Anisotropic conduction in the myocardium due to fibrosis: the effect of texture on wave propagation

Abstract

Cardiac fibrosis occurs in many forms of heart disease. It is well established that the spatial pattern of fibrosis, its texture, substantially affects the onset of arrhythmia. However, in most modelling studies fibrosis is represented by multiple randomly distributed short obstacles that mimic only one possible texture, diffuse fibrosis. An important characteristic feature of other fibrosis textures, such as interstitial and patchy textures, is that fibrotic inclusions have substantial length, which is suggested to have a pronounced effect on wave propagation. In this paper, we study the effect of the elongation of inexcitable inclusions (obstacles) on wave propagation in a 2D model of cardiac tissue described by the TP06 model for human ventricular cells. We study in detail how the elongation of obstacles affects various characteristics of the waves. We quantify the anisotropy induced by the textures, its dependency on the obstacle length and the effects of the texture on the shape of the propagating wave. Because such anisotropy is a result of zigzag propagation we show, for the first time, quantification of the effects of geometry and source-sink relationship, on the zigzag nature of the pathway of electrical conduction. We also study the effect of fibrosis in the case of pre-existing anisotropy and introduce a procedure for scaling of the fibrosis texture. We show that fibrosis can decrease or increase the preexisting anisotropy depending on its scaled texture.

Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

“…Upper panels A, B show the results we obtained in a 3D monolayer of the tissue (0.25 mm depth, 1 z-layer). As this case is equivalent to 2D model, we use it as a reference for comparison of 2D and 3D models, in particular with the results reported earlier [29]. We see that the velocity significantly decreases with an increase in the fibrosis percentage.…”

“…Similarly to Nezlobinsky et al [29], we uniformly distributed fibrosis elements and varied length of elements (in x-axis direction) and density of elements distribution. To distribute fibrosis elements through the mesh we implemented two approaches.…”

“…To distribute fibrosis elements through the mesh we implemented two approaches. Fibrosis pattern was generated in the same manner as described in [29], namely, we subdivided each X × Y × Z matrix in x or y direction into Y • Z or X • Z rows with size 1 × 200 × 1 or 200 × 1 × 1 respectively. Then we subdivided each row into blocks of length n and assign it as fibrotic with a probability p. This approach allowed us to set fibrosis percentage precisely close to desired value.…”

“…One of the first works demonstrating the importance of the texture and the characteristic dimensions of unexcitable obstacles in the tissue for the onset of spiral waves was the work of A. Pertsov's group (see [28]). In our recent study, [29], we made a first attempt to study the effects of fibrotic texture representing some features of interstitial fibrosis with primarily linear accumulations of collagen separating bundles of myocytes with little alteration in the alignment of myocytes or bundles [30]. One of main features of this pattern is that inexcitable inclusions to cardiac tissue here have some directional dependency laying between myofibers.…”

“…In idealised representation they can be seen as thin elongated obstacles directed along cardiac fibers. In [29], we considered case of parallel fibers, thus texture of linear inexcitable elements which all have the same orientation and we studied propagation in such 2D models of myocardium for wave along this direction (longitudinal) and perpendicular to it (transversal) propagation. Main findings of this study revealed an opposite change in the conduction velocity (CV) with the obstacle length depending on the direction of the wavefront propagation.…”