jean-Pierre Simone, Kaat Desloovereb,c, Ilse Jonkersa

a. KU Leuven, Department of Kinesiology, Human Movement Biomechanics Research

Group, Tervuursevest 101 B-3001 Heverlee, Belgium. mariska.wesseling@kuleuven.be

Ilse.Jonkers@kuleuven.be friedl.degroote@kuleuven.be

b. KU Leuven, Department of Rehabilitation Sciences, Neuromotor Rehabilitation,

Tervuursevest 101 B-3001 Heverlee, Belgium. christophe.meyer@faber.kuleuven.be

c. Clinical Motion Analysis laboratory, University Hospitals Leuven, Weligerveld 1, B-

3212 Pellenberg, Belgium. kaat.desloovere@uzleuven.be

d. Hip Unit, Orthopaedic Department, Ziekenhuis Oost-limburg, Schiepse Bos 6, B-

3600 Genk, Belgium. kristoffcorten@me.com

e. UZ Pellenberg Orthopedic Department, University Hospitals Leuven, Weligerveld 1

blok 1, B-3212 Pellenberg, Belgium. jean-pierre.simon@uzleuven.be

Corresponding author:

Mariska Wesselingmariska.wesseling@med.kuleuven.be

Tel.: +32 16 376463

All work was conducted at KU Leuven.

This work was supported by the Agency for Innovation by Science and Technology

under Grant 100786. The funders had no role in any part of this study.

Disclosure statement

The authors hereby declare there are no financial and personal conflicts of interest.

Word count: 3682

Subject-specific musculoskeletal modelling in patients before and after

total hip arthroplasty

The goal of this study was to define the effect on hip contact forces of including

subject-specific moment generating capacity in the musculoskeletal model by

scaling isometric muscle strength and by including geometrical information in

control subjects, hip osteoarthritis and total hip arthroplasty patients. Scaling

based on dynamometer measurements decreased the strength of all flexor and

abductor muscles. This resulted in a model that lacked the capacity to generate

joint moments required during functional activities. Scaling muscle forces based

on functional activities and inclusion of MRI-based geometrical detail did not

compromise the model strength and resulted in hip contact forces comparable to

previously reported measured contact forces.

Keywords: musculoskeletal modelling; patient-specific modelling; imaging;

moment generating capacity; hip osteoarthritis; total hip arthroplasty

Introduction

Altered joint loading has been defined as a risk factor for the onset of osteoarthritis

(OA) (Andriacchi et al. 2004) as well as a factor affecting the stress around and fixation

of a joint implant (Jonkers et al. 2008; Szwedowski et al. 2012). In vivo joint loading

can be calculated using musculoskeletal modelling and dynamic simulations of motion

based on integrated three dimensional motion capture data. Using this methodology,

joint loading in hip OA and total hip arthroplasty (THA) patients was found to be

substantially decreased as a result of altered kinematics and kinetics (Lenaerts, Mulier,

et al. 2009; Foucher et al. 2009; Wesseling et al. 2016).

However, muscle weakness was reported as a common problem in hip pathology

patients, while this is mostly not taken into account in musculoskeletal modelling. OA

patients have decreased hip abductor and flexor strength (Arokoski et al. 2002) and

although improved strength was found after THA, deficits may remain. Therefore,

rather than relying on the generic moment generating capacity, it is important to account

for subject-specific moment generating capacity in the musculoskeletal model

(Anderson & Pandy 2001; Ackland et al. 2012; Valente et al. 2014). Specifically for

patients presenting weakness, including this information can be relevant.

Isometric dynamometer measurements of joint moments have already been used

to estimate parameters of the musculotendon actuators (Anderson & Pandy 2001;

Garner & Pandy 2003; Van Campen et al. 2014). Only moderate or low sensitivity of

calculated muscle and contact forces to perturbing maximal isometric muscle force was

reported (De Groote et al. 2010; Ackland et al. 2012; Valente et al. 2014). Since it was

shown that the model’s moment generating capacity is highly sensitive to tendon slack

length and optimal fibre length, focus has been on the estimation of these parameters in

healthy subjects (Garner & Pandy 2003; Van Campen et al. 2014). Given that hip OA

and THA patients present hip muscle weakness, the effect of scaling muscle strength is

more relevant in these patients compared to healthy controls. Therefore, a scaling

approach to determine muscle strength based on dynamometer results could be

promising to account for weakness in the musculoskeletal model and evaluate the effect

of muscle weakness on calculated power output (Thelen 2003) and muscle forces (De

Groote et al. 2010; van der Krogt et al. 2012; Valente et al. 2013) as well as the

resulting contact forces.

However, dynamometer measurements of the hip might not be representative for

the moment generating capacity of these patients during functional activities, since OA

and total joint replacement patients present a decreased voluntary activation (Stevens et

al. 2003). As an alternative, functional scaling of the moment generating capacity could

be considered, an approach already successfully adopted for the knee (Lloyd & Besier

2003). During functional scaling, the parameters determining the muscle force

generating capacity are adapted through optimization. This method has been previously

used in EMG-driven models, to optimize the musculotendon parameters such that

modelled knee joint moments were in good agreement with experimentally measured

knee joint moments during functional activities (Lloyd & Besier 2003). Specifically

more demanding tasks were used as these motions are expected to result in increased

joint moments and therefore in increased muscle forces.

Besides subject-specific muscle forces, also subject-specific geometrical detail is

important in defining muscle forces and joint loading (Valente et al. 2014; Bosmans et

al. 2015). Medical imaging techniques have been used to include subject-specific

geometrical detail into the model (Scheys et al. 2006; Hainisch et al. 2012). Joint

moments (Bartels et al. 2015) as well as muscle and contact forces (Lenaerts, Bartels, et

al. 2009; Bosmans et al. 2014; Martelli et al. 2015) were affected when accounting for

subject-specific joint definition and muscle-tendon paths. In hip OA patients, it was

reported that subject-specific hip geometry and joint centre location affect calculated

hip contact forces (Lenaerts et al. 2008; Lenaerts, Bartels, et al. 2009). Therefore,

although decreased hip contact forces were reported in hip pathology patients,

differences in hip contact forces between patients and controls might be different when

using subject-specific models that account for the individual muscle force generation.

Although several studies reported the isolated effect of including subject-

specific geometry as well as scaling the moment generating capacity on calculated

muscle and contact forces, no study so far reported the combined effect of including all

these subject-specific factors in the musculoskeletal model on hip contact forces.

Therefore, the goal of this study was to define the effect of including subject-specific

moment generating capacity in the musculoskeletal model by scaling the isometric

muscle force and by including MRI-based geometrical information in a group of control

subjects and hip pathology patients before and after total hip replacement. The added

value of scaling the isometric muscle strength of hip abductor and flexor muscles

statically, using dynamometer measurements, as well as functionally, based on

functional activities, was investigated. This is highly relevant given the reported

analytical and functional muscle weakness as well as geometrical alterations in these

patients.

Methods

Experimental procedure

Five patients with unilateral OA and four of these patients three months after THA

surgery as well as four healthy controls were included in the study (table 1). One patient

after THA surgery was discarded due to erroneous force plate data. All THA patients

were operated by a single experienced orthopaedic surgeon via the direct anterior

approach. All subjects performed three gait trials as well as three stair ascent and

descent trials at self-selected speed. 3D marker trajectories were measured using a 3D

motion analysis system (VICON®, recording at 100 Hz, Oxford Metrics, Oxford, UK)

and ground reaction forces were synchronously measured using two AMTI force

platforms (1500 Hz, Advanced Mechanical Technology Inc., Watertown, MA). A Plug-

in-gait marker set (Davis et al. 1991) of the lower limb and trunk was used and

additionally three-cluster markers were placed on the upper and lower legs. For the

static trials, additional markers were placed on the medial femoral condyle as well as

the medial malleolus, resulting in a total of 40 markers. For the stair ascent and descent

trials a two-step staircase was placed on top of the force platforms. All subjects

performed a strength test measuring the moment generating capacity of the hip abductor

and flexor muscles using a Biodex dynamometer (Meyer et al. 2013). For hip abduction

and hip flexion three maximal voluntary isometric contractions (MVIC) of 6 seconds

were performed (with a 30 second rest period in between) at three different joint

positions, i.e. hip abduction angles of 0°, 10 and 20° and hip flexion angles of 30°, 45°

and 60°. Pre-operatively, two OA patients were unable to deliver an abduction moment

against the dynamometer at an abduction angle of 20°. For these patients, the moment

during the MVIC was set to be the moment required to hold up the leg, assuming that

the patients were capable of holding up their leg but not to provide additional moment

against the dynamometer. MVIC moments were reported as absolute moments and were

also normalized to body mass times height.

Finally, four series of axial MR images (Philips Ingenia 3.0T) were acquired for

all subjects while lying supine. A full leg image series was created from the overlapping

images. The images ranged from the superior rim of the iliac spine to the distal margins

of the toes. For the patients after THA, a magnetic artefact reduction sequence was

additionally used to minimize the artefact due to the prosthesis. Markers placed during

the gait analysis were outlined on the subject’s skin and replaced by radio-opaque, non-

ferromagnetic markers for the MRI scans (Scheys et al. 2008).

Musculoskeletal model

For all subjects, MRI based models were created consisting of 14 segments, 19 degrees

of freedom and 88 musculotendon actuators (Delp et al. 1990). The models were created

using in-house developed software (Scheys et al. 2006). First, the bone structures of the

pelvis, femora, patellae and tibiae were segmented from the images (Mimics Innovation

Suite, Materialise, Leuven, Belgium). Hip joint centres and knee axes were determined

based on the femoral bone structures. Next, muscle attachment and via points on the

pelvis, femora and proximal tibiae were defined in the MR images. The number of

muscle points as well as their relative position was defined similar to the generic model.

All muscle points on the lower leg were adopted from the scaled generic model.

Additionally, two wrapping surfaces around the hip joint were included. The

workflow to define the wrapping surfaces is described in Wesseling et al. (in review).

Briefly, the wrapping spheres were defined based on nine points for both the mm.

iliacus and psoas major that describe the path of the muscles around the hip joint

capsule. A circle was fit through these nine points to define the two wrapping spheres

for each hip joint. Care was taken that the muscles fully wrapped over the surface,

therefore the second points of the mm. iliacus and psoas major were moved more

proximally. The mm. rectus femoris and sartorius were constrained to wrap over the

surface defined for the m. iliacus.

Muscle-tendon parameters were linearly scaled from the generic model based on

the muscle-tendon length. Prior to static and functional scaling the maximal isometric

muscle forces in all models were identical to the maximal isometric forces in the

Gait2392 OpenSim model (Delp et al. 2007) and the Thelen muscle model (Thelen

2003) was used.

Moment generating capacity

Subject-specific moment generating capacity of the hip flexors and abductors was

determined for all models by scaling the maximal isometric muscle force of the hip

abductor (mm. piriformis, anterior and middle gluteus maximus, middle and posterior

gluteus medius, anterior, middle and posterior gluteus minimus) and flexor (mm.

iliacus, psoas major, rectus femoris and sartorius) muscles in the musculoskeletal

model. Since the m. tensor fasciae latae and the anterior part of the m. gluteus medius

contribute both to hip abduction and flexion, the maximal isometric force of these

muscles was scaled using the average of the abduction and flexion scale factors. Scale

factors were determined in two different ways. On the one hand, a static scaling

procedure estimated the scale factors of the muscles based on the absolute abduction

and flexion moments measured during the MVIC dynamometer experiments. The

maximal moments at the three different joint angles were used as input for a linear

optimization problem that solved for scale factors that minimized the differences

between the modelled joint angle-moment curves for abduction and flexion and the

measured moment generating capacity (Matlab R2014a, The Mathworks Inc., Natick,

MA, USA). The maximal isometric muscle forces of the hip abductors and flexors were

scaled using the respective static scale factors.

On the other hand, functional scaling determined the scale factors based on the

joint moments calculated either during gait, stair ascent or stair descent for the same

muscles as for the static scaling. This way, the functional scaling enforced the scaled

model strength to be sufficient to generate the functionally observed joint motions.

Scale factors were determined by optimizing two conflicting criteria. Firstly, we were

interested in finding the smallest possible scale factors that resulted in sufficient model

strength to perform the functional movements. Secondly, muscle activations could not

be unreasonably high during the measured tasks, since we assumed that those tasks did

not require sustained maximal muscle activation. This way, no arbitrary high scale

factors could be selected by the algorithm. Scale factors for the abductors and flexors

were determined for each trial separately by creating a pareto set of optimal solutions,

i.e. a set of scale factors corresponding to different relative costs for the two criteria

(Matlab R2014a, The Mathworks Inc., Natick, MA, USA) (Logist et al. 2010). From the

pareto set of solutions, the minimal scale factors for which no maximal activations were

found were selected. Finally, from all simulated trials, the trial that was most

demanding, i.e. the trial that resulted in the highest sum of all scale factors, being either

gait, stair ascent or descent, determined the functional scale factors for each subject

separately. Then, the maximal isometric muscle forces of the abductor and flexor

muscles were scaled based on the static and functional scale factors. Finally, dynamic

simulations of gait were generated.

Dynamic simulations of motion

Simulations of gait were generated in OpenSim 3.1 (Delp et al. 2007). An inverse

kinematics procedure was used to calculate joint angles based on the measured 3D

marker trajectories (Lu & O’Connor 1999). Joint moments were calculated using

inverse dynamics. A static optimization procedure was used to calculate muscle forces

that minimized the instantaneous sum of squared muscle activations (Matlab R2014a,

The Mathworks Inc., Natick, MA, USA). The optimization problem was constrained to

allow only for physiological increase and decrease rates of muscle activation

(characterized by activation and deactivation time constants of 11 ms and 68 ms

respectively (Raasch et al. 1997)). Instead of strictly imposing that muscle forces

generated the internal joint moments, the cost function included a weight factor for each

joint moment allowing for deviations of the muscle generated moments from the

internal joint moments (Wesseling et al. 2015). The absolute deviation of the muscle

generated moments was expressed as a fraction of the maximal absolute internal joint

moment. Finally, hip contact forces were calculated using a JointReaction analysis

(Steele et al. 2012) and were normalized to body weight. Also force orientation in the

frontal, sagittal and transversal plane was calculated (figure 1). Calculated hip contact

force magnitude and orientation were reported descriptively and compared to measured

contact forces as reported by Bergmann et al. (2001) (HIP98).

Results

During the dynamometer experiments, OA and THA patients generated slightly lower

normalized hip flexion and abduction moments although absolute moments were

comparable to controls (table 2). Static scaling based on the dynamometer

measurements decreased the maximal isometric force for the abductors as well as

flexors for all subjects (table 3). This decrease was higher for hip flexor muscles than

for hip abductor muscles. The functionally scaled models were mostly stronger than the

statically scaled models and several functionally scaled models were even stronger

compared to the unscaled models (table 3). Most often, gait resulted in the highest scale

factor (10 gait, 1 stair ascent and 2 stair descent trials resulted in the highest sum of

scale factors).

The statically scaled musculoskeletal models lacked the strength to generate the

joint moments required for the functional trials. In these models, muscle generated

moments deviated more from the internal joint moments compared to the unscaled

models (figure 2). As these deviations were unreasonably large, further results, i.e. hip

contact forces, were not reliable (supplementary material A).

The functionally scaled models were sufficiently strong to generate the joint

moments required for the functional trials, since this was the criterion to determine the

functional scale factors. Simulation results for the functionally scaled and unscaled

models were similar in terms of the deviation of the muscle generated moments from

the internal joint moments (figure 2) and hip contact force magnitude (figure 3). Also

orientation of the contact forces was not importantly affected by the functional scaling

(figure 4). Given the limited effect of scaling isometric muscle forces, further results are

reported based on the unscaled models.

In comparison to the hip contact forces of the HIP98 dataset, calculated hip

contact forces for controls were higher at both the first and second peak, (figures 3 and

5). As calculated hip contact forces for both OA and THA patients were lower than for

controls, these were more comparable to HIP98. Hip contact force magnitudes of

patients compared well with HIP98 (figure 3). Orientation in the frontal plane was also

more comparable to HIP98 (figure 4), while in the transversal and sagittal planes the

orientation deviated more and variation was large.

Discussion

The goal of this study was to define the effect on hip contact forces of including subject-

specific moment generating capacity in the musculoskeletal model by using a static and

a functional scaling approach for isometric muscle strength when including MRI-based

geometrical information into the musculoskeletal model.

Static scaling based on the dynamometer experiments decreased the maximal

isometric muscle forces of specifically the hip flexor muscles (table 3). Measured hip

flexion torques reported in this study were much lower than torques reported by Meyer

et al. (2013), which might be explained by the older subjects in the present study. Use of

the statically scaled models resulted in increased deviations of the muscle generated

moments from the internal joint moments required to balance the external joint

moments (figure 2) indicating that the scaled maximal muscle forces were too low.

Especially for controls, the deviation of the muscle generated moments from the internal

joint moments increased when statically scaling muscle forces. Since the absolute

isometric joint moments measured with the dynamometer were only minimally different

between controls and patients, muscle forces were decreased to a similar extent.

However, the gait pattern adopted by the controls required higher hip flexion and

abduction joint moments than the gait pattern adopted by the patients, therefore the

muscle generated moments deviated more. As the statically scaled models were not

strong enough to generate the internal joint moments, further results, i.e. hip contact

forces, could not be reliably calculated and are therefore not further discussed. Static

scaling based on the isometric dynamometer measurements resulted in models that were

unable to generate sufficient functional joint moments, which indicates that maximal

moment generating capacity during dynamometer measurements are not representative

for the moment generating capacity during gait, even in healthy controls.

Previous research reported that altered maximal isometric muscle force does not

largely affect calculated muscle forces (De Groote et al. 2010; Ackland et al. 2012) and

we also did not find a large effect on contact forces during gait when using functional

scaling. Also deviations of the muscle generated moments from the internal joint

moments were more similar to the unscaled models (figure 3). Only in hip rotation the

deviation of the muscle generated moments from the internal joint moment was larger

for all models. This follows directly from the imposed weights during the static

optimization, as the weight penalizing deviations in the transverse plane was smaller to

account for the higher measurement errors in this plane.

When comparing hip contact forces between controls and patients, contact

forces in both OA and THA patients were decreased over the entire gait cycle compared

to controls, as has been reported before (Stansfield & Nicol 2002; Li et al. 2014; Li et

al. 2015). This was independent of scaling muscle forces. This suggests that, in

agreement with previous research, pre-operative adaptations remained after surgery

(Stansfield & Nicol 2002; Foucher et al. 2007). Also, hip contact forces were

comparable between OA and THA patients, indicating that hip contact forces did not

return to normal three months after THA.

Estimated hip contact forces in this study were higher than measured contact

forces (Bergmann et al. 2001), also when scaling muscle forces, specifically at the

second peak. However, the difference was much smaller for patients than for controls.

Increased hip contact force magnitudes in controls compared to measured forces has

been reported before (Klein Horsman 2007; Mellon et al. 2013; Wesseling et al. 2015).

This might partially be attributed to differences in subject and gait characteristics, such

as gait speed and external hip moments (Wesseling et al. 2015). Since hip contact forces

in OA and THA subjects were more comparable to HIP98 forces than for control

subjects, this might imply that HIP98 data is not representative for hip contact forces in

healthy control subjects.

A limitation of this study is the limited number of subjects in each group. As

only four or five subjects were available in each group, statistical tests deemed to be

inappropriate and only relevant trends were described. Hence, in future research a larger

number of subjects should be included to allow statistical testing. Another limitation is

the supine position of the subjects for acquiring the MRI scans. This potentially affects

the muscle paths derived from MRI, particularly for mm. iliacus and psoas major that

wrap over the hip capsule and the posterior muscles that are flattened when lying

supine. The supine position may also introduce skin and marker movement, affecting

the joint kinematics and therefore calculated contact forces. Further, based on the

dynamometer measurements only the maximal isometric muscle force was scaled.

However, other muscle-tendon parameters, i.e. tendon slack length and optimal fibre

length, also influence the moment generating capacity. It might not be representative to

only adjust the maximal isometric muscle forces (Thelen 2003), as inclusion of other

muscle tendon parameters can have a larger effect on muscle forces (De Groote et al.

2010; Ackland et al. 2012) and therefore on contact forces. Also, dynamometer

measurements of the hip might not be representative for the moment generating capacity

of the OA patients during functional activities, since OA patients present a decreased

voluntary activation due to pain and impairments in the central nervous system (Mizner

et al. 2003; Stevens et al. 2003). This could affect calculated scale factors. However,

dynamometry is the only method to measure the moment generating capacity. As

electrical stimulation of the hip muscles is not evident, the central activation ratio could

not be determined in the present study and therefore the voluntary activation is

unknown. Besides that, moments were measured at only three different joint angles. The

availability of only three data points for static scaling of the joint angle-moment curve

could have affected the accuracy of the calculated scale factors.

Conclusion

In conclusion, scaling muscle strength based on isometric dynamometer measurements

reduced the force generating capacity of all hip flexor and abductor muscles and

resulted in models that were too weak to perform functional movements. This indicates

that isometric dynamometer measurements were not representative for the functional

demands of gait in hip pathology patients as well as in healthy control subjects.

Functional scaling of muscle forces resulted in models that were strong enough to

perform the functional tasks and calculated hip contact forces that resembled the hip

contact forces computed using the unscaled models. This indicates that scaling muscle

forces is not needed when only considering hip contact forces, as long as the model

remains strong enough.

Acknowledgement

The support of the Agency for Innovation by Science and Technology (IWT-TBM no

100786) is gratefully acknowledged. The funders had no role in any part of this study.

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Tables

Table 1. Mean ± standard deviation of the subject characteristics.

Controls OA THABMI (kg/m2) 22.0±2.94 25.4±5.16 23.3±2.7Walking speed (m/s)

1.27±0.25 1.06±0.10 1.21±0.23

Age (yrs.) 56±3.0 54±8.6 53±9.8Height (m) 1.68±0.14 1.77±0.07 1.75±0.06Weight (kg) 62.7±16.1 80.5±22.2 71.6±11.4

Table 2. Median (range) of the absolute and normalized maximal moment generating

capacity measured using the dynamometer measurements for the controls, osteoarthritis

(OA) and total hip arthroplasty (THA) patients.

Absolute torque (Nm)Abduction Flexion

0° 10° 20° 30° 45° 60°Control 105.4

(72.7-126.7)85.0

(64.4-116.8)

73.1(58.8-104)

85.6(54.2-123)

67.8(35.3-94.1)

57.2(38.6-80.3)

OA 88.7(77.2-125)

80.8(41.4-110.8)

77.2(46-95.7)

79.6(58.3-135.2)

52.3(39.2-108.9)

70.1(30.4-89.9)

THA 106.7(65.4-138.2)

85.4(49.6-110.1)

76.4(35-101.7)

96.0(58.2-121.4)

77.7(41.5-96.8)

58.2(26.3-65)

Normalized torque (Nm/(kg*m))Abduction Flexion

0° 10° 20° 30° 45° 60°Control 1.01

(0.84-1.04)0.83

(0.78-0.98)0.71

(0.58-0.78)0.82

(0.74-0.86)0.57

(0.48-0.77)0.53

(0.47-0.62)OA 0.83

(0.37-0.94)0.60

(0.46-0.84)0.63

(0.32-0.72)0.81

(0.33-0.99)0.62

(0.18-0.80)0.45

(0.33-0.66)THA 0.79

(0.69-0.87)0.62

(0.54-0.70)0.55

(0.38-0.65)0.72

(0.59-1.04)0.56

(0.45-0.72)0.42

(0.29-0.52)

Table 3. Median (range) of scale factors for the hip abductors and flexors with static

scaling, using the dynamometer measurements, and functional scaling, using the

functional activities for controls, osteoarthritis (OA) and total hip arthroplasty (THA)

patients.

StaticAbductors Flexors

Controls 0.68(0.49-0.78)

0.43(0.28-0.54)

OA 0.54(0.41-0.67)

0.41(0.30-0.66)

THA 0.56(0.37-0.61)

0.43(0.26-0.52)

FunctionalAbductors Flexors

Controls 1.08(0.43-1.23)

1.02(0.36-1.15)

OA 1.10(0.56-1.31)

0.94(0.87-1.12)

THA 0.63(0.47-0.72)

0.82(0.62-1.05)

Figures

Figure 1. The calculated orientation angles in the frontal (Ax), transversal (Ay) and

sagittal (Az) planes and the different hip contact force components in posterior-anterior

(Fx), inferior-superior (Fy) and medio-lateral (Fz) direction indicated on a right femur.

Figure 2. The absolute deviation of the muscle generated moments expressed as a

fraction of the maximal absolute internal joint moment in hip flexion (left), abduction

(middle) and rotation (right). Dark grey boxplots represent unscaled models, white

boxplots represent the functionally scaled models and light grey boxplots represent the

statically scaled models.

Figure 3. Hip contact forces at the first (left) and second (right) peak. Dark grey

boxplots represent unscaled models and white boxplots represent the functionally scaled

models. The grey area represents the range of measured hip contact forces by Bergmann

et al. (2001).

Figure 4. Orientation of the hip contact forces at the first (left) and second (right) peak

in the frontal (Ax), transversal (Ay) and sagittal (Az) planes. Dark grey boxplots

represent unscaled models and white boxplots represent the functionally scaled models.

The grey area represents the range of measured hip contact forces by Bergmann et al.

(2001).

Figure 5. Averaged hip contact forces for controls and osteoarthritis (OA) and total hip

arthroplasty (THA) patients without scaling muscle forces. The grey area represents the

range of measured forces by Bergmann et al. (2001).