Excessive knee joint loading (i.e., compressive and shear loads) has been associated with numerous knee pathologies and injuries (e.g., osteoarthritis, ligament injury). Therefore, accurate assessment of knee joint loading during functional activities may be useful for understanding normal and pathological movement. Traditionally, the inverse dynamics solution has been used to estimate the net joint forces and moments at selected joints (6,11). The net joint force calculated using inverse dynamics, however, does not consider individual muscle forces and their contributions to joint loading (11). The development of EMG-driven modeling methods provides a means by which the individual muscle forces acting at a joint can be estimated (7,11,18).
Muscle forces estimated from an EMG-driven model are usually based on a Hill-type muscle model that considers the influence of muscle length, muscle contraction velocity, and level of activation (18). Because of the difficulty in measuring muscle forces in vivo, the accuracy and validity of an EMG-driven model have been evaluated by comparing the net joint moments calculated by the model with the net joint moment calculated or measured by standard net joint measurements (i.e., inverse dynamics and/or dynamometry) (18). To estimate muscle forces and joint moments accurately, several muscle parameters must be estimated or calibrated for an EMG-driven model (11,25). In general, these parameters can be divided into two categories: 1) muscle anatomic or structural parameters, such as muscle physiological cross-sectional areas (PCSA), moment arms, fiber length, and pennation angles; and 2) muscle contractile parameters (i.e., muscle length–tension and force–velocity relationships, tendon slack length).
Accurate muscle anatomic parameters are prerequisites to the creation of a musculoskeletal model and can be derived in three ways: 1) use of a generic anatomic model based on anthropometric values obtained from existing literature; 2) scaling of a generic model based on subject-specific anthropometric measures (i.e., segment length, body mass, etc.); and 3) direct measurements of in vivo muscle anatomic parameters using various imaging techniques such as magnetic resonance imaging (MRI) and ultrasound (3,21,27,28,33). Although it may seem intuitive that the direct measurement of muscle anatomic parameters may yield more accurate results, most investigators use a generic or a scaling approach when developing an EMG-driven musculoskeletal model (3,5,16,18,38). To date, the influence of incorporating direct measurements of muscle anatomic parameters on joint moment predictions has not been reported.
The purpose of this study was to investigate how incorporating direct measurements of muscle anatomic parameters (i.e., muscle volumes and moment arms) affects knee joint moment predictions when compared with generic and scaled musculoskeletal models. We hypothesized that the knee moment calculated from an EMG-driven knee model that incorporates direct measurements of subject-specific muscle volumes and moment arms of the lower extremity musculature would compare more favorably with the knee moment estimated by standard joint moment calculations (i.e., inverse dynamics and dynamometry) than generic and scaled musculoskeletal models.
Four males (25.7 ± 3.8 yr, 73.2 ± 6.8 kg, 1.75 ± 0.04 m) and three females (29.7 ± 5.5 yr, 54.3 ± 2.5 kg, 1.64 ± 0.02 m) between the ages of 23 and 36 yr were recruited for this study. Subjects were healthy and pain free at the time of the study. Subjects were excluded from participation if they had previous knee surgery, ligamentous instability, or any medical condition that would impair their ability to perform the tasks described below. Before participation, all procedures were explained to each subject, and informed consent was obtained as approved by the Institutional Review Board of the University of Southern California Health Sciences Campus.
All subjects participated in two data collection sessions: 1) an MRI scan to obtain subject-specific muscle volumes and moment arms and 2) biomechanical testing. To measure subject-specific muscle volumes and moment arms, sagittal and axial MRIs of each subject’s dominant leg (defined as the leg used to kick a ball) were obtained using a 3.0-T MRI system (GE Signa HDx 3.0T, Fairfield, CT). Axial images of the leg (ankle mortise to the iliac crest) were acquired using a spin-echo pulse sequence (TR = 2600–3700 ms, TE = 11.3 ms, slice thickness = 10 mm, matrix = 512 × 512). Sagittal plane images of the knee joint were obtained using a spin-echo pulse sequence (TR = 1100 ms, TE = 37 ms, slice thickness = 3 mm, matrix = 512 × 512). Sagittal plane images were acquired at 0°, 15°, 30°, 45°, and 60° of knee flexion during static partial weight bearing by having subjects push against a load of 111 N provided by a custom-made nonferromagnetic MRI loading device (35). MRIs were obtained while subjects pushed against a load because it has been suggested that muscle moment arm data measured during muscle contraction provide a better representation of the actual values during functional activities (20).
For the biomechanical testing session, each subject performed a drop land task and isokinetic knee extension exercise on an isokinetic dynamometer (Kin-Com; Isokinetic International, Harrison, TN). The drop land task was selected because this activity is commonly used to study knee injury risk and/or pathology (6). Data were obtained from the dominant leg.
Muscle activation levels during the two tasks were recorded from the vastus lateralis (VL), vastus medialis (VM), rectus femoris (RF), semitendinosus (ST), biceps femoris long head (BFL), medial gastrocnemius (MG), and lateral gastrocnemius (LG) using preamplified bipolar surface electrodes (MA300 EMG System; Motion Lab Systems, Baton Rouge, LA). The preamplifiers had a double-differential input design (CMRR >100 dB at 65 Hz, gain at 1 kHz × 20% ± 1%, input impedance > 100,000,000Ω) and a signal bandwidth from 20 Hz to 3000 Hz. EMG signals were transferred to a 16-bit analog-to-digital converter. The disposable surface EMG electrode consisted of two 9-mm silver/silver chloride discs (20-mm interelectrode spacing). The electrode placement for each muscle was consistent with previously reported guidelines (26). Before testing, EMG signals from each muscle were obtained while performing a series of three maximum voluntary isometric contractions. These tests were conducted for normalization purposes.
Kinematic data during the drop landing task were recorded at a rate of 250 Hz using an eight-camera motion analysis system (Vicon 612; Oxford Metrics, Oxford, UK). Ground reaction forces were collected at a rate of 1500 Hz using two AMTI force plates (AMTI, Newton, MA). Twenty-one reflective markers (14-mm spheres) were attached to the following bony landmarks: distal first toe, first and fifth metatarsal heads, medial and lateral malleoli, medial and lateral femoral epicondyles, greater trochanters, anterior superior iliac spines, iliac crests, and the L5–S1 junction. In addition, noncollinear tracking cluster markers were placed on the heels (three markers), lateral shanks (four markers), and lateral thighs (four markers). For the drop landing task, subjects started from a standing position on a platform (height = 35 cm) in front of the two force plates. Subjects were instructed to land with one foot on each plate and then jump upward as high as possible. Three trials were collected.
For the isokinetic knee extension task, subjects were placed in a seated position on the dynamometer with the hip in 80° of flexion. Subjects moved through a 60° arc of motion (75°–15° of knee flexion) at a rate of 60°·s−1 and were instructed to straighten their knee as hard and fast as possible against the resistance pad of the dynamometer. The range of motion (75°–15° of knee flexion) of the knee extension task was chosen for subjects’ comfort and to assist subjects in performing knee extension with the required rate of 60°·s−1. All dynamometer data were gravity corrected. Three trials were obtained.
To calculate the volume of each muscle of interest, the cross-sectional area of quadriceps, hamstrings, and gastrocnemius muscles was measured from each axial MRI. The muscle volume of each slice was computed by multiplying the cross-sectional area of the muscle by the slice thickness of the image. The sum of the measured muscle volumes from all slices (i.e., total muscle volume) was combined with the muscle pennation angle and fiber length reported in previous in vitro studies (12,36) to calculate the PCSA (muscle volume × cosine of the pennation angle/fiber length) (13) for each muscle. The PCSA was then multiplied by a previously reported specific tension value of 23 N·cm−2 (9,29) to approximate the maximum isometric muscle force for each muscle.
Moment arms of the quadriceps, semimembranosus (SM), ST, biceps femoris, and MG and LG tendons were measured from the sagittal plane images at each of the five different knee flexion angles using ImageJ software (National Institutes of Health, Bethesda, MD). Each muscle’s moment arm was defined as the perpendicular distance from the line of action of the muscle tendon to the knee joint center. The knee joint center was defined as the intersection of the anterior and posterior cruciate ligaments (35). A second-order polynomial curve fitting procedure was used to estimate moment arms from 0° to 90° of knee flexion.
The Visual3D software (C-motion, Rockville, MD) was used to compute the segmental kinematics and kinetics of the dominant lower extremity. Raw trajectory and ground reaction force data were filtered using a fourth-order zero-lag Butterworth low-pass filter at 6 Hz. Three-dimensional net joint moments during drop landing were calculated using standard inverse dynamics equations (8). Segment mass, center of mass location, and segment moment of inertia were approximated from the data of Dempster (10). Net knee joint moments were normalized to body mass and are presented as internal moments.
Raw EMG signals collected during the two tasks were band-pass filtered (35–500 Hz), rectified, and smoothed with a 6-Hz low-pass filter. For each muscle, the highest EMG value recorded from the maximum voluntary isometric contraction, drop land, or isokinetic knee extension trials was determined. The smoothed EMG data of each muscle were then normalized to its highest EMG value. EMG data were postprocessed using a custom MATLAB program (MathWorks, Natick, MA).
Development of generic, scaled, and MRI knee models
The SIMM software (MusculoGraphics, Inc., Chicago, IL) was used to create a generic lower extremity model that represents the skeleton of a young adult male (height = 1.8 m) (9). The model included 10 musculotendon actuators: VL, VM, vastus intermedius (VI), RF, ST, SM, BFL, biceps femoris short head (BFS), MG, and LG. The muscle anatomic parameters of the 10 muscles were based on the values reported by Friederich and Brand (12) and Wickiewicz et al. (36). Tendon slack lengths of the 10 muscles were based on the average values reported by Delp (9) and Lloyd and Buchanan (19) for each subject.
Normalized muscle EMG and lower extremity kinematics (hip flexion/extension, hip adduction/abduction, hip internal/external rotation, knee flexion/extension, and ankle plantarflexion/dorsiflexion) were used as input variables for the generic EMG-driven model. Lower extremity kinematic data were used to determine individual muscle tendon lengths and contraction velocities for the Hill-type muscle model built in SIMM. Normalized EMG data were used to represent muscle activation levels. Muscle activation of the VI was estimated as the average of the VM and VL normalized EMG amplitudes during each task. SM was assumed to have the same activation as ST, and BFS was assumed to have the same activation as the BFL (18). A 40-ms electromechanical delay was used to adjust for the time difference between the onset of EMG signals and onset of force output (18). The force (FM) of each muscle was then calculated using the equation below:
where FT is the tendon force; FMax is the maximum isometric contraction muscle force; f(l) and f(v) are the generic muscle length–tension and force–velocity relationships, respectively; a is muscle activation; fp(l) is the length–tension of the parallel elastic element; and θ is the pennation angle (9,18).
To create a scaled lower extremity model for each subject, the dimensions of the pelvis, femur, tibia, patella, and ankle and foot complex of the generic SIMM model were adjusted on the basis of the measured distance between the anterior superior iliac spines, the distance from hip to knee joint center, the distance from knee to ankle joint center, patella thickness, and foot length, respectively (27). This was done to scale the muscle moment arms for each subject. The maximum isometric muscle force of each muscle was scaled on the basis of the power of two-thirds of the body mass for each subject (40). Individual muscle forces calculated from the generic model (FM) were then adjusted for each subject using this scaling factor.
To create the MRI knee model, the maximum isometric muscle forces derived from MRI-estimated PCSA of the 10 muscles were used to adjust the muscle forces calculated from the generic SIMM model (FM) for each subject. The adjusted muscle force was then multiplied by the moment arm data estimated from MRI to calculate the muscle moment at the knee for each muscle. The net sagittal plane moments at the knee during the drop landing and isokinetic knee extension task were calculated from each of the three models by summing all muscle moments (muscle force × its corresponding moment arm) generated from the quadriceps, hamstring, and gastrocnemius muscles for the knee joint. Only the sagittal moment was analyzed because the rotational motion of the knee joint modeled in SIMM is limited to this plane.
The coefficient of multiple correlation (15,39) was calculated to examine the level of agreement between the joint moment time series curve of each of the three EMG-driven models and the standard net joint moment measurements (inverse dynamics for the drop landing task and dynamometer for the isokinetic knee extension task). The mean absolute difference also was calculated for each task to examine the overall error of each model in predicting the net sagittal plane knee moment. Given the small sample size, the Friedman test for nonparametric repeated-measures comparisons (SPSS version 15.0; Chicago, IL) was performed to compare the differences in the mean absolute difference among the three models for each task. If significance was found (P ≤ 0.05), post hoc pairwise comparisons were performed using Wilcoxon signed rank tests. Effect sizes for the significant post hoc comparison were calculated using Cohen d.
The net knee sagittal plane moments calculated using the three modeling approaches during drop landing and isokinetic knee extension tasks are presented in Figures 1 and 2, respectively. For both tasks, the model with MRI direct measurements of muscle volumes and moment arms had a higher coefficient of multiple correlation value than the generic and scaled models, indicating better agreement with standard net joint moment measurements (Table 1). The scaled model had a lower coefficient of multiple correlation value than the generic model for both tasks, indicating that the agreement with standard net joint moment measurements did not improve when a generic musculoskeletal model was scaled on the basis of segment size and body mass (Table 1).
The Friedman test assessing the mean absolute differences among the three models reached statistical significance for the drop landing task (P ≤ 0.05). Post hoc testing revealed that the model with the MRI-measured muscle volumes and moment arms had a significantly smaller mean absolute difference than both the generic (0.33 ± 0.12 vs 0.54 ± 0.23 N·m·kg−1, effect size = 0.99) and the scaled models (0.33 ± 0.12 vs 0.65 ± 0.31 N·m·kg−1, effect size = 1.14) (Table 1). Although the mean absolute difference of the scaled model was greater than that of the generic model, this difference did not reach statistical significance.
For the isokinetic knee extension task, the Friedman test assessing the mean absolute difference among the three models also reached statistical significance (P ≤ 0.05). Post hoc testing revealed that the MRI model had a significantly smaller mean absolute difference than both the generic (0.50 ± 0.17 vs 0.87 ± 0.40 N·m·kg−1, effect size = 1.07) and the scaled models (0.50 ± 0.17 vs 1.03 ± 0.46 N·m·kg−1, effect size = 1.37). In addition, the mean absolute difference of the scaled model was significantly greater than that of the generic model (1.03 ± 0.46 vs 0.87 ± 0.40 N·m·kg−1, effect size = 1.36) (Table 1).
Consistent with our hypothesis, the net knee joint moment calculated by the EMG-driven knee model that incorporated MRI measurements of muscle volumes and moment arms exhibited better agreement and a smaller error when compared with the standard knee joint moment measurements than the generic and scaled models. Given that the net joint moment is the sum of each individual muscle moment (force × moment arm) and moments from passive structures surrounding the joint, it is reasonable to assume that direct measurements of muscle volumes and moment arms would compare more favorably to standard measures of joint kinetics. As such, this type of modeling approach may provide a more accurate assessment of knee joint loading.
By using direct MRI measurements of muscle volumes and moment arms, the errors observed for the knee joint moment predictions were reduced by 40%–50% when compared with using generic or scaled muscle anatomic parameters. These findings emphasize the importance of acquiring accurate subject-specific muscle anatomic parameters (i.e., muscle volumes and moment arms) when using a computational model to quantify or evaluate joint kinetics during functional activities. This may be especially critical if a knee model is used to compare certain populations that have been shown to have altered muscle morphology (i.e., reduction in muscle volume) after knee injury or pathology (e.g., ligament injury, meniscal lesion) (1,37).
Although the model using direct MRI measurements of muscle volumes and moment arms outperformed the generic and scaled models, all three approaches demonstrated errors when compared with the standard net joint moment measurements. The errors in each of the models may be attributed to the estimation of muscle activation directly from normalized EMG and the use of generic muscle contractile parameters and tendon slack lengths. Muscle contractile parameters and tendon slack lengths are difficult to measure in vivo and are often estimated through a mathematical optimization procedure by minimizing the differences between the joint moments calculated by an EMG-driven model and standard joint moment measurements (5,16,18,38). For example, Lloyd and Besier (18) used optimization procedures to estimate three EMG-to–muscle activation parameters and 15 muscle contractile parameters for a generic EMG-driven knee model. The knee joint moments calculated by their model had good agreement and small errors (mean errors ranging from 0.13 to 0.19 N·m·kg−1) with the joint moments calculated by inverse dynamics and moments measured by dynamometer. In contrast, the mean error of the subject-specific model for the drop landing task in the current study was 0.33 ± 0.15 N·m·kg−1. This finding is encouraging considering that the current model only accounted for subject-specific muscle volumes and moment arms without optimizing or calibrating any muscle contractile or EMG-to–muscle activation parameters. In addition, the large reduction (i.e., 40%–50%) in the errors of joint moment prediction with MRI-measured muscle volumes and moment arms would be expected to result in more representative muscle contractile parameters estimations if subsequent optimization procedures are performed. Future modeling approaches that combine both direct measurements of muscle anatomic parameters and optimization procedures for muscle contractile parameters may further improve the accuracy and advance the application of an EMG-driven knee joint model.
On average, the errors in predicting knee joint moment of the three models were greater in the isokinetic knee extension task when compared with the drop landing task. This finding is consistent with the results of Lloyd and Besier (18), who reported greater errors in their EMG-driven knee model for the isokinetic knee extension tasks performed on a dynamometer when compared with dynamic tasks such as cutting and running. The greater errors during isokinetic knee extension are difficult to explain; however, one possible explanation is that the isokinetic task was performed with a constant velocity. For example, if the generic muscle force–velocity relationship underestimated or overestimated the muscle force at the velocity in which the isokinetic test was performed, significant errors would be expected through the entire task. Future studies that incorporate various speeds of isokinetic tasks and other forms of muscle performance testing (e.g., isotonic contractions) may provide insight into this issue.
Although scaling a generic musculoskeletal model on the basis of anthropometric measurements is commonly used to create a model representative of subjects enrolled in a particular study (5,38), our results show that the joint moment prediction did not improve with this approach when compared with the generic musculoskeletal model. The greater errors with the scaled model may result from the scaling methods that were used. More specifically, the moment arm of a muscle depends not only on the size of the bones but also on the attachment sites of the muscle. Simply scaling the dimensions of the bones on the basis of segment length may not account for the variability of the muscle attachment sites across individuals (27). For example, Scheys et al. (27) demonstrated that the lower extremity muscle moment arms measured from an MRI-derived musculoskeletal model differed significantly from the moment arms of a scaled model created by scaling a generic model on the basis of bone dimensions.
Although muscle size may be somewhat associated with body mass, body mass alone cannot predict how much force a muscle can generate (22,41). Scaling the maximum isometric muscle force on the basis of body mass or any other single value of anthropometry measurements assumes that the percent difference in the maximum muscle force between two individuals is constant for all muscles. However, the maximum isometric force of a muscle is proportional to its PCSA (17). Data from in vitro studies have demonstrated that the percent differences in muscle PCSA among individuals vary across muscles (12,36). Therefore, a single scaling value would not be expected to account for between-subject differences in muscle force potential.
Although the direct measurements of muscle volumes and moment arms improved joint moment predictions of an EMG-driven model, the use of MRI can be expensive or time-consuming. A scaling approach provides a convenient and inexpensive way to create a subject-specific musculoskeletal model. However, the scaled model in the current study demonstrated the greatest errors. Therefore, future studies are needed to develop alternative scaling methods that can better estimate or predict muscle forces and moment arms.
The differences in the values of the coefficient of multiple correlation and mean absolute difference among the three models can be explained by the differences in estimated muscle forces for each model. On average, the maximum forces of the quadriceps and gastrocnemius muscles estimated on the basis of MRI-measured muscle volumes (Table 2) were greater than the forces derived from the generic and scaled models (Table 3). Conversely, the maximum hamstring muscle forces estimated from MRI were somewhat similar to or slightly lower than those from the generic and scaled models. As expected, the maximum muscle forces estimated using MRI demonstrated greater between-subject variability (i.e., greater SD) for all muscles than the generic and scaled models (Table 3). Considering that the average height and weight of the subjects in the current study were smaller than the male model built in the generic SIMM model, one would expect that scaling of the generic model would lead to further discrepancies in muscle force predictions.
Although the generic SIMM model is commonly used in biomechanical studies (5,38), its muscle anatomic parameters are derived from a relatively small sample of cadavers (12,36). Recently, Arnold et al. (3) have developed a lower extremity musculoskeletal model that incorporates the muscle anatomic parameters measured from a sample of cadavers (n = 21) larger than what was used in the development of the original SIMM model (34). Future studies are warranted to evaluate the joint moment predictions of more contemporary models.
Although the MRI-measured muscle volumes (Table 2) in our study are comparable to previous reports examining muscle volumes in young adults (2,23,31), the use of a 10-mm slice thickness when obtaining the MRIs may have introduced a degree of measurement error. Another limitation of the current study is that our PCSA calculations incorporated pennation angles and muscle fiber lengths reported from existing literature (12,36). On the basis of previous in vitro cadaveric studies, the fiber lengths and pennation angles of the 10 muscles included in our knee model were remarkably similar among cadaver bodies (12,36). Although we feel that it is appropriate to use existing values for our study, the use of cadaver-based pennation angles and fiber lengths may have limited the accuracy of calculating a subject-specific PCSA for each muscle. As such, care must be taken in using the modeling approach used in the current study to evaluate individuals with trophic changes after injury and/or surgery where alterations in muscle fiber lengths and pennation angles may be present. Future modeling approaches that incorporate direct measurements of muscle fiber lengths and pennation angles using MRI or ultrasound (21) would strengthen the clinical application of subject-specific EMG-driven models.
Apart from the differences in predicted muscle forces, the ability of each of the three models to predict knee joint moments was influenced by muscle moment arm estimations. On average, the moment arms of the quadriceps and gastrocnemius muscles measured from MRI were greater than the moment arms from the generic and scaled models (Fig. 3). In contrast, the moment arms of the SM and ST were similar among the three modeling approaches for the majority of knee flexion angles (Fig. 3). The moment arms of the biceps femoris muscles measured from MRI were greater than those from the generic and scaled models with small knee flexion angles (i.e., <30°) but were smaller than those from the generic and scaled models as knee flexion angle increased (i.e., >40°).
The differences in muscle moment arms among the three modeling approaches may be the result of the varying methods that were used to obtain these data (24). For example, the generic and scaled models calculate muscle moment arms using the tendon excursion method, whereas the moment arms of the MRI-based model were measured from the MRIs as the perpendicular distance from the line of action of the muscle tendon to the knee joint center. In addition, the method used in estimating the location of the knee joint center also could have affected the moment arm measurements in the MRI model. Two landmarks are commonly used to define the knee joint center on a two-dimensional image: 1) the tibiofemoral contact point and 2) the intersection of cruciate ligaments (32). The choice of using the intersection of cruciate ligaments as the knee joint center was based on the work of Baker and Ronsky (4), who demonstrated that this measurement resulted in better agreement with the estimation of the knee instantaneous center of rotation using the helical axis approach as compared with the tibiofemoral contact point method.
The magnitudes and patterns of the polynomial curve relationships between moment arms and joint angles for the muscles included in the model are similar to the moment arms reported in previous in vitro studies (14,30). However, it should be noted that the polynomial moment arm curves were estimated using curve fitting procedures based on images obtained at only five knee flexion angles. Moment arms estimated from a limited number of knee positions may not provide sufficient information to predict the moment arm of the muscles at every knee joint angle. In addition, the sagittal plane images used to obtain the moment arm data were obtained while subjects pushed against a load of only 111 N. Although 111 N was selected to avoid motion artifact during image acquisition, this load would not be expected to result in muscle forces that would be comparable to those experienced during the drop land and isokinetic knee extension tasks used in the current study. It is possible that the application of a higher load may affect the moment arm measurements.
In the current study, the net knee moment predictions of the three modeling approaches were examined during two tasks (drop landing and isokinetic knee extension) that are knee extensor dominant. Whether or not the MRI model would provide better moment predictions during tasks that are knee flexor dominant remains to be seen. In addition, future studies are needed to evaluate other sports-related activities (e.g., running, cutting) to broaden the generalizability of the findings.
The present study was, in part, supported by the American Society of Biomechanics Graduate Student Grant-in-Aid program.
The authors report no conflicts of interest.
The study was approved by the Institutional Review Board of the University of Southern California Health Sciences Campus.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
1. Akima H, Furukawa T. Atrophy of thigh muscles after meniscal lesions and arthroscopic partial menisectomy. Knee Surg Sports Traumatol Arthrosc. 2005; 13 (8): 632–7.
2. Albracht K, Arampatzis A, Baltzopoulos V. Assessment of muscle volume and physiological cross-sectional area of the human triceps surae muscle in vivo
. J Biomech. 2008; 41 (10): 2211–8.
3. Arnold EM, Ward SR, Lieber RL, Delp SL. A model of the lower limb for analysis of human movement. Ann Biomed Eng. 2010; 38 (2): 269–79.
4. Baker N, Ronsky J. Use of instantaneous helical axes to determine knee joint centre on magnetic resonance images. Abstract presented at: XVIIIth Congress of the International Society of Biomechanics; 2001 July 8–13; Zurich, Switzerland.
5. Besier TF, Fredericson M, Gold GE, Beaupre GS, Delp SL. Knee muscle forces during walking and running in patellofemoral pain patients and pain-free controls. J Biomech. 2009; 42 (7): 898–905.
6. Chappell JD, Herman DC, Knight BS, Kirkendall DT, Garrett WE, Yu B. Effect of fatigue on knee kinetics and kinematics in stop-jump tasks. Am J Sports Med. 2005; 33 (7): 1022–9.
7. Cholewicki J, McGill SM, Norman RW. Comparison of muscle forces and joint load from an optimization and EMG assisted lumbar spine model: towards development of a hybrid approach. J Biomech. 1995; 28 (3): 321–31.
8. Davis RB 3rd, Ounpuu S, Tyburski D, Gage JR. A gait analysis data collection and reduction technique. Hum Mov Sci. 1991; 10 (5): 575–87.
9. Delp SL. Surgery Simulation: A Computer-Graphics System to Analyze and Design Musculoskeletal Reconstructions of the Lower Limb [dissertation]. Stanford (CA): Stanford University; 1990. p. 117.
10. Dempster WT. Space Requirements of the Seated Operator: Geometrical, Kinematic, and Mechanical Aspects of the Body with Special Reference to the Limbs. Wright-Patterson Air Force Base (OH): US Air Force: Wright Air Development Center Technical Report no. 55-159; 1955. p. 1–241.
11. Erdemir A, McLean S, Herzog W, van den Bogert AJ. Model-based estimation of muscle forces exerted during movements. Clin Biomech (Bristol, Avon). 2007; 22 (2): 131–54.
12. Friederich JA, Brand RA. Muscle fiber architecture in the human lower limb. J Biomech. 1990; 23 (1): 91–5.
13. Fukunaga T, Roy RR, Shellock FG, et al.. Physiological cross-sectional area of human leg muscles based on magnetic resonance imaging. J Orthop Res. 1992; 10 (6): 928–34.
14. Herzog W, Read LJ. Lines of action and moment arms of the major force-carrying structures crossing the human knee joint. J Anat. 1993; 182: 213–30.
15. Kadaba MP, Ramakrishnan HK, Wootten ME, Gainey J, Gorton G, Cochran GV. Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res. 1989; 7 (6): 849–60.
16. Koo TK, Mak AF. Feasibility of using EMG driven neuromusculoskeletal model for prediction of dynamic movement of the elbow. J Electromyogr Kinesiol. 2005; 15 (1): 12–26.
17. Lieber RL. Skeletal Muscle Structure, Function, & Plasticity: The Physiological Basis of Rehabilitation. Philadelphia (PA): Lippincott Williams & Wilkins; 2009. p. 1–40.
18. Lloyd DG, Besier TF. An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo
. J Biomech. 2003; 36 (6): 765–76.
19. Lloyd DG, Buchanan TS. A model of load sharing between muscles and soft tissues at the human knee during static tasks. J Biomech Eng. 1996; 118 (3): 367–76.
20. Maganaris CN. Imaging-based estimates of moment arm length in intact human muscle-tendons. Eur J Appl Physiol. 2004; 91 (2–3): 130–9.
21. Manal K, Roberts DP, Buchanan TS. Optimal pennation angle of the primary ankle plantar and dorsiflexors: variations with sex, contraction intensity, and limb. J Appl Biomech. 2006; 22 (4): 255–63.
22. Maughan RJ, Watson JS, Weir J. Strength and cross-sectional area of human skeletal muscle. J Physiol. 1983; 338: 37–49.
23. Morse CI, Degens H, Jones DA. The validity of estimating quadriceps volume from single MRI cross-sections in young men. Eur J Appl Physiol. 2007; 100 (3): 267–74.
24. Pal S, Langenderfer JE, Stowe JQ, Laz PJ, Petrella AJ, Rullkoetter PJ. Probabilistic modeling of knee muscle moment arms: effects of methods, origin-insertion, and kinematic variability. Ann Biomed Eng. 2007; 35 (9): 1632–42.
25. Pandy MG. Computer modeling and simulation of human movement. Annu Rev Biomed Eng. 2001; 3: 245–73.
26. Perotto AO, Delagi EF. Anatomic Guide for the Electromyographer: The Limbs and Trunk. 3rd ed. Springfield (IL): Charles C Thomas; 1994. p. 309.
27. Scheys L, Spaepen A, Suetens P, Jonkers I. Calculated moment-arm and muscle-tendon lengths during gait differ substantially using MR based versus rescaled generic lower-limb musculoskeletal models. Gait Posture. 2008; 28 (4): 640–8.
28. Shelburne KB, Pandy MG. A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions. J Biomech. 1997; 30 (2): 163–76.
29. Spector SA, Gardiner PF, Zernicke RF, Roy RR, Edgerton VR. Muscle architecture and force–velocity characteristics of cat soleus and medial gastrocnemius: implications for motor control. J Neurophysiol. 1980; 44 (5): 951–60.
30. Spoor CW, van Leeuwen JL. Knee muscle moment arms from MRI and from tendon travel. J Biomech. 1992; 25 (2): 201–6.
31. Tate CM, Williams GN, Barrance PJ, Buchanan TS. Lower extremity muscle morphology in young athletes: an MRI-based analysis. Med Sci Sports Exerc. 2006; 38 (1): 122–8.
32. Tsaopoulos DE, Maganaris CN, Baltzopoulos V. Can the patellar tendon moment arm be predicted from anthropometric measurements? J Biomech. 2007; 40 (3): 645–51.
33. van den Bogert AJ, Gerritsen KG, Cole GK. Human muscle modeling from a user’s perspective. J Electromyogr Kinesiol. 1998; 8 (2): 119–24.
34. Ward SR, Eng CM, Smallwood LH, Lieber RL. Are current measurements of lower extremity muscle architecture accurate? Clin Orthop Relat Res. 2009; 467 (4): 1074–82.
35. Ward SR, Terk MR, Powers CM. Influence of patella alta on knee extensor mechanics. J Biomech. 2005; 38 (12): 2415–22.
36. Wickiewicz TL, Roy RR, Powell PL, Edgerton VR. Muscle architecture of the human lower limb. Clin Orthop Relat Res. 1983; 179: 275–83.
37. Williams GN, Snyder-Mackler L, Barrance PJ, Buchanan TS. Quadriceps femoris muscle morphology and function after ACL injury: a differential response in copers versus non-copers. J Biomech. 2005; 38 (4): 685–93.
38. Winby CR, Lloyd DG, Besier TF, Kirk TB. Muscle and external load contribution to knee joint contact loads during normal gait. J Biomech. 2009; 42 (14): 2294–300.
39. Yu B, Kienbacher T, Growney ES, Johnson ME, An KN. Reproducibility of the kinematics and kinetics of the lower extremity during normal stair-climbing. J Orthop Res. 1997; 15 (3): 348–52.
40. Zoeller RF, Ryan ED, Gordish-Dressman H, et al.. Allometric scaling of biceps strength before and after resistance training in men. Med Sci Sports Exerc. 2007; 39 (6): 1013–9.
41. Zoeller RF, Ryan ED, Gordish-Dressman H, et al.. Allometric scaling of isometric biceps strength in adult females and the effect of body mass index. Eur J Appl Physiol. 2008; 104 (4): 701–10.
Keywords:©2012The American College of Sports Medicine
MAGNETIC RESONANCE IMAGING; PHYSIOLOGICAL CROSS-SECTIONAL AREAS; MUSCLE VOLUME; MUSCLE MOMENT ARM; SIMM