Invasive cardiac catheterisation is a precursor to ablation therapy for ventricular tachycardia. Invasive cardiac diagnostics are fraught with risks. Decades of research has been conducted on the inverse problem of electrocardiography, which can be used to reconstruct Heart Surface Potentials (HSPs) from Body Surface Potentials (BSPs), for non-invasive cardiac diagnostics. State of the art solutions to the inverse problem are unsatisfactory, since the inverse problem is known to be ill-posed. In this paper we propose a novel approach to reconstructing HSPs from BSPs using a Time-Delay Artificial Neural Network (TDANN). We first design the TDANN architecture, and then develop an iterative search space algorithm to find the parameters of the TDANN, which results in the best overall HSP prediction. We use recorded BSPs and HSPs from individuals suffering from serious cardiac conditions to validate our TDANN. The results are encouraging, in that the predicted and recorded HSPs have an average correlation coefficient of 0.7 under diseased conditions.
Given @math BSPs, represented by the vector @math and @math HSPs, represented by vector @math . The inverse problem is given by the linear matrix equation @math . A number of techniques from standard numerical analysis have been proposed to approximate solutions to the transfer matrix @math . A good overview is provided in @cite_10 . The primary idea in all proposed techniques and their variants is to select elements of the matrix @math such that the error @math @math is the l2-norm. , is minimized.
@cite_10
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This article summarizes the theoretical underpinnings of both the forward and inverse problems of electrocardiography. Space limitations prohibit describing all of the research work done in these areas, and the author apologizes in advance for any omissions on this account or due to oversight. The article should enable one to gain a better qualitative and quantitative understanding of the heart's electrical activity.