Reentry via high-frequency pacing in a mathematical model for human-ventricular cardiac tissue with a localized fibrotic region

Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue.

(c) The averaged power spectrum of these time series; this is the average of the power spectra of the time series from the four representative points mentioned above. The spiral-wave frequency ω is the value of the frequency of the dominant peak in this spectrum ,i.e, the peak at 6.4 Hz.

Model of fibroblast clump with remodelling in gap-junctional coupling and four ionic currents
We divide the medium into three regions (see fig. S5), namely, the normal region, the border zone (BZ), and the central zone (CZ); CZ lies inside the fibroblast clump; the BZ region is the region between CZ and the normal region. In the BZ region we reduce the conductances of I N a by 50%, I CaL by 50%, I Kr and I Ks by 30%. In the CZ region we reduce the conductances of I N a by 70%, I CaL by 70%, I Kr and I Ks by 60%. Furthermore, the value of the diffusion coupling is linearly reduced from its control value in the normal region to 60% of its original value in the CZ region.

Video captions
Video S1: Wave distortions around a fibroblast clump via highfrequency PP protocol. Video showing the formation of wave distortions and spiral waves around a fibroblast clump of p f = 30% and radius R = 1 cm. For this video, we use 10 frames per second with each frame separated from the succeeding frame by 20ms in real time.
Video S2: Absence of wave distortions around the fibroblast clump at low-frequency PP protocol. Video showing that no wave distortions occur around a fibroblast clump of p f = 30% and radius R = 1 cm if we use low-frequency PP protocol. For this video, we use 10 frames per second with each frame separated from the succeeding frame by 20ms in real time.
Video S3: Delayed occurrence of wave distortions around the fibroblast clump with higher excitability. Video showing that the formation of wave distortions around a fibroblast clump is delayed if we increase the excitability inside the clump and around it by increasing the conductance of I Na (G Na ) by 1.1 times. The wave distortion occur at 17.7s, which is higher than the averaged value of 15.4 s in the case of normal excitability. For this video, we use 10 frames per second with each frame separated from the succeeding frame by 20ms in real time.
Video S4: Re-entry via the TP protocol. Video showing the initiation of reentry, because of our high-frequency pacing (TP protocol), in a medium with a fibroblast clump with R=2.4 cm and p f =33% (left panel) and 43% (right panel). For this video, we use 10 frames per second with each frame separated from the succeeding frame by 20ms in real time.
Video S5: TP-pacing induced reentry in our 3D simulations with a cylindrical fibroblast clump. Video showing the formation of reentry, via our TP stimulation protocol with PCL= 152 ms, in a 3D domain with a cylindrical fibroblast clump, p f = 65%, and R=2.4 cm. For this video, we use 10 frames per second with each frame separated from the succeeding frame by 20ms in real time.