Dual regulation by subcellular calcium heterogeneity and heart rate variability on cardiac electromechanical dynamics

Abstract

Heart rate constantly varies under physiological conditions, termed heart rate variability (HRV), and in clinical studies, low HRV is associated with a greater risk of cardiac arrhythmias. Prior work has shown that HRV influences the temporal patterns of electrical activity, specifically the formation of pro-arrhythmic alternans, a beat-to-beat alternation in the action potential duration (APD), or intracellular calcium (Ca) levels. We previously showed that HRV may be anti-arrhythmic by disrupting APD and Ca alternations in a homogeneous cardiac myocyte. Here, we expand on our previous work, incorporating variation in subcellular Ca handling (also known to influence alternans) into a nonlinear map model of a cardiac myocyte composed of diffusively coupled Ca release units (CRUs). Ca-related parameters and initial conditions of each CRU are varied to mimic subcellular Ca heterogeneity, and a stochastic pacing sequence reproduces HRV. We find that subcellular Ca heterogeneity promotes the formation of spatially discordant subcellular alternans patterns, which decreases whole cell Ca and APD alternation for low and moderate HRV, while high subcellular Ca heterogeneity and HRV both promote electromechanical desynchronization. Finally, we find that for low and moderate HRV, both the specific subcellular Ca-related parameters and the pacing sequences influence measures of electromechanical dynamics, while for high HRV, these measures depend predominantly on the pacing sequence. Our results suggest that pro-arrhythmic subcellular discordant alternans tend to form for low levels of HRV, while high HRV may be anti-arrhythmic due to mitigated influence from subcellular Ca heterogeneity and desynchronization of APD from Ca instabilities.

FIG. 1.

Subcellular discordant alternans form with increasing initial condition heterogeneity in the absence of heart rate variability (HRV). APD, whole cell peak Ca, and CRU peak Ca are plotted as a function of beat number for different initial condition (IC) heterogeneity levels. Parameters: IC heterogeneity of (a) 2$\mathrm{\%}$ and (b) 12$\mathrm{\%}$; $T_0=250$ ms, $\sigma =0$  ms.

FIG. 2.

The formation of subcellular discordant alternans due to initial condition heterogeneity dampens APD and whole cell peak Ca alternation in the absence of heart rate variability (HRV). (a) The magnitude of the beat-to-beat difference in APD ($\mathrm{\Delta }a$) and whole cell peak Ca ($\mathrm{\Delta }{c}^p$) and (b) the in-phase fraction measurements between APD/whole cell peak Ca ($f_{Ca,APD}$), CRU Ca/whole cell peak Ca ($f_{CRU,Ca}$), and CRU Ca/APD ($f_{CRU,APD}$) are shown as a function of pacing period ($T_0$) for different initial condition (IC) heterogeneity levels. Parameter: $\sigma =0$ ms.

FIG. 3.

High heart rate variability (HRV) promotes the formation of subcellular concordant alternans. APD, whole cell peak Ca, and CRU peak Ca are shown as a function of beat number for increasing levels of heart rate variability, $\sigma =$ (a) 2, (b) 6, and (c) 12 ms. Parameters: $T_0=250$ ms, IC heterogeneity of $12\mathrm{\%}$.

FIG. 4.

The propensity for subcellular discordant alternans formation is greater at lower levels of heart rate variability (HRV). Magnitude of the beat-to-beat differences in APD ($\mathrm{\Delta }a$) and whole cell peak Ca ($\mathrm{\Delta }{c}^p$) are plotted as a function of pacing period ($T_0$), for different initial condition (IC) heterogeneity levels. Parameters: $\sigma =$ (a) 2, (b) 6, and (c) 12 ms.

FIG. 5.

Heart rate variability (HRV) promotes CRU peak Ca synchronization and APD-Ca desynchronization. (a) The in-phase fraction between whole cell peak Ca and APD, (b) CRU peak Ca and whole cell peak Ca, and (c) CRU peak Ca and APD are shown as a function of period rates ($T_0$), for different initial condition (IC) heterogeneity levels and levels of HRV [$\sigma =2$ (left), 6 (middle), and 12 (right) ms].

FIG. 6.

Subcellular Ca heterogeneity and subcellular discordant alternans formation are more prominent for low heart rate variability (HRV). APD, whole cell peak Ca, and CRU peak Ca are shown as a function of beat number for increasing levels of heart rate variability, $\sigma =$ (a) 2, (b) 6, and (c) 12 ms. Parameters: (Top) $T_0=250$ ms, heterogeneity of $12\mathrm{\%}$.

FIG. 7.

The formation of subcellular discordant alternans at high HRV does not reduce APD alternation. Magnitude of the beat-to-beat differences in APD ($\mathrm{\Delta }a$) and whole cell peak Ca ($\mathrm{\Delta }{c}^p$) are plotted as a function of pacing period ($T_0$), for different subcellular Ca heterogeneity levels. Parameters: $\sigma =$ (a) 2, (b) 6, and (c) 12 ms.

FIG. 8.

Subcellular heterogeneity reduces whole cell peak Ca and APD alternations for low heart rate variability (HRV). (a) The magnitude of the beat-to-beat difference in APD ($\mathrm{\Delta }a$) and (b) whole cell peak Ca ($\mathrm{\Delta }{c}^p$) are shown as a function of HRV level $\sigma$ and level of subcellular Ca heterogeneity, for pacing periods ($T_0$) of 230 (left), 250 (middle), and 300 (right) ms.

FIG. 9.

Subcellular Ca heterogeneity and heart rate variability (HRV) promote desynchronization between subcellular Ca and APD. The in-phase fraction between (a) whole cell peak Ca and APD, (b) CRU peak Ca and whole cell peak Ca, and (c) CRU peak Ca and APD are shown as a function of period ($T_0$), for different heterogeneity levels and levels of HRV [$\sigma =2$ (left), 6 (middle), and 12 (right) ms].

FIG. 10.

Subcellular Ca heterogeneity has a more prominent influence on APD-Ca synchronization for low heart rate variability (HRV) and at longer pacing period. The in-phase fraction between (a) whole cell Ca fraction in-phase with APD ($f_{Ca,APD}$), (b) CRU fraction in-phase with whole cell peak Ca ($f_{CRU,Ca}$), and (c) CRU fraction in-phase with APD ($f_{CRU,APD}$) are shown as a function of HRV level $\sigma$ and level of subcellular Ca heterogeneity, for pacing periods ($T_0$) of 230 (left), 250 (middle), and 300 (right) ms.

FIG. 11.

Subcellular discordant alternans formation depends on both the specific pacing sequence and subcellular Ca handling parameters. APD, whole cell peak Ca, and CRU peak Ca are shown as a function of beat number for [(a)–(c)] three different combinations of pacing sequences and parameter sets. Note that the pacing sequence and parameter set numbers correspond with the rows and columns, respectively, in Figs. 12 and 13. Parameters: $T_0=250\text{ms}$, $\sigma =2\text{ms}$, and subcellular Ca $\text{heterogeneity}=16\mathrm{\%}$.

FIG. 12.

The magnitude of beat-to-beat difference in APD ($\mathrm{\Delta }a$) depends on the specific parameter set and pacing sequence for low and moderate heart rate variability (HRV) and predominately on the pacing sequence for high HRV. The $\mathrm{\Delta }a$ value is plotted for 50 parameter sets and 50 pacing sequences for each HRV level [$\sigma$ = (a) 2, (b) 6, and (c) 12 ms], and level of subcellular Ca heterogeneity [4$\mathrm{\%}$ (left), 10$\mathrm{\%}$ (middle), and 16$\mathrm{\%}$ (right)]. Parameter: $T_0=250$ ms.

FIG. 13.

The magnitude of whole cell peak Ca beat-to-beat difference ($\mathrm{\Delta }{c}^p$) depends on specific parameter set at all levels of heart rate variability (HRV). The $\mathrm{\Delta }{c}^p$ value is plotted for 50 parameter sets and 50 pacing sequences for each HRV level [$\sigma$ = (a) 2, (b) 6, and (c) 12 ms], and level of subcellular Ca heterogeneity [4$\mathrm{\%}$ (left), 10$\mathrm{\%}$ (middle), and 16$\mathrm{\%}$ (right)]. Parameter: $T_0=250$ ms.