Parameter sensitivity from single atrial cell to tissue: How much does it matter? A simulation and multivariate regression study

We previously performed parameter sensitivity analysis in the Courtemanche-Ramirez-Nattel (CRN) human atrial cell model, and sought to extend this to address sensitivities across spatial scales. Thus, we investigated how input variability and uncertainty at cellular level propagates through to affect tissue level dynamics. We simulated action potential (AP) propagation in a strip of cardiac tissue, using the monodomain and CRN tissue/cell models. Input maximal conductances (p=12) within the CRN model were varied within 1/3 of baseline, and points in parameter space selected by Latin hypercube sampling. The tissue was paced for twenty beats at 1Hz (S1), and 6 metrics of AP shape were derived for the final beat (max dV/dt, max voltage, resting voltage, action potential duration to 90% repolarisation (APD90), resting voltage and APD to 50% repolarisation (APD50)). S1 pacing was followed by a single ectopic beat (S2) at different intervals, at one end and the midpoint of the tissue. Additional tissue metrics were calculated, including conduction velocity (CV), CV and APD restitution curves and the size of the tissue vulnerable window. Subsequently, parameter sensitivity on both tissue and cell level outputs was performed using Partial Least Squares regression. Simulations and postprocessing were performed in Nektar++ and Matlab (Mathworks). Regression values were smaller in tissue compared to cell (APD90/max dV/dt R2=0.43/0.27 in tissue vs R2=0.92/0.97 in cells). AP metrics exhibited stronger sensitivities to maximal ionic conductances in single cell compared to tissue simulations (sensitivity indices 0.98/0.99 for max dVdt/max voltage to GNa in cell vs 0.48/0.59 in tissue) while CV was sensitive to GNa (0.61) and VW to GNa (-0.58) and GK1 (-0.61). Further analysis offunctional metrics in tissue will determine sensitivity of tissue to cellular changes.