Sensitivity of transvenous defibrillation models to adaptive mesh density and resolution: the potential for interactive solution times

Abstract

The voltage gradients induced in ventricular myocardium by an electric shock have been shown to correlate to the probability of the shock producing a successful defibrillation. Finite element modeling is one method for computing these voltage gradients, although the meshing of complex biomedical domains is difficult on a patient-specific basis. We recently described an adaptive algorithm that automates the generation of finite element meshes for complex 3-D domains from bitmapped images. This article examines the sensitivity of the computed distribution of ventricular voltage gradients to the resolution of the images and to the adapted density of the mesh. The results allow us to establish an adaptation stopping criterion and a minimum input image resolution for modeling transvenous defibrillation. The sensitivity to adapted mesh density was analyzed by comparing voltage gradient histograms from successively finer meshes to histograms from a uniform mesh at the maximum possible density. Comparisons were made using the Kolmogorov-Smirnov test with the number of samples required to detect a 5% difference in the histograms at the 0.05 significance level. Adaptation to a global current density error estimate of 5% or less was required in order to achieve acceptance of the null hypothesis that the distributions were the same in all cases. Defibrillation efficacy, however, is predicted from the voltage gradient in the first quartile, and the results suggest that this region of the cumulative histogram converges faster during mesh adaptation than the histogram as a whole. We also compared histograms from models generated from successively finer input images. The histogram of each model was compared with the histogram obtained from the finest possible resolution. In all cases, the null hypothesis of no difference was accepted at resolutions of 2.3 × 2.3 × 3.0 mm. The average time required to build and adapt models to a 5% accuracy at the first quartile at this resolution was 1.8 min. on a common workstation. We believe that this demonstrates a potential for the eventual synthesis of finite element computations into interactive electrode placement tools on a subject-specific basis.