An automated near-real time computational method for induction and treatment of scar-related ventricular tachycardias

Highlights • Model-based real-time detection of unique ventricular tachycardia (VT) circuits• Automated detection of isthmus’ exit sites• Computerized fully automated detection of optimal sites for VT ablation• Three orders of magnitude faster than standard based on reaction-diffusion models

∇ · (σ m ∇V m ) = β (I m − I s ) (1) where V m is the transmembrane voltage, σ m is the conductivity tensor, β is the surfaceto-volume ratio, I s is an applied stimulus current for initiating propagation and I m is the transmembrane current given by: where C m is the membrane capacitance per unit area, I ion is the current density flowing through the ionic channels depending on the membrane state and concentrations of ion species represented by a state vector, η, which is described by Eq.(4) according to the chosen ionic model. Cellular dynamics was simulated using the ten Tusscher-Panfilov model (epicardial phenotype) [2], which was modified to reproduce action potential duration values reported in the porcine heart [3]. Modifications of the default parameters of the model were implemented in both healthy and border zone (BZ) cells. In healthy cells, maximum channel conductance of both slow and rapid delayed rectifier potassium currents was increased by 230%. In BZ cells, peak sodium current was reduced by 62%, peak L-type calcium current by 69%, and peak delayed rectifier potassium currents by 31% and 54%. An initial state vector was generated by pacing each cell at a cycle length of 600 ms for 100 cycles.
The conductivity tensor σ m in Eq.1 is given by: where ξ = l|t are the eigendirections of the tissue along the cardiac fiber direction (ξ = l) and transverse (ξ = t) to it within the intracellular (i) and extracellular (e) domain. The eigenvalues of the tensors are given below in Table 1.

Numerical solution
For the spatial discretization of the the monodomain equation a standard finite element method was used as detailed in the openCARP manual, Sec. 30.1). An operator splitting scheme was employed, see openCARP manual, Sec. 30.3). For the temporal discretization a Crank-Nicolson approach was used, openCARP manual, Sec. 30.3.2). The discretized system was solved using the conjugate gradient method with an incomplete LU preconditioner.

Simulations in openCARP
An idealized 2D cardiac infarct model designed with the purpose of replicating the setup used in this study (see Figure 1A) is available for download from RADAR4KIT. The data set includes: ilu_cg_opts parameters.par run.sh vm.mshz Software for validation of our setup is available for download from the openCARP web page. Execution requires mesher for creating the test mesh, openCARP for running the simulations and meshalyzer for visualization of the simulation results.
Snapshots of V m showing reentry induction following the pacing protocol are shown in Figure  1B. Note that the set of tissue conductivities used here resulted in a propagation pattern with enhanced anisotropy (t = 4380 ms). Note also that conduction velocity is slower in the isthmus due to the assigned reduced tissue conductivity. In this setup, reentry was induced by a S2 beat with a coupling interval of 250 ms in respect to the last paced S1 beat (t = 4200 ms -8 pulses with a pacing cycle length of 600 ms). The S2 beat blocked at the isthmus' mouth proximal to the stimulus site at t = 4550 ms, traveled around the scar and reentered the isthmus from its distal mouth (t = 4900 ms) from where it propagated back to the myocardium.
Details of the parameter file used to simulated cardiac excitation within the idealized model are summarized below. To ascertain reproducibility of our simulation setup, all parameters are explicitly given as simulator input that can be directly used with the openCARP simulator [1]. Simulations were tested under both Linux and Mac OSX.

Electrophysiology definition
Two types of viable tissues, healthy and BZ, were defined as follows: