Enabling Detailed, Biophysics-Based Skeletal Muscle Models on HPC Systems

Investigating the spatial resolution of EMG and MMG based on a systemic multi-scale model

While electromyography (EMG) and magnetomyography (MMG) are both methods to measure the electrical activity of skeletal muscles, no systematic comparison between both signals exists. Within this work, we propose a novel in silico model for EMG and MMG and test the hypothesis that MMG surpasses EMG in terms of spatial selectivity, i.e. the ability to distinguish spatially shifted sources. The results show that MMG provides a slightly better spatial selectivity than EMG when recorded directly on the muscle surface. However, there is a remarkable difference in spatial selectivity for non-invasive surface measurements. The spatial selectivity of the MMG components aligned with the muscle fibres and normal to the body surface outperforms the spatial selectivity of surface EMG. Particularly, for the MMG’s normal-to-the-surface component the influence of subcutaneous fat is minimal. Further, for the first time, we analyse the contribution of different structural components, i.e. muscle fibres from different motor units and the extracellular space, to the measurable biomagnetic field. Notably, the simulations show that for the normal-to-the-surface MMG component, the contribution from volume currents in the extracellular space and in surrounding inactive tissues, is negligible. Further, our model predicts a surprisingly high contribution of the passive muscle fibres to the observable magnetic field.

Characterization of Electromechanical Delay Based on a Biophysical Multi-Scale Skeletal Muscle Model

Skeletal muscles can be voluntary controlled by the somatic nervous system yielding an active contractile stress response. Thereby, the active muscle stresses are transmitted to the skeleton by a cascade of connective tissue and thus enable motion. In the context of joint perturbations as well as the assessment of the complexity of neural control, the initial phase of the muscle-tendon system's stress response has a particular importance and is analyzed by means of electromechanical delay (EMD). EMD is defined as the time lag between the stimulation of a muscle and a measurable change in force output. While EMD is believed to depend on multiple structures / phenomena, it is hard to separate their contributions experimentally. We employ a physiologically detailed, three-dimensional, multi-scale model of an idealized muscle-tendon system to analyze the influence of (i) muscle and tendon length, (ii) the material behavior of skeletal muscle and tendon tissue, (iii) the chemo-electro-mechanical behavior of the muscle fibers and (iv) neural control on EMD. Comparisons with experimental data show that simulated EMD values are within the physiological range, i.e., between 6.1 and 68.6 ms, and that the model is able to reproduce the characteristic EMD-stretch curve, yielding the minimum EMD at optimal length. Simulating consecutive recruitment of motor units increases EMD by more than 20 ms, indicating that during voluntary contractions neural control is the dominant factor determining EMD. In contrast, the muscle fiber action potential conduction velocity is found to influence EMD even of a 27 cm long muscle by not more than 3.7 ms. We further demonstrate that in conditions where only little pre-stretch is applied to a muscle-tendon system, the mechanical behavior of both muscle and tendon tissue considerably impacts EMD. Predicting EMD for different muscle and tendon lengths indicates that the anatomy of a specific muscle-tendon system is optimized for its function, i.e., shorter tendon lengths are beneficial to minimize the neural control effort for muscles primary acting as motor in concentric contractions.

Modelling the electrical activity of skeletal muscle tissue using a multi-domain approach

Electromyography (EMG) can be used to study the behaviour of the motor neurons and thus provides insights into the physiology of the central nervous system. However, due to the high complexity of neuromuscular control, EMG signals are challenging to interpret. While the exact knowledge of the excitation patterns of a specific muscle within an in vivo experimental setting remains elusive, simulations allow to systematically investigate EMG signals in a controlled environment. Within this context, simulations can provide virtual EMG data, which, for example, can be used to validate and optimise signal analysis methods that aim to estimate the relationship between EMG signals and the output of motor neuron pools. However, since existing methods, which are employed to compute EMG signals, exhibit deficiencies with respect to the physical model itself as well as with respect to numerical aspects, we propose a novel homogenised continuum model that closely resolves the electro-physiological behaviour of skeletal muscle tissue. The proposed model is based on an extension of the well-established bidomain model and includes a biophysically detailed description of the electrical activity within the tissue, which is due to the depolarisation of the muscle fibre membranes. In contrast to all other published EMG models, which assume that the electrical potential field for each muscle fibre can be calculated independently, the proposed model assumes that the electrical potential in the muscle fibres is coupled to the electrical potential in the extracellular space. We show that the newly proposed model is able to simulate realistic EMG signals and demonstrate the potential to employ the predicted virtual EMG signal in order to evaluate the goodness of automated decomposition algorithms.

An Efficient Modelling-Simulation-Analysis Workflow to Investigate Stump-Socket Interaction Using Patient-Specific, Three-Dimensional, Continuum-Mechanical, Finite Element Residual Limb Models

The lack of an efficient modelling-simulation-analysis workflow for creating and utilising detailed subject-specific computational models is one of the key reasons why simulation-based approaches for analysing socket-stump interaction have not yet been successfully established. Herein, we propose a novel and efficient modelling-simulation-analysis workflow that uses commercial software for generating a detailed subject-specific, three-dimensional finite element model of an entire residual limb from Diffusion Tensor MRI images in <20 min. Moreover, to complete the modelling-simulation-analysis workflow, the generated subject-specific residual limb model is used within an implicit dynamic FE simulation of bipedal stance to predict the potential sites of deep tissue injury. For this purpose, a nonlinear hyperelastic, transversely isotropic skeletal muscle constitutive law containing a deep tissue injury model was implemented in LS-DYNA. To demonstrate the feasibility of the entire modelling-simulation-analysis workflow and the fact that detailed, anatomically realistic, multi-muscle models are superior to state-of-the-art, fused-muscle models, an implicit dynamic FE analysis of 2-h bipedal stance is carried out. By analysing the potential volume of damaged muscle tissue after donning an optimally-fitted and a misfitted socket, i.e., a socket whose volume was isotropically shrunk by 10%, we were able to highlight the differences between the detailed individual- and fused-muscle models. The results of the bipedal stance simulation showed that peak stresses in the fused-muscle model were four times lower when compared to the multi-muscle model. The peak interface stress in the individual-muscle model, at the end of bipedal stance analysis, was 2.63 times lower than that in the deep tissues of the stump. At the end of the bipedal stance analysis using the misfitted socket, the fused-muscle model predicted that 7.65% of the residual limb volume was injured, while the detailed-model predicted 16.03%. The proposed approach is not only limited to modelling residual limbs but also has applications in predicting the impact of plastic surgery, for detailed forward-dynamics simulations of normal musculoskeletal systems.