A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential

Abstract

HighlightsSimplified cardiomyocyte electrophysiology model optimised for patient specific modelling.Modified Mitchell and Schaeffer model.No spurious pacemaker behaviour.Suitable for parameter fitting.Consistent leading order APD approximation.

A Predictive Personalised Model for the Left Atrium

“…We described the local tissue electrophysiology with a heterogeneous isotropic monodomain approximation [7], and the mMS ionic model described in [5]; similarly to the original Mitchell-Schaeffer (MS) model [8], mMS is able to capture the measured CV and ERP restitution properties with the smallest numbers of parameters to constrain, it is proven to be stable to pacemaker behaviour independently of the choice of the parameter values and it is possible to analytically estimate the action potential duration (APD) and the CV restitutions with leading order approximations. We obtained locally personalised patient-specific models with the algorithm described in [6], by fitting the measured local CV restitution and the ERP to a set of pre-computed restitution curves, obtained from the solution of a 1D computational model on a set of known parameters.…”

“…We obtained locally personalised patient-specific models with the algorithm described in [6], by fitting the measured local CV restitution and the ERP to a set of pre-computed restitution curves, obtained from the solution of a 1D computational model on a set of known parameters. To achieve an optimal range of parameters and improve the sensitivity with respect to the measured quantities, we built the data set of pre-computed solutions by sweeping on the parameter set defined by the maximum value of APD (APD max ), the minimum value of the gate variable on the null-cline (h min ) defined in [5], the maximum CV (CV max ) and the τ in and τ open ionic parameters. We then obtained the original parameters by inverting the analytical leading order formulations.…”

“…At each location, an S1-S2 pacing protocol [4] was applied at both the CS and HRA catheters to generate two conduction velocity (CV) restitution curves and an estimate of the effective refractory period (ERP) for each pair of electrodes. We fitted a modified Mitchell-Schaeffer (mMS) cardiac cell model [5] that does not exhibit pacemaker behaviour to the restitution curves recorded during CS pacing with the algorithm developed in [6]. We then interpolated the fitted cell model parameters across the atrial anatomy derived from the anatomical mapping system.…”

Predicting Spiral Wave Stability by Personalized Electrophysiology Models

“…The source term was modeled with mMS model, [11]. This model has the smallest numbers of parameters to constrain while capturing the measured CV and ERP restitution properties and it is proven to be stable to pacemaker behavior.…”

“…From the effective refractory period (ERP) and the conduction velocity (CV) restitutions the fitting algorithm uniquely identified the 5 parameters describing the local electrophysiology of the tissue. In this work we apply the algorithm developed in [10] to constrain the parameters of the modified Mitchell-Schaeffer (mMS) ionic model [11] and we predict if the tissue is capable to sustain arrhythmias. Tissue properties were predicted analyzing the spiral wave stability and the pattern of the rotor tip on a personalized 2D homogeneous tissue slab.…”