Using Animatlab for Neuromechanical Analysis
411
Muscles are complex organs whose activity is varied over time and dependent largely
on biological and situational context. Reducing a muscle to a spring-damper system disregards certain biological aspects of muscle, such as fatigue [31], the dynamic response
to fast and slow contractions [32], and muscle energetics [33]. Additionally, a linear
model does not include the asymmetric velocity profile in which the muscle activity
differs while lengthening or contracting [19]. Understanding the limitations incurred by
reduced models can help guide future implementations of neuromechanical models and
contextualize analytical results when compared to experimental data.
When actual muscle is not activated and below its resting length, it, like the model,
will not generate any tension. The model, though, treats tension like a switch and sets it
to zero discontinuously when a critical combination of stimulation and length is crossed.
Unlike real muscle, which generates a continuous tension profile while activation and
deactivating. As a result, muscles in Animatlab are susceptible to oscillations in the
tension profile when the muscle is resting near the discontinuous tension region.
For instance, while in a resting state and supported by a network of muscles, the
weight of the leg itself can lengthen a muscle and pull it in to or out of a discontinuous
tension region. In the case where the muscle is pulled out of a discontinuous tension
region, the tension will suddenly be “switched on”, causing the muscle to contract. When
the length shortens, the tension turns off again. This leads to an oscillatory cycle in which
the muscle is constantly moving in and out of the discontinuous tension region.
Abiding by the limitations described in this work, it is possible to mitigate many
of the problems associated with modeling muscles in Animatlab. However, the nonbiological aspects of a spring-damper system can still cause problems when trying to
represent muscle. The inclusion of biological components may provide a solution for
the limitations described.
Incorporating a series element damper in the model would be a way to represent
energy loss in the tendon that may prevent the muscle from oscillating. The current
series element is simply represented as an undamped spring, which could lead to oscillations. Minimizing the passive tension by reducing the magnitude of the parallel spring
element could shrink the size of the discontinuous tension region. The parallel element
stiffness is one of the only “free” muscle parameters that can be adjusted to change the
discontinuous tension region but doing so would also change the tension output proposed
by the optimization process. Modifying these elements would require changing how the
program calculates muscle tension at a fundamental level that is beyond the scope of
this work.
5 Conclusion
In this work, we have presented a methodology for formulating parameters for linear
Hill muscles in Animatlab. We have shown the mathematical basis for the derivation of
specific active and passive parameters, as well as the limitations for simulating muscles in
a discrete form. Through this work, it is possible to create neuromechanical simulations
that can be used to evaluate experimental data and develop our understanding of the
underlying mechanisms that control locomotion.
Future implementations of Animatlab could enhance the existing linear Hill model
through the inclusion of additional components in the spring-damper model, possibly
411
Muscles are complex organs whose activity is varied over time and dependent largely
on biological and situational context. Reducing a muscle to a spring-damper system disregards certain biological aspects of muscle, such as fatigue [31], the dynamic response
to fast and slow contractions [32], and muscle energetics [33]. Additionally, a linear
model does not include the asymmetric velocity profile in which the muscle activity
differs while lengthening or contracting [19]. Understanding the limitations incurred by
reduced models can help guide future implementations of neuromechanical models and
contextualize analytical results when compared to experimental data.
When actual muscle is not activated and below its resting length, it, like the model,
will not generate any tension. The model, though, treats tension like a switch and sets it
to zero discontinuously when a critical combination of stimulation and length is crossed.
Unlike real muscle, which generates a continuous tension profile while activation and
deactivating. As a result, muscles in Animatlab are susceptible to oscillations in the
tension profile when the muscle is resting near the discontinuous tension region.
For instance, while in a resting state and supported by a network of muscles, the
weight of the leg itself can lengthen a muscle and pull it in to or out of a discontinuous
tension region. In the case where the muscle is pulled out of a discontinuous tension
region, the tension will suddenly be “switched on”, causing the muscle to contract. When
the length shortens, the tension turns off again. This leads to an oscillatory cycle in which
the muscle is constantly moving in and out of the discontinuous tension region.
Abiding by the limitations described in this work, it is possible to mitigate many
of the problems associated with modeling muscles in Animatlab. However, the nonbiological aspects of a spring-damper system can still cause problems when trying to
represent muscle. The inclusion of biological components may provide a solution for
the limitations described.
Incorporating a series element damper in the model would be a way to represent
energy loss in the tendon that may prevent the muscle from oscillating. The current
series element is simply represented as an undamped spring, which could lead to oscillations. Minimizing the passive tension by reducing the magnitude of the parallel spring
element could shrink the size of the discontinuous tension region. The parallel element
stiffness is one of the only “free” muscle parameters that can be adjusted to change the
discontinuous tension region but doing so would also change the tension output proposed
by the optimization process. Modifying these elements would require changing how the
program calculates muscle tension at a fundamental level that is beyond the scope of
this work.
5 Conclusion
In this work, we have presented a methodology for formulating parameters for linear
Hill muscles in Animatlab. We have shown the mathematical basis for the derivation of
specific active and passive parameters, as well as the limitations for simulating muscles in
a discrete form. Through this work, it is possible to create neuromechanical simulations
that can be used to evaluate experimental data and develop our understanding of the
underlying mechanisms that control locomotion.
Future implementations of Animatlab could enhance the existing linear Hill model
through the inclusion of additional components in the spring-damper model, possibly