Computational model for the analysis of cartilage and cartilage tissue constructs.

We propose a new non-linear poroelastic model that is suited to the analysis of soft tissues. In this paper the model is tailored to the analysis of cartilage and the engineering design of cartilage constructs. The proposed continuum formulation of the governing equations enables the strain of the individual material components within the extracellular matrix (ECM) to be followed over time, as the individual material components are synthesized, assembled and incorporated within the ECM or lost through passive transport or degradation. The material component analysis developed here naturally captures the effect of time-dependent changes of ECM composition on the deformation and internal stress states of the ECM. For example, it is shown that increased synthesis of aggrecan by chondrocytes embedded within a decellularized cartilage matrix initially devoid of aggrecan results in osmotic expansion of the newly synthesized proteoglycan matrix and tension within the structural collagen network. Specifically, we predict that the collagen network experiences a tensile strain, with a maximum of ~2% at the fixed base of the cartilage. The analysis of an example problem demonstrates the temporal and spatial evolution of the stresses and strains in each component of a self-equilibrating composite tissue construct, and the role played by the flux of water through the tissue.

Multiscale modeling of gastrointestinal electrophysiology and experimental validation.

Normal gastrointestinal (GI) motility results from the coordinated interplay of multiple cooperating mechanisms, both intrinsic and extrinsic to the GI tract. A fundamental component of this activity is an omnipresent electrical activity termed slow waves, which is generated and propagated by the interstitial cells of Cajal (ICCs). The role of ICC loss and network degradation in GI motility disorders is a significant area of ongoing research. This review examines recent progress in the multiscale modeling framework for effectively integrating a vast range of experimental data in GI electrophysiology, and outlines the prospect of how modeling can provide new insights into GI function in health and disease. The review begins with an overview of the GI tract and its electrophysiology, and then focuses on recent work on modeling GI electrical activity, spanning from cell to body biophysical scales. Mathematical cell models of the ICCs and smooth muscle cell are presented. The continuum framework of monodomain and bidomain models for tissue and organ models are then considered, and the forward techniques used to model the resultant body surface potential and magnetic field are discussed. The review then outlines recent progress in experimental support and validation of modeling, and concludes with a discussion on potential future research directions in this field.

A mathematical model of fatigue in skeletal muscle force contraction.

The ability for muscle to repeatedly generate force is limited by fatigue. The cellular mechanisms behind muscle fatigue are complex and potentially include breakdown at many points along the excitation-contraction pathway. In this paper we construct a mathematical model of the skeletal muscle excitation-contraction pathway based on the cellular biochemical events that link excitation to contraction. The model includes descriptions of membrane voltage, calcium cycling and crossbridge dynamics and was parameterised and validated using the response characteristics of mouse skeletal muscle to a range of electrical stimuli. This model was used to uncover the complexities of skeletal muscle fatigue. We also parameterised our model to describe force kinetics in fast and slow twitch fibre types, which have a number of biochemical and biophysical differences. How these differences interact to generate different force/fatigue responses in fast- and slow- twitch fibres is not well understood and we used our modelling approach to bring new insights to this relationship.

Anatomically based lower limb nerve model for electrical stimulation.

BACKGROUND: Functional Electrical Stimulation (FES) is a technique that aims to rehabilitate or restore functionality of skeletal muscles using external electrical stimulation. Despite the success achieved within the field of FES, there are still a number of questions that remain unanswered. One way of providing input to the answers is through the use of computational models. METHODS: This paper describes the development of an anatomically based computer model of the motor neurons in the lower limb of the human leg and shows how it can be used to simulate electrical signal propagation from the beginning of the sciatic nerve to a skeletal muscle. One-dimensional cubic Hermite finite elements were used to represent the major portions of the lower limb nerves. These elements were fit to data that had been digitised using images from the Visible Man project. Nerves smaller than approximately 1 mm could not be seen in the images, and thus a tree-branching algorithm was used to connect the ends of the fitted nerve model to the respective skeletal muscle. To simulate electrical propagation, a previously published mammalian nerve model was implemented and solved on the anatomically based nerve mesh using a finite difference method. The grid points for the finite difference method were derived from the fitted finite element mesh. By adjusting the tree-branching algorithm, it is possible to represent different levels of motor-unit recruitment. RESULTS: To illustrate the process of a propagating nerve stimulus to a muscle in detail, the above method was applied to the nerve tree that connects to the human semitendinosus muscle. A conduction velocity of 89.8 m/s was obtained for a 15 mum diameter nerve fibre. This signal was successfully propagated down the motor neurons to a selected group of motor units in the muscle. CONCLUSION: An anatomically and physiologically based model of the posterior motor neurons in the human lower limb was developed. This model can be used to examine the effect of external stimulation on nerve and muscle activity, as may occur, for example, in the field of FES.