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K. Deng et al.
4 Discussion
In this manuscript, we present a biomechanical model of a rat hindlimb with biarticular
muscles. This model is an expansion of our previous monoarticular model [1]. The
largest difference in biomechanics between the new model and the previous one is that
the number of muscles was increased from 6 to 8. This causes the forces acting about
the knee joint to be substantially different from those in our previous model. The knee
is now mostly controlled by biarticular muscles. The other joints’ muscles are perturbed
by the contraction of the biarticular muscles, but they function largely in the same way
as in the previous model (i.e. as antagonistic pairs of muscles). Another difference is the
knee and ankle synergies. Rather than producing a synergy by actuating these muscle
sets with the same pattern formation network [1], in this model, they are mechanically
coupled by the GA muscle.
In order to calculate the desired motoneuron activations, we used several new strategies in the inverse kinematics analysis. With the implementation of biarticular muscles,
our previous method to estimate muscle parameter values is no longer suitable. We
developed a more biomimetic technique which combines rat muscle data [12, 13] with
other researchers’ studies on muscle [15–18] to determine those parameter values. When
compared with other researchers’ reports [19, 20] of muscle parameter values, the similarities support that our approach is a feasible method for modeling biomimetic muscles.
Moreover, the new analysis includes the falling phase of the length-tension curve, which
models active tension production more accurately. Our previous work obtained the tension from the Hill muscle model, but the force buildup curve was different from that of
actual muscle. The fact that our calculated parameters are consistent with experimental
reports of the tension of rat soleus [21–24] suggests that our new method of tuning
length-tension characteristics is an improvement over our previous method. Also, when
analyzing the passive tension in different phases of walking, we found that the passive
tension in the muscles is strongly related to joint motion.
Calculating the desired motoneuron activity makes it possible to develop a neural
controller that produces that activity. Animatlab natively supports neural control modeling alongside the mechanical modeling, which is the main deference between it and
other simulation software like OpenSim. Similar studies on cat [4, 5] and human [11,
25] have proposed control strategies that could help us develop a SNS that does so. The
resulting neural controller would expand upon our previous work using a two-level neural system [1]. The increased number and types of muscles in the system would require
the Pattern Formation Layer and muscle activation neurons to be expanded.
This hypothetical neural hierarchy (Fig. 8B) is similar to our previous designs
(Fig. 8A), but more complex. As was done previously, the new SNS will use separate rhythm generator and pattern formation layers to activate muscles in the leg and
generate forward walking. The main difference will be in the pattern formation network:
Instead of using two pairs of synergies to control 6 muscles, we will use 3 pairs of synergies to control 8 muscles. These 8 muscles are organized into muscle groups and color
coded in the SNS in Fig. 8B. Orange connections represent hip flexion; blue connections
represent hip extension; brown connections represent knee extension; black connections
represent knee flexion; green connections represent ankle plantarflexion; and the cyan
K. Deng et al.
4 Discussion
In this manuscript, we present a biomechanical model of a rat hindlimb with biarticular
muscles. This model is an expansion of our previous monoarticular model [1]. The
largest difference in biomechanics between the new model and the previous one is that
the number of muscles was increased from 6 to 8. This causes the forces acting about
the knee joint to be substantially different from those in our previous model. The knee
is now mostly controlled by biarticular muscles. The other joints’ muscles are perturbed
by the contraction of the biarticular muscles, but they function largely in the same way
as in the previous model (i.e. as antagonistic pairs of muscles). Another difference is the
knee and ankle synergies. Rather than producing a synergy by actuating these muscle
sets with the same pattern formation network [1], in this model, they are mechanically
coupled by the GA muscle.
In order to calculate the desired motoneuron activations, we used several new strategies in the inverse kinematics analysis. With the implementation of biarticular muscles,
our previous method to estimate muscle parameter values is no longer suitable. We
developed a more biomimetic technique which combines rat muscle data [12, 13] with
other researchers’ studies on muscle [15–18] to determine those parameter values. When
compared with other researchers’ reports [19, 20] of muscle parameter values, the similarities support that our approach is a feasible method for modeling biomimetic muscles.
Moreover, the new analysis includes the falling phase of the length-tension curve, which
models active tension production more accurately. Our previous work obtained the tension from the Hill muscle model, but the force buildup curve was different from that of
actual muscle. The fact that our calculated parameters are consistent with experimental
reports of the tension of rat soleus [21–24] suggests that our new method of tuning
length-tension characteristics is an improvement over our previous method. Also, when
analyzing the passive tension in different phases of walking, we found that the passive
tension in the muscles is strongly related to joint motion.
Calculating the desired motoneuron activity makes it possible to develop a neural
controller that produces that activity. Animatlab natively supports neural control modeling alongside the mechanical modeling, which is the main deference between it and
other simulation software like OpenSim. Similar studies on cat [4, 5] and human [11,
25] have proposed control strategies that could help us develop a SNS that does so. The
resulting neural controller would expand upon our previous work using a two-level neural system [1]. The increased number and types of muscles in the system would require
the Pattern Formation Layer and muscle activation neurons to be expanded.
This hypothetical neural hierarchy (Fig. 8B) is similar to our previous designs
(Fig. 8A), but more complex. As was done previously, the new SNS will use separate rhythm generator and pattern formation layers to activate muscles in the leg and
generate forward walking. The main difference will be in the pattern formation network:
Instead of using two pairs of synergies to control 6 muscles, we will use 3 pairs of synergies to control 8 muscles. These 8 muscles are organized into muscle groups and color
coded in the SNS in Fig. 8B. Orange connections represent hip flexion; blue connections
represent hip extension; brown connections represent knee extension; black connections
represent knee flexion; green connections represent ankle plantarflexion; and the cyan