Formation of spatially discordant alternans due to fluctuations and diffusion of calcium

Abstract

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.

Figure 1. Schematic illustration of the multi-scale computational model.

Each cell consists of 75 diffusively coupled sarcomeres. Ca concentrations within each sarcomere are modeled using phenomenological equations describing Ca cycling. Ca sensitive ion channels are labeled with a superscript k, while non Ca sensitive channels are the same for all sarcomeres. Neighboring cells are coupled via gap junctions in tissue.

Figure 2. APD and peak CaT during development of alternans after a change in CL.

(A) APD (top) and peak Ca transient (bottom) vs beat number n. (B) The amplitude of APD (Δa _n) and Ca transient (Δc _n) alternans amplitude vs. beat number for five independent simulations with identical parameters and initial conditions. Differences between each simulation run are due only to the Ca cycling fluctuations present. (C) The amplitude (Δc _n) of Ca transient alternans vs beat number n at the early stages of pacing.

Figure 3. Subcellular Ca dynamics in a single cell during development of alternans.

(A-D) Four independent simulations with the same parameters and initial conditions are shown. Each panel has the amplitude of APD alternans (top) and space-time plot of the amplitude of Ca transient alternans (bottom).

Figure 4. Subcellular Ca dynamics when a cell is paced with an AP clamp waveform.

(A) Periodic AP clamp. (B-C) AP clamp alternating in a LSLS and SLSL sequence respectively. AP clamp is taken from a recording of a single sarcomere paced at CL= 300 ms with stable Ca cycling (u=1.5 ms^-1). Initial conditions are chosen so that sarcomeres above (below) the 12th sarcomere start with opposite alternans phase.

Figure 5. Development and synchronization of alternans within 5 coupled cells.

The amplitude of APD alternans (top) and a space-time plot of subcellular Ca (bottom). Dashed lines indicate cell boundaries.

Figure 6. Development of SDA in a cable of 200 cells (3cm).

The profiles of the amplitudes of APD and CaT alternans at (A) beat 110, (B) beat 140, and (C) beat 400. (D) Details of the profiles at 400 beat between 100 and 115 cells. Green lines indicate cell boundaries. Since the amplitude of APD alternans is small, it will take time to synchronize these subcellular SDA. Space-time plots of the APD alternans amplitude (E) and the CaT alternans amplitude (F).

Figure 7. Steady state patterns of APD and CaT alternans in 2D tissue.

Two independent simulations with D _v=2.5×10^-3 cm²/ms (A-B), and D _v=6.25×10^-4 cm²/ms (C-D).

Figure 8. Tissue paced from the end.

Steady state APD (A) and Ca (B) alternans amplitude when PCL is changed from 300 ms to 280 ms. The leftmost 5 cell (at 0 cm) are paced in the 1D cable.

Figure 9. Initiation of ventricular tachycardia and fibrillation.

14 snapshots of the membrane voltage and [Ca]_i in 3 cm x 3 cm tissue. Tissue paced from the left edge. White lines indicate nodal lines, which separate opposite phase of alternans. At 320 ms S2 wave hit the S1 waveback (induced by *). Then a spiral wave (i.e. ventricular tachycardia) is initiated (460-960 ms). The spiral wave spontaneously brakes up at 1040 ms.

Figure 10. Summary of the mechanism for the formation of SDA.