Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies

Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly distributed source strength

The solution of the mixed boundary value problem of potential theory involves the computation of the potential field generated by monolayer and double layer source distributions on surfaces at which boundary conditions are known. Closed-form analytical expressions have been described in the literature for the potential field generated by double layers having a linearly distributed strength over triangular source elements. This contribution presents the corresponding expression for the linearly distributed monolayer strength. The solution is shown to be valid for all observation points in space, including those on the interior, edges and vertices of the source triangle

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

BACKGROUND: Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level. METHODS: We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG. RESULTS: We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given. CONCLUSIONS: Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described

ECG marker of adverse electrical remodeling post-myocardial infarction predicts outcomes in MADIT II study

PMC3522579Background Post-myocardial infarction (MI) structural remodeling is characterized by left ventricular dilatation, fibrosis, and hypertrophy of the non-infarcted myocardium. Objective The goal of our study was to quantify post-MI electrical remodeling by measuring the sum absolute QRST integral (SAI QRST). We hypothesized that adverse electrical remodeling predicts outcomes in MADIT II study participants. Methods Baseline orthogonal ECGs of 750 MADIT II study participants (448 [59.7%] ICD arm) were analyzed. SAI QRST was measured as the arithmetic sum of absolute QRST integrals over all three orthogonal ECG leads. The primary endpoint was defined as sudden cardiac death (SCD) or sustained ventricular tachycardia (VT)/ventricular fibrillation (VF) with appropriate ICD therapies. All-cause mortality served as a secondary endpoint. Results Adverse electrical remodeling in post-MI patients was characterized by wide QRS, increased magnitudes of spatial QRS and T vectors, J-point deviation, and QTc prolongation. In multivariable Cox regression analysis after adjustment for age, QRS duration, atrial fibrillation, New York Heart Association heart failure class and blood urea nitrogen, SAI QRST predicted SCD/VT/VF (HR 1.33 per 100 mV*ms (95%CI 1.11–1.59); P=0.002), and all-cause death (HR 1.27 per 100 mV*ms (95%CI 1.03–1.55), P=0.022) in both arms. No interaction with therapy arm and bundle branch block (BBB) status was found. Conclusions In MADIT II patients, increased SAI QRST is associated with increased risk of sustained VT/VF with appropriate ICD therapies and all-cause death in both ICD and in conventional medical therapy arms, and in patients with and without BBB. Further studies of SAI QRST are warranted.JH Libraries Open Access Fun

Mathematical Modeling and Simulation of Ventricular Activation Sequences: Implications for Cardiac Resynchronization Therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy

Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem

The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso-heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition and statistical approaches such as Bayesian Maximum A Posteriori estimation and Kalman filter have been applied. Statistical methods have yielded accurate inverse solutions; however, they require knowledge of a good a priori probability density function, or state transition definition. Minimum relative entropy (MRE) is an approach for inferring probability density function from a set of constraints and prior information, and may be an alternative to those statistical methods since it operates with more simple prior information definitions. However, success of the MRE method also depends on good choice of prior parameters in the form of upper and lower bound values, expected uncertainty in the model and the prior mean. In this paper, we explore the effects of each of these parameters on the solution of inverse ECG problem and discuss the limitations of the method. Our results show that the prior expected value is the most influential of the three MRE parameters