A localized meshless approach for modeling spatial–temporal calcium dynamics in ventricular myocytes

Abstract

SUMMARY Spatial-temporal calcium dynamics due to calcium release, buffering and re-uptaking plays a central role in studying excitation-contraction (E-C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ a meshless method, namely, the local radial basis function collocation method (LRBFCM) to model such calcium behaviors by solving a nonlinear system of reaction-diffusion partial differential equations. In particular, a simplified structural unit containing a single transverse-tubule (or t-tubule) and its surrounding half sarcomeres is investigated using the meshless method. Numerical results are compared to those generated by finite element methods, showing the capability and efficiency of the LRBFCM in modeling calcium dynamics in ventricular myocytes. The single t-tubule model is also extended to the whole-cell scale with t-tubules excluded to demonstrate the scalability of the proposed meshless method in handling very large domains. The experiments have shown that the LRBFCM is suitable to multi-scale modeling of calcium dynamics in ventricular myocytes with high accuracy and efficiency.

Numerical Analysis of the Effect of T-tubule Location on Calcium Transient in Ventricular Myocytes

“…The kinetics satisfies the equilibrium condition R B m = R B s = 0 and gives the following initial conditions, [ CaB 1 ] = 11.917µ M , [ CaB 2 ] = 0.968µ M , [ CaB 3 ] = 0.130µ M , [ CaB s ] = 6.364µ M . Following [10], we define the J Ca flux through the cell surface and T-tubule as: J Ca flux = J Ca + J NCX − J pCa + J Cab , where J Ca denotes the total Ca 2+ influx via the L-type Ca 2+ channels (LCCs), J NCX the total Ca 2+ influx (or efflux) via the Na + - Ca 2+ exchangers (NCXs), J pCa the total Ca 2+ pumps efflux and J Cab the total background Ca 2+ leak influx. In order to compute the value of the fluxes J Ca , J NCX , J pCa and J Cab we define their respective current densities I Ca , I NCX , I pCa and I Cab .…”

“…In order to compute the value of the fluxes J Ca , J NCX , J pCa and J Cab we define their respective current densities I Ca , I NCX , I pCa and I Cab . I NCX and I Cab are functions of the holding potential of voltage-clamp protocol V : with V = 10 mV , for t ∈ (0, 70 ms ], and V = −50 mV , for t ∈ (70 ms , ∞], (see Yao et al [10]) The given current densities I i (µ M/ms ), i = Ca, NCX, pCa, Cab are converted to Ca 2+ influx/efflux J i (µ M/ms ), i = Ca, NCX, pCa, Cab by using an experimentally estimated capacitance to rendered volume ratio, ( C m /V cell = 8.8 pF/pL ) in adult rat ventricular myocytes [10]: $$J_i={\beta }_i\frac{V_{mc}}{S_j}true(\frac{1}{2F}\frac{C_m}{V_{\text{italiccell}}}true)I_i,$$ where C m ( pF ) is the cell capacitance, V cell ( pL ) is the cell volume, V mc (µ m 3 ) is the compartment volume of the geometric model used to represent the cell in the numerical experiment, S j (µ m 2 ) is the total surface area where the channel i resides in the geometric model, F is the Faraday’s constant, and β i , i = Ca, NCX, pCa, Cab is a model-dependent scaling parameter for LCCs, NCXs, Ca 2+ pumps and background leak respectively. The values of the scaling parameters are as follows β Ca = 232.3, β NCX = 133.7, β pCa = 390.0, and β Cab = 1345.0.…”

“…Their study highlights the need to understand the regulation and signalling of Ca 2+ within microdomains along with its pathophysiological and therapeutic implications. In Lu et al [8], Cheng et al [9] and Yao et al [10], Ca 2+ interactions and concentrations were studied with SR activity inhibited in order to assess the effect of the distribution of sarcolemma and T-tubule ion channels on Ca 2+ regulation in myocytes. Results from these studies show that Ca 2+ transient in myocytes could be influenced by variations in the distribution of ion channels along the sarcolemma and T-tubule.…”

“…This is motivated by the need to understand the pathophysiological implications of T-tubule remodeling/relocation on myocytes. This study is carried out by utilizing a mathematical model describing the Ca 2+ interactions via the sarcolemma and the T-tubule of myocytes [8, 10]. Numerical experiments are carried out on three separate geometric models incorporated with realistic T-tubule structures extracted from 3D electron microscopy images at a high resolution.…”

Parallel Acceleration for Modeling of Calcium Dynamics in Cardiac Myocytes

“…At these scales, deterministic methods utilizing partial differential equations (PDEs) are more appropriate than stochastic methods [4,5]. The local radial basis function collocation method (LRBFCM) developed by S̃arler and Vertnik [6] has been applied to solving the PDEs in our earlier work [7]. This meshless method eliminates the generation of meshes, as commonly required in finite element methods.…”