Arrhythmogenicity of cardiac fibrosis: fractal measures and Betti numbers

Infarction- or ischaemia-induced cardiac fibrosis can be arrythmogenic. We use mathematcal models for diffuse fibrosis (\(\mathcal{DF}\)), interstitial fibrosis (\(\mathcal{IF}\)), patchy fibrosis (\(\mathcal{PF}\)), and compact fibrosis (\(\mathcal{CF}\)) to study patterns of fibrotic cardiac tissu...

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Bibliographic Details
Published in:arXiv.org 2021-05
Main Authors: Mulimani, Mahesh Kumar, Lawson, Brodie A J, Pandit, Rahul
Format: Article
Language:English
Subjects:
Algorithms
Fibrosis
Fractal geometry
Fractals
Infarction
Mathematical models
Online Access:Get full text
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Summary:Infarction- or ischaemia-induced cardiac fibrosis can be arrythmogenic. We use mathematcal models for diffuse fibrosis (\(\mathcal{DF}\)), interstitial fibrosis (\(\mathcal{IF}\)), patchy fibrosis (\(\mathcal{PF}\)), and compact fibrosis (\(\mathcal{CF}\)) 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.
ISSN:2331-8422