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Aalborg Universitet
Musculoskeletal model-based inverse dynamic analysis under ambulatory conditions
using inertial motion capture
Karatsidis, Angelos; Jung, Moonki; Schepers, Martin; Bellusci, Giovanni; de Zee, Mark;
Veltink, Peter H.; Andersen, Michael Skipper
Published in:
Medical Engineering & Physics
Publication date:
2019
Document Version
Accepted author manuscript, peer reviewed version
Link to publication from Aalborg University
Citation for published version (APA):
Karatsidis, A., Jung, M., Schepers, M., Bellusci, G., de Zee, M., Veltink, P. H., & Andersen, M. S. (Accepted/In
press). Musculoskeletal model-based inverse dynamic analysis under ambulatory conditions using inertial
motion capture. Medical Engineering & Physics.
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Title:
Musculoskeletal model-based inverse dynamic analysis under ambulatory con-
ditions using inertial motion capture
Authors:
Angelos Karatsidis1,2, Moonki Jung3, H. Martin Schepers1, Giovanni Bellusci1,
Mark de Zee4, Peter H. Veltink2, Michael Skipper Andersen5
Affiliations:
1Xsens Technologies B.V., Enschede 7521 PR, The Netherlands
2Department of Biomedical Signals and Systems, Faculty of Electrical Engineer-
ing, Mathematics and Computer Science, University of Twente, Enschede 7500
AE, The Netherlands
3AnyBody Technology A/S, Aalborg 9220, Denmark
4Department of Health Science and Technology, Aalborg University, Aalborg
9220, Denmark
5Department of Materials and Production, Aalborg University, Aalborg 9220,
Denmark
Corresponding author:
Angelos Karatsidis, Address: Xsens Technologies B.V., Pantheon 6-8, Enschede
7521 PR, The Netherlands, E-mail: angelos.karatsidis@xsens.com, Tel.: +31 88
97367 36, Fax: +31 88 97367 01
Keywords:
musculoskeletal modeling, inertial motion capture, inverse dynamics, ground
reaction forces and moments, gait analysis
Wordcount:
Abstract: 197 words
Main text: 3582 words
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Accepted manuscript
Abstract1
Inverse dynamic analysis using musculoskeletal modeling is a powerful tool,2
which is utilized in a range of applications to estimate forces in ligaments, mus-3
cles, and joints, non-invasively. To date, the conventional input used in this4
analysis is derived from optical motion capture (OMC) and force plate (FP)5
systems, which restrict the application of musculoskeletal models to gait labo-6
ratories. To address this problem, we propose the use of inertial motion cap-7
ture to perform musculoskeletal model-based inverse dynamics by utilizing a8
universally applicable ground reaction force and moment (GRF&M) prediction9
method. Validation against a conventional laboratory-based method showed10
excellent Pearson correlations for sagittal plane joint angles of ankle, knee, and11
hip (ρ= 0.95, 0.99, and 0.99, respectively) and root-mean-squared-differences12
(RMSD) of 4.1±1.3◦, 4.4±2.0◦, and 5.7±2.1◦, respectively. The GRF&M pre-13
dicted using IMC input were found to have excellent correlations for three com-14
ponents (vertical: ρ= 0.97, RMSD=9.3±3.0 %BW, anteroposterior: ρ= 0.91,15
RMSD=5.5±1.2 %BW, sagittal: ρ= 0.91, RMSD=1.6±0.6 %BW*BH), and16
strong correlations for mediolateral (ρ= 0.80, RMSD=2.1±0.6 %BW ) and17
transverse (ρ= 0.82, RMSD=0.2±0.1 %BW*BH). The proposed IMC-based18
method removes the complexity and space-restrictions of OMC and FP systems19
and could enable applications of musculoskeletal models in either monitoring20
patients during their daily lives or in wider clinical practice.21
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1. Introduction22
Assessment of muscle, joint, and ligament forces is important to understand23
the mechanical and physiological mechanisms of human movement. To date,24
the measurement of such in-vivo forces is a challenging task. For this reason,25
computer-based musculoskeletal models have been widely used to estimate the26
variables of interest non-invasively [1, 2].27
The most common approach used in musculoskeletal modeling is the method28
of the inverse dynamics [3]. This analysis utilizes the equations of motion with29
input from human body kinematics in conjunction with kinetics obtained from30
external forces [4], to estimate joint reaction and muscle forces, as well as net31
joint moments using muscle recruitment methods [5]. Measurements of the32
external forces are typically required and measured using force plates (FPs),33
however, the use of FPs has several limitations. First, subjects tend to alter34
their natural gait patterns in order to hit the small and fixed measurement area35
of a plate [6]. In addition, this static and limited measurement area, impedes36
the assessment of several consecutive steps, when only a couple of FPs are37
available. Finally, the combined use of FP with motion input introduces a38
dynamic inconsistency, which results to residual forces and moments in the39
inverse dynamics. [7, 8].40
Several studies have proposed replacing the FP input with wearable de-41
vices such as shoes with three-dimensional force and torque sensors beneath42
the sole [9, 10, 11]. In a similar fashion, pressure insoles were proposed to re-43
construct the complete ground reaction forces and moments (GRF&M) from44
pressure distributions [12, 13, 14]. Although these wearable devices are suitable45
for the assessment of external forces, the increased height and weight of the46
shoes equipped with force/torque sensors [15, 16], as well as the repeatability47
of the pressure sensors [17] are considered important limitations.48
Recent research has suggested the replacement of the force input with predic-49
tions derived solely from motion input [18, 19, 20, 21, 22, 23]. In these studies,50
human body kinematics are combined with the inertial properties of the body51
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segments, from which Newton-Euler equations are utilized to compute the exter-52
nal forces and moments. Since the system of equations becomes indeterminate53
during the double stance of gait, each of the aforementioned studies focused on54
methods to solve this issue. Ren et al. [19] suggested a gait event-based func-55
tion which is only applicable in gait, while Oh et al. [20] and Choi et al. [21]56
suggested methods based on a machine learning that require a training database57
and thus are not applicable for movements not included in that database. A58
last approach enables the universal application of these methods using a muscle59
recruitment approach has shown promising performance for various activities of60
daily living [22] and sports [23].61
The majority of the existing research which studied the prediction of GRF&M,62
used conventional optical motion capture (OMC) input. Despite the high ac-63
curacy of this method in tracking marker trajectories, its dependence on lab-64
oratory equipment restricts possible applications during daily life activities or65
in wider clinical practice. In the previous decade, ambulatory motion tracking66
systems based on inertial measurement units (IMUs), have been proposed as a67
suitable alternative for estimating 3D segment kinematics [24, 25, 26, 27]. A68
key benefit of such systems is that they can be applied in virtually any environ-69
ment without depending on external infrastructure, such as cameras. Driven70
by these advances in inertial motion capture (IMC), recent work of the authors71
demonstrated its ability to estimate three-dimensional GRF&M [28], which were72
distributed between the feet using a smooth transition assumption concept [19].73
However, limitations of that approach is that it is only valid for gait and has no74
muscle, bone or ligament force estimate capabilities.75
To date, the use of detailed musculoskeletal modeling with kinematic inputs76
from IMUs has only received limited attention. Koning et al. [29] previously77
demonstrated the feasibility of kinematically driving a musculoskeletal model78
using only orientations from IMUs. However, that study only compared the79
kinematics of the musculoskeletal model, without any inverse dynamic calcula-80
tions.81
The aim of this study was to develop a workflow to perform musculoskeletal82
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model-based inverse dynamics using exclusively IMC input, applicable in am-83
bulatory environments and validate it against a conventional laboratory-based84
approach.85
2. Methods86
2.1. Subjects87
The experimental data was collected at the Human Performance Labora-88
tory, at the Department of Health Science and Technology, Aalborg University,89
Aalborg, Denmark following the ethical guidelines of The Scientific Ethical Com-90
mittee for the Region of North Jutland (Den Videnskabsetiske Komit for Region91
Nordjylland). Eleven healthy male individuals with no present musculoskeletal92
or neuromuscular disorders volunteered for the study (age: 31.0 ±7.2 years;93
height: 1.81 ±0.06 m; weight: 77.3 ±9.2 kg; body mass index (BMI): 23.6 ±94
2.4 kg/m2). All participants provided written informed consent, prior to data95
collection.96
2.2. Instrumentation97
Full-body IMC data were collected using the Xsens MVN Link (Xsens Tech-98
nologies B.V., Enschede, the Netherlands), in which 17 IMUs were mounted on99
the head, sternum, pelvis, upper legs, lower legs, feet, shoulders, upper arms,100
forearms and hands using the dedicated clothing. The exact location of each101
sensor on the respective segment followed the manufacturer guidelines described102
in the manual of Xsens MVN [30]. The affiliated software Xsens MVN Studio103
4.2.4 was used to track the IMU orientations with respect to an earth-based104
coordinate frame [24, 25]. Segment orientations were obtained by applying the105
IMU-to-segment alignment, found using a known upright pose (N-pose) per-106
formed by the subject at a known moment in time, while taking specific care107
to minimize the effect of magnetic disturbances. In addition, this information108
is fused with updates regarding the joints and external contacts to limit the109
position drift [26].110
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For validation purposes, an OMC system utilizing 8 infrared high speed111
cameras (Oqus 300 series, Qualisys AB, Gothenburg, Sweden) and the software112
Qualisys Track Manager 2.12 (QTM) were used to track the trajectories of 53113
reflective markers mounted on the human body, as described in the Appendix of114
[28]. In addition, three FP systems (AMTI OR6-7-1000, Advanced Mechanical115
Technology, Inc.,Watertown, MA, USA) embedded in the floor of the laboratory,116
were utilized using QTM to record the GRF&Ms. Both IMC and OMC systems117
sampled data at a frequency of 240 Hz, while the FP system sampled data at118
2400 Hz and subsequently downsampled to 240 Hz to match the IMC and OMC119
sampling rate.. A second-order forward-backward low-pass Butterworth filter120
was applied to the reflective marker trajectories and measured GRF&M, with121
cut-off frequencies of 6 Hz and 15 Hz, respectively.122
2.3. Experimental protocol123
For each participant, the body dimensions were extracted using a conven-124
tional tape following the guidelines of Xsens. During the data collection, the125
subjects were instructed to walk barefoot in three different walking speeds (com-126
fortable; CW, fast; FW, and slow; SW). The walking speeds performed experi-127
mentally were quantified as 1.28±0.14 m/s (mean ±standard deviation) for CW,128
1.58±0.09 m/s for FW (CW + 23%) and 0.86±0.11 m/s for SW (CW−33%).129
For every walking speed, five successful trials were assessed. A successful trial130
was obtained when a single foot hit one of the FPs entirely, followed by an entire131
hit of the other foot on the successive FP.132
2.4. Overall description of the components in the musculoskeletal models133
Three musculoskeletal models have been constructed in AnyBodyTM Mod-134
eling System (AMS) v.6.0.7 (AnyBodyTM Technology A/S, Aalborg, Denmark)135
[1]:136
a model in which the kinematics are driven by IMC and the GRF&M are137
predicted from the kinematics (IMC-PGRF).138
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a model in which the kinematics are driven by OMC and the GRF&M are139
predicted from the kinematics (OMC-PGRF).140
a model in which the kinematics are driven by OMC and the GRF&M are141
measured from FPs (OMC-MGRF).142
In the IMC-PGRF model, a Biovision Hierarchy (BVH) file is exported from143
Xsens MVN Studio and imported in AMS, in which a stick figure model is ini-144
tially reconstructed. The BVH file contains a hierarchy part with a description145
of the linked segment model in a static pose, as well as a motion part that146
contains, for each time frame, the absolute position and orientation of the root147
pelvis segment, and the joint angles between the segments described in the hier-148
archy. The generated stick figure model contains 72 degrees-of-freedom (DOF).149
In order to match the stick figure model with the musculoskeletal model, we150
utilize a concept of virtual markers (VMs) demonstrated in a previous Kinect-151
based study [31]. The VMs are mapped to particular points of each model that152
are well defined in both models, such as joint centers and segment end points.153
The VM placement is illustrated in Figure 1 and described in more detail in154
the supplementary material. Following this step, the VMs are treated as actual155
experimental markers, as if they were derived from an OMC system and they156
are assigned weights in three directions in the segmentframe. Contrary to OMC,157
no filtering was applied to the VM trajectories.158
In all models, the GaitFullBody template of the AnyBodyTM Managed159
Model Repository (AMMR) 1.6.2 was used to reconstruct the musculoskele-160
tal models in AMS. The lumbar spine model was derived from the study of161
de Zee et al. [32], the lower limb model was derived from the Twente Lower162
Extremity Model Klein-Horsman et al. [33], and the shoulder and upper limb163
models were based on the model of the Delft Shoulder Group [34, 35, 36]. The164
full-body kinematic model contained 39 DOF in total. Specifically, a pelvis165
segment with three rotational and three translational DOF, two spherical hip166
joints, two revolute knee joints, two universal ankle joints, a spherical pelvic-167
lumbar joint, two glenohumeral joints with five DOF each, two universal elbow168
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joints, and two universal wrist joints. The motion of the neck joint was locked169
to a neutral position.170
2.5. Scaling and kinematics analysis of the musculoskeletal models171
For each subject, a standing reference trial with an anatomical pose was172
utilized to identify the parameters of segment lengths and the (virtual) marker173
positions, using a least-square minimization between the model and input (vir-174
tual or skin-mounted) marker positions [37]. In the IMC-PGRF musculoskeletal175
model, the lengths of the shanks, thighs, head, upper arm and forearms were176
derived directly from the stick figure, as generated from Xsens MVN studio us-177
ing the measured body dimensions. In contrast, the pelvis width, foot length,178
and trunk height were optimized based on the above-mentioned least-square179
minimization method. The estimated segment lengths were used in all subse-180
quent dynamic trials to perform the kinematic analysis based on the method of181
Andersen et al. [38].182
2.6. Inertial and geometric scaling of the musculoskeletal models183
The mass of each segment was linearly scaled based on the total body mass184
and the segment mass ratio values reported by Winter [4]. The inertial pa-185
rameters were calculated by considering the segments as cylinders with uniform186
density. In addition, geometric scaling of each segment, where the longitudinal187
axis was defined as the second entry, was achieved using the following matrix:188
S=
qms
ls0 0
0ls0
0 0 qms
ls
(1)
where Sis the scaling matrix, lsis the ratio between the unscaled and scaled189
lengths of the segment, msis the mass ratio of the segment.190
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2.7. Muscle recruitment191
The muscle recruitment problem was solved by defining an optimization192
problem where a system of equations minimizes the cost function, subject to193
the dynamic equilibrium equations and non-negativity constraints, so that each194
muscle can only pull, but not push, while its force remains below its strength195
[1, 31, 39].196
The strengths of the muscles were derived from previous studies which de-197
scribed the models of the body parts, and were considered constant for different198
lengths and contraction velocities [32, 33, 34, 35, 36]. To scale the muscle199
strengths, fat percentage was used as in Veeger et al. [35], calculated from the200
body mass index [40]. The model of the lower body contained 110 muscles,201
distributed into 318 individual muscle paths. In contrast, in the upper body202
model, ideal joint torque generators were utilized. Actuators for residual forces203
and moments with capacity up to 10 N and Nm, respectively, were placed at the204
origin of the pelvis and included in the muscle recruitment problem previously205
described.206
2.8. Ground reaction force and moment prediction207
The GRF&M were predicted by adjusting a method of Skals et al. [23]. A208
set of eighteen dynamic contact points were overlaid 1 mm beneath the inferior209
surface of each foot. Each dynamic contact point consisted of five unilateral210
force actuators, which could generate a positive vertical force perpendicular to211
the ground, and static friction forces in the anterior, posterior, medial, and212
lateral directions using a friction coefficient of 0.5. In addition, the height and213
velocity activation thresholds were set to 0.03 m and 1.2 m/s, respectively.214
2.9. Data Analysis215
Lower limb joint angles calculated in the IMC-PGRF model were compared216
to the OMC-PGRF/OMC-MGRF. In addition, GRF&M and JRF&M of the217
IMC-PGRF and OMC-PGRF were compared to OMC-MGRF.218
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Forces were normalized to body weight (BW) and moments to body weight219
times body height (BW*BH). The time axis of the curves was normalized to220
100% of the gait cycle for the kinematics (time between two consecutive heel-221
strike events of the analyzed limb) and 100% of the stance phase (time between222
heel-strike and toe-off events of the analyzed limb) for the kinetics. Measured223
and estimated GRF&M were expressed on the right handed coordinate frame224
defined by the walking direction within the trial (given that the subjects walked225
straight) and the vertical axis equal to the vertical axis of the respective mo-226
tion capture system used. On the other hand, JRF&M were expressed on the227
coordinate frame of the segment distal to the body in both IMC and OMC228
methods.229
The above-mentioned comparisons of kinematic and kinetic variables to their230
respective references were performed using absolute and relative root-mean-231
square-differences (RMSD and rRMSD, respectively)as described by Ren et al.232
[19]. In addition, for every curve, the magnitude (M) and phase (P) differ-233
ence metrics [41] have been utilized. Pearson correlation coefficient (ρ) were234
calculated, averaged using Fisher’s z transformation method [42], and cate-235
gorized similarly to Taylor et al. [43], as ”weak” (ρ≤0.35), ”moderate”236
(0.35 < ρ ≤0.67), ”strong” (0.67 < ρ ≤0.90), and ”excellent” (ρ > 0.90).237
3. Results238
3.1. Estimated kinematics of the musculoskeletal model239
Table 1 presents the results for the accuracy analysis for the joint angles240
of the IMC-driven model versus the OMC-driven model. Similarly, Figure 2241
illustrates the curves for the joint angles of the lower extremities averaged across242
all gait cycles performed by the eleven subjects. Excellent Pearson correlation243
coefficients have been found in all sagittal plane angles for ankle, knee, and hip244
(0.95,0.99, and 0.99, respectively). For the same variables, the RMSDs across a245
gait cycle were found as 4.1±1.3◦, 4.4±2.0◦and 5.7±2.1◦, respectively (mean246
±standard deviation). Hip flexion angles were overall underestimated (M=247
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−4.0±13.9%), whereas knee and ankle magnitude differences showed an average248
overestimation (0.7±6.2% and 8.6±16.4%). The hip abduction showed excellent249
correlations (ρ= 0.91) with an RMSD of 4.1±2.0◦and a mean underestimation250
with a magnitude difference M=−12.2±34.7%. Strong correlation values (ρ=251
0.68) were observed in the hip internal-external rotation angle with an RMSD252
of 6.5±2.8◦and an underestimation of magnitude difference M= 5.5±39.0%.253
Finally, the subtalar eversion angle showed strong correlation (ρ= 0.82), RMSD254
of 9.66 ±3.07◦and M= 24.0±34.7%.255
3.2. Predicted kinetics using inertial and optical motion capture256
The results of the accuracy analysis for GRF&M and JRF&M are presented257
in Table 2 and 3, for IMC-PGRF and OMC-PGRF, respectively. The mean258
values and standard deviations of the curves from IMC-PGRF, OMC-PGRF,259
and OMC-MGRF models, are illustrated in Figures 3 and 4, for the forces and260
moments, respectively.261
The Pearson correlation coefficients of the IMC-PGRF model were excellent262
for vertical (ρ= 0.97) and anteroposterior GRF&M (ρ= 0.91) and strong for263
mediolateral GRF&M (ρ= 0.80). For the same components, RMSD values264
observed were of 9.3±3.0, 5.5±1.2 and 2.1±0.6 %BW, respectively (mean265
±standard deviation). The OMC-PGRF model performed better in the an-266
teroposterior GRF&M components (ρ= 0.96, RMSD = 3.7±1.1 %BW), and267
similarly to IMC-PGRF for the other two GRF&M components (mediolateral:268
ρ= 0.79, RMSD = 1.9±0.5 BW, vertical: ρ= 0.99, RMSD = 5.9±1.9 BW).269
Concerning GRM, the sagittal plane was predicted with similar excellent270
correlations in both IMC-PGRF (ρ= 0.91) and OMC-PGRF (ρ= 0.94) driven271
models. The correlation coefficients for frontal and transverse GRM components272
found in the IMC-PGRF model were ρ= 0.64, ρ= 0,82, respectively, whereas273
in the OMC-PGRF model (ρ= 0.66, ρ= 0,81, respectively). The RMSDs274
found in the IMC-PGRF approach were 0.9±0.6, 1.6±0.6 , and 0.2±0.001275
%BW*BH for frontal, sagittal and transverse GR&M, respectively, which were276
either slightly higher or similar to the RMSDs of the OMC-PGRF approach277
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(0.7±0.2, 1.2±0.4, and 0.2±0.1 %BW*BH, respectively).278
4. Discussion279
We have presented a method to perform musculoskeletal model-based in-280
verse dynamics using exclusively IMC input (IMC-PGRF). First, we compared281
the kinematic joint angle estimates of the lower limbs against those assessed282
through a conventional, laboratory-based OMC input. In addition, we tested283
the performance of the approach in calculating the JRF&M, while predicting284
the GRF&M from the kinematics, against a similarly constructed model (OMC-285
MGRF) which uses input from both FP and OMC. Finally, we performed a sim-286
ilar comparison to evaluate the predicted kinetics of a model driven exclusively287
by OMC input (OMC-PGRF).288
Regarding the IMC-based joint angles in the musculoskeletal model, all three289
sagittal plane angles provided excellent correlations (range: 0.95-0.99) and aver-290
age RMSD values remained below 6◦. Slightly lower correlations were observed291
in the frontal and transverse plane angles, which can be explained due to the292
smaller range of motion within these planes. For instance, even though the293
hip abduction and external rotation joint angles present absolute RMSD values294
similar to the flexion component, their rRMSDs which take into account the295
range of motion are two and three times higher, respectively.296
Both GRF&M and JRF&M of the vertical axis presented higher correlations297
and lower RMSDs than the ones in the anteroposterior and mediolateral axes.298
Similarly, sagittal plane moments were found in most cases to be more accurate299
than frontal and transverse plane moments. By visual inspection of the curves,300
we observe that the magnitude of the IMC-PGRF anteroposterior GRF&M301
seems to be underestimated both in the negative early stance and positive late302
stance peak, which can be confirmed by the magnitude difference for that curve303
(M=−28.3%). However, this behaviour is not observed in the OMC-PGRF,304
nor during the single stance of the IMC-PGRF curve. Despite the higher rRMSD305
found in the non-sagittal joint angles, the performance of the IMC-PGRF in306
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the mediolateral, frontal and transverse plane GRF&M components matched307
closely the OMC-PGRF approach. This observation reveals that OMC-based308
kinematics suffer from errors of similar size, when capturing the typically small309
movements of the frontal and transverse planes, given the fact that both IMC-310
PGRF and OMC-PGRF had the same model characteristics. Therefore, OMC-311
MGRF should also be used with caution, when comparing either kinematic or312
JRF&M quantities of the non-sagittal planes.313
A number of error sources contribute to discrepancies in the OMC kinemat-314
ics. First, soft tissue artefacts can create a relative movement of the marker315
with respect to the bone [44, 45]. In addition, mismatches between the experi-316
mental and modelled marker positions can lead to errors in segment orientations317
calculated during inverse kinematics. Both error sources would have a relatively318
larger impact on the kinematics of the frontal and transverse plane, than on the319
sagittal plane. Finally, the JRF&M of the OMC-PGRF were compared against320
a non-independent OMC-MGRF reference, which could have contributed to un-321
derestimation of the actual errors.322
The IMC-PGRF approach has a number of possible sources of errors which323
would influence the performance. Similarly to OMC models, soft-tissue ar-324
tifacts may compromise the kinematic estimates. Further errors in segment325
kinematics may stem due to the N-pose calibration assumptions. In particular,326
mismatches between the practised and modelled N-pose could result in offsets327
in the estimated positions. Other common error sources in IMC include manual328
measurements of segment lengths as well as IMU inaccuracies. In addition, the329
stick figure model, which was utilized to recreate the VMs, has a higher number330
of DOF, compared to the musculoskeletal model used.331
A possible source of error in all inverse dynamic approaches concerns the332
inertial parameters (masses and moments of inertia), as well as the center of333
mass (CoM) locations of each human body segment, which were calculated334
based on anthropometric tables found in the literature.335
This study focused on presenting and evaluating a general workflow for mus-336
culoskeletal model-based inverse dynamic simulations using ambulatory IMC337
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systems. The presentation of results in this study was performed on the level of338
ground and joint reaction forces and moments. These measures are calculated339
from muscle force estimates derived from a muscle recruitment optimization340
technique. Given the high number of muscles in the model (110) and without341
a clear medical research question, it is challenging to choose which muscles are342
more important to present and analyze. Future studies could examine specific343
applications and pathologies in order to identify the most important muscles344
and evaluate their respective force estimates.345
A limitation of this study is that, even though the method has been pre-346
viously shown to be universally applicable in OMC-based studies [22, 23], we347
only evaluated its performance in gait of three different speeds. In addition,348
our experiments included only young healthy male subjects, but the underlying349
methods to predict kinetics from kinematics have been recently shown to be350
applicable in Parkinson’s patients [46]. Future studies could investigate the ap-351
plication of IMC systems combined with musculoskeletal modeling in groups of352
larger sample size than the current study, including patients, as well as female353
subjects.354
5. Conclusion355
In this study, we have demonstrated a workflow to perform musculoskeletal356
model-based inverse dynamics using input from a commercially available IMC357
system. Our validation findings indicate that the prediction of GRF&M as well358
as JRF&M using musculoskeletal model-based inverse dynamics based on only359
IMC data provides comparable performance to both OMC-PGRF and OMC-360
MGRF methods. The proposed method allows assessment of kinetic variables361
outside the laboratory.362
Ethical approval363
The ethical guidelines of The Scientific Ethical Committee for the Region of364
North Jutland (Den Videnskabsetiske Komit for Region Nordjylland) were fol-365
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lowed and all volunteers signed written informed consent after receiving detailed366
information prior to data collection.367
Conflict of interest statement368
Three of the authors are employees of Xsens Technologies B.V. that manu-369
factures and sells the Xsens MVN. One of the authors is employee of AnyBody370
Technology A/S that owns and sells the AnyBody Modeling System.371
Acknowledgements372
This study was performed in the context of KNEEMO Initial Training Net-373
work, funded by the European Unions Seventh Framework Programme for re-374
search, technological development, and demonstration under Grant Agreement375
No. 607510 (www.kneemo.eu). This work was also supported by the Danish376
Council for Independent Research under grant no. DFF-4184-00018 to M. S.377
Andersen. Finally, this research received funding in part from the European378
Unions Horizon 2020 research and innovation programme under grant agree-379
ment No. 680754 (The MovAiD project, www.movaid.eu).380
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21
Accepted manuscript
List of Figures546
1 Illustration of the pipeline used in the IMC-PGRF approach. A547
recording from Xsens MVN Studio (a) is exported to a BVH548
file to generate a stick figure model (b), in which virtual markers549
(blue) are placed. Virtual markers (red) are also placed on points550
of the musculoskeletal model (c), and by projecting b on c the551
kinematics of the musculoskeletal model are solved. Finally, in-552
verse dynamic analysis using prediction of ground reaction forces553
and moments is performed to estimate the kinetics. . . . . . . . . 24554
2 Ankle, knee, and hip joint angle estimates (standard deviation555
around mean) of the IMC-PGRF (orange shaded area around556
orange dotted line) and OMC-PGRF models (blue shaded area557
around blue dashed line) versus OMC-MGRF model (thin black558
solid lines around thick black solid line). . . . . . . . . . . . . . . 25559
3 Ground and lower limb joint reaction force estimates (standard560
deviation around mean) of the IMC-PGRF (orange shaded area561
around orange dotted line) and OMC-PGRF models (blue shaded562
area around blue dashed line) versus OMC-MGRF model (thin563
black solid lines around thick black solid line). . . . . . . . . . . . 26564
4 Ground reaction and lower limb net joint moment estimates (stan-565
dard deviation around mean) of the IMC-PGRF (orange shaded566
area around orange dotted line) and OMC-PGRF models (blue567
shaded area around blue dashed line) versus OMC-MGRF model568
(thin black solid lines around thick black solid line). . . . . . . . 27569
23
Accepted manuscript
Figure 1
24
Accepted manuscript
Figure 2
HS TO HS TO HS
-30
-20
-10
0
10
Angle (degrees)
Subtalar Eversion
HS TO HS TO HS
-10
0
10
20
30
Ankle Plantar Flexion
HS TO HS TO HS
-60
-40
-20
0
Knee Flexion
HS TO HS TO HS
-5
0
5
10
15
Angle (degrees)
Hip Abduction
HS TO HS TO HS
0
10
20
30
Hip External Rotation
HS TO HS TO HS
-20
0
20
40
Hip Flexion
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
25
Accepted manuscript
HS TO HS TO
-0.2
0
0.2
Force (BW)
Ground Anteroposterior
HS TO HS TO
-0.05
0
0.05
0.1
Ground Mediolateral
HS TO HS TO
0
0.5
1
Ground Vertical
HS TO HS TO
-1
-0.5
0
Force (BW)
Ankle Anteroposterior
HS TO HS TO
-2
-1.5
-1
-0.5
0
Ankle Mediolateral
HS TO HS TO
0
2
4
6
8
Ankle Proximodistal
HS TO HS TO
0
0.5
1
1.5
Force (BW)
Knee Anteroposterior
HS TO HS TO
-1
-0.5
0
Knee Mediolateral
HS TO HS TO
0
2
4
6
Knee Proximodistal
HS TO HS TO
-0.4
-0.2
0
0.2
0.4
0.6
Force (BW)
Hip Anteroposterior
HS TO HS TO
-1.5
-1
-0.5
0
Hip Mediolateral
HS TO HS TO
0
2
4
6
Hip Proximodistal
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 3
26
Accepted manuscript
HS TO HS TO
-0.03
-0.02
-0.01
0
0.01
0.02
Moment (BW*BH)
Ground Frontal
HS TO HS TO
-0.1
-0.05
0
Ground Sagittal
HS TO HS TO
-5
0
5
10
10-3 Ground Transverse
HS TO HS TO
0
0.01
0.02
Moment (BW*BH)
Subtalar Eversion
HS TO HS TO
0
0.05
0.1
Ankle Plantar Flexion
HS TO HS TO
-0.01
0
0.01
Ankle Axial
HS TO HS TO
-0.06
-0.04
-0.02
0
Moment (BW*BH)
Knee Abduction
HS TO HS TO
-0.04
-0.02
0
0.02
0.04
0.06
Knee Flexion
HS TO HS TO
-5
0
5
10
10-3 Knee Axial
HS TO HS TO
-0.02
0
0.02
0.04
0.06
Moment (BW*BH)
Hip Abduction
HS TO HS TO
-0.1
-0.05
0
0.05
0.1
Hip Flexion
HS TO HS TO
-0.01
-0.005
0
0.005
0.01
0.015
Hip External Rotation
OMC-MGRF Mean ± SDIMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 4
27
Accepted manuscript
List of Tables570
1 Comparison of lower limb joint angles between musculoskele-571
tal model driven by the inertial (IMC-PGRF) and optical mo-572
tion capture (OMC-PGRF/OMC-MGRF), using Pearson corre-573
lation coefficient (ρ), absolute and relative root-mean-squared-574
differences (RM SD in degrees and rRMS D in %, respectively).575
Mand Pdenote the % magnitude and phase differences . . . . . 29576
2 IMC-PGRF-based ground and joint reaction forces (first three577
quantities) and net moments (second three quantities) versus578
OMC-MGRF. Pearson correlation coefficient is denoted with ρ.579
Absolute per body weight (or body weight times height) and580
relative root-mean-squared-difference are denoted with RM SD581
(%BW or %BW*BH) and rRM SD (%), respectively. Mand P582
indicate the magnitude and phase differences (%). . . . . . . . . 30583
3 OMC-PGRF-based ground and joint reaction forces (first three584
quantities) and net moments (second three quantities) versus585
OMC-MGRF. Pearson correlation coefficient is denoted with ρ.586
Absolute per body weight (or body weight times height) and587
relative root-mean-squared-difference are denoted with RM SD588
(%BW or %BW*BH) and rRM SD (%), respectively. Mand P589
indicate the magnitude and phase differences (%). . . . . . . . . 31590
28
Accepted manuscript
Table 1
ρRMSD rRMSD M P
Subtalar Eversion 0.81 9.7 (3.2) 32.6 (10.3) 24.0 (34.7) 19.3 (10.2)
Ankle Plantarflexion 0.95 4.1 (1.3) 14.0 ( 4.8) 8.6 (16.4) 9.8 ( 3.9)
Knee Flexion 0.99 4.4 (2.0) 7.2 (3.4) 0.7 (6.2) 4.8 (2.7)
Hip Abduction 0.91 4.1 (2.0) 25.9 (10.7) -12.2 (34.7) 21.2 (9.3)
Hip External Rotation 0.68 6.5 (2.8) 36.9 (15.2) 5.5 (39.0) 12.6 (6.2)
Hip Flexion 0.99 5.7 (2.1) 12.7 ( 5.3) -4.0 (13.9) 8.8 (4.2)
29
Accepted manuscript
Table 2
ρRMSD rRMSD M P
Ground
Anteroposterior 0.91 5.5 (1.2) 15.0 (2.4) -25.4 ( 7.3) 14.4 (3.2)
Mediolateral 0.80 2.1 (0.6) 18.5 (3.2) 7.3 (19.3) 15.4 (3.8)
Vertical 0.97 9.3 (3.0) 7.7 (2.1) -1.5 ( 1.5) 3.4 (1.0)
Frontal 0.64 0.9 (0.6) 38.0 (23.1) 125.5 (319.9) 30.6 (17.3)
Sagittal 0.91 1.6 (0.6) 17.5 ( 6.8) 14.3 ( 18.2) 12.1 ( 4.5)
Transverse 0.82 0.2 (0.1) 23.3 ( 7.2) -8.5 ( 41.9) 17.8 ( 5.3)
Ankle
Anteroposterior 0.84 22.2 (10.3) 26.1 (10.2) 49.0 (45.8) 10.8 (2.1)
Mediolateral 0.93 24.3 ( 8.9) 15.2 ( 5.3) 14.3 (17.1) 7.9 (2.7)
Proximodistal 0.93 88.5 (30.6) 13.6 ( 4.6) 9.8 (14.1) 7.2 (2.3)
Eversion 0.76 0.6 (0.2) 33.3 (20.2) 107.7 (220.3) 18.9 (10.7)
Plantar Flexion 0.93 1.6 (0.6) 15.1 ( 6.6) 10.6 ( 18.1) 9.9 ( 3.6)
Axial 0.67 0.5 (0.2) 30.4 (12.2) 46.5 ( 49.1) 27.2 (13.5)
Knee
Anteroposterior 0.82 30.6 (10.3) 25.8 (9.7) 43.7 (53.5) 13.0 (4.5)
Mediolateral 0.91 12.0 ( 3.5) 14.1 (3.8) 6.6 ( 8.6) 7.0 (2.0)
Proximodistal 0.90 63.1 (26.9) 14.3 (6.6) 5.1 ( 9.1) 7.2 (2.8)
Abduction 0.81 1.1 (0.4) 18.9 ( 6.8) -2.7 (16.1) 10.7 ( 3.8)
Flexion 0.58 1.9 (0.5) 29.8 ( 7.6) 17.9 (45.0) 32.8 ( 9.6)
Axial 0.73 0.3 (0.1) 25.4 (10.3) 2.3 (30.5) 27.9 (13.8)
Hip
Anteroposterior 0.71 17.6 ( 7.6) 27.2 (9.6) 6.8 (24.4) 27.6 (10.9)
Mediolateral 0.73 27.0 (12.5) 23.0 (7.4) 7.7 (14.6) 10.6 ( 4.1)
Proximodistal 0.78 102.8 (30.6) 21.7 (4.5) 20.2 (10.0) 9.0 ( 2.5)
Abduction 0.83 1.4 (0.7) 19.7 (5.8) 6.3 (16.9) 13.7 ( 7.9)
Flexion 0.92 2.2 (0.6) 19.4 (4.2) 73.2 (26.3) 14.8 ( 4.2)
External Rotation 0.50 0.5 (0.2) 31.6 (6.6) -3.9 (36.4) 25.6 (10.1)
30
Accepted manuscript
Table 3
ρRMSD rRMSD M P
Ground
Anteroposterior 0.96 3.7 (1.1) 8.3 (2.0) 7.7 (12.0) 8.8 (1.8)
Mediolateral 0.79 1.9 (0.5) 18.6 (4.1) 2.4 (10.8) 15.2 (4.9)
Vertical 0.99 5.9 (1.9) 4.9 (1.4) -1.2 ( 1.1) 2.1 (0.7)
Frontal 0.66 0.7 (0.2) 30.3 (9.3) 71.0 (122.2) 24.5 (9.1)
Sagittal 0.94 1.2 (0.4) 13.1 (3.8) 15.9 ( 15.3) 9.2 (3.2)
Transverse 0.81 0.2 (0.1) 20.7 (7.5) 7.1 ( 22.9) 17.5 (7.5)
Ankle
Anteroposterior 0.83 18.9 ( 6.9) 23.0 (6.1) 37.3 (28.6) 10.8 (2.3)
Mediolateral 0.96 16.1 ( 4.2) 10.7 (2.6) 6.8 ( 9.6) 5.8 (2.1)
Proximodistal 0.96 62.2 (17.6) 9.8 (2.7) 7.1 ( 9.0) 5.2 (1.8)
Eversion 0.76 0.5 (0.1) 25.5 (7.0) 45.3 (64.1) 18.7 (10.2)
Plantar Flexion 0.96 1.0 (0.3) 10.1 (3.3) 5.9 (10.0) 7.0 ( 2.6)
Axial 0.64 0.5 (0.1) 27.2 (7.3) 33.3 (36.9) 27.5 (11.5)
Knee
Anteroposterior 0.93 11.9 ( 4.5) 12.3 (4.3) -7.3 (8.7) 7.4 (2.0)
Mediolateral 0.96 7.2 ( 2.0) 8.8 (2.6) -4.2 (5.6) 4.4 (1.0)
Proximodistal 0.95 41.7 (12.0) 9.3 (2.6) -2.7 (5.8) 4.9 (1.2)
Abduction 0.91 0.8 (0.2) 12.6 (2.6) -0.1 (10.5) 7.7 (1.6)
Flexion 0.86 0.9 (0.3) 16.7 (4.8) -1.7 (14.3) 16.9 (5.2)
Axial 0.82 0.2 (0.1) 18.5 (6.6) -3.4 (17.7) 20.6 (8.0)
Hip
Anteroposterior 0.89 9.9 ( 3.6) 16.0 (6.7) -10.4 (10.6) 16.6 (7.6)
Mediolateral 0.92 14.7 ( 4.0) 12.7 (3.1) -1.9 ( 6.9) 6.2 (1.5)
Proximodistal 0.92 50.0 (15.9) 11.5 (2.6) -4.6 ( 6.1) 5.5 (1.2)
Abduction 0.91 0.8 (0.2) 13.3 (2.6) -3.2 ( 6.3) 8.7 (2.4)
Flexion 0.86 1.3 (0.4) 16.4 (3.4) -9.3 (12.3) 18.0 (4.1)
External Rotation 0.68 0.3 (0.1) 22.5 (3.7) 6.5 (15.8) 18.8 (4.8)
31
Accepted manuscript
Supplementary material
Title:
Musculoskeletal model-based inverse dynamic analysis under ambulatory conditions using inertial motion
capture
Authors:
Angelos Karatsidis1,2, Moonki Jung3, H. Martin Schepers1, Giovanni Bellusci1, Mark de Zee4, Peter H.
Veltink2, Michael Skipper Andersen5
Affiliations:
1Xsens Technologies B.V., Enschede 7521 PR, The Netherlands
2Institute for Biomedical Technology and Technical Medicine (MIRA), University of Twente, Enschede
7500 AE, The Netherlands
3AnyBody Technology A/S, Aalborg 9220, Denmark
4Department of Health Science and Technology, Aalborg University, Aalborg 9220, Denmark
5Department of Materials and Production, Aalborg University, Aalborg 9220, Denmark
Corresponding author:
Angelos Karatsidis, Address: Xsens Technologies B.V., Enschede 7521 PR, The Netherlands, E-mail:
angelos.karatsidis@xsens.com, Tel.: +31 88 97367 36, Fax: +31 88 97367 01
Keywords:
musculoskeletal modeling, inertial motion capture, inverse dynamics, ground reaction forces and mo-
ments, gait analysis
1
Accepted manuscript
1. Virtual marker placement
Table 1: Desription of the placement of virtual markers (VM) on the segments of the Xsens MVN model (stick figure model)
and the musculoskeletal model constructed based on the AnyBody Managed Model Repository (AMMR).
VM Name VM Placement on MVN VM Placement on AMMR VM Weight
T1C7 jT1C7 T1/C7 Joint (1,1,1)
SPNE jT9T8 Inferior to T1/C7 Joint (1,1,1)
CHST Anterior to jT9T8 Inferior and Anterior to T1/C7 Joint (1,1,1)
SACR jL5S1 Anterior to Pelvis/Sacrum Joint (10,0,0)
RHJC jRightHip Right Hip Joint (10,10,10)
RKJC jRightKnee Right Knee Joint (2,2,2)
RKJL Lateral to jRightKnee Lateral to Right Knee Joint (1,0,0)
RAJC jRightAnkle Right Ankle Joint (1,1,1)
RTOE jRightBallFoot Right Big Toe Node (1,1,1)
RTOL Lateral to jRightBallFoot Lateral to Right Big Toe Node (0,1,0)
RSJC jRightShoulder Right Glenohumeral Joint (0,2,2)
REJC jRightElbow Elbow Joint (2,2,2)
RELA Lateral to jRightElbow Lateral to Elbow Joint (1,1,1)
RWJC jRightWrist Right Wrist Joint (2,2,2)
RHT1 Inferior and Medial to jRightWrist Inferior and Medial to Right Wrist Joint (0.5,0.5,0.5)
RHT2 Inferior and Lateral to jRightWrist Inferior and Lateral to Right Wrist Joint (0.5,0.5,0.5)
LHJC jLeftHip Left Hip Joint (10,10,10)
LKJC jLeftKnee Left Knee Joint (2,2,2)
LKJL Lateral to jLeftKnee Lateral to Left Knee Joint (1,0,0)
LAJC jLeftAnkle Left Ankle Joint (1,1,1)
LTOE jLeftBallFoot Left Big Toe Node (1,1,1)
LTOL Lateral to jLeftBallFoot Lateral to Left Big Toe Node (0,1,0)
LSJC jLeftShoulder Left Glenohumeral Joint (0,2,2)
LEJC jLeftElbow Elbow Joint (2,2,2)
LELA Lateral to jLeftElbow Lateral to Elbow Joint (1,1,1)
LWJC jLeftWrist Left Wrist Joint (2,2,2)
LHT1 Inferior and Medial to jLeftWrist Inferior and Medial to Left Wrist Joint (0.5,0.5,0.5)
LHT2 Inferior and Lateral to jLeftWrist Inferior and Lateral to Left Wrist Joint (0.5,0.5,0.5)
2
Accepted manuscript
(a) Xsens MVN (stick-figure) model (b) AnyBody Musculoskeletal Model (AMMR)
Figure 1: Illustration of the placement of the virtual markers (VM) on the segments of the Xsens MVN model (stick figure
model) and the musculoskeletal model constructed based on the AnyBody Managed Model Repository (AMMR).
3
Accepted manuscript
2. Accuracy analysis per walking speed
2.1. Comfortable walking speed
Table 2: Comfortable walking speed; comparison of lower limb joint angles between musculoskeletal model driven by the inertial
(IMC-PGRF) and optical motion capture (OMC-PGRF/OMC-MGRF), using Pearson correlation coefficient (ρ), absolute and
relative root-mean-squared-differences (RMSD in degrees and rRM SD in %, respectively). Mand Pdenote the % magnitude
and phase differences .
Normal Walking
ρRMSD rRMSD M P
Subtalar Eversion 0.79 9.7 (3.1) 32.6 (10.1) 25.5 (36.2) 18.9 (9.6)
Ankle Plantarflexion 0.95 4.0 (1.3) 13.1 ( 4.9) 10.3 (16.6) 9.3 (3.6)
Knee Flexion 0.98 4.6 (2.0) 7.4 (3.1) 2.1 (5.5) 4.9 (2.3)
Hip Abduction 0.91 3.9 (1.9) 25.2 ( 9.1) -15.9 (28.8) 20.4 (8.0)
Hip External Rotation 0.66 6.5 (2.6) 35.7 (14.1) 7.9 (36.7) 12.6 (5.5)
Hip Flexion 0.99 5.6 (2.2) 12.5 ( 5.5) -3.7 (13.0) 8.8 (4.4)
Figure 2: Comfortable walking speed; ankle, knee, and hip joint angle estimates (standard deviation around mean) of the
IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue dashed
line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
HS TO HS TO HS
-30
-20
-10
0
10
Angle (degrees)
Subtalar Eversion
HS TO HS TO HS
-10
0
10
20
30
Ankle Plantar Flexion
HS TO HS TO HS
-60
-40
-20
0
Knee Flexion
HS TO HS TO HS
-5
0
5
10
15
Angle (degrees)
Hip Abduction
HS TO HS TO HS
0
10
20
30
Hip External Rotation
HS TO HS TO HS
-20
0
20
40
Hip Flexion
OMC-MGRF Mean ± SDIMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
4
Accepted manuscript
Table 3: Comfortable walking speed; IMC-PGRF-based ground and joint reaction forces (first three quantities) and net moments
(second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body weight
(or body weight times height) and relative root-mean-squared-difference are denoted with RMS D (%BW or %BW*BH) and
rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.91 5.5 (1.1) 14.6 (2.4) -24.8 ( 6.6) 14.2 (3.0)
Mediolateral 0.80 2.1 (0.5) 18.7 (2.5) 4.8 (17.4) 15.5 (3.0)
Vertical 0.97 8.6 (2.3) 7.1 (1.8) -1.4 ( 1.4) 3.1 (0.8)
Frontal 0.66 0.8 (0.5) 34.1 (15.3) 105.5 (334.8) 28.5 (13.8)
Sagittal 0.91 1.5 (0.6) 16.8 ( 7.0) 12.2 ( 17.2) 11.6 ( 4.4)
Transverse 0.83 0.2 (0.1) 22.3 ( 6.4) -11.7 ( 31.7) 17.4 ( 4.3)
Ankle
Anteroposterior 0.84 21.9 (10.3) 25.7 (10.1) 48.0 (47.2) 10.9 (2.1)
Mediolateral 0.93 23.9 ( 8.3) 14.8 ( 4.9) 12.8 (15.4) 8.0 (2.5)
Proximodistal 0.93 85.6 (27.7) 13.0 ( 4.4) 8.0 (12.6) 7.2 (2.2)
Eversion 0.75 0.6 (0.2) 31.5 (16.3) 98.7 (234.1) 18.3 ( 8.6)
Plantar Flexion 0.94 1.5 (0.6) 14.3 ( 6.0) 8.2 ( 15.3) 9.6 ( 3.5)
Axial 0.70 0.5 (0.2) 29.2 (11.6) 38.7 ( 46.6) 25.4 (12.8)
Knee
Anteroposterior 0.84 29.8 ( 9.3) 26.0 (9.8) 49.4 (50.6) 12.3 (4.7)
Mediolateral 0.93 11.4 ( 3.0) 13.5 (3.8) 8.1 ( 8.7) 6.4 (2.2)
Proximodistal 0.92 58.4 (29.2) 13.3 (6.9) 5.1 ( 8.1) 6.7 (3.1)
Abduction 0.83 1.0 (0.4) 17.6 (6.4) -2.1 (14.7) 10.3 ( 4.0)
Flexion 0.59 1.8 (0.5) 29.8 (6.8) 16.7 (38.8) 32.9 ( 8.2)
Axial 0.73 0.3 (0.2) 25.4 (9.9) 2.7 (31.6) 27.8 (13.1)
Hip
Anteroposterior 0.74 16.7 ( 7.4) 26.2 (8.8) 5.7 (17.7) 26.6 (8.8)
Mediolateral 0.75 26.1 (13.4) 22.7 (7.6) 7.1 (15.4) 10.3 (4.2)
Proximodistal 0.81 99.0 (25.3) 21.6 (4.4) 21.2 (10.1) 8.5 (2.7)
Abduction 0.84 1.3 (0.7) 18.8 (5.5) 9.5 (17.9) 12.8 (8.2)
Flexion 0.92 2.2 (0.6) 18.9 (3.5) 69.5 (20.9) 14.6 (4.6)
External Rotation 0.47 0.5 (0.2) 30.9 (6.9) -6.7 (32.6) 25.6 (9.9)
5
Accepted manuscript
Table 4: Comfortable walking speed; OMC-PGRF-based ground and joint reaction forces (first three quantities) and net
moments (second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body
weight (or body weight times height) and relative root-mean-squared-difference are denoted with RM SD (%BW or %BW*BH)
and rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.96 3.6 (1.0) 8.2 (1.8) 5.8 ( 8.5) 8.9 (1.8)
Mediolateral 0.77 1.9 (0.4) 19.1 (3.7) 1.6 (10.8) 15.4 (4.1)
Vertical 0.99 5.7 (1.2) 4.8 (1.0) -1.2 ( 0.9) 2.1 (0.5)
Frontal 0.66 0.7 (0.2) 30.9 (9.4) 68.9 (139.9) 24.7 (8.2)
Sagittal 0.94 1.1 (0.2) 12.0 (2.6) 15.8 ( 11.3) 8.4 (2.0)
Transverse 0.82 0.2 (0.1) 19.8 (7.2) 3.8 ( 21.4) 16.6 (6.4)
Ankle
Anteroposterior 0.85 18.8 ( 6.5) 23.2 (6.6) 40.1 (29.7) 10.3 (2.1)
Mediolateral 0.96 15.0 ( 2.9) 9.8 (1.9) 6.7 ( 7.5) 5.5 (1.6)
Proximodistal 0.97 57.2 (12.6) 8.8 (2.0) 7.0 ( 6.7) 4.8 (1.3)
Eversion 0.75 0.5 (0.1) 25.5 (6.8) 45.4 (75.0) 18.0 ( 8.7)
Plantar Flexion 0.97 0.9 (0.2) 8.9 (2.0) 5.7 ( 7.3) 6.3 ( 1.7)
Axial 0.63 0.5 (0.1) 27.3 (6.5) 29.9 (35.3) 26.6 (10.1)
Knee
Anteroposterior 0.93 11.0 (4.3) 11.2 (2.7) -6.9 (5.4) 7.2 (1.4)
Mediolateral 0.97 6.5 (1.6) 8.0 (1.8) -4.2 (3.8) 4.1 (0.7)
Proximodistal 0.96 37.7 (7.8) 8.4 (1.7) -2.7 (4.0) 4.6 (0.9)
Abduction 0.91 0.7 (0.1) 11.9 (2.3) -0.3 ( 8.1) 7.8 (1.7)
Flexion 0.86 0.9 (0.2) 16.7 (4.5) -1.2 (12.9) 17.2 (5.2)
Axial 0.81 0.2 (0.1) 18.7 (6.2) -6.5 (17.2) 20.6 (6.9)
Hip
Anteroposterior 0.89 9.6 ( 3.0) 15.6 (6.2) -11.8 (9.3) 16.8 (7.0)
Mediolateral 0.91 14.7 ( 3.2) 12.6 (2.2) -2.2 (7.0) 6.4 (1.0)
Proximodistal 0.92 47.5 (13.1) 11.2 (2.2) -4.9 (4.9) 5.4 (1.0)
Abduction 0.90 0.8 (0.1) 13.3 (2.4) -3.6 ( 5.7) 8.9 (2.0)
Flexion 0.86 1.3 (0.3) 16.0 (2.6) -9.0 (11.8) 17.6 (3.4)
External Rotation 0.67 0.3 (0.1) 22.7 (3.5) 7.0 (15.7) 18.8 (4.4)
6
Accepted manuscript
HS TO HS TO
-0.2
-0.1
0
0.1
0.2
0.3
Force (BW)
Ground Anteroposterior
HS TO HS TO
-0.05
0
0.05
0.1
Ground Mediolateral
HS TO HS TO
0
0.5
1
Ground Vertical
HS TO HS TO
-1
-0.5
0
Force (BW)
Ankle Anteroposterior
HS TO HS TO
-2
-1.5
-1
-0.5
0
Ankle Mediolateral
HS TO HS TO
0
2
4
6
8
Ankle Proximodistal
HS TO HS TO
0
0.5
1
1.5
Force (BW)
Knee Anteroposterior
HS TO HS TO
-1
-0.8
-0.6
-0.4
-0.2
0
Knee Mediolateral
HS TO HS TO
0
1
2
3
4
5
Knee Proximodistal
HS TO HS TO
-0.4
-0.2
0
0.2
0.4
0.6
Force (BW)
Hip Anteroposterior
HS TO HS TO
-1.5
-1
-0.5
0
Hip Mediolateral
HS TO HS TO
0
2
4
6
Hip Proximodistal
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 3: Comfortable walking speed; ground and lower limb joint reaction force estimates (standard deviation around mean)
of the IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue
dashed line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
7
Accepted manuscript
HS TO HS TO
-0.03
-0.02
-0.01
0
0.01
0.02
Moment (BW*BH)
Ground Frontal
HS TO HS TO
-0.1
-0.05
0
Ground Sagittal
HS TO HS TO
-5
0
5
10
10-3 Ground Transverse
HS TO HS TO
0
0.01
0.02
Moment (BW*BH)
Subtalar Eversion
HS TO HS TO
0
0.05
0.1
Ankle Plantar Flexion
HS TO HS TO
-0.015
-0.01
-0.005
0
0.005
0.01
Ankle Axial
HS TO HS TO
-0.06
-0.04
-0.02
0
Moment (BW*BH)
Knee Abduction
HS TO HS TO
-0.04
-0.02
0
0.02
0.04
Knee Flexion
HS TO HS TO
-5
0
5
10
10-3 Knee Axial
HS TO HS TO
-0.02
0
0.02
0.04
0.06
Moment (BW*BH)
Hip Abduction
HS TO HS TO
-0.1
-0.05
0
0.05
0.1
Hip Flexion
HS TO HS TO
-0.01
-0.005
0
0.005
0.01
0.015
Hip External Rotation
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 4: Comfortable walking speed; ground reaction and lower limb net joint moment estimates (standard deviation around
mean) of the IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around
blue dashed line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
8
Accepted manuscript
2.2. Slow walking speed
Table 5: Slow walking speed; comparison of lower limb joint angles between musculoskeletal model driven by the inertial
(IMC-PGRF) and optical motion capture (OMC-PGRF/OMC-MGRF), using Pearson correlation coefficient (ρ), absolute and
relative root-mean-squared-differences (RMSD in degrees and rRM SD in %, respectively). Mand Pdenote the % magnitude
and phase differences .
Slow Walking
ρRMSD rRMSD M P
Corr RMSE rRMSE M P
Subtalar Eversion 0.81 10.1 (3.5) 32.9 (9.6) 29.5 (36.3) 17.6 (10.1)
Ankle Plantarflexion 0.96 3.9 (1.2) 13.7 (4.0) 5.1 (14.0) 9.5 ( 3.4)
Knee Flexion 0.99 4.1 (2.4) 7.0 (4.3) -0.3 (7.5) 4.7 (3.6)
Hip Abduction 0.91 4.1 (2.1) 27.6 (12.4) -3.3 (42.8) 23.2 (10.9)
Hip External Rotation 0.76 6.7 (3.1) 39.5 (17.9) 12.9 (46.9) 13.0 ( 6.7)
Hip Flexion 0.99 5.2 (1.9) 13.3 ( 5.7) -3.8 (16.4) 8.6 ( 4.2)
Figure 5: Slow walking speed; ankle, knee, and hip joint angle estimates (standard deviation around mean) of the IMC-PGRF
(orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue dashed line) versus
OMC-MGRF model (thin black solid lines around thick black solid line).
HS TO HS TO HS
-40
-20
0
20
Angle (degrees)
Subtalar Eversion
HS TO HS TO HS
-10
0
10
20
30
Ankle Plantar Flexion
HS TO HS TO HS
-60
-40
-20
0
Knee Flexion
HS TO HS TO HS
-5
0
5
10
15
Angle (degrees)
Hip Abduction
HS TO HS TO HS
0
10
20
30
Hip External Rotation
HS TO HS TO HS
-10
0
10
20
30
40
Hip Flexion
OMC-MGRF Mean ± SDIMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
9
Accepted manuscript
Table 6: Slow walking speed; IMC-PGRF-based ground and joint reaction forces (first three quantities) and net moments
(second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body weight
(or body weight times height) and relative root-mean-squared-difference are denoted with RMS D (%BW or %BW*BH) and
rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.88 4.7 (0.8) 16.3 (2.3) -26.3 ( 8.6) 15.8 (3.4)
Mediolateral 0.84 1.7 (0.5) 17.6 (3.6) 13.2 (23.1) 13.3 (3.5)
Vertical 0.97 8.1 (2.3) 7.4 (2.1) -1.5 ( 1.2) 3.0 (0.9)
Frontal 0.64 1.0 (0.8) 45.7 (32.5) 177.8 (340.9) 32.6 (21.9)
Sagittal 0.90 1.5 (0.7) 18.7 ( 8.2) 10.2 ( 20.2) 12.2 ( 4.9)
Transverse 0.81 0.2 (0.1) 23.3 ( 5.8) -0.7 ( 56.1) 17.5 ( 4.7)
Ankle
Anteroposterior 0.85 22.8 (12.2) 29.0 (12.1) 56.5 (52.1) 10.7 (2.5)
Mediolateral 0.93 24.2 (11.3) 16.0 ( 6.7) 12.9 (21.3) 7.7 (2.9)
Proximodistal 0.93 87.4 (38.0) 14.3 ( 5.6) 8.2 (18.1) 7.1 (2.3)
Eversion 0.78 0.6 (0.3) 37.6 (27.2) 140.7 (259.7) 18.7 (13.5)
Plantar Flexion 0.93 1.6 (0.8) 16.8 ( 8.5) 9.6 ( 24.0) 10.1 ( 4.1)
Axial 0.65 0.5 (0.2) 33.7 (14.9) 47.8 ( 61.5) 27.9 (15.2)
Knee
Anteroposterior 0.84 23.6 ( 6.8) 25.9 (11.3) 50.0 (65.3) 11.5 (3.0)
Mediolateral 0.89 10.5 ( 3.1) 14.7 ( 4.2) 3.8 ( 7.4) 7.3 (2.1)
Proximodistal 0.87 65.0 (29.7) 16.8 ( 7.3) 5.2 (11.7) 8.1 (3.1)
Abduction 0.74 1.2 (0.5) 23.2 ( 7.5) -5.8 (20.4) 12.0 ( 4.5)
Flexion 0.46 1.8 (0.5) 34.5 ( 7.2) 35.3 (59.5) 36.9 (10.3)
Axial 0.60 0.3 (0.1) 29.8 (10.7) 8.2 (32.3) 33.0 (14.6)
Hip
Anteroposterior 0.55 17.3 ( 7.2) 32.5 (10.3) 11.0 (30.6) 34.7 (12.2)
Mediolateral 0.66 23.8 (11.1) 25.1 ( 7.4) 5.8 (15.0) 11.1 ( 4.4)
Proximodistal 0.71 88.4 (23.7) 23.1 ( 3.8) 17.8 ( 8.4) 9.3 ( 2.4)
Abduction 0.83 1.4 (0.7) 21.0 (6.9) -1.1 (13.4) 14.0 ( 8.3)
Flexion 0.92 2.0 (0.4) 22.8 (3.5) 93.3 (23.2) 15.5 ( 4.1)
External Rotation 0.57 0.4 (0.2) 32.4 (7.0) -0.2 (40.5) 24.8 (10.4)
10
Accepted manuscript
Table 7: Slow walking speed; OMC-PGRF-based ground and joint reaction forces (first three quantities) and net moments
(second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body weight
(or body weight times height) and relative root-mean-squared-difference are denoted with RMS D (%BW or %BW*BH) and
rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.97 3.2 (1.2) 8.8 (2.6) 16.5 (13.0) 8.5 (1.7)
Mediolateral 0.82 1.5 (0.3) 17.2 (2.8) 4.4 (10.9) 13.8 (4.3)
Vertical 0.99 5.1 (1.6) 4.7 (1.5) -1.4 ( 1.4) 1.8 (0.6)
Frontal 0.70 0.6 (0.2) 29.7 (10.2) 83.9 (124.3) 22.3 (9.5)
Sagittal 0.94 1.1 (0.4) 13.4 ( 5.0) 5.0 ( 12.4) 9.7 (4.2)
Transverse 0.80 0.2 (0.1) 21.2 ( 6.9) 16.2 ( 24.5) 18.1 (7.9)
Ankle
Anteroposterior 0.83 16.8 ( 6.8) 22.7 (6.2) 32.4 (31.0) 11.2 (2.8)
Mediolateral 0.96 14.4 ( 3.8) 10.6 (3.1) 1.9 (10.0) 5.6 (2.4)
Proximodistal 0.97 55.3 (16.7) 9.8 (3.5) 1.2 ( 8.9) 5.2 (2.3)
Eversion 0.79 0.4 (0.1) 24.7 (8.3) 43.2 (59.0) 18.0 (13.3)
Plantar Flexion 0.96 0.9 (0.4) 10.6 (4.4) -0.9 ( 9.2) 7.2 ( 3.2)
Axial 0.68 0.4 (0.1) 27.3 (7.3) 37.2 (42.0) 25.6 (11.9)
Knee
Anteroposterior 0.92 9.9 ( 3.5) 14.8 (5.7) -11.4 (11.5) 7.6 (2.7)
Mediolateral 0.96 7.0 ( 2.4) 9.9 (3.5) -7.3 ( 6.1) 4.6 (1.3)
Proximodistal 0.95 39.1 (14.7) 10.1 (3.6) -6.8 ( 5.6) 5.0 (1.6)
Abduction 0.90 0.7 (0.1) 14.0 (2.9) -5.3 (11.3) 7.7 (1.6)
Flexion 0.84 0.8 (0.2) 18.7 (5.4) -2.8 (18.0) 18.2 (5.8)
Axial 0.73 0.2 (0.1) 21.7 (7.0) 2.7 (16.2) 24.7 (9.2)
Hip
Anteroposterior 0.87 8.3 ( 2.7) 17.0 (7.4) -10.0 (9.0) 18.4 (9.3)
Mediolateral 0.90 12.9 ( 4.3) 13.7 (3.9) -2.3 (5.7) 6.5 (2.0)
Proximodistal 0.91 44.3 (13.9) 12.4 (3.0) -6.0 (5.9) 5.5 (1.3)
Abduction 0.93 0.7 (0.1) 12.4 (2.7) -2.4 ( 6.2) 7.1 (1.7)
Flexion 0.81 1.1 (0.3) 19.2 (2.4) -12.4 (11.7) 20.7 (3.3)
External Rotation 0.71 0.3 (0.1) 22.4 (4.1) 12.5 (16.0) 16.9 (4.2)
11
Accepted manuscript
HS TO HS TO
-0.2
-0.1
0
0.1
0.2
Force (BW)
Ground Anteroposterior
HS TO HS TO
-0.05
0
0.05
0.1 Ground Mediolateral
HS TO HS TO
0
0.5
1
Ground Vertical
HS TO HS TO
-1
-0.5
0
Force (BW)
Ankle Anteroposterior
HS TO HS TO
-1.5
-1
-0.5
0
Ankle Mediolateral
HS TO HS TO
0
2
4
6
8Ankle Proximodistal
HS TO HS TO
0
0.5
1
1.5
Force (BW)
Knee Anteroposterior
HS TO HS TO
-0.8
-0.6
-0.4
-0.2
0
Knee Mediolateral
HS TO HS TO
0
1
2
3
4
Knee Proximodistal
HS TO HS TO
-0.4
-0.2
0
0.2
0.4
Force (BW)
Hip Anteroposterior
HS TO HS TO
-1
-0.5
0
Hip Mediolateral
HS TO HS TO
0
1
2
3
4
5
Hip Proximodistal
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 6: Slow walking speed; ground and lower limb joint reaction force estimates (standard deviation around mean) of the
IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue dashed
line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
12
Accepted manuscript
HS TO HS TO
-0.03
-0.02
-0.01
0
0.01
Moment (BW*BH)
Ground Frontal
HS TO HS TO
-0.08
-0.06
-0.04
-0.02
0
0.02
Ground Sagittal
HS TO HS TO
0
5
10
10-3 Ground Transverse
HS TO HS TO
0
0.01
0.02
Moment (BW*BH)
Subtalar Eversion
HS TO HS TO
0
0.05
0.1
Ankle Plantar Flexion
HS TO HS TO
-15
-10
-5
0
5
10-3 Ankle Axial
HS TO HS TO
-0.06
-0.04
-0.02
0
Moment (BW*BH)
Knee Abduction
HS TO HS TO
-0.04
-0.02
0
0.02
0.04
Knee Flexion
HS TO HS TO
-5
0
5
10-3 Knee Axial
HS TO HS TO
-0.04
-0.02
0
0.02
0.04
0.06
Moment (BW*BH)
Hip Abduction
HS TO HS TO
-0.05
0
0.05
Hip Flexion
HS TO HS TO
-0.01
-0.005
0
0.005
0.01
0.015
Hip External Rotation
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 7: Slow walking speed; ground reaction and lower limb net joint moment estimates (standard deviation around mean)
of the IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue
dashed line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
13
Accepted manuscript
2.3. Fast walking speed
Table 8: Fast walking speed; comparison of lower limb joint angles between musculoskeletal model driven by the inertial
(IMC-PGRF) and optical motion capture (OMC-PGRF/OMC-MGRF), using Pearson correlation coefficient (ρ), absolute and
relative root-mean-squared-differences (RMSD in degrees and rRM SD in %, respectively). Mand Pdenote the % magnitude
and phase differences .
Fast Walking
ρRMSD rRMSD M P
Subtalar Eversion 0.83 9.3 (2.8) 32.2 (11.4) 16.1 (29.9) 21.6 (10.9)
Ankle Plantarflexion 0.95 4.6 (1.3) 15.4 ( 5.1) 10.4 (18.3) 10.8 ( 4.7)
Knee Flexion 0.98 4.6 (1.6) 7.3 (2.6) -0.0 (5.0) 4.6 (1.9)
Hip Abduction 0.9 4.2 (2.0) 25.0 (10.3) -17.6 (29.6) 20.0 (8.4)
Hip External Rotation 0.62 6.2 (2.6) 35.3 (12.8) -5.4 (29.1) 12.0 (6.4)
Hip Flexion 0.99 6.3 (1.9) 12.5 ( 4.4) -4.6 (12.0) 9.1 (3.8)
Figure 8: Fast walking speed; ankle, knee, and hip joint angle estimates (standard deviation around mean) of the IMC-PGRF
(orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue dashed line) versus
OMC-MGRF model (thin black solid lines around thick black solid line).
HS TO HS TO HS
-30
-20
-10
0
10
Angle (degrees)
Subtalar Eversion
HS TO HS TO HS
-20
-10
0
10
20
30
Ankle Plantar Flexion
HS TO HS TO HS
-60
-40
-20
0
Knee Flexion
HS TO HS TO HS
-10
0
10
20
Angle (degrees)
Hip Abduction
HS TO HS TO HS
0
10
20
30
Hip External Rotation
HS TO HS TO HS
-20
0
20
40
Hip Flexion
OMC-MGRF Mean ± SDIMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
14
Accepted manuscript
Table 9: Fast walking speed; IMC-PGRF-based ground and joint reaction forces (first three quantities) and net moments
(second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body weight
(or body weight times height) and relative root-mean-squared-difference are denoted with RMS D (%BW or %BW*BH) and
rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.92 6.5 (1.2) 14.1 (2.0) -25.2 ( 6.6) 13.0 (2.7)
Mediolateral 0.75 2.5 (0.7) 19.3 (3.4) 3.9 (15.2) 17.5 (3.8)
Vertical 0.95 11.5 (3.2) 8.8 (2.2) -1.7 ( 1.8) 4.1 (1.1)
Frontal 0.61 0.9 (0.5) 34.1 (15.5) 91.7 (269.9) 30.9 (15.0)
Sagittal 0.90 1.7 (0.4) 17.1 ( 4.2) 21.6 ( 15.2) 12.7 ( 4.1)
Transverse 0.81 0.2 (0.1) 24.4 ( 9.3) -13.1 ( 33.0) 18.4 ( 6.8)
Ankle
Anteroposterior 0.84 22.0 ( 8.0) 23.4 (6.9) 41.8 (34.5) 10.7 (1.5)
Mediolateral 0.94 25.0 ( 6.2) 14.9 (3.7) 17.7 (13.1) 8.0 (2.9)
Proximodistal 0.93 93.3 (23.8) 13.6 (3.2) 13.8 ( 9.3) 7.5 (2.5)
Eversion 0.75 0.7 (0.2) 30.7 (13.7) 81.9 (137.1) 19.8 ( 9.8)
Plantar Flexion 0.93 1.6 (0.4) 14.1 ( 4.2) 14.8 ( 12.5) 10.1 ( 3.3)
Axial 0.65 0.6 (0.1) 28.3 ( 8.4) 54.9 ( 33.2) 28.6 (12.1)
Knee
Anteroposterior 0.75 39.4 ( 8.2) 25.3 (7.4) 29.3 (38.3) 15.7 (4.6)
Mediolateral 0.90 14.5 ( 3.0) 14.3 (3.3) 8.0 ( 8.9) 7.3 (1.5)
Proximodistal 0.92 66.8 (19.0) 12.8 (4.0) 5.0 ( 7.0) 6.7 (1.8)
Abduction 0.86 1.1 (0.2) 15.5 (3.3) 0.1 (10.9) 9.8 ( 2.1)
Flexion 0.67 2.0 (0.4) 24.6 (5.3) -0.2 (18.7) 28.2 ( 8.3)
Axial 0.83 0.3 (0.1) 20.6 (8.1) -4.9 (25.8) 22.2 (11.5)
Hip
Anteroposterior 0.80 19.0 ( 8.3) 22.5 (6.7) 3.3 (23.4) 20.7 (5.9)
Mediolateral 0.77 31.8 (11.6) 21.1 (6.8) 10.5 (13.0) 10.6 (3.7)
Proximodistal 0.82 123.9 (32.5) 20.3 (4.9) 21.7 (11.2) 9.2 (2.4)
Abduction 0.80 1.5 (0.6) 19.5 (4.5) 10.7 (16.6) 14.4 (6.9)
Flexion 0.91 2.6 (0.6) 16.4 (3.1) 55.2 (20.0) 14.5 (3.8)
External Rotation 0.44 0.5 (0.2) 31.7 (5.6) -4.5 (36.2) 26.6 (9.9)
15
Accepted manuscript
Table 10: Fast walking speed; OMC-PGRF-based ground and joint reaction forces (first three quantities) and net moments
(second three quantities) versus OMC-MGRF. Pearson correlation coefficient is denoted with ρ. Absolute per body weight
(or body weight times height) and relative root-mean-squared-difference are denoted with RMS D (%BW or %BW*BH) and
rRM SD (%), respectively. Mand Pindicate the magnitude and phase differences (%).
ρRMSD rRMSD M P
Ground
Anteroposterior 0.96 4.2 (0.8) 7.9 (1.5) 0.1 ( 7.4) 9.0 (1.7)
Mediolateral 0.76 2.2 (0.5) 19.4 (5.3) 1.2 (10.6) 16.5 (6.0)
Vertical 0.98 7.2 (2.3) 5.4 (1.6) -1.0 ( 0.9) 2.6 (0.8)
Frontal 0.59 0.8 (0.2) 30.1 (8.1) 59.1 (92.8) 26.9 (9.3)
Sagittal 0.94 1.5 (0.3) 14.3 (2.9) 28.3 (13.3) 9.7 (2.8)
Transverse 0.80 0.2 (0.1) 21.0 (8.5) 1.1 (19.8) 17.9 (8.3)
Ankle
Anteroposterior 0.83 21.3 ( 7.0) 22.9 (5.2) 39.4 (23.6) 11.0 (1.9)
Mediolateral 0.95 19.4 ( 4.2) 11.9 (2.3) 12.5 ( 8.6) 6.6 (2.2)
Proximodistal 0.96 76.4 (15.8) 11.0 (2.0) 13.7 ( 6.9) 5.7 (1.7)
Eversion 0.72 0.6 (0.1) 26.2 (5.6) 47.5 (55.2) 20.3 ( 7.5)
Plantar Flexion 0.96 1.3 (0.3) 10.9 (2.6) 13.8 ( 8.0) 7.7 ( 2.7)
Axial 0.60 0.5 (0.1) 27.0 (8.2) 33.3 (32.7) 30.6 (12.1)
Knee
Anteroposterior 0.94 15.2 (4.1) 10.8 (2.3) -3.0 (5.8) 7.4 (1.6)
Mediolateral 0.96 8.2 (1.6) 8.5 (1.4) -0.6 (4.7) 4.5 (0.8)
Proximodistal 0.95 49.6 (9.0) 9.4 (1.6) 1.7 (4.7) 5.3 (0.9)
Abduction 0.92 0.9 (0.2) 11.8 (1.8) 6.1 ( 9.0) 7.6 (1.5)
Flexion 0.90 1.2 (0.3) 14.6 (3.4) -1.1 (11.2) 15.2 (4.0)
Axial 0.89 0.2 (0.1) 14.8 (4.7) -6.5 (18.5) 16.1 (4.9)
Hip
Anteroposterior 0.91 11.9 ( 4.0) 15.4 (6.4) -9.1 (13.3) 14.4 (5.4)
Mediolateral 0.94 16.6 ( 3.5) 11.7 (2.4) -1.2 ( 7.9) 5.8 (1.2)
Proximodistal 0.93 59.5 (17.0) 10.8 (2.5) -2.6 ( 7.2) 5.5 (1.3)
Abduction 0.88 1.0 (0.2) 14.3 (2.5) -3.5 ( 7.2) 10.4 (2.4)
Flexion 0.89 1.6 (0.3) 13.8 (2.9) -6.1 (13.0) 15.3 (3.8)
External Rotation 0.67 0.4 (0.1) 22.2 (3.5) -0.9 (12.6) 20.7 (5.3)
16
Accepted manuscript
HS TO HS TO
-0.2
0
0.2
Force (BW)
Ground Anteroposterior
HS TO HS TO
-0.05
0
0.05
0.1
Ground Mediolateral
HS TO HS TO
0
0.5
1
1.5
Ground Vertical
HS TO HS TO
-1
-0.5
0
Force (BW)
Ankle Anteroposterior
HS TO HS TO
-2
-1.5
-1
-0.5
0
Ankle Mediolateral
HS TO HS TO
0
2
4
6
8
Ankle Proximodistal
HS TO HS TO
0
0.5
1
1.5
2
Force (BW)
Knee Anteroposterior
HS TO HS TO
-1
-0.5
0
Knee Mediolateral
HS TO HS TO
0
2
4
6
Knee Proximodistal
HS TO HS TO
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Force (BW)
Hip Anteroposterior
HS TO HS TO
-1.5
-1
-0.5
0
Hip Mediolateral
HS TO HS TO
0
2
4
6
8
Hip Proximodistal
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 9: Fast walking speed; ground and lower limb joint reaction force estimates (standard deviation around mean) of the
IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue dashed
line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
17
Accepted manuscript
HS TO HS TO
-0.03
-0.02
-0.01
0
0.01
0.02
Moment (BW*BH)
Ground Frontal
HS TO HS TO
-0.1
-0.05
0
0.05
Ground Sagittal
HS TO HS TO
0
5
10
10-3 Ground Transverse
HS TO HS TO
-0.01
0
0.01
0.02
Moment (BW*BH)
Subtalar Eversion
HS TO HS TO
-0.05
0
0.05
0.1
Ankle Plantar Flexion
HS TO HS TO
-0.02
-0.01
0
0.01
0.02
Ankle Axial
HS TO HS TO
-0.08
-0.06
-0.04
-0.02
0
Moment (BW*BH)
Knee Abduction
HS TO HS TO
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Knee Flexion
HS TO HS TO
-0.01
-0.005
0
0.005
0.01
0.015
Knee Axial
HS TO HS TO
-0.02
0
0.02
0.04
0.06
0.08
Moment (BW*BH)
Hip Abduction
HS TO HS TO
-0.1
-0.05
0
0.05
0.1
Hip Flexion
HS TO HS TO
-0.01
-0.005
0
0.005
0.01
0.015
Hip External Rotation
OMC-MGRF Mean ± SD
IMC-PGRF Mean ± SD OMC-PGRF Mean ± SD
Figure 10: Fast walking speed; ground reaction and lower limb net joint moment estimates (standard deviation around mean)
of the IMC-PGRF (orange shaded area around orange dotted line) and OMC-PGRF models (blue shaded area around blue
dashed line) versus OMC-MGRF model (thin black solid lines around thick black solid line).
18
Accepted manuscript