Arun V. Holden

Computational Biology of the Heart

Partial table of contents: Modelling Cardiac Excitation and Excitability (M. Boyett, et al.). Modelling Propagation in Excitable Media (A. Holden & A. Panfilov). Rotors, Fibrillation and Dimensionality (A. Winfree). A Mathematical Model of Cardiac Anatomy (P. Hunter, et al.). Finite Element Methods for Modelling Impulse Propagation in the Heart (J. Rogers, et al.). The Effects of Geometry and Fibre Orientation on Propagation and Extracellular Potentials in Myocardium (J. Keener & A. Panfilov). Forward and Inverse Problems in Electrocardiography (A. van Oosterom). Computational Electromechanics of the Heart (P. Hunter, et al.). Index.

Heterogeneous three-dimensional anatomical and electrophysiological model of human atria

Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmanns bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of , and were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing , but including , , and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1 : 9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6 m s−1 for AWM, 1.2 m s−1 for CT, 1.6 m s−1 for PM and 1.1 m s−1 for BB at a rate of 63 bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.

Tension of organizing filaments of scroll waves

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria--the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

Reentrant waves and their elimination in a model of mammalian ventricular tissue

The vulnerability to reentrant wave propagation, its characteristics (period, meander, and stability), the effects of rotational transmural anisotropy, and the control of reentrant waves by small amplitude perturbations and large amplitude defibrillating shocks are investigated theoretically and numerically for models based on high order, stiff biophysically derived excitation equations.

From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity

Abstract The Rose-Hindmarsh equations are a system of three nonlinear ordinary differential equations that provide a phenomenological model for repetitive, patterned and irregular activity in molluscan neurones. We obtain bifurcation diagrams for this system, and obtain interval maps that reproduce the behaviour of the differential system. These maps are used to explore the bifurcations from simple to complex oscillatory behaviour.

Analysis of the Chronotropic Effect of Acetylcholine on Sinoatrial Node Cells

Analysis of Chronotropic Effect of ACh. Introduction: The ionic basis underlying the negative chronotropic effect of acetylcholine (ACh) on sinoatrial (SA) node cells is unresolved and controversial. In the present study, mathematical modeling was used to address this issue.

Application of Micro-Computed Tomography With Iodine Staining to Cardiac Imaging, Segmentation, and Computational Model Development

Micro-computed tomography (micro-CT) has been widely used to generate high-resolution 3-D tissue images from small animals nondestructively, especially for mineralized skeletal tissues. However, its application to the analysis of soft cardiovascular tissues has been limited by poor inter-tissue contrast. Recent ex vivo studies have shown that contrast between muscular and connective tissue in micro-CT images can be enhanced by staining with iodine. In the present study, we apply this novel technique for imaging of cardiovascular structures in canine hearts. We optimize the method to obtain high-resolution X-ray micro-CT images of the canine atria and its distinctive regions-including the Bachmanns bundle, atrioventricular node, pulmonary arteries and veins-with clear inter-tissue contrast. The imaging results are used to reconstruct and segment the detailed 3-D geometry of the atria. Structure tensor analysis shows that the arrangement of atrial fibers can also be characterized using the enhanced micro-CT images, as iodine preferentially accumulates within the muscular fibers rather than in connective tissues. This novel technique can be particularly useful in nondestructive imaging of 3-D cardiac architectures from large animals and humans, due to the combination of relatively high speed ( ~ 1 h/per scan of the large canine heart) and high voxel resolution (36 μm) provided. In summary, contrast micro-CT facilitates fast and nondestructive imaging and segmenting of detailed 3-D cardiovascular geometries, as well as measuring fiber orientation, which are crucial in constructing biophysically detailed computational cardiac models.

From simple to simple bursting oscillatory behaviour via chaos in the Rose-Hindmarsh model for neuronal activity

Abstract The bifurcation diagrams for the Rose-Hindmarsh model are obtained from the Poincare maps which govern the dynamics of this differential system. This and a sequence of burst pattern that undergoes transition from simple to simple bursting oscillatory behaviour via chaos are presented. This burst pattern simulates the repetitive, patterned and irregular activity seen in molluscan neurones. Additionally, some maps are used to qualitatively analyze the period-2 chaos exhibited in this system.

Gradient Model Versus Mosaic Model of the Sinoatrial Node

Background —A radical reinterpretation (mosaic model) of the makeup of the sinoatrial (SA) node has been proposed to explain the characteristic regional differences in electrical activity between the periphery and center of the SA node. According to the mosaic model, the differences result from a change in the mix of atrial cells and uniform SA node cells from periphery to center, whereas according to the alternative gradient model, there are no atrial cells within the functional SA node, and the differences result from a change in the intrinsic properties of SA node cells from periphery to center. Methods and Results —A mosaic model of peripheral and central tissue has been constructed computationally by use of a coupled ordinary differential equation network (CODE) in a 2D lattice (20×20), with each node of the lattice designated randomly as an atrial cell or SA node cell (in correct proportions for periphery and center). The mosaic model fails to predict the characteristic differences in action potential rate and shape between the periphery and center, whereas the existing gradient model can do so. Conclusions —The mosaic model of the SA node is untenable, and the SA node is adequately described by the gradient model.