Multiparameter Optimization of Nonuniform Conduction Properties for Creating Continuous Equivalent Models

Éric IRAKOZE1 and Vincent Jacquemet2
1University of Montreal, 2Université de Montréal


Introduction: The arrhythmogenic role of discrete propagation may be assessed by comparing discrete and equivalent continuous models. We aim to develop an optimization algorithm for estimating the smooth conductivity field that best reproduces the conduction properties of a given discrete model. Methods: Our algorithm iteratively adjusts local conductivity of the continuous model by simulating passive diffusion for 3 ms from a white noise initial condition and computing the RMS error with respect to the discrete model. We derived an approximate formula for the gradient of the cost function that requires (in 2D) only two additional simulations regardless of the number of estimated parameters. Conjugate gradient solver facilitated simultaneous optimization of multiple conductivity parameters. The method was validated in 2D anisotropic tissues with uniform or nonuniform conductivity (slow region with Gaussian profile) and random diffuse fibrosis (84 substrates), as well as in an interconnected cable model of the left atrium (uniform with fibrosis). In nonuniform tissues, the continuous conductivity field was interpolated from its value at 1 to 32 control points. Slow conduction (respectively, fast) was defined as conduction velocity (CV) smaller than 15 cm/s (respectively, larger). Differences in CV or RMS differences of activation maps between discrete and continuous models were reported. Results: Convergence was reached after around 8 iterations. In uniform 2D tissues, longitudinal and transverse CV differences were 1.2% (fast conduction) and 3.1% (slow). In nonuniform 2D tissues, the RMS difference of activation times improved from 4.8 ms (1 control point) to 0.6 ms (32 control points). In the atria, RMS difference of activation times was 1.5 ms (fast) and 2.0 ms (slow). Conclusion: Our approach based on the comparison of passive properties (3 ms simulation) avoids performing active propagation simulations (> 100 ms) at each iteration while reproducing activation maps, with possible applications to large-scale models.