Subject-specific, multiscale simulation of electrophysiology: a software pipeline for image-based models and application examples

Many simulation studies in biomedicine are based on a similar sequence of processing steps, starting from images and running through geometric model generation, assignment of tissue properties, numerical simulation and visualization of the results--a process known as image-based geometric modelling and simulation. We present an overview of software systems for implementing such a sequence both within highly integrated problem-solving environments and in the form of loosely integrated pipelines. Loose integration in this case indicates that individual programs function largely independently but communicate through files of a common format and support simple scripting, so as to automate multiple executions wherever possible. We then describe three specific applications of such pipelines to translational biomedical research in electrophysiology.

A software framework for solving bioelectrical field problems based on finite elements

Computational modeling and simulation can provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Commonly, the modeling is based on Maxwell's and Poisson's equations for electromagnetic and electric fields, respectively, and numerical techniques are applied for field calculation such as the finite element and finite differences methods. Focus of this work are finite element methods, which are based on an element-wise discretization of the spatial domain. These methods can be classified on the element's geometry, e.g. triangles, tetrahedrons and hexahedrons, and the underlying interpolation functions, e.g. polynomials of various order. Aim of this work is to describe finite element-based approaches and their application to extend the problem-solving environment SCIRun/BioPSE. Finite elements of various types were integrated and methods for interpolation and integration were implemented. General methods for creation of finite element system matrices and boundary conditions were incorporated. The extension provides flexible means for geometric modeling, physical simulation, and visualization with particular application in solving bioelectric field problems.

A Model of 3D Propagation in Discrete Cardiac Tissue

A model was developed of a bundle of cardiac fibers embedded in an extracellular space. In contrast to the classical bidomain approach, the model is constructed such that the intracellular and extracellular spaces are spatially distinct. The model was used to test the hypothesis that the distribution of the extracellular fluid in the tissue can affect the conduction velocity. The preliminary results suggest that under nominally normal conditions, the propagation speed depends on the fraction of extracellular space and less on the actual distribution of extracellular space within the bundle.

Modelling passive cardiac conductivity during ischaemia

The results of a geometric model of cardiac tissue, used to compute the bidomain conductivity tensors during three phases of ischaemia, are described. Ischaemic conditions were simulated by model parameters being changed to match the morphological and electrical changes of three phases of ischaemia reported in literature. The simulated changes included collapse of the interstitial space, cell swelling and the closure of gap junctions. The model contained 64 myocytes described by 2 million tetrahedral elements, to which an external electric field was applied, and then the finite element method was used to compute the associated current density. In the first case, a reduction in the amount of interstitial space led to a reduction in extracellular longitudinal conductivity by about 20%, which is in the range of reported literature values. Moderate cell swelling in the order of 10-20% did not affect extracellular conductivity considerably. To match the reported drop in total tissue conductance reported in experimental studies during the third phase of ischaemia, a ten fold increase in the gap junction resistance was simulated. This ten-fold increase correlates well with the reported changes in gap junction densities in the literature.

Clinical implications of fetal magnetocardiography

OBJECTIVES

To test the usefulness and reliability of fetal magnetocardiography as a diagnostic or screening tool, both for fetuses with arrhythmias as well as for fetuses with a congenital heart defect.

METHODS

We describe 21 women with either a fetal arrhythmia or a congenital heart defect discovered during prenatal evaluation by sonography. Four fetuses showed a complete atrioventricular block, two an atrial flutter, nine ventricular extrasystole, and one a complete irregular heart rate. Five fetuses were suspected to have a congenital heart defect. In all cases magnetocardiograms were recorded.

RESULTS

Nine fetuses with extrasystole showed a range of premature atrial contractions, premature junctional beats or premature ventricular contractions. Two fetuses with atrial flutter showed typical flutter waves and four fetuses with complete atrioventricular block showed an uncoupling of P-wave and QRS complex. One fetus showed a pattern suggestive of a bundle branch block. In three of four fetuses with confirmed congenital heart defects the magnetocardiogram showed abnormalities.

CONCLUSION

Fetal magnetocardiography allows an insight into the electrophysiological aspects of the fetal heart, is accurate in the classification of fetal arrhythmias, and shows potential as a tool in defining a population at risk for congenital heart defects.

The influence of fetoabdominal tissues on fetal ECGs and MCGs

Both fetal electrocardiography and fetal magnetocardiography are influenced by the volume conduction within the abdomen of the pregnant woman. In this paper, various models are used to simulate this influence. Such models are helpful to determine where to attach electrodes at the maternal abdomen in case fetal ECGs are measured and where to position the magnetocardiograph in case fetal MCGs are measured. Another goal is to assess the influence of individual differences, such as the amount of amniotic fluid. Seven models based on MR-images have been created, four for the third trimester of gestation, with the fetus in left occiput position, and three for the second trimester. The models consist of four compartments; the fetus, the vernix caseosa, the amniotic fluid, and the remainder of the maternal abdomen. It turns out that individual differences have a large impact on the fetal MCG and that the best measurement positions are expected over the centre of the abdomen near the fetal heart. The fetal ECG is dependent on the vernix caseosa and when this layer is present, the fetal ECG is best measured by two electrodes, one over the fetal mouth and the other over the bottom of the fetus.

The passive DC conductivity of human tissues described by cells in solution

The electrical conductivity of human tissue at low frequencies is discussed when a uniform electric field is applied to some tissue containing many cells. Human tissue is described as a suspension of particles in a conducting solution. Relations are derived for the apparent conductivity of a cell surrounded by a membrane. These relations can be used to estimate the accuracy of a model that considers the cell as a non-conducting particle. Usually, a tissue is composed of several types of particles. A relationship that expresses the effective conductivity of a suspension of one type of ellipsoidal particles could be found in the literature. The orientation of the particles could be uniform or they could be randomly distributed. For non-conducting particles, this expression is known as Archie's law. The expression is extended such that also the effective conductivity of a suspension of various types of particles can be calculated. The result is evaluated for the cortex of the brain using experimental data given in the literature.

The volume conductor may act as a temporal filter on the ECG and EEG

The influence of the volume conductor on the EEG, MEG, fetal ECG and fetal MCG is studied by means of simulations. The assumption that the Maxwell equations can be used in a quasi-static approximation is reconsidered and the fact that the conductivity of human tissue is frequency dependent is taken into account. It is found that displacement currents have a substantial effect on the fetal ECG and to a lesser degree on the fetal MCG. Moreover, the frequency dependence of the conductivity of the tissues within the head may have a considerable effect on the EEG.