Simulation of the Effects of Extracellular Calcium Changes Leads to a Novel Computational Model of Human Ventricular Action Potential With a Revised Calcium Handling

Abstract

The importance of electrolyte concentrations for cardiac function is well established. Electrolyte variations can lead to arrhythmias onset, due to their important role in the action potential (AP) genesis and in maintaining cell homeostasis. However, most of the human AP computer models available in literature were developed with constant electrolyte concentrations, and fail to simulate physiological changes induced by electrolyte variations. This is especially true for Ca²⁺, even in the O'Hara-Rudy model (ORd), one of the most widely used models in cardiac electrophysiology. Therefore, the present work develops a new human ventricular model (BPS2020), based on ORd, able to simulate the inverse dependence of AP duration (APD) on extracellular Ca²⁺ concentration ([Ca²⁺]_o), and APD rate dependence at 4 mM extracellular K⁺. The main changes needed with respect to ORd are: (i) an increased sensitivity of L-type Ca²⁺ current inactivation to [Ca²⁺]_o; (ii) a single compartment description of the sarcoplasmic reticulum; iii) the replacement of Ca²⁺ release. BPS2020 is able to simulate the physiological APD-[Ca²⁺]_o relationship, while also retaining the well-reproduced properties of ORd (APD rate dependence, restitution, accommodation and current block effects). We also used BPS2020 to generate an experimentally-calibrated population of models to investigate: (i) the occurrence of repolarization abnormalities in response to hERG current block; (ii) the rate adaptation variability; (iii) the occurrence of alternans and delayed after-depolarizations at fast pacing. Our results indicate that we successfully developed an improved version of ORd, which can be used to investigate electrophysiological changes and pro-arrhythmic abnormalities induced by electrolyte variations and current block at multiple rates and at the population level.

Keywords: calcium handling; computational modeling; extracellular concentrations; human ventricular action potential; population of models.

FIGURE 1

Summary of the design and validation of the new I_CaL model. (A) Schematic representation of the Markov model structure: voltage-dependent inactivation (VDI) and Ca²⁺-dependent inactivation (CDI) are represented as two separate loops, with four states each (C, closed; O, open; I₁ and I₂, inactivated). Inactivation rates in the CDI loop are K_CDI times faster than the corresponding rates in the VDI loop. VDI and CDI loops are interconnected by up/down rates (r_up/r_down), dependent on the n-gate, which directly depends on intracellular Ca²⁺ and its binding to Calmodulin (CaM), as shown in the equation at the bottom of the panel, modified from Decker et al. (2009); O’Hara et al. (2011), and Passini and Severi (2013). (B,C) Comparison of the simulated I_CaL I–V curve (B) and steady state inactivation curve (C) between ORd (light blue), BPS2020 (dark blue), and the experimental data from Magyar et al. (2000) (black squares). (D) Evaluation of the effect of CDI inactivation, by comparing VDI-only and VDI+CDI voltage clamp protocols for I_CaL: both ORd (light blue, left) and BPS2020 (dark blue, right) show a faster inactivation when CDI is included, in agreement with experimental recordings with and without Ba²⁺ from O’Hara et al. (2011) (not shown). (E) Comparison of the recovery from inactivation between ORd (light blue), BPS2020 (dark blue), and the experimental data from Fülöp et al. (2004) (black diamonds), obtained using the P1/P2 protocol.

FIGURE 2

Comparison of ORd and BPS2020 behavior for [Ca²⁺]_o variations. (A) Simulated action potential (AP) for the original ORd and the BPS2020 models (left and right panels, respectively) for three different [Ca²⁺]_o. In control conditions ([Ca²⁺]_o = 1.8 mM, solid lines), results with the two models are quite similar. However, when [Ca²⁺]_o increases ([Ca²⁺]_o = 2.7 mM, dashed lines) or decreases ([Ca²⁺]_o = 0.9 mM, dotted lines), they behave in two opposite ways. Only BPS2020 reproduces the inverse APD-[Ca²⁺]_o relationship observed experimentally. (B) APD-[Ca²⁺]_o relationship for ORd (light blue) vs. BPS2020 (dark blue). (C) Changes observed in the APD-[Ca²⁺]_o relationship of BPS2020 when restoring I_CaL (dotted line) or J_rel (dashed line) to the original ORd formulations.

FIGURE 3

Rate dependence properties of BPS2020 vs. ORd. In all panels, simulation results for BPS2020 and ORd are shown in dark blue and light blue, respectively. Experimental data from O’Hara et al. (2011); Pieske et al. (2002) and Schmidt et al. (1998) are shown as black squares, black circles and black diamonds, respectively. (A) Steady state action potential duration (APD) rate dependence (CL – cycle length) and APD restitution obtained with the S₁S₂ protocol (DI – diastolic interval). APDs computed at 30, 50, 70, and 90% of repolarization are labeled on the right. (B) Steady state APD₉₀ rate dependence changes induced by specific current blocks; stars are the APD₉₀ values in control conditions. (C) APD₉₀ restitution changes induced by specific current blocks. (D) [Na⁺]_i (left) and peak [Ca²⁺]_i (middle and right) vs. pacing frequency.

FIGURE 4

APD₉₀ accommodation. At t = 0 s, the pacing cycle length (CL) is abruptly reduced from 750 to 480 ms (black circles) or 410 ms (white circles). At t = 180 s, the CL is abruptly increased to its original value. (A) Action potential duration (APD) accommodation measured experimentally by Franz et al. (1988). (B) APD accommodation simulated with the ORd model. (C) APD accommodation with the BPS2020 model. (A,B) Are adapted from O’Hara et al. (2011).

FIGURE 5

Experimentally calibrated population. (A) Action potentials and (B) Ca²⁺ transients with the BPS2020 model (baseline, white traces), the experimentally calibrated population (blue traces, representing 342 APs) and the rejected models (gray traces). (C) Biomarker distributions in the experimentally calibrated population. The black vertical lines are the experimental boundaries Passini et al. (2017) used to calibrate the population. APD, AP duration at the % specified repolarization; Tri_90–40, APD₉₀-APD₄₀; dV/dt_max, maximum upstroke velocity; Vpeak, AP peak voltage; RMP, resting membrane potential.

FIGURE 6

Repolarization abnormalities – EADs. (A) Examples of different responses to dofetilide (0.1 μM), CL = 4,000 ms (Guo et al., 2011). Top: repolarizing models (black, REP); middle: models developing early afterdepolarizations (magenta, EAD) and bottom panel failing to repolarize (cyan, RF). (B) Distribution of the scaling factors which show statistically significant differences between the three categories: models repolarizing (REP, black), models developing EADs (EAD, magenta) and models failing to repolarize (RF, cyan) (*p < 0.05). Red crosses represent outliers. (C) EAD induced by I_CaL reactivation (left) and EAD induced by Ca²⁺ release from SR (right).

FIGURE 7

Repolarization abnormalities – DADs. (A) Illustrative action potential (AP) traces for four models that produced delayed afterdepolarizations (DADs). (B) Illustrative model producing a DAD. (C) Example of DAD degenerating into an anticipated spontaneous AP. In both models the leakage J_leak from the overloaded SR increased the Ca²⁺ concentrations in cytosol ([Ca²⁺]_i) and subspace ([Ca²⁺]_SS). The RyR-sensitive channels sensed the increased [Ca²⁺]_SS and triggered a spontaneous SR Ca²⁺ release (through J_rel) that was translated by the Na⁺/Ca²⁺ exchanger (I_Naca) into the depolarization of the membrane potential, thus determining the DAD and the anticipated AP.

FIGURE 8

Repolarization abnormalities – alternans. Action potentials (APs) at different cycle lengths (CLs) (pacing at 30 s if CL ≥ 300 ms, otherwise 15 s) and APD₉₀-CL relationship for three models from the in silico population. The model (black) in (A,B) belongs to the ADAPT class. The model (green) in (C,D) from the ALT class showed alternans and produced a bifurcation. (E,F) Show an ADAPT FAIL model (red, whose AP fails to adapt for CL shorter than 250 ms). The magenta trace in (C,D) show the alternans suppression due to 30% J_up upregulation. (G) Distribution of the scaling factors showing statistically significant differences (^∗p < 0.05) between the three categories: models adapting to changes in pacing rate (ADAPT, black), models failing to adapt (ADAPT FAIL, red) and models developing alternans (ALT, green). Red crosses represent outliers.

FIGURE 9

Ca²⁺-dependence inactivation. Left: framework for isolating the Ca²⁺-dependent inactivation (CDI) (from Limpitikul et al., 2018). Top: voltage step. Middle: [Ca²⁺]_ss example of concentration step. Bottom: I_CaL current in response to voltage activation at baseline [Ca²⁺]_ss (black) and in response to a [Ca²⁺]_ss step (magenta). Right: Steady state CDI (evaluated as a/b) as a function of [Ca²⁺]_ss with ORd (light blue) and BPS2020 model (dark blue), fitted with a Boltzmann curve; CDI quantification are also highlighted for different [Ca²⁺]_o values (magenta for BPS2020 and purple for ORd).