Examining the Effect of Introducing a Link From Electrical Excitation to Calcium Dynamics in a Cardiomyocyte

Abstract

Calcium dysregulation is a significant cause of fatal cardiac arrythmias, but it is an incompletely understood phenomenon and difficult to predict. Cardiac calcium levels can be modeled as a system of partial differential equations linking the electrical excitation, calcium signaling, and mechanical contraction dynamics of the heart. A complete calcium-induced calcium release model uses reaction-diffusion equations to fully link these three systems. Simulations examine the effect of introducing the link from calcium signaling to electrical excitation. In particular, we perform a parameter study on the strength of the feedback connection with both links between calcium signaling and electrical excitation enabled. Simulations indicate that the feedback and feedforward between electrical excitation and calcium signaling can influence the voltage in a physiologically realistic way.

Examining the Electrical Excitation, Calcium Signaling, and Mechanical Contraction Cycle in a Heart Cell

“…Section 3.2 describes the electrical excitation that is connected to the calcium signaling in both the feedforward and feedback directions represented by link 1 ○ and link 2 ○ in Figure 1.1. Link 1 ○ from electrical system to the calcium dynamics was first established in [1], and link 2 ○ was established in [2]. Finally, Section 3.3 presents the mechanical contraction component that is also connected to the calcium signaling in both the feedback and feedforward directions represented by links 3 ○ and 4 ○ in Figure 1.1 and was established in [2].…”

“…This section details the seven-variable model used in this work. It is a special case of the eight-variable model fully established in [2], obtained by not including all variables so as to focus the simulations on one new effect only. Namely, the full model consists of calcium in the cytosol c(x, t), n sc = 3 many cytosol buffer species b 3 (x, t), cal-cium in the SR s(x, t), voltage V (x, t), and the potassium gating function n(x, t).…”

“…The model was extended for the first time to include the Electrical Excitation component in Figure 1.1 in [1], which implemented a one-way interaction from electrical excitation to calcium signaling indicated by link 1 ○ in Figure 1.1. Studies with six variables in [2] extended the coupling to include a two-way cycle between electrical excitation and calcium signaling by incorporating both links 1 ○ and 2 ○ in Figure 1.1. The 2016 paper [2] also introduced the formulation of the complete eight-variable model for all components in Figure 1.1, but not all model variables were used in the simulations, and the studies did not incorporate the mechanical system.…”

“…Studies with six variables in [2] extended the coupling to include a two-way cycle between electrical excitation and calcium signaling by incorporating both links 1 ○ and 2 ○ in Figure 1.1. The 2016 paper [2] also introduced the formulation of the complete eight-variable model for all components in Figure 1.1, but not all model variables were used in the simulations, and the studies did not incorporate the mechanical system. This work studies the introduction of the Mechanical Contraction component in Figure 1.1 by activating the links 3 ○ and 4 ○ in Figure 1.1.…”

Parameter Identification for Calcium Release in a Heart Cell with Modified Patankar–Runge–Kutta Schemes

“…where c denotes the concentration of calcium in the cytosol, and b i and B i , i = 1, 2, represent the free and bound concentration of buffer species in the cytosol, respectively. See [6] for a description of all occurring parameters and the definition of the reaction terms. In particular, the term J CRU , which depends on various parameters collected in the parameter vector p, models the injection of calcium into the cell as point sources.…”