Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology

Abstract

Reaction -diffusion computational models of cardiac electrophysiology require both dynamic excitation models that reconstruct the action potentials of myocytes as well as datasets of cardiac geometry and architecture that provide the electrical diffusion tensor D, which determines how excitation spreads through the tissue. We illustrate an experimental pipeline we have developed in our laboratories for constructing and validating such datasets. The tensor D changes with location in the myocardium, and is determined by tissue architecture. Diffusion tensor magnetic resonance imaging (DT-MRI) provides three eigenvectors e i and eigenvalues l i at each voxel throughout the tissue that can be used to reconstruct this architecture. The primary eigenvector e 1 is a histologically validated measure of myocyte orientation (responsible for anisotropic propagation). The secondary and tertiary eigenvectors (e 2 and e 3 ) specify the directions of any orthotropic structure if l 2 is significantly greater than l 3 -this orthotropy has been identified with sheets or cleavage planes. For simulations, the components of D are scaled in the fibre and cross-fibre directions for anisotropic simulations (or fibre, sheet and sheet normal directions for orthotropic tissues) so that simulated conduction velocities match values from optical imaging or plunge electrode experiments. The simulated pattern of propagation of action potentials in the models is partially validated by optical recordings of spatio-temporal activity on the surfaces of hearts. We also describe several techniques that enhance components of the pipeline, or that allow the pipeline to be applied to different areas of research: Q ball imaging provides evidence for multi-modal orientation distributions within a fraction of voxels, infarcts can be identified by changes in the anisotropic structure-irregularity in myocyte orientation and a decrease in fractional anisotropy, clinical imaging provides human ventricular geometry and can identify ischaemic and infarcted regions, and simulations in human geometries examine the roles of anisotropic and orthotropic architecture in the initiation of arrhythmias.

Electrophysiological and structural determinants of electrotonic modulation of repolarization by the activation sequence

“…Diffusion tensors, and the eigenvectors and eigenvalues of these tensors, were calculated from the diffusion measurements at each voxel throughout the tissue using in-house software. No smoothing or interpolation of the diffusion measurements was necessary: see Benson et al (2011b) for examples of the calculated fiber directions in rat hearts.…”

Antenatal architecture and activity of the human heart

“…For every voxel within the cardiac tissue these angles are all defined within a coordinate system formed by three orthogonal axes: (i) the base-apex axis of the left ventricle (figure 2b), (ii) the radial axis joining the centroid of the left ventricle with the voxel within the transverse plane normal to the base-apex axis and (iii) the tangential axis normal to the transverse plane [17]. These angles define the architecture of the ventricular myocardium and are of modulus 1808.…”

Orthogonal Invariant Sets of the Diffusion Tensor and the Development of a Curvilinear Set Suitable for Low-Anisotropy Tissues

“…Fluids in partially-ordered biological tissues such as brain [1], muscle [2,3] and cartilage [4][5][6] have been shown to exhibit anisotropic translational diffusion when measured with techniques such as diffusion tensor imaging (DTI) [7]. The fluids, which usually consist primarily of water, are inherently isotropic liquids and therefore any measured anisotropy in their translational motion is a result of the influence of a locally anisotropic environment on the motional statistics of the liquid molecules.…”