Arrhythmogenicity of cardiac fibrosis: fractal measures and Betti numbers

Abstract

Infarction- or ischaemia-induced cardiac fibrosis can be arrythmogenic. We use mathematcal models for diffuse fibrosis ($\mathcal{D}\mathcal{F}$), interstitial fibrosis ($\mathcal{I}\mathcal{F}$), patchy fibrosis ($\mathcal{P}\mathcal{F}$), and compact fibrosis ($\mathcal{C}\mathcal{F}$) to study patterns of fibrotic cardiac tissue that have been generated by new mathematical algorithms. We show that the fractal dimension $\mathbb{D}$, the lacunarity $\mathcal{L}$, and the Betti numbers ${\beta }_0$ and ${\beta }_1$ of such patterns are \textit{fibrotic-tissue markers} that can be used to characterise the arrhythmogenicity of different types of cardiac fibrosis. We hypothesize, and then demonstrate by extensive \textit{in silico} studies of detailed mathematical models for cardiac tissue, that the arrhytmogenicity of fibrotic tissue is high when ${\beta }_0$ is large and the lacunarity parameter $b$ is small.

Manuscript: 6 pages 7 figures Supplemental Material: 4 pages 6 figures

References in corpus (1)

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