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Multi-Scale Modelling of the Neuromuscular System -- Coupling Received: 21 January 2019 Revised: 13 May 2019 Accepted: 14 May 2019 DOI: 10.1002/wsbm.1457 ADVANCED REVIEW Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics Oliver Röhrle1,2 | Utku S¸. Yavuz1,3 | Thomas Klotz1,2 | Francesco Negro4 | Thomas Heidlauf5 1Institute for Modelling and Simulation of Biomechanical Systems, University of Abstract Stuttgart, Stuttgart, Germany Mathematical models and computer simulations have the great potential to substan- 2Stuttgart Center for Simulation Sciences tially increase our understanding of the biophysical behavior of the neuromuscular (SC SimTech), University of Stuttgart, system. This, however, requires detailed multiscale, and multiphysics models. Stuttgart, Germany Once validated, such models allow systematic in silico investigations that are not 3Biomedical Signals and Systems, Universiteit Twente, Enschede, necessarily feasible within experiments and, therefore, have the ability to provide The Netherlands valuable insights into the complex interrelations within the healthy system and for 4 Department of Clinical and Experimental pathological conditions. Most of the existing models focus on individual parts of Sciences, Universià degli Studi di Brescia, Brescia, Italy the neuromuscular system and do not consider the neuromuscular system as an 5EPS5 – Simulation and System Analysis, integrated physiological system. Hence, the aim of this advanced review is to facili- Hofer pdc GmbH, Stuttgart, Germany tate the prospective development of detailed biophysical models of the entire neu- romuscular system. For this purpose, this review is subdivided into three parts. The Correspondence Oliver Röhrle, Institute for Modelling and first part introduces the key anatomical and physiological aspects of the healthy Simulation of Biomechanical Systems, neuromuscular system necessary for modeling the neuromuscular system. The sec- University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany. ond part provides an overview on state-of-the-art modeling approaches rep- Email: [email protected] resenting all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system Funding information Baden Württemberg Stiftung, Grant/Award model is introduced. The integrated system model combines existing models of the Number: High Performance Computing II; motor neuron pool, of the sensory system and of a multiscale model describing the Deutsche Forschungsgemeinschaft, mechanical behavior of skeletal muscles. Since many sub-models are based on Grant/Award Number: ExC 310/2 and ExC 2075 strictly biophysical modeling approaches, it closely represents the underlying phys- iological system and thus could be employed as starting point for further improve- ments 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 KEYWORDS biophysical modeling, continuum mechanics, motor neuron, multiphysics, multiscale, neuromuscular system, skeletal muscle WIREs Syst Biol Med. 2019;e1457. wires.wiley.com/sysbio © 2019 Wiley Periodicals, Inc. 1of43 https://doi.org/10.1002/wsbm.1457 2of43 RÖHRLE ET AL. 1 | INTRODUCTION The complex interplay between the neural system and the musculoskeletal system leads to movement. The muscles act hereby as actuators transforming signals from specialized neurons (motor neurons) into mechanical force and contractile motion. The nervous system is responsible for processing the signals from central (conscious and automatic control) and peripheral (sen- sory) pathways to consciously control movement. In this sense, the neuromuscular system consists of a complex control sys- tem that integrates supraspinal (descending) and sensory (afferent) inflow, and actuators (contracting skeletal muscles). The supraspinal control comprises neural information from higher centers, that is, the motor cortex, the brain stem, cere- bellum and the basal ganglia. These higher centers provide voluntary (conscious) movement initiated by thoughts or emotions as a consequence of will (Krakauer & Ghez, 2000), as well as excitation patterns for sequential performance of automated movements (Yuste, MacLean, Smith, & Lansner, 2005). The sensory controls, that is, the reflex loops, control the amount of contraction by sensing the length and rate of change of length (contraction velocity) of muscle fibers and tendons to provide information about the position of our body in physical space as well as tactile information about objects and environment enclosing our body. The resulting neural drive is highly adaptable and changes due to aging, fatigue, motor skill or pain, neu- romuscular degeneration and spinal cord injury. The actuators, that is, the muscle-tendon-complexes, are composed of a hier- archical structure of extracellular matrix, of excitable (active) skeletal muscle cells and of tendinous structures connecting the excitable cells to the skeleton. Body movement is the result of a cascade of molecular processes turning chemical energy, for example, provided by the hydrolysis of adenosine triphosphate (ATP), into mechanical (contraction) and nonmechanical (heat) work. The overall system, the neuromuscular system, is a complex adaptive system, in which the biophysical state of individual elements can change according to various types of tasks and conditions (physiological and pathological). There exist numer- ous experimental studies that scrutinize the interplay between the neural drive and the corresponding motor output under dif- ferent conditions, such as aging (Enoka et al., 2003), fatigue (Gandevia, Allen, Butler, & Taylor, 1996), motor skill (Shadmehr, Smith, & Krakauer, 2010) or pain (Yavuz, Negro, Falla, & Farina, 2015), neuromuscular degeneration (Schmied, Pouget, & Vedel, 1999) and spinal cord injury (Shields, 2002). To investigate the neuromuscular system, many experimental studies link force and position control tasks to evaluate the performance of the motor system and its components, such as motor units (De Luca & Hostage, 2010; Negro, Yavuz, & Farina, 2016), spinal cord circuits (Magalhães et al., 2015; Yavuz et al., 2013), and the activity of descending tracts (Kristeva, Patino, & Omlor, 2007; Ushiyama et al., 2012). Despite substan- tial amount of experimental research, there exist due to the inherent complexity and the many cross-dependencies (feedback system) still substantial gaps in our physiological knowledge. The fact that many biophysical quantities are, from an experi- mental or ethical point of view, difficult or even impossible to determine (in particular, in human subjects and in vivo) makes our endeavor to gain a deeper understanding of the neuromuscular system an even harder challenge. Hence, to improve our understanding of the causality relation between neural input and motor output, one can, in addition to the experimental studies, use mathematical models to systematically analyze the physiological system and/or to augment missing data with in silico data. In this respect, mathematical modeling has the advantage to generate data in a controlled envi- ronment. This is usually impossible in experiments. Furthermore, detailed biophysical mathematical modeling provides an efficient mean to systematically analyze and reveal complex dependencies and interactions. Although there exist already some (mainly phenomenological) models of the neuromuscular system that significantly contributed to the knowledge of neuromus- cular physiology, for example, the works by Fuglevand, Winter, and Patla (1993) and Heckman and Binder (1991), detailed structural and biophysical models of skeletal muscle contraction and the motor neurons innervating the skeletal muscle, that is, the muscle control, are almost nonexistent. However, detailed biophysical models are essential for revealing the full power of an in silico laboratory to investigate the behavior of the modeled system under normal and pathological conditions. The aim of this advanced review is to ease the barrier of developing and utilizing detailed biophysical, multiscale models of the healthy neuromuscular system. In this sense, we split the review into three parts. The first part (Section 2) is concerned with key aspects of the anatomy and physiology of the neuromuscular system and thus represents the basis for developing bio- physical models of the neuromuscular system. The second part (Section 3) provides an extensive overview of existing compu- tational models and modeling approaches of parts of the neuromuscular system. While an integrated physiological model of the neuromuscular system ideally would resolve all structures and phenomena presented in Section 2, the state-of-the-art review section also includes a brief overview on the capabilities and limitations of existing modeling approaches. In the last part (Section 4), we pick specific examples of cutting-edge models of parts of the neuromuscular system and outline how they join together to obtain a comprehensive, biophysically based model of the neuromuscular system. The specific examples, which can also be downloaded or are provided within the Supporting Information, can be considered as a tutorial. They are RÖHRLE ET AL. 3of43 chosen to introduce the general concepts of biophysical models, that is, by describing the original model of
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