Modelling the passive and nerve activated response of the rectus femoris muscle to a flexion loading: a finite element framework.

A muscle modelling framework is presented which relates the mechanical response of the rectus femoris muscle (at the organ level) to tissue level properties, with the capability of linking to the cellular level as part of the IUPS Physiome Project. This paper will outline our current approach to muscle modelling incorporating micro-structural passive and active properties including fibre orientations and nerve innervation. The technique is based on finite deformation (using FE analysis) coupled to electrical nerve initiated muscle activation, and we present the influence of active tension through an eccentric contraction at specific flexion angles. Finally we discuss the future goals of incorporating cell mechanics and validating at the organ level to provide a complete diagnostic tool with the ability to relate mechanisms of failure across spatial scales.

An anatomical model of the gastric system for producing bioelectric and biomagnetic fields.

Between 60 and 70 million people in the United States are affected by gastrointestinal disorders. Many of these conditions are difficult to assess without surgical intervention and accurate noninvasive techniques to aid in clinical assessment are needed. Through the use of a superconducting quantum interference device (SQUID) gradiometer, the weak magnetic field generated as a result of muscular activity in the digestive system can be measured. However, the interpretation of these magnetic recordings remains a significant challenge. We have created an anatomically realistic biophysically based mathematical model of the human digestive system and using this model normal gastric electrical control activity (ECA) has been simulated. The external magnetic fields associated with this gastric ECA have also been computed and are shown to be in qualitative agreement with recordings taken from normal individuals. The model framework thus provides a rational basis from which to begin interpreting magnetic recordings from normal and diseased individuals.

Anatomically realistic torso model for studying the relative decay of gastric electrical and magnetic fields.

Non-invasive assessment of the gastro-intestinal system has not obtained widespread clinical acceptance despite the fact that the first electrogastrograms were recorded almost a century ago. One technique that is gaining acceptance for non-invasively assessing the gastrointestinal system is the recording of cutaneous electrogastrograms. It has been proposed that measurement of the gastric magnetic field (magnetogastrogram) may produce more reliable signals in the form of a vector field and also allows the signals to be obtained with non-contact sensors. In this study, an anatomically realistic torso model of the gastrointestinal system is used to investigate the relative decay of electrical and magnetic fields resulting from gastric electrical activity. Typically the electrical fields are measured on the skin surface while the magnetic fields are recorded at locations close to, but not in contact with the skin surface. This is the first study which has used a temporal and multiple dipole source model to simulate resultant electrical and magnetic fields.

Computational simulations of the human magneto- and electroenterogram.

Many functional pathologies of the small intestine are difficult to diagnose clinically without an invasive surgical intervention. Often such conditions are associated with a disruption of the normal electrical activity occurring within the musculature of the small intestine. The far field electrical signals on the torso surface arising from the electrical activity within the small intestine cannot be reliably measured. However, it has been shown that abnormal electrical activity in the small intestine can be distinguished by recording the magnetic fields of intestinal origin immediately outside the torso surface. We have developed an anatomically-based computational model to simulate slow wave propagation in the small intestine, the resulting cutaneous electrical field and the magnetic field outside the torso. Using both a one-dimensional and a three-dimensional model of the duodenum we investigate the degree of detail that is required to realistically simulate this far field activity. Our results indicate that some of the qualitative behavior in the far field activity can be replicated using a one-dimensional model, although there are clear situations where the greater level modeling detail is required.

Multiscale modelling of human gastric electric activity: can the electrogastrogram detect functional electrical uncoupling?

During recent years there has been a growing interest in the assessment of gastric electrical health through cutaneous abdominal recordings. The analysis of such recordings is largely limited to an inspection of frequency dynamics, and this has raised doubts as to whether functional gastric electrical uncoupling can be detected using this technique. We describe here a computational approach to the problem in which the equations governing the underlying physics of the problem have been solved over an anatomically detailed human torso geometry. Cellular electrical activity was embedded within a stomach tissue model, and this was coupled to the torso using an equivalent current source approach. Simulations were performed in which normal and functionally uncoupled (through the introduction of an ectopic antral pacemaker) gastric slow wave activity was present, and corresponding cutaneous electrogastrograms were produced. These were subsequently analysed using the currently recommended techniques, and it was found that the functionally uncoupled situation was indistinguishable from normal slow wave activity using this approach.

From cell to body surface: a fully coupled approach.

Different types of equivalent cardiac sources are often used in the forward problem of electrocardiology. These may not be adequate to accurately reproduce the body surface potentials that are the result of cellular electrical activity, because they do not guarantee current conservation across the myocardial surfaces. Presented here are the outlines of 2 new coupling techniques that seek to overcome this problem by creating a continuous electrical pathway from the cellular level through to the body surface. The first technique directly couples the extracellular cardiac bidomain region to the surrounding passive torso regions creating a single system of equations without the need for matrix inversions. The second technique uses a fixed point iteration across each myocardial surface that has the goal of matching the potential fields and current flows across the cardiac boundaries into the neighbouring tissues. These techniques can be combined, directly coupling some regions and iterating across other region boundaries. Simulations on a transverse two-dimensional slice through a human male torso are presented, showing the convergence of these methods.

Computing work in the ischemic heart.

This study analyzes the effect of a poorly perfused (ischemic) region on active tension and strain at a point in a model of the cardiac ventricles. The cellular active mechanics and electrophysiology were calculated using a coupled electromechanical cell model. The deformation of the heart was calculated combining an anisotropic constitutive law with the active tension generated by the cell models. An ischemic cell model was developed by adapting the Noble 98-HMT cell model parameters. The ischemic model exhibits a raised resting potential, shortened action potential duration and reduced amplitude. Ischemic cells were introduced into the heart model in the anterior wall of the left ventricle. The model was solved with and in the absence of the ischemic region. The stress and strains at a point located in the ischemic region were calculated. The ischemic cell model produced negligible amounts of active tension and this reduced the work load of ischemic cells by several orders of magnitude. The ischemic region had a significant effect on pump function in both the left and right ventricles.

An anatomically based model of small intestine excitation.

Electrical and magnetic fields are generated by the smooth muscle's electrical activity in the walls of the gastrointestinal system. These fields can be measured on the torso surface. We present a computational model that is capable of simulating the electrical activity occurring within the small intestine. Finite elements were used to represent the geometry of the small intestine. A finer resolution finite difference mesh was defined within this geometrical mesh and used to solve the equations governing the activation of the intestinal smooth muscle. Initial simulations were performed to illustrate the spread of potential along the small intestine. With further development this model will provide a basis for understanding and interpreting noninvasive magnetic measurements from intestinal smooth muscle.