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Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

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Abstract Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state‐of‐the‐art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub‐models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Electrical circuit model for the motor neuron model. Again, resistors with an arrow indicate voltage‐dependent conductance. The dendritic membrane potential, Vmd, equals the difference between the dendritic intracellular potential, ϕid, and the extracellular potential, ϕe. The somatic membrane potential, Vms, equals the difference between the somatic intracellular potential, ϕis, and the extracellular potential, ϕe. The driving forces in the model are the differences between the membrane potentials and the corresponding equilibrium potentials, which are represented by batteries
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Illustration electrical equivalent circuit, which was used by Hodgkin and Huxley () to mimic the electrical behavior of the membrane of the squid giant axon. Resistors with an arrow indicate voltage‐dependent conductances. The membrane potential, Vm, equals the difference between the intracellular potential, ϕi, and the extracellular potential, ϕe. The driving forces in the model are the differences between the membrane potential and the corresponding equilibrium potentials, which are represented by batteries
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Schematic representation of the excitation‐contraction coupling in a muscle fiber (Adapted from Röhrle, Neumann, and Heidlauf ())
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The influence of the contraction velocity on the force generation of a skeletal muscle
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Normalized active force‐length relationship derived from the geometrical overlap of the thin and the thick filaments (cf. Gordon et al., ). The gray color highlights the working range of most of the sarcomeres
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Structure of a sarcomere. On the left side, an image of a sarcomere is shown, while the right side shows the schematic structure of a sarcomere including thick, thin, and titin filaments as well as the Z‐discs and M‐disc (Figure modified from Sameerb at http://en.wikipedia.org/ with permission)
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Structure of a skeletal muscle. Original image© by OpenStax Anatomy and Physiology
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Schematic drawing of an action potential
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The neuromuscular pathway of movement: The figure illustrates the simplified flow of neuromuscular interaction with its three essential components: (a) neural drive comprises projection from supraspinal centers (solid lines), afferent feedbacks (dashed lines) from two exemplary proprioceptive sensory cells, that is, muscle spindle and Golgi tendon organs (Golgi TO) on spinal motor neurons (αMN) and gamma motor neurons (γMNs). The scheme includes ascending branches of sensory afferents which contribute primary somatosensory cortex (orange shade on the brain figure). (b) The excitation‐contraction part shows excitation of extrafusal and intrafusal muscle fibers by αMN and γMNs, respectively. (c) The multidirectional joint torque is depicted as a resultant of the neuromuscular interaction
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Schematic drawing of the motor neuron pool model; the figure illustrates the structure of a model that simulates a pool with 100 αMNs. Thereby the size and thus the electrical properties of the MNs changes through the pool exponentially. Motor neurons receive inputs from different classes of inputs signals. The independent input, that is, IINi, is represented by Gaußian noise with a bandwidth of 0–100 Hz. The common input signal represents the linear combination of a mean component, that is, ICIm, a Gaußian noise component (bandwidth 0.5–40 Hz), that is, ICIn, and the secondary common input, that is, ISI, corresponding to oscillations generated from other structures of the central nervous system and which is also modeled as zero mean Gaußian noise (bandwidth 0–100 Hz). The output of the model is the firing trains of αMNs
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Schematic representation of the model of Shorten et al. (), indicating its components and their interactions. Therein, (a) indicates the model of the membrane ionic currents, (b) is the Ca2+‐release model, (c) denotes the Ca2+‐dynamics model, (d) is the model of the XB dynamics, and (e) shows the fatigue model. The figure is taken from Heidlauf ()
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Schematic representation of the structure of the biophysical model of the neuromuscular system. The MN pools integrate descending inputs from the central nervous system and feedback signals from sensory organs such as the muscle spindles. Note that currently there exists no suitable model for the γMN pool and thus simulations of the integrated model rely on assumptions such as co‐activation between the αMN pool and the corresponding γMN pool. The discharge trains calculated by the motor neuron model are used to drive the multiscale skeletal muscle model by stimulating the membranes of the muscle fibers belonging to the corresponding MU. Thereby both macroscopic quantities such as the overall muscle force output and internal states such as the concentrations of specific ions can be observed. Furthermore, the sensory feedback of the muscle spindles is calculated based on the current deformation, the rate of deformation and the applied γ‐activation
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Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Analytical and Computational Methods > Computational Methods
Physiology > Mammalian Physiology in Health and Disease

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