Complex restitution behavior and reentry in a cardiac tissue model for neonatal mice

Abstract

Spatiotemporal dynamics in cardiac tissue emerging from the coupling of individual cardiomyocytes underlie the heart's normal rhythm as well as undesired and possibly life-threatening arrhythmias. While single cells and their transmembrane currents have been studied extensively, systematically investigating spatiotemporal dynamics is complicated by the nontrivial relationship between single-cell and emergent tissue properties. Mathematical models have been employed to bridge this gap and contribute to a deepened understanding of the onset, development, and termination of arrhythmias. However, no such tissue-level model currently exists for neonatal mice. Here, we build on a recent single-cell model of neonatal mouse cardiomyocytes by Wang and Sobie (Am. J. Physiol. Heart Circ. Physiol 294:H2565) to predict properties that are commonly used to gauge arrhythmogenicity of cardiac substrates. We modify the model to yield well-defined behavior for common experimental protocols and construct a spatially extended version to study emergent tissue dynamics. We find a complex action potential duration (APD) restitution behavior characterized by a nonmonotonic dependence on pacing frequency. Electrotonic coupling in tissue leads not only to changes in action potential morphology but can also induce spatially concordant and discordant alternans not observed in the single-cell model. In two-dimensional tissue, our results show that the model supports stable functional reentry, whose frequency is in good agreement with that observed in adult mice. Our results can be used to further constrain and validate the mathematical model of neonatal mouse cardiomyocytes with future experiments.

Keywords: Alternans; cardiac tissue; mathematical modeling; neonatal mice; reentry; restitution.

Figure 1

Sketch of the components of the Wang–Sobie model. The model distinguishes 14 sarcolemmal currents and describes intracellular calcium cycling between different model compartments (myoplasm, subspace, junctional sarcoplasmic reticulum [JSR], network sarcoplasmic reticulum [NSR]). The calcium concentrations are buffered by troponin, calmodulin, and calsequestrin [CSQN].

Figure 2

Effects of long‐term pacing: The original model drift upon pacing at 1 Hz is eliminated by conservative stimulation and removal of I _Cl,Ca. The time course of the intracellular potassium concentration (solid lines) and of an aggregate measure of drift ∆_tot (dotted lines) is shown.

Figure 3

(A) Action potential (AP) in a single cell and in tissue. Time t = 0 ms was defined as the time point, when the upstroke surpasses −60 mV to align the two APs. (B) Time course of the stimulus current (single cell) and the electrotonic current (tissue). The upper inset shows a magnified view of the fast dynamics at the start of the action potential (AP), whereas the lower inset shows the small amplitude electrotonic currents during repolarization.

Figure 4

(A) action potential duration (APD) as a function of basic cycle length (BCL). Three examples of S1–S2 restitution curves (fixed S1, varying S2) and the dynamic restitution curve (S1 = S2) is shown. (B) Diastolic sodium and calcium concentration at steady state as a function of the pacing frequency. (C,D) Membrane potential and intracellular calcium concentration, respectively, during different steady‐state action potentials (APs).

Figure 5

Restitution in a cable. Properties of action potential (AP) #45 and 46 after start of stimulation are shown for each basic cycle length (BCL). (A) Action potential duration (APD) measured at a cell 1 cm from the left of the cable. (B) CV measured between 1 and 2 cm from the left of the cable. (C) Spatial variations in APD at BCL = 130 ms. (D) Spatial variations in APD at BCL = 140 ms.

Figure 6

Spiral wave dynamics. (A) Snapshots of the membrane potential at time t/s ∈ {0.25, 1.0, 2.5, 5.0} (from left to right). (B) Histogram of the periods of the electrical activity during t/s ∈ [1.0, 2.0]. (bin size 1 ms). (C) Meandering of the spiral core for t/s ∈ [1.0, 2.5]. (D) Meandering of the spiral core for t/s ∈ [3.5, 5.0].