Modelling the Musculoskeletal System

Mathematical models and computer simulations have great potential to increase our understanding of the neuromuscular system. In particular, integrated physiological system models allow us to test hypotheses and observe variables that cannot be recorded in vivo. Our group aims to develop a detailed biophysical model of the entire neuromuscular system (see Röhrle et al. 2019). This integrated physiological system model combines sub-models describing motor neuron pools, the sensory system, and skeletal muscles.

Active research focus areas:

• The integration of sensory signals by motor neuron pools, e.g., Schmid et al. 2024
• The impact of the 3D motor unit architecture in muscles, e.g., Saini et al. 2023 
• Integration of model components in biophysical system models, e.g., Haggie et al. 2023

Human movement requires the coordinated interaction of multiple muscles. However, the influence of many biomechanical factors, such as a muscle's pre-stretch, contact stresses, tissue anatomy, and neuromuscular physiology, is not well-explored. We have developed unique 3D continuum mechanical musculoskeletal system models to perform such investigations.

Active research focus areas:

• Upper arm modelling, consisting of six muscles capable of flexion/extension and supination/pronation to investigate muscle and motor-unit synergies for applications in ergonomics, human-machine -interaction, and sports and rehabilitation
• Pervasive simulation to bridge the gap between resource-poor systems like laptops or tablets and complex biomechanical simulation tasks (PerSiVal project). This enables real-time simulation, e.g., for visualization or in virtual/augmented reality environments. 

This is in close collaboration with the IPVS and VISUS at the University of Stuttgart and the Fraunhofer IPA.

The central nervous system can voluntarily control skeletal muscles, enabling us to move and interact with the outside world. This is achieved through a complex signaling cascade: (i) the neural control signals cause electric signals, known as action potentials, to transmit this control signal through the whole muscle; (ii) the action potentials trigger the release of biochemical signaling molecules that (iii) activate microscopic molecular motors. Modeling this signaling pathway requires considering phenomena on different time and length scales. Our chemo-electro-mechanical models tackle this challenge and resolve the most relevant aspects of skeletal muscle anatomy and physiology within organ-scale continuum models.

The chemo-electro-mechanical skeletal muscle model has multiple applications:

• Simulation-enhanced investigations of EMG and MMG signals
  
• Quantification of the delay between the electric muscle activation and a measurable force response.
• Influence of muscle fiber types and the 3D motor unit architecture. 

The chemo-electro-mechanical skeletal muscle model is computationally expensive. Optimizing the utilized numerical methods is also a focus area in our research group.

Modelling skeletal muscle tissue within the framework of continuum mechanics demands suitable constitutive material models on the macroscopic (organ) scale. This is also the fundamental requirement for reliable three-dimensional muscle simulations using the finite-element method. Commonly used phenomenological constitutive approaches, which have to be calibrated to macroscopic experimental material tests, suffer from the high inter- and intra-tissue variability of skeletal muscle tissue and the lack of individual experiments for the specific type of muscle to be modelled. The high variations in the tissue properties are hereby originated in the highly heterogeneous microstructure of the tissue.

Hence, our research group focuses on the development and consistent formulation of novel multi-scale material models for skeletal muscle tissue. These models directly take into account the significant microstructural features, for which a lot of experimental data is available. For instance, the model directly incorporates a comprehensive formulation for the collagenous structures of the extracellular matrix, including the description of collagen fibre stiffness and the dispersion of collagen fibres. Suitable homogenisation methods are developed and applied to get the wanted macroscopic constitutive behaviour. In contrast to phenomenological approaches, the proposed multi-scale model and its underlying idea of a rigorous bottom-up framework is able to answer questions like, for instance:

• How do microstructural changes (for example, due to diseases) influence the overall behaviour of skeletal muscles?
• What kind of direction-dependent behaviour on the organ scale results from the arrangement of structures on the microscale?
• How does the stiffness of single collagen fibres influence the stress distribution of the whole muscle?

The novel multi-scale model is an important step towards subject-specific material models.

This is done in close collaboration with the University of Pennsylvania, USA.

Human motion ranges from sprinting to marathon running. This is only possible as skeletal muscles are highly adaptive, and skeletal muscle fibers have evolved to be the only cells that can deal with a 100-fold range of energy demands. However, the control mechanisms of ATP homeostasis (i.e., the fuel of a cell) and, hence, muscle fatigue are only partially understood. We are developing a computational model that captures the undelaying cellular biochemical reactions to test different hypotheses regarding the regulation of ATP metabolism and to investigate how muscle manages perturbations in energy demands. This allows us to relate the cellular function with in vivo biomechanical data recorded during physical exercise. This is essential to improve therapies for patients showing abnormal fatigability (e.g., chronic fatigue syndrome) and training in athletics.

Skeletal muscles play an important role in overall health; from movement range, resistance and strength, to protein reservoir, muscles have the ability to adapt to any specific intensity of physical activity. A particular adaptation feature can be targeted by means of exercise. In principle, there are two kinds of training protocols: training for resistance and training for endurance, but a combination of these two protocols lead to intermediate outcomes.

Exercise, mechanical, or electrical stimuli trigger biochemical responses known as signaling pathways. These pathways control the adaptation processes at the cell level. Muscle cells are also known as muscle fibers, and there are many fiber types that share characteristics with one of two categories: some muscle cells (known as Type I fibers) adapt to sustained activities such as walking, or running a marathon, and are fatigue resistant; other cells (known as Type II fibers) adapt to activities that require force or power, such as sprinting, but are easily fatigable. As any muscle has a different proportion of fiber types, an adaptation process involves the transition between fiber types.

The aim of this research is to model the hypertrophy, atrophy, and fiber shifting processes of muscle tissue as the outcome of different training protocols. We assume that the training input stimulates a biochemical system that drives the protein content and fiber shifting of the tissue, and as a consequence, the model predicts force and fatigue adaptation. This is in collaboration with the National University of Colombia (Bogotá).