Daniel N. Bassett, Qi Shao, Kurt Manal, Thomas S. Buchanan
Center for Biomedical Engineering Research, University of Delaware, Newark, DE
Introduction
The biomedical field thrives on computational devices. Clinicians, physical therapists, and researchers frequently use models as tools. The key to proper implementation of these tools is a good understanding of the limitations, advantages, and options available. Previous research on EMG-driven models demonstrated the ability of single joint models to predict joint moments with reasonable accuracy [1]. The advantage provided is the possibility of studying muscle and intersegmental forces in vivo.
In a continued effort to expand our understanding of EMG-driven models, we looked at the multiple contributions of biarticular muscles to the two joints they span. The focus was placed on the gastrocnemii in modeling the ankle and knee. Single joint EMG-driven models have been shown to perform well at both of the major joints in the lower leg [1,2,3]. Our aim was to compare these models to one that includes the gastrocnemii as flexors of the knee and plantarflexors of the ankle. That is, a two joint model with bi-articular gastrocnemii.
The results were anticipated to show the different model’s ability to predict joint moments to be comparable. However, the muscle force predictions were expected to vary with the inclusion of another joint – especially when accounting for the multi-joint roles of biarticular muscles (such as the gastrocnemii).
Methods
Data Collection
Six healthy individuals possessing normal gait were included in this study. Data were collected using a six camera Qualysis system for motion, AMTI force plate for ground reaction forces, and electromyography (EMG) for muscle activity. Surface electrodes were used to acquire EMG from the rectus femoris, vastus lateralis, vastus medialis, semitendinosus, and biceps femoris long head. For muscles about the ankle, EMGs were collected from the soleus and tibialis anterior beyond the medial and lateral gastrocnemii also included at the knee. Throughout the experiment the subjects performed a series of maximum voluntary isometric contractions (MVIC), and three sets of motion trials. The three types of motion were normal walking, hopping, and hop and stop; where we defined hopping as starting from a stationary position, jumping 1.3 meters to land with the markered leg on the in-floor force plate, and immediately jumping again in the same direction. Hop-and-stop was defined similarly to hopping, except after landing on the force plate, the position was held balancing on the markered leg.
Data Processing
A total of eleven muscles were included in the model by estimating the EMG for the vastus intermedius as the average of the other two vasti, and the short head of biceps femoris as activating the same as the long head. All of the EMG signals were then relieved of bias, rectified, filtered, and normalized. The muscle-tendon lengths and moment arms were estimated by SIMM from the kinematic data to be input to the model with the processed EMG activations [4].
Biomechanical Model
The force (FM) for each of the muscles was calculated using a forward dynamic Hill-type model that included active (FA), passive (FP), velocity-dependent (FV), and damping (bm) elements as shown in equation 1. Which are dependent on muscle fiber length (lm) and fiber velocity (vm).
The biomedical field thrives on computational devices. Clinicians, physical therapists, and researchers frequently use models as tools. The key to proper implementation of these tools is a good understanding of the limitations, advantages, and options available. Previous research on EMG-driven models demonstrated the ability of single joint models to predict joint moments with reasonable accuracy [1]. The advantage provided is the possibility of studying muscle and intersegmental forces in vivo.
In a continued effort to expand our understanding of EMG-driven models, we looked at the multiple contributions of biarticular muscles to the two joints they span. The focus was placed on the gastrocnemii in modeling the ankle and knee. Single joint EMG-driven models have been shown to perform well at both of the major joints in the lower leg [1,2,3]. Our aim was to compare these models to one that includes the gastrocnemii as flexors of the knee and plantarflexors of the ankle. That is, a two joint model with bi-articular gastrocnemii.
The results were anticipated to show the different model’s ability to predict joint moments to be comparable. However, the muscle force predictions were expected to vary with the inclusion of another joint – especially when accounting for the multi-joint roles of biarticular muscles (such as the gastrocnemii).
Methods
Data Collection
Six healthy individuals possessing normal gait were included in this study. Data were collected using a six camera Qualysis system for motion, AMTI force plate for ground reaction forces, and electromyography (EMG) for muscle activity. Surface electrodes were used to acquire EMG from the rectus femoris, vastus lateralis, vastus medialis, semitendinosus, and biceps femoris long head. For muscles about the ankle, EMGs were collected from the soleus and tibialis anterior beyond the medial and lateral gastrocnemii also included at the knee. Throughout the experiment the subjects performed a series of maximum voluntary isometric contractions (MVIC), and three sets of motion trials. The three types of motion were normal walking, hopping, and hop and stop; where we defined hopping as starting from a stationary position, jumping 1.3 meters to land with the markered leg on the in-floor force plate, and immediately jumping again in the same direction. Hop-and-stop was defined similarly to hopping, except after landing on the force plate, the position was held balancing on the markered leg.
Data Processing
A total of eleven muscles were included in the model by estimating the EMG for the vastus intermedius as the average of the other two vasti, and the short head of biceps femoris as activating the same as the long head. All of the EMG signals were then relieved of bias, rectified, filtered, and normalized. The muscle-tendon lengths and moment arms were estimated by SIMM from the kinematic data to be input to the model with the processed EMG activations [4].
Biomechanical Model
The force (FM) for each of the muscles was calculated using a forward dynamic Hill-type model that included active (FA), passive (FP), velocity-dependent (FV), and damping (bm) elements as shown in equation 1. Which are dependent on muscle fiber length (lm) and fiber velocity (vm).
(1)Furthermore the muscle activations (a(t)) were obtained by passing the EMG activations through a recursive filter and non-linearizing it [4].
The core function of the model’s algorithm was to forward integrate equation 1 evaluating muscle fiber length, which was then subtracted from the muscle-tendon length to estimate force from the known tendon-force relationship. Using the musculoskeletal geometry from SIMM the muscle moments were calculated and then summed into joint moments.
Each portion of the model described in this paper relies on parameters, values for which are often difficult to obtain in vivo, and must therefore be calibrated. The kinematic and ground reaction force data were used to compute the inverse dynamic joint moments, which in turn were used as “measured” benchmarks for the optimization process [5] assigning values to the model parameters.
The model was tuned in three separate ways on a walking trial: single joint at the ankle, single joint at the knee, and multi joint at the ankle and knee combined. Once this was done, the calibrated parameters were used to predict joint moments and muscle forces for new trials to which the model had not been calibrated.
Results & Discussion
The core function of the model’s algorithm was to forward integrate equation 1 evaluating muscle fiber length, which was then subtracted from the muscle-tendon length to estimate force from the known tendon-force relationship. Using the musculoskeletal geometry from SIMM the muscle moments were calculated and then summed into joint moments.
Each portion of the model described in this paper relies on parameters, values for which are often difficult to obtain in vivo, and must therefore be calibrated. The kinematic and ground reaction force data were used to compute the inverse dynamic joint moments, which in turn were used as “measured” benchmarks for the optimization process [5] assigning values to the model parameters.
The model was tuned in three separate ways on a walking trial: single joint at the ankle, single joint at the knee, and multi joint at the ankle and knee combined. Once this was done, the calibrated parameters were used to predict joint moments and muscle forces for new trials to which the model had not been calibrated.
Results & Discussion
Figure 1: Correlation between the predicted and measured joint moments for all subjects over all trials
As expected, Figure 1 shows the joint moment prediction results as being similar between single and multi joint models. Since the calibration was performed on walking trials, it was anticipated that the correlations would be best for walking predictions (RMS-error approximately 20%). The hopping trial results proved interesting, as they demonstrated the ability of all three models to accurately predict joint moments of a novel task.
Figure 2: Subject average gastrocnemius force predictions for walking and hopping (Subject 4)
Figure 2 shows the average gastrocnemius muscle force predictions for one subject during walking and hopping. Comparing the single ankle joint with the multi-joint model the variation is minimal. On the other hand, the force magnitude of the gastrocnemii predicted by the single knee joint model is noticeably higher for both walking and hopping predictions. It should also be noted that the values found by all three models were reasonable compared to literature [3].
Figure 1: Correlation between the predicted and measured joint moments for all subjects over all trials
A sensitivity analysis showed that some model parameters had greater influence on the resultant muscle force predictions than others. For example, for subject 4 (cf. Figure 2), the medial gastrocnemius tendon slack length was the most sensitive parameter. For other subjects, different parameters were observed to be the most sensitive for estimating muscle forces and it is likely that subject specific sensitivity analyses are warranted in this approach.
Conclusion
Based on this study, we believe the multi-joint model is supplying improved muscle force predictions due to better accountability of biarticular muscles. The results need to be explored in more detail on a larger population to gain a better understanding. Studying synergistic motions of the ankle and knee, both joints may need to be included in the model to account for the multiple contributions of the biarticular gastrocnemii.
References
1. Buchanan, T.S., Lloyd, D.G., Manal, K.T., & Besier, T.F., 2005, “Estimation of muscle forces and joint moments using a forward-inverse dynamics model,” Medicine & Science in Sports & Exercise, pp. 1911-1916.
2. Lloyd, D.G., & Besier, T.F., 2002, “An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo,” Journal of Biomechanics, 36, pp. 765-776.
3. Bogey, R.A., Perry, J., & Gitter, J., (2005). “An EMG-to-force processing approach for determining ankle muscle forces during normal human gait,” IEEE Transaction on Neural Systems and Rehabilitation Engineering, 13, pp. 302-310.
4. Buchanan, T.S., Lloyd, D.G., Manal, K.T., & Besier, T.F., 2004, “Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command,” Journal of Applied Biomechanics, 20, pp. 367-395.
5. Goffe, W.L., Ferrier, G.D., & Rogers, J., 1994, “Global optimization of statistical functions with simulated annealing. Journal of Econometrics,” 60, pp. 65-99.
Acknowledgements
NIH R01-HD38582 and P20-RR16458.
Figure 2 shows the average gastrocnemius muscle force predictions for one subject during walking and hopping. Comparing the single ankle joint with the multi-joint model the variation is minimal. On the other hand, the force magnitude of the gastrocnemii predicted by the single knee joint model is noticeably higher for both walking and hopping predictions. It should also be noted that the values found by all three models were reasonable compared to literature [3].
Figure 1: Correlation between the predicted and measured joint moments for all subjects over all trials
A sensitivity analysis showed that some model parameters had greater influence on the resultant muscle force predictions than others. For example, for subject 4 (cf. Figure 2), the medial gastrocnemius tendon slack length was the most sensitive parameter. For other subjects, different parameters were observed to be the most sensitive for estimating muscle forces and it is likely that subject specific sensitivity analyses are warranted in this approach.
Conclusion
Based on this study, we believe the multi-joint model is supplying improved muscle force predictions due to better accountability of biarticular muscles. The results need to be explored in more detail on a larger population to gain a better understanding. Studying synergistic motions of the ankle and knee, both joints may need to be included in the model to account for the multiple contributions of the biarticular gastrocnemii.
References
1. Buchanan, T.S., Lloyd, D.G., Manal, K.T., & Besier, T.F., 2005, “Estimation of muscle forces and joint moments using a forward-inverse dynamics model,” Medicine & Science in Sports & Exercise, pp. 1911-1916.
2. Lloyd, D.G., & Besier, T.F., 2002, “An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo,” Journal of Biomechanics, 36, pp. 765-776.
3. Bogey, R.A., Perry, J., & Gitter, J., (2005). “An EMG-to-force processing approach for determining ankle muscle forces during normal human gait,” IEEE Transaction on Neural Systems and Rehabilitation Engineering, 13, pp. 302-310.
4. Buchanan, T.S., Lloyd, D.G., Manal, K.T., & Besier, T.F., 2004, “Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command,” Journal of Applied Biomechanics, 20, pp. 367-395.
5. Goffe, W.L., Ferrier, G.D., & Rogers, J., 1994, “Global optimization of statistical functions with simulated annealing. Journal of Econometrics,” 60, pp. 65-99.
Acknowledgements
NIH R01-HD38582 and P20-RR16458.
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