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 (DF ), interstitial fibrosis (IF), patchy fibrosis (PF), and compact fibrosis (CF) to study patterns of fibrotic cardiac tissue that have been generated by new mathematical algorithms. We show that the fractal dimension D, the lacunarity L, and the Betti numbers β0 and β1 of such patterns are fibrotic-tissue markers that can be used to characterise the arrhythmogenicity of different types of cardiac fibrosis. We hypothesize, and then demonstrate by extensive in silico studies of detailed mathematical models for cardiac tissue, that the arrhytmogenicity of fibrotic tissue is high when β0 is large and the lacunarity parameter b is small.