From in vivo plasma composition to in vitro cardiac electrophysiology and in silico virtual heart: the extracellular calcium enigma

In spite of its potential impact on simulation results, the problem of setting the appropriate Ca(2+) concentration ([Ca(2+)](o)) in computational cardiac models has not yet been properly considered. Usually [Ca(2+)](o) values are derived from in vitro electrophysiology. Unfortunately, [Ca(2+)](o) in the experiments is set significantly far (1.8 or 2 mM) from the physiological [Ca(2+)] in blood (1.0-1.3 mM). We analysed the inconsistency of [Ca(2+)](o) among in vivo, in vitro and in silico studies and the dependence of cardiac action potential (AP) duration (APD) on [Ca(2+)](o). Laboratory measurements confirmed the difference between standard extracellular solutions and normal blood [Ca(2+)]. Experimental data on human atrial cardiomyocytes confirmed literature data, demonstrating an inverse relationship between APD and [Ca(2+)](o). Sensitivity analysis of APD on [Ca(2+)](o) for five of the most used cardiac cell models was performed. Most of the models responded with AP prolongation to increases in [Ca(2+)](o), i.e. opposite to the AP shortening observed in vitro and in vivo. Modifications to the Ten Tusscher-Panfilov model were implemented to demonstrate that qualitative consistency among in vivo, in vitro and in silico studies can be achieved. The Courtemanche atrial model was used to test the effect of changing [Ca(2+)](o) on quantitative predictions about the effect of K(+) current blockade. The present analysis suggests that (i) [Ca(2+)](o) in cardiac AP models should be changed from 1.8 to 2 mM to approximately 1.15 mM in order to reproduce in vivo conditions, (ii) the sensitivity to [Ca(2+)](o) of ventricular AP models should be improved in order to simulate real conditions, (iii) modifications to the formulation of Ca(2+)-dependent I(CaL) inactivation can make models more suitable to analyse AP when [Ca(2+)](o) is set to lower physiological values, and (iv) it could be misleading to use non-physiological high [Ca(2+)](o) when the quantitative analysis of in vivo pathophysiological mechanisms is the ultimate aim of simulation.