The thesis was successfully defended on Friday April 13th at 9:30 AM in Spencer Lab 209 at the University of Delaware. The thesis manuscript is also available here.
This thesis is a collection of two papers on EMG-driven modeling. In both papers, the modeling approach employs forward dynamics to estimate joint moments from muscle forces. During the optimization process, inverse dynamics is used as a benchmark to which the joint moments are compared to obtain values for necessary physiological parameters. Once the models are calibrated, they are used to predict muscle forces and joint moments on new trials and tasks. The papers deal with issues at the forefront of modeling in the field of biomechanics.
The first paper was published in the book Computational Intelligence for Movement Sciences: Neural Networks and Other Emerging Techniques edited by Begg & Palaniswami. The focus of that book was to expose the reader to computational intelligence methods as applied to biomedical and human movement research areas. It was intended to provide an instructional approach to a very complex field. For this reason, chapter two is presented in a more detailed form than usually found in scientific journals – particularly outlining each of the steps necessary to implement a forward dynamic model. Two examples of the application of EMG-driven models are presented in the final sections of chapter two. The first is of a single-joint model applied to the ankle of an unimpaired subject during normal walking. In contrast, the second example is of the same model applied to a stroke subject during gait.
The second paper presented is the first report of a multi-joint EMG-driven model, and will be submitted to be published in a technical journal. The focus of the paper is the comparison between single-joint and multi-joint modeling. Of particular interest was the proper inclusion of biarticular muscles, which contribute to the joint moments produced at two joints. Accounting for the multiple actions of the gastrocnemii was hypothesized to deliver different muscle forces with similar joint moment estimations. The results supported the hypothesis, and generated some of the groundwork for proper implementation of multi-joint models.
Tuesday, April 10, 2007
ASME Summer Bioengineering 2007
Predicting muscle forces and joint moments using single joint and multi joint EMG-driven models
(1)
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.
Orthopaedic Biomechanics & Sports Rehabilitation 2006
EVALUATION OF SINGLE AND MULTI JOINT MODELS OF THE ANKLE USING HYBRID EMG-DRIVEN APPROACHES
Daniel N. Bassett, Qi Shao, Daniel L. Benoit, Kurt T. Manal, and Thomas S. Buchanan
Center for Biomedical Engineering Research
University of Delaware, Newark, DE, USA
E-mail: bassett@me.udel.edu Web: http://www.cber.udel.edu/
INTRODUCTION
The evaluation of individual muscle forces is important in the study of ankle injuries or pathological gait. EMG-driven models can be very powerful tools in this regard, though they must be understood to be properly applied. In this study we compared the performance of a single-joint model of the ankle with a multi-joint model of the ankle and knee combined. Estimations of gastrocnemii muscle forces were hypothesized to be different when accounting for their contributions at the knee.
METHODS
Data were collected during the stance phase of healthy gait. EMG data were collected from the semitendinosus, biceps femoris, rectus femoris, vastus lateralis, vastus medialis about the knee (Lloyd & Besier, 2002), the tibialis anterior and soleus about the ankle, and the gastrocnemii as biarticular muscles that span both the ankle and knee. Kinematic data were used to obtain joint angles for the hip, knee, and ankle and subsequently muscle-tendon lengths and muscle moment arms using SIMM. Inverse dynamic joint moments were calculated for the knee and ankle from the kinematic data and ground reaction forces.
Our EMG-driven model is built on a forward dynamic approach using a Hill-type model (Buchanan et al., 2005). The equation relating components of our Hill-type model was integrated to calculate fiber length and tendon length ultimately giving muscle forces and joint moments (Buchanan et al., 2004).
Due to the difficulty of in vivo measurement of subject specific muscle parameters, such as tendon slack length, we used a hybrid model to tune these parameters (Goffe et al., 1994) using the inverse dynamic joint moments as the standard. The tuned models were then used to predict ankle joint moments for other walking trials.
RESULTS AND DISCUSSION
Figure 1: Ankle Joint Moment Comparison
As shown in Figure 1, the model’s ability to estimate joint moments was consistent between single and multiple joint calibrations. More importantly, however, deviations in muscle force predictions were observed in the multi-joint model. The inclusion of the knee resulted in a 15-20% increase in gastrocnemii forces (Figure 2).
Figure 2: Muscle force change between single and multi joint models throughout stance phase.
In this preliminary study, the changes in muscle forces during the latter portion of the stance phase are most likely due to the gastrocnemii being important contributors to knee flexion. The multi-joint model, which accounted for knee moments, predicted higher forces in these muscles than the single joint ankle model. Therefore, when studying ankle injuries the motion in question should be considered. Synergistic kinetic activity of the ankle and knee may need to be modeled by including both joints.
REFERENCES
Buchanan, T.S., Lloyd, D.G., Manal, K.T., Besier, T.F. (2004). J. App. Biomech, 20, 367-395.
Buchanan, T.S., Lloyd, D.G., Manal, K.T., Besier, T.F. (2005). Med Sci Sports Exerc., 1911-1916.
Goffe, W.L., Ferrier, G.D., Rogers, J. (1994). J. Econom., 60, 65-99.
Lloyd, D.G., Besier, T.F. (2002). J. Biomech., 36, 765-776.
ACKNOWLEDGEMENTS
NIH R01-HD38582 and P20-RR16458
Daniel N. Bassett, Qi Shao, Daniel L. Benoit, Kurt T. Manal, and Thomas S. Buchanan
Center for Biomedical Engineering Research
University of Delaware, Newark, DE, USA
E-mail: bassett@me.udel.edu Web: http://www.cber.udel.edu/
INTRODUCTION
The evaluation of individual muscle forces is important in the study of ankle injuries or pathological gait. EMG-driven models can be very powerful tools in this regard, though they must be understood to be properly applied. In this study we compared the performance of a single-joint model of the ankle with a multi-joint model of the ankle and knee combined. Estimations of gastrocnemii muscle forces were hypothesized to be different when accounting for their contributions at the knee.
METHODS
Data were collected during the stance phase of healthy gait. EMG data were collected from the semitendinosus, biceps femoris, rectus femoris, vastus lateralis, vastus medialis about the knee (Lloyd & Besier, 2002), the tibialis anterior and soleus about the ankle, and the gastrocnemii as biarticular muscles that span both the ankle and knee. Kinematic data were used to obtain joint angles for the hip, knee, and ankle and subsequently muscle-tendon lengths and muscle moment arms using SIMM. Inverse dynamic joint moments were calculated for the knee and ankle from the kinematic data and ground reaction forces.
Our EMG-driven model is built on a forward dynamic approach using a Hill-type model (Buchanan et al., 2005). The equation relating components of our Hill-type model was integrated to calculate fiber length and tendon length ultimately giving muscle forces and joint moments (Buchanan et al., 2004).
Due to the difficulty of in vivo measurement of subject specific muscle parameters, such as tendon slack length, we used a hybrid model to tune these parameters (Goffe et al., 1994) using the inverse dynamic joint moments as the standard. The tuned models were then used to predict ankle joint moments for other walking trials.
RESULTS AND DISCUSSION
Figure 1: Ankle Joint Moment Comparison
As shown in Figure 1, the model’s ability to estimate joint moments was consistent between single and multiple joint calibrations. More importantly, however, deviations in muscle force predictions were observed in the multi-joint model. The inclusion of the knee resulted in a 15-20% increase in gastrocnemii forces (Figure 2).
Figure 2: Muscle force change between single and multi joint models throughout stance phase.
In this preliminary study, the changes in muscle forces during the latter portion of the stance phase are most likely due to the gastrocnemii being important contributors to knee flexion. The multi-joint model, which accounted for knee moments, predicted higher forces in these muscles than the single joint ankle model. Therefore, when studying ankle injuries the motion in question should be considered. Synergistic kinetic activity of the ankle and knee may need to be modeled by including both joints.
REFERENCES
Buchanan, T.S., Lloyd, D.G., Manal, K.T., Besier, T.F. (2004). J. App. Biomech, 20, 367-395.
Buchanan, T.S., Lloyd, D.G., Manal, K.T., Besier, T.F. (2005). Med Sci Sports Exerc., 1911-1916.
Goffe, W.L., Ferrier, G.D., Rogers, J. (1994). J. Econom., 60, 65-99.
Lloyd, D.G., Besier, T.F. (2002). J. Biomech., 36, 765-776.
ACKNOWLEDGEMENTS
NIH R01-HD38582 and P20-RR16458
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