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Effects of an Obesity-Specific Marker Set on Estimated Muscle and Joint Forces in Walking

LERNER, ZACHARY F.1; BOARD, WAYNE J.2; BROWNING, RAYMOND C.1,2

Author Information
Medicine & Science in Sports & Exercise: June 2014 - Volume 46 - Issue 6 - p 1261-1267
doi: 10.1249/MSS.0000000000000218

Abstract

Accurate estimates of muscle and joint contact forces (JCF) from dynamic simulations of human locomotion provide critical insight into normal and pathological function of the musculoskeletal system (5–7,23,26). For example, musculoskeletal simulations can be used to enhance our understanding of the biomechanical mechanisms linking obesity and large joint osteoarthritis. The accuracy of experimentally driven musculoskeletal simulations is dependent upon the ability to collect accurate kinematic data. Using passive reflective markers placed on the surface of the skin to determine the kinematics of the underlying skeleton can result in inaccurate marker placement and soft tissue artifact (STA), particularly in overweight and obese subjects (20). As our population becomes progressively overweight and obese (19), participants in locomotor biomechanics studies, especially those using obese participants, will likely include individuals with substantial subcutaneous adiposity. The majority of studies that use motion capture for gait analysis, even those directly assessing obesity (9,15,24), use standard kinematic marker sets/methodologies developed for nonobese individuals that do not attempt to account for adiposity, namely, some version of the Helen Hayes marker set methodology (14).

Inaccurate marker placement and STA can lead to gross errors in basic biomechanical measures, such as hip and knee joint kinematics and net muscle moments (3). In addition, when a generic musculoskeletal model is scaled to the anthropometrics of a subject, using markers placed on the skin to represent the size and motion of the underlying skeleton of an overweight or obese individual may lead to inaccurate scale factors and marker trajectories, respectively. Although various methods have been proposed to account for excess soft tissue obscuring the underlying bone, such as lateral relocation of the anterior superior iliac spines (ASIS) markers (2), dual-energy X-ray absorptiometry-derived anthropometric measures (2,10,12), biplane fluorscopy (28), and functional joint locating methods (21), they are not consistently used and are limited by effectiveness, practicality, and/or cost. A methodology to account for excess soft tissue in overweight and obese individuals that is relatively accurate, relatively simple, and inexpensive to use would aid researchers who conduct biomechanical analyses of obese individuals (25). In addition, investigating the influence of marker set methodology on musculoskeletal simulation outputs will provide insights into the sensitivity of kinematics and muscle/joint forces to how the musculoskeletal system is modeled.

The purpose of this study was threefold: first, to develop an obesity-specific motion capture methodology that was easy to implement and accounted for subcutaneous adiposity; second, to demonstrate the ability of the new methodology to replicate the kinematics of nonobese individuals using a standard methodology; and third, to determine the effect of using a methodology specifically developed for obese individuals to estimate muscle (vasti, hamstring, rectus femoris, and iliopsoas) and axial hip and knee contact forces during walking in obese adults. We hypothesized that 1) there would not be significant differences in lower-extremity joint angles, lower-extremity muscle forces, and axial hip and knee JCF between the obesity-specific methodology and a modified Helen Hayes methodology in nonobese individuals, but 2) there would be significant differences in these same parameters between the methodologies in obese individuals.

METHODS

Subjects

Nine obese adults with a body mass index (BMI) of 35.0 (3.78) kg·m−2 (mean (SD)), of which eight were female, and nine nonobese adults with a BMI of 22.1 (1.02) kg·m−2, of which five were female, in good health with no known acute/chronic diseases or limitations to physical activity, participated in our study. All subjects gave written informed consent approved by the Colorado State University’s Human Research Institutional Review Board.

Experimental protocol

As part of a larger study, participants walked at nine randomized speed grade combinations, ranging from 0.50 to 1.75 m·s−1 at grades ranging from 0° to 9°. The biomechanics data were collected for the last 30 s of the 6-min trials, and there were 5 min of rest between trials. For the purposes of this study, we used data from the 1.25 m·s−1, level (0°) trials.

Experimental data

Ground reaction forces were collected using a dual-belt, force-measuring treadmill (Fully Instrumented Treadmill; Bertec Corp., Columbus, OH) recording at 1000 Hz, whereas kinematics were collected using a 10-camera motion capture system (Nexus, Vicon, Centennial, CO) recording at 100 Hz. Marker trajectory and ground reaction force data were digitally low-pass filtered at 5 and 12 Hz, respectively, using fourth-order zero-lag Butterworth filters. EMG data (Noraxon, Scottsdale, AZ) from bipolar surface electrodes recording at 1000 Hz was collected for the soleus, lateral gastrocnemius, vastus lateralis, vastus medialis, biceps femoris long head, and semimembranosus muscles using standard procedures (17). The EMG signal was band-pass filtered (16–380 Hz), fully rectified, and finally low-pass filtered at 7 Hz.

Kinematic marker sets

The obesity-specific methodology was developed for use in obese individuals and consisted of a combination of physical reflective markers, marker clusters, and digitally defined markers (Fig. 1, see Figure, Supplemental Digital Content 1, http://links.lww.com/MSS/A332, Marker and marker cluster placements of the obesity-specific methodology on a representative subject). Reflective markers were placed over the following anatomical landmarks identified via palpation: 7th cervical vertebrae, acromion processes, right scapular inferior angle, sternoclavicular notch, xyphoid process, 10th thoracic vertebrae, posterior–superior iliac spines, ASIS, iliac crests (IC), medial and lateral epicondyles of the femurs, medial and lateral malleoli, calcanei, first metatarsal heads, second metatarsal heads, and proximal and distal heads of the 5th metatarsals. Marker clusters (four noncollinear markers affixed to a rigid plate) were adhered to the thighs, shanks, and sacrum to aid in three-dimensional tracking. A spring-loaded digitizing pointer (C-Motion, Germantown, MD) was used to digitally mark the ASIS and IC. We placed the tip of the digitizing pointer on the soft tissue directly over the anatomical landmark and depressed the digitizing pointer until it reached the underlying bone to mark the location for postprocessing. This process was also used to define the location of the digital ASIS and IC landmarks relative to three markers on the sacral cluster using Visual 3D (C-Motion/Visual 3D, Germantown, MD). This relation was used during the motion trials to calculate the digital ASIS and IC trajectories during postprocessing in Visual 3D. Coordinate data (i.e., marker trajectories) for all additional markers were determined in Visual 3D as well. A modified Helen Hayes (basic) methodology (14) was defined as a subset of the previously described passive reflective markers as follows: five markers on the torso (excluding the acromion processes), ASIS, posterior–superior iliac spines, one marker from each thigh cluster (posterior–superior marker), the lateral condyles of the femur, one marker from each shank cluster (posterior–superior marker), the lateral malleoli, the calcanei, and second metatarsal heads.

FIGURE 1
FIGURE 1:
Marker placements of the obesity-specific methodology and the subset of markers comprising the basic methodology relative to skeletal landmarks.

Dynamic musculoskeletal simulation

For each participant and methodology, we used OpenSim to scale a generic musculoskeletal model, determine joint angles, and quantify muscle and JCF (16). The OpenSim model was composed of 12 body segments with 19 degrees of freedom, 92 muscle–tendon actuators, and a knee joint that included a planar patellofemoral joint that articulated with the femur (6,8,27). The distance between the experimental ASIS markers (i.e., inter-ASIS distance between physical ASIS markers in the case of the basic methodology, or digitized ASIS markers in the case of the obesity-specific methodology) was used to uniformly scale the pelvis of each subject-specific musculoskeletal model. The distance between the experimental ASIS and lateral femoral epicondyle markers was used to scale each thigh segment, whereas the distance between lateral femoral epicondyle and lateral malleoli markers was used to scale each shank segment. The joint angles during each gait trial were calculated using OpenSim’s inverse kinematics analysis with standard marker weighting factors used to generate joint angles in nonobese individuals that follow guidelines from gait analysis software including Visual 3D, Vicon, and OpenSim (16,26). We used a weighted static optimization approach to resolve individual muscle forces from the net joint toques determined through the method of inverse dynamics (16,26). The static optimization objective function minimized the sum of squared muscle activations while incorporating individual muscle weighting constants of seven for the gastrocnemius, three for the hamstrings and one for all other muscles in the model. These weighting constants, established by Steele et al., resulted in the best agreement between model-estimated tibiofemoral forces and those measured experimentally from an instrumented knee joint replacement (see Figure, Supplemental Digital Content 2, http://links.lww.com/MSS/A333, Axial tibiofemoral contact forces across a single gait cycle from an individual with an instrumented knee joint replacement during walking at 1.25 m·s−1 measured experimentally, estimated using a weighted static optimization method, and estimated using an unweighted static optimization method) (11,16,26). Residual actuators were applied to the pelvis during static optimization to account for dynamic inconsistencies resulting from modeling assumptions and small errors in the experimental data. OpenSim’s Joint Reaction analysis was used to determine JCF (16,26), which represents the forces and moments that each joint structure carries because of all muscle forces, external loads, and inertial loads of the model. The compressive knee contact force was computed as the component of the resultant force acting on the tibia and parallel to the long axis of the tibia, whereas the compressive hip contact force was computed as the component of the resultant force acting on the femoral head, parallel to the long axis of the femur.

Joint kinematics (sagittal plane joint angles of the pelvis, hip, and knee), muscle forces (vasti, hamstring, rectus femoris, and iliopsoas), and axial JCF (hip and knee) are reported from the right leg, normalized, and averaged across two representative gait cycles per subject, and then averaged across subjects for each methodology. Muscle forces and axial knee JCF were normalized to the body weight (BW) of each subject.

Statistical analysis

Student’s t-tests were used to determine whether there were significant differences in kinematic and kinetic variables (averages, maximums, and/or minimums) between the basic and obesity-specific methodologies within each group. A criterion of P < 0.05 defined significance. SigmaPlot version 11.0 (Systat Software, Inc., San Jose, CA) was used to perform the statistical analyses.

RESULTS

We present the results of eight obese individuals, as Static Optimization failed, despite repeated attempts, to find a solution using the basic methodology for one obese participant. The mean residual force in each coordinate direction applied to the center of mass of the pelvis was less than 4.1% BW for each completed simulation. In the nonobese participants, joint angles, muscle forces, and first peak hip and knee JCF were not significantly different between the basic and obesity-specific methodologies (Table 1). In the obese individuals, peak hip flexion during stance and pelvic tilt angles were significantly different between the kinematic marker set methodologies (Fig. 2). First peak rectus femoris muscle forces were significantly smaller (0.27 BW vs 0.73 BW, P < 0.001) in the obesity-specific methodology versus the basic methodology, whereas all other muscle forces were similar (Fig. 3, Table 1). A qualitative comparison between estimated muscle forces and experimental EMG revealed relatively good agreement for the activation timing of the vasti and biceps femoris long head muscles (Fig. 3). Compared with the basic methodology, the obesity-specific methodology resulted in smaller first peak axial hip (2.82 BW vs 3.58 BW, P = 0.002) and knee (2.12 BW vs 2.54 BW, P = 0.021) contact forces (Fig. 4).

TABLE 1
TABLE 1:
Differences in joint angles, peak muscle forces, and JCF between the obesity-specific methodology relative to the basic methodology for the obese and nonobese participants.
FIGURE 2
FIGURE 2:
Sagittal plane pelvic (top panel), hip (middle panel), and knee (bottom panel) joint angles in obese individuals determined using the obesity-specific (black solid line) and basic (gray dashed line) methodologies. Hip flexion angle and anterior pelvic tilt were significantly greater in the basic versus obesity-specific methodologies.
FIGURE 3
FIGURE 3:
BW normalized muscle forces in obese individuals, estimated using the obesity-specific methodology (black solid line) and the basic methodology (dashed gray line). *Denotes significant differences across marker set methodologies. Vasti and biceps femoris long head EMG was included in the first and second panels, respectively. Vasti (first panel), hamstring (second panel), and iliopsoas (fourth panel) BW normalized muscle forces were similar between methodologies, whereas the rectus femoris (third panel) muscle had greater BW normalized force output in the basic versus the obesity-specific methodology. The stance phase occurs during ∼0%–60% of the gait cycle.
FIGURE 4
FIGURE 4:
BW normalized axial hip (top panel) and knee (bottom panel) contact forces in obese individuals, estimated using the obesity-specific methodology (black solid line) and the basic methodology (dashed gray line). *Denotes significant differences across marker set methodologies. First peak hip and knee contact forces were significantly greater in the basic versus the obesity specific methodologies.

DISCUSSION

We accept our first hypothesis that sagittal plane joint angles, muscle forces, and JCF would be similar between the methodologies in nonobese individuals. This demonstrates the ability of the obesity-specific methodology to replicate lower-extremity kinematics determined from the well-established, modified Helen Hayes methodology. We found significant differences in hip flexion and pelvic tilt joint angles, rectus femoris muscle forces, and first peak axial hip and knee JCF between marker methodologies in the obese group, and therefore also accept our second hypothesis.

To account for additional subcutaneous adipose tissue at the pelvis and lower extremities in overweight and obese versus nonobese individuals, we created an obesity-specific methodology by probing and digitally marking several key pelvic landmarks directly on the underlying bone and adding additional marker clusters. As reported in the literature, but not in this current evaluation, segment tracking in the frontal and transverse planes is likely more accurate when utilizing marker clusters (4). We elected to define the location and trajectory of the ASIS and IC digital markers relative to a cluster placed on the sacrum because the sacrum moves in unison with the pelvis, has reduced subcutaneous adipose tissue, and is likely to be less susceptible to STA than other locations on the pelvis.

During the musculoskeletal model scaling process, it is possible to adjust the location of the model’s virtual markers relative to the skeleton to reduce the error in relation to the experimental markers. However, to be accurate, this method requires some knowledge of the actual location of the skeleton (e.g., via an MRI image) relative to the skin and may be prone to inaccuracy when used to adjust markers by many centimeters, as required in obese individuals. In addition, merely measuring the depth of the soft tissue separating a marker placed on the skin and the bone, and adjusting the virtual marker in the model accordingly, may not be adequate at the pelvis because physical markers attached on the abdomen in obese experience substantial STA and tend to move with the torso rather than the pelvis. Using a digitizing pointer to provide a physical measure of the location of underlying bony landmarks and defining those digital locations relative to skeletal landmarks less susceptible to STA are likely more accurate and repeatable.

There was substantial subcutaneous abdominal adiposity positioned between the ASIS markers placed on the skin and the actual ASIS bony landmarks on the bone in all of the obese subjects. This made it difficult to accurately track the underlying pelvic skeleton when the basic methodology was used to generate joint angles. The inverse kinematics analysis, which solves the least squares equation for all of the markers, resulted in a kinematic solution that caused significant anterior rotation (anterior pelvic tilt) of the pelvis in the basic methodology. This is because musculoskeletal models capable of estimating muscle and joint forces are fully constrained, and a translation, as opposed to a rotation, of the pelvis to reduce the pelvic region marker errors would increase the marker errors on the body segments down the kinematic chain (i.e., the thigh and shank). We systematically tested a range of pelvic region marker weighting factors, yet the significant rotation of the pelvis remained when the adipose tissue was not accounted for (i.e., the basic methodology). Because of the kinematic relation between the pelvis and femur, a more anterior rotated pelvis will increase the hip flexion angle even if the femur has not changed its own global orientation. Thus, the basic methodology resulted in likely inaccurate pelvic tilt and hip flexion angles.

It was surprising that sagittal plane knee joint angles were similar between methodologies in the obese individuals because, although we did not expect differences in the sagittal plane orientation of the shank and foot, we did expect differences in the sagittal plane orientation of the femur. However, as mentioned previously, this is due to how the inverse kinematic solution of a fully constrained musculoskeletal model accounts for inaccurate marker placements around the pelvis (i.e., a preference to modulate the orientation of the pelvis rather than the hip joint center location).

With similar vasti and hamstring forces during early stance between the methodologies in the obese group (Fig. 3A, B), it was initially counterintuitive to find significantly different axial knee JCF. On closer inspection, however, because the basic methodology elicited greater rectus femoris force output, there was a net increase in the axial knee contact force during early stance versus the obesity-specific methodology. During mid-late stance, axial knee JCF was not significantly different between methodologies because the force outputs from the muscles crossing the knee joint were generally similar during that portion of the gait cycle.

The first peak axial hip and knee contact forces estimated using the obesity-specific methodology (hip, 2.82 BW; knee, 2.12 BW) were in closer agreement to values reported in the literature from instrumented implants at similar walking speeds and in a similar population (hip, ∼2.75 BW (13); knee, ∼2.15 BW (29)) than those estimated from the basic methodology (hip, 3.58 BW; knee, 2.54 BW). Heller et al. (13) compared model-estimated and experimentally measured in vivo hip contact forces and reported a tendency for musculoskeletal simulations to overestimate forces at that joint. Interestingly, they used a kinematic marker set, similar to the basic marker set used in this study, composed solely of passive reflective markers affixed to the skin even though half of their subjects were overweight (BMI > 25 kg·m−2), whereas the other half was obese (BMI > 30 kg·m−2). Our results demonstrate that failing to account for soft tissue at the pelvis may result in artificially large force output from certain hip flexor muscles, which might explain the tendency for their simulations to overestimate hip contact forces in this population.

The primary limitation of this study was the small sample size, yet we believe our primary goal to establish the importance of accounting for adipose tissue during kinematic data collection was demonstrated, nevertheless. Surface EMG has been shown to be a viable way to measure muscle activity in the lower extremity of obese adults (18); however, the effectiveness of this method in this population can be limited and must be regarded as a limitation. Another limitation of this study was that scaling of each model’s pelvis segment based on the digital ASIS locations did not directly account for the overlying mass of adipose tissue. However, it has been reported that body mass distributions are generally similar between obese and nonobese adults (1), and the inertial properties of the body segments likely have limited influence on model kinetics during the stance phase of gait (22). Thus, uniform scaling of the inertial properties in obese adults should have limited effect on the presented results. A subsequent limitation of this study was that we used a weighted static optimization approach to indirectly validate muscle force estimates on the basis of comparing estimated and experimentally measured contact forces at the knee joint alone. However, we are confident in the ability of these static optimization weighting factors to provide reasonable estimates of both hip and knee contact forces because much of the primary hip musculature (i.e., rectus femoris, biceps femoris long head, semimembranosus, semitendinosus, and sartorius) crosses both the hip and knee joints and was accounted for in the knee joint validation. In addition, we have found that relative differences between conditions (e.g., marker set methodologies or weight status) are insensitive to the Static Optimization weighting factors themselves. Finally, results from inverse kinematic and inverse dynamic analyses generated using unconstrained (i.e., 6 degree of freedom) models common to gait analysis software such as Vicon and Visual 3D were not included in this study but warrant further investigation.

In summary, the effect of marker set methodology on estimates of muscle forces and axial hip and knee JCF in obese individuals was significant, with the basic methodology yielding larger muscle and JCF. There were no significant differences in these same measures between the methodologies in the nonobese participants. The measured differences between the two methodologies can likely be attributed to tracking the motion of the pelvis using the digital ASIS and IC marker locations in the case of the obesity-specific methodology versus the physical ASIS and IC markers placed on the skin in the case of the basic methodology. These findings are not only relevant for studies directly assessing the biomechanics of obese individuals but also for studies in which a subset of the subjects are overweight or obese, because applying a basic methodology to all of the subjects, or different methodologies to separate subject groups, may act as confounding factors. The results of this study support the need for biomechanists to adopt kinematic data collection protocols that account for adipose tissue in overweight and obese individuals.

Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award Number R03AR059264.

The authors declare no conflict of interest.

Results of the present study do not constitute endorsement by the American College of Sports Medicine.

REFERENCES

1. Browning RC, Baker EA, Herron JA, Kram R. Effects of obesity and sex on the energetic cost and preferred speed of walking. J Appl Physiol. 2006; 100 (2): 390–8.
2. Browning RC, Kram R. Effects of obesity on the biomechanics of walking at different speeds. Med Sci Sports Exerc. 2007; 39 (9): 1632–41.
3. Cappozzo A, Catani F, Della Croce U, Leardini A. Position and orientation in space of bones during movement: anatomical frame definition and determination. Clin Biomech. 1995; 10 (4): 171–8.
4. Collins TD, Ghoussayni SN, Ewins DJ, Kent JA. A six degrees-of-freedom marker set for gait analysis: repeatability and comparison with a modified Helen Hayes set. Gait Posture. 2009; 30 (2): 173–80.
5. Correa TA, Crossley KM, Kim HJ, Pandy MG. Contributions of individual muscles to hip joint contact force in normal walking. J Biomech. 2010; 43 (8): 1618–22.
6. Delp SL, Anderson FC, Arnold AS, et al. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng. 2007; 54 (11): 1940–50.
7. Delp SL, Arnold AS, Speers RA, Moore CA. Hamstrings and psoas lengths during normal and crouch gait: implications for muscle-tendon surgery. J Orthop Res. 1996; 14 (1): 144–51.
8. Delp SL, Loan JP, Hoy MG, Zajac FE, Topp EL, Rosen JM. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng. 1990; 37 (8): 757–67.
9. DeVita P, Hortobagyi T. Obesity is not associated with increased knee joint torque and power during level walking. J Biomech. 2003; 36: 1355–62.
10. Ehlen K, Reiser R, Browning R. Energetics and biomechanics of inclined treadmill walking in obese adults. Med Sci Sports Exerc. 2011; 43 (7): 1251–9.
11. Fregly BJ, Besier TF, Lloyd DG, et al. Grand challenge competition to predict in vivo knee loads. J Orthop Res. 2012; 30 (4): 503–13.
12. Ganley KJ, Powers CM. Determination of lower extremity anthropometric parameters using dual energy X-ray absorptiometry: the influence on net joint moments during gait. Clin Biomech (Bristol, Avon). 2004; 19 (1): 50–6.
13. Heller MO, Bergmann G, Deuretzbacher G, et al. Musculo-skeletal loading conditions at the hip during walking and stair climbing. J Biomech. 2001; 34 (7): 883–93.
14. Kadaba MP, Ramakrishnan HK, Wootten ME. Measurement of lower extremity kinematics during level walking. J Orthop Res. 1990; 8 (3): 383–92.
15. Lai PP, Leung AK, Li AN, Zhang M. Three-dimensional gait analysis of obese adults. Clin Biomech (Bristol, Avon). 2008; 23 (1 Suppl): S2–6.
16. Lerner ZF, Haight DJ, Demers MS, Board WJ, Browning RC. The effects of walking speed on tibiofemoral loading estimated via musculoskeletal modeling. J Appl Biomech. In press.
17. Merletti R. Standard for reporting EMG data. J Electromyogr Kinesiol. 1999; 9: III–IV.
18. Minetto MA, Botter A, Šprager S, et al. Feasibility study of detecting surface electromyograms in severely obese patients. J Electromyogr Kinesiol. 2013; 23 (2): 285–95.
19. Mokdad AH, Bowman BA, Ford ES, Vinicor F, Marks JS, Koplan JP. The continuing epidemics of obesity and diabetes in the United States. J Am Med Assoc. 2001; 286 (10): 1195–200.
20. Peters A, Galna B, Sangeux M, Morris M, Baker R. Quantification of soft tissue artifact in lower limb human motion analysis: a systematic review. Gait Posture. 2010; 31 (1): 1–8.
21. Piazza SJ, Erdemir A, Okita N, Cavanagh PR. Assessment of the functional method of hip joint center location subject to reduced range of hip motion. J Biomech. 2004; 37 (3): 349–56.
22. Rao G, Amarantini D, Berton E, Favier D. Influence of body segments’ parameters estimation models on inverse dynamics solutions during gait. J Biomech. 2006; 39 (8): 1531–6.
23. Shelburne KB, Torry MR, Steadman JR, Pandy MG. Effects of foot orthoses and valgus bracing on the knee adduction moment and medial joint load during gait. Clin Biomech (Bristol, Avon). 2008; 23 (6): 814–21.
24. Spyropoulos P, Pisciotta J, Pavlou K, Cairns M, Simon S. Biomechanical gait analysis in obese men. Arch Phys Med Rehabil. 1991; 72 (13): 1065.
25. Stagni R, Leardini A, Cappozzo A, Grazia Benedetti M, Cappello A. Effects of hip joint centre mislocation on gait analysis results. J Biomech. 2000; 33 (11): 1479–87.
26. Steele KM, DeMers MS, Schwartz MH, Delp SL. Compressive tibiofemoral force during crouch gait. Gait Posture. 2012; 35 (4): 556–60.
27. Yamaguchi GT, Zajac FE. A planar model of the knee joint to characterize the knee extensor mechanism. J Biomech. 1989; 22 (1): 1–10.
28. You BM, Siy P, Anderst W, Tashman S. In vivo measurement of 3-D skeletal kinematics from sequences of biplane radiographs: Application to knee kinematics. IEEE Trans Med Imaging. 2001; 20 (6): 514–25.
29. Zhao D, Banks SA, Mitchell KH, D’Lima DD, Colwell CW, Fregly BJ. Correlation between the knee adduction torque and medial contact force for a variety of gait patterns. J Orthop Res. 2007; 25 (6): 789–97.
Keywords:

BIOMECHANICS; KINEMATIC DATA COLLECTION; MUSCULOSKELETAL MODELING; GAIT; JOINT CONTACT FORCES

Supplemental Digital Content

© 2014 American College of Sports Medicine