Abstract Early afterdepolarization (EAD), an abnormal condition of cardiac myocytes defined as the reversal of action potential during its repolarization phase, can initiate spiral waves in cardiac tissue, which may eventually develop into spiral turbulence. In addition to EAD, fibrosis, a process during aging or as a result of injury and a major cause of tissue heterogeneities in cardiac tissue, can also destabilize waves, resulting in spiral breakup. In this paper, we study excitation wave propagation in two-dimensional (2D) and three-dimensional (3D) tissue models using two EAD-capable mathematical models for cardiac cells, the minimal model and the reduced model, in the presence of randomly distributed fibrosis under pacing; we find that pacing generates spiral waves or non-spiral waves in 2D, and scroll waves or non-scroll waves in 3D, depending on the pacing cycle length (PCL) and the percentage of fibrosis (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$P_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation>). Our systematic numerical studies reveal that increasing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$P_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> promotes the transition from non-spiral to spiral states, including spiral turbulence. However, increasing PCL leads to a transition from spiral to non-spiral states. In particular, near the transition boundaries, the occurrence of spiral and non-spiral states depends on the realization of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$P_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation>. We find that the spiral turbulence state in the minimal model is maintained by high <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$P_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> fibrosis, which promotes discontinuous propagation of waves, whereas both EAD-induced trigger activity and fibrosis-driven conduction discontinuity maintained spiral turbulence in the reduced model. In particular, focal waves initiated by EAD-induced trigger activity in the reduced model break up due to fibrosis, showing the combined role of EAD and fibrosis in sustaining spiral turbulence. Furthermore, our scroll wave studies reveal that a spiral turbulence state in 2D can be suppressed in 3D due to possible complex interaction between EAD-capable cells, fibrosis and tissue thickness, leading to a non-scroll state. We observe that the reduced model exhibits phase wave state, which is absent in the minimal model due to the lack of EAD oscillations; we further observe that neither <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$P_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> nor PCL affects the phase wave state, as this state arises predominantly from oscillatory behavior driven by cellular activity. One of our key findings is that it can help estimate the safety limit for pacing to prevent spiral breakup in EAD-susceptible fibrotic tissue, thereby reducing the risk of fibrillation in the heart. Graphical abstract

Fibrosis and pacing driven wave dynamics in early afterdepolarization cardiac models

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发表日期：

2026年4月28日

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Duryodhan Prusty,
Alok Ranjan Nayak

摘要

Abstract

Early afterdepolarization (EAD), an abnormal condition of cardiac myocytes defined as the reversal of action potential during its repolarization phase, can initiate spiral waves in cardiac tissue, which may eventually develop into spiral turbulence. In addition to EAD, fibrosis, a process during aging or as a result of injury and a major cause of tissue heterogeneities in cardiac tissue, can also destabilize waves, resulting in spiral breakup. In this paper, we study excitation wave propagation in two-dimensional (2D) and three-dimensional (3D) tissue models using two EAD-capable mathematical models for cardiac cells, the minimal model and the reduced model, in the presence of randomly distributed fibrosis under pacing; we find that pacing generates spiral waves or non-spiral waves in 2D, and scroll waves or non-scroll waves in 3D, depending on the pacing cycle length (PCL) and the percentage of fibrosis ( $P_f$ $P_{f}$ ). Our systematic numerical studies reveal that increasing $P_f$ $P_{f}$ promotes the transition from non-spiral to spiral states, including spiral turbulence. However, increasing PCL leads to a transition from spiral to non-spiral states. In particular, near the transition boundaries, the occurrence of spiral and non-spiral states depends on the realization of $P_f$ $P_{f}$ . We find that the spiral turbulence state in the minimal model is maintained by high $P_f$ $P_{f}$ fibrosis, which promotes discontinuous propagation of waves, whereas both EAD-induced trigger activity and fibrosis-driven conduction discontinuity maintained spiral turbulence in the reduced model. In particular, focal waves initiated by EAD-induced trigger activity in the reduced model break up due to fibrosis, showing the combined role of EAD and fibrosis in sustaining spiral turbulence. Furthermore, our scroll wave studies reveal that a spiral turbulence state in 2D can be suppressed in 3D due to possible complex interaction between EAD-capable cells, fibrosis and tissue thickness, leading to a non-scroll state. We observe that the reduced model exhibits phase wave state, which is absent in the minimal model due to the lack of EAD oscillations; we further observe that neither $P_f$ $P_{f}$ nor PCL affects the phase wave state, as this state arises predominantly from oscillatory behavior driven by cellular activity. One of our key findings is that it can help estimate the safety limit for pacing to prevent spiral breakup in EAD-susceptible fibrotic tissue, thereby reducing the risk of fibrillation in the heart.

Graphical abstract