Piero Colli-Franzone

A mathematical procedure for solving the inverse potential problem of electrocardiography. analysis of the time-space accuracy from in vitro experimental data☆

Abstract The inverse potential problem of electrocardiography leads to a Cauchy problem for an elliptic operator and is strongly ill posed. Its solution must be determined by some regularization technique in which a parameter controls the amount of regularization of the solution. Therefore the choice of this smoothing parameter is important for achieving the best accuracy attainable given the discrete approximation errors and the noise level on the data. A regularized inverse procedure is applied to data from an in vitro experiment, and a new criterion for the choice of a quasi-optimal value of the smoothing parameter is described. The performance of this criterion is investigated, and a detailed analysis of the accuracy of the results is carried out. This analysis concerns both the recovered epicardial maps (space analysis) and the ECGs (time analysis).

ACCURATE COMPUTATION OF ELECTROGRAMS IN THE LEFT VENTRICULAR WALL

An integral representation of electrograms is used for large scale simulations in an anisotropic model of the whole left ventricle. Numerical artifacts, like spurious oscillations or peaks, may appear if the computational grid is not fine enough. To avoid an excessive increase in the number of elements and nodes, we present a numerical procedure based on a combination of: a special refinement of the grid, a sub-element technique, a nonlinear interpolation and a split form of the integral. The numerical simulations show that in this way it is possible to suppress the numerical artifacts thus allowing an accurate computation of electrograms in any point inside or outside the myocardial wall.

Localization of ventricular ectopic beats from intracavitary potential distributions: an inverse model in terms of sources

The mathematical model used for estimating the spatial location of the site of origin of paced beats from intracavitary potential maps provided encouraging results despite the oversimplifying assumptions. The robustness of the procedure, which is relatively insensitive to the assigned value of the distance between the dipoles, has been explained from the property of the equivalent quadrupole source. A more general equivalent source should comprise two mutually perpendicular pairs of oppositely directed dipoles to account for the effects of fiber rotation in the area of the wavefront plus a single dipole to account for the normal dipole layer component when the wavefront surface is open.<<ETX>>

Exploring anodal and cathodal make and break cardiac excitation mechanisms in a 3D anisotropic bidomain model

Published studies have investigated the relevance of cardiac virtual electrode responses to unipolar cathodal and anodal stimulations for explaining the make and break excitation mechanisms. Most of these studies have considered 2D bidomain models or cylindrical domains that by symmetry reduce to the 2D case, so the triggering mechanisms and onset of excitation have not yet been fully elucidated in 3D anisotropic models. The goal of this work is to revisit these excitation mechanisms with 3D bidomain simulations considering two tissue types with unequal anisotropy ratio, including transmural fiber rotation and augmenting the Luo-Rudy I membrane model with the so-called funny and the electroporation currents. In addition to usual snapshots of transmembrane potential patterns, we compute from the action potential waveforms the activation time and associated isochrone sequences, yielding a detailed 3D description of the instant and location of excitation origin, shape and propagation of activation wavefronts. A specific aim of this work is to detect the location of the excitation onset and whether its trigger mechanism is (a) electrotonic, i.e. originating from discharge diffusion of currents flowing between virtual cathodes and anodes and/or (b) membrane-based, i.e. arising only from intrinsic depolarizing membrane currents. Our results show that the electrotonic mechanism is observed independently of the degree of unequal anisotropy in diastolic anode make and systolic cathode break. The membrane-based mechanism is observed in diastolic cathode make, diastolic anode break, only for a relative weak anisotropy, and systolic anode break. The excitation trigger mechanism, the location of the excitation origin and the pattern of the isochrone sequence are independent of the degree of anisotropy for diastolic cathode make, systolic cathode and anode break, while they might depend on the degree of anisotropy for diastolic anode make and break. Moreover, the tissue anisotropy has a strong influence on the threshold amplitude of the stimulation pulse triggering these mechanisms.

A parallel solver for anisotropic cardiac models

A parallel solver for numerical simulations of a full cardiac cycle in three dimensional domains, based on the anisotropic monodomain and bidomain models, is presented. The solver employs structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale parallel computations have been run, simulating anisotropic dispersion of the action potential duration.

Mathematical and numerical methods for reaction-diffusion models in electrocardiology

This paper presents a review of current mathematical and numerical models of the bioelectrical activity in the ventricular myocardium, describing cardiac cells excitability and the action-potential propagation in cardiac tissue. The degenerate reaction-diffusion system called the Bidomain model is introduced and interpreted as macroscopic averaging of a cellular model on a periodic assembling of myocytes. The main theoretical results for the cellular and Bidomain models are given. Various approximate models based on some relaxed approaches are also considered, such as Monodomain and eikonal-curvature models. The main numerical methods for the Bidomain and Monodomain models are then reviewed. In particular, we focus on isoparametric finite elements, semi-implicit time discretizations and a parallel iterative solver based on a multilevel Schwarz preconditioned conjugate gradient method. The Bidomain solver is finally applied to the study of the excitation processes generated by virtual electrode response in 3D orthotropic blocks of myocardial tissue.

Anode Make and Break Excitation Mechanisms and Strength-Interval Curves: Bidomain Simulations in 3D Rotational Anisotropy

The shape of anodal strength-interval curves and make and break excitation mechanisms are investigated in a 2D anisotropic Bidomain model, with different membrane models and action potential durations, and in a 3D rotational anisotropic Bidomain model, with axisymmetric or orthotropic conductivity properties. The results have shown that the LRd model with a long intrinsic APD exhibits a systolic dip threshold lower than the diastolic threshold, in agreement with previous experimental data. The spatial and temporal analysis of the excitation patterns indicates a novel anode make excitation mechanism with delayed propagation within the transition from break to make mechanisms.

Relationship Between Cardiac Electrical and Mechanical Activation Markers by Coupling Bidomain and Deformation Models

The aim of this study is to simulate the electromechanical behavior of a cardiac wedge following an endo- or epicardial stimulation, and to study different markers of mechanical contraction times. We investigate how tissue anisotropy affects the performance of the mechanical markers and we evaluate their delay distributions with respect to the electrical activation time. The main results of this study show that: the electrical and mechanical activation sequences are very well correlated; the electromechanical delay displays heterogeneous distributions even if the electrical and mechanical cellular properties are assumed homogeneous; the electromechanical delay is larger in the regions where depolarization proceeds along fiber than across fiber.

Effects of anodal cardiac stimulation on V m and Ca i 2+ distributions: a bidomain study

The aim of this work is to study make and break excitation mechanisms elicited by anodal pulses at different coupling intervals using 2D and 3D anisotropic Bidomain simulations. Two different S1-S2 stimulation protocols are considered, one with the S2 pulse delivered at the same location of the S1 pulse and the other at a distant location. Anodal strength-interval (S-I) curves are computed for both S1-S2 protocols showing results consistent with experimental S-I curves, both in terms of stimulus threshold amplitude and depth of the anodal dip during the break phase. The intracellular calcium concentration (

Modeling ventricular excitation: axial and orthotropic anisotropy effects on wavefronts and potentials

Ca_i^{2+}