During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

Cerebral palsy results from an upper motor neuron lesion and has significant effects on skeletal muscle stiffness throughout the body. The increased stiffness that occurs is partly a result of changes in the microstructural components of muscle. In particular, alterations in extracellular matrix, sarcomere length, fibre diameter, and fat content have been reported; however, experimental studies have shown wide variability in the degree to which each component is altered. Many studies have reported alterations in the extracellular matrix, while others have reported no changes. A consistent finding throughout the literature is increased sarcomere length in cerebral palsy muscle. Often more than one component is altered, making it difficult to determine the individual effects on stiffness. The purpose of this study is to use a modeling approach to isolate individual effects of microstructural alterations that typically occur during cerebral palsy on whole muscle behavior; in particular, the extracellular matrix volume fraction, stiffness, and sarcomere length. These microstructural effects can be captured using a three dimensional model of muscle. We found that the extracellular matrix volume fraction has a larger effect on stiffness compared to sarcomere length, even when coupled with decreased extracellular matrix stiffness. Additionally, the effects of sarcomere length in passive stiffness are mitigated by the increased extracellular matrix volume fraction. Using this model, we can achieve a better understanding of the possible combinations of microstructural changes that can occur during cerebral palsy. Developing these insights into diseased muscle tissue will help to direct future clinical and experimental procedures.

Pulmonary arterial hypertension (PAH) is a rare disorder characterized by elevated blood pressure and pulmonary vascular resistance, often followed by right ventricular hypertrophy and heart failure. The effect of PAH and its treatments on the mechanics, function, and remodelling of the right ventricle (RV) is currently not well understood. To study cardiac biomechanics and functionality as PAH progresses, we implemented a computational model of the heart simulating right ventricular maladaptive remodelling. Our Windkessel-based model, which accounts for direct ventricular interaction and the presence of the pericardium, is utilized to simulate various disease stages of PAH. We find that the pericardium has a larger effect on heart performance than ventricular interaction through the septum.We also examined the effectiveness of two treatments, ventricular assist device (RVAD) and atrial septostomy, on diseased hearts. We show that while both pulsatile and continuous RVADs restore cardiac function, pulsatile RVAD improves cardiac output 29.4% more than continuous RVAD. We also demonstrate that atrial septostomy improves cardiac output by 19.5%. Our model can be further extended by simulating the heart’s response to other treatments such as extracorporeal membrane oxygenation (ECMO), and by incorporating ventricular remodelling growth simulations and finite-element ventricular modelling.

Cerebral palsy results from an upper motor neuron lesion and significantly affects skeletal muscle stiffness. The increased stiffness that occurs is partly a result of changes in the microstructural components of muscle. In particular, alterations in extracellular matrix, sarcomere length, fibre diameter, and fat content have been reported; however, experimental studies have shown wide variability in the degree of alteration. Many studies have reported changes in the extracellular matrix, while others have reported no differences. A consistent finding is increased sarcomere length in cerebral palsy affected muscle. Often many components are altered simultaneously, making it difficult to determine the individual effects on muscle stiffness. In this study, we use a three dimensional modelling approach to isolate individual effects of microstructural alterations typically occurring due to cerebral palsy on whole muscle behaviour; in particular, the effects of extracellular matrix volume fraction, stiffness, and sarcomere length. Causation between the changes to the microstructure and the overall muscle response is difficult to determine experimentally, since components of muscle cannot be manipulated individually; however, utilising a modelling approach allows greater control over each factor. We find that extracellular matrix volume fraction has the largest effect on whole muscle stiffness and mitigates effects from sarcomere length.