A physiologically based, multi-scale model of skeletal muscle structure and function

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Abstract

Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle's response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modeling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle's response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modeling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibers and their grouping. Together with a well-established model of motor-unit recruitment, the electro-physiological behavior of single muscle fibers within motor units is computed and linked to a continuummechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenization. The effect of homogenization has been investigated by varying the number of embedded skeletal muscle fibers and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the tibialis anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modeling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behavior ranging from motor-unit recruitment to force generation and fatigue. © 2012 Röhrle, Davidson and Pullan.

Figures

  • FIGURE 1 |The tri-quadratic FE mesh of the tibialis anterior (TA). The shaded section represents the element boundaries that are aligned with the aponeurosis separating the superficial and deep compartments of the TA.
  • FIGURE 2 | Subfigure (A) shows the location of theTA within the lower limb; (B–D) show the muscle fibers associated with motor units 1, 5, and 10. Further (B) depicts the motor-unit territory center midpoint, C1, for motor unit 1 and (the sphere with) radius R1 that was used to select the fibers for motor unit 1.
  • Table 3 |Values of the coefficients and variables of the recruitment and rate coding model used within this framework.
  • Table 1 | Values for the fiber model (bidomain equations).
  • Table 2 | Computed conduction velocities based on different grid spacing for slow- and fast-twitch muscle fibers.
  • FIGURE 3 |The stimulation times of every second motor unit are shown with vertical strikes. It can be seen that the larger motor units become active later in the simulation and the average frequency of all motor units increases throughout the simulation. The sigmoidal shape of the force curve can be seen, with a slow average change in curvature at the beginning and
  • FIGURE 4 |The force output ofTA muscle simulation with mechanical fiber spacings of 2000, 1000, and 500 µm.
  • FIGURE 5 |The force output profiles of theTA with 10, 30, and 50 motor units. The sigmoidal shapes of the force profile can be clearly seen in the best-fit curves of the plots of 30 motor units and 50 motor units (dashed lines). The change in curvature of the 10 motor-unit simulation is more subtle. The variations in the base line force of the simulations are due to the changing location of the slow and fast fiber types. Increasing the number of motor units increases the maximum value of the force, which is also a result of fiber type location.

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APA

Röhrle, O., Davidson, J. B., & Pullan, A. J. (2012). A physiologically based, multi-scale model of skeletal muscle structure and function. Frontiers in Physiology, 3 SEP. https://doi.org/10.3389/fphys.2012.00358

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