Identifying myocardial ischemia by inversely computing transmembrane potentials from body-surface potential maps

We attempted to solve the inverse electrocardio-graphic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to estimate the size and location of myocardial ischemia. We modeled the bioelectric process by combining a static bidomain heart model with a torso conduction model. Although the task of computing myocardial TMPs at an arbitrary time instance is still an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the inverse solutions yielded a good estimate of ischemic regions, which is of more clinical interest than merely reporting the voltage values. We formulated the inverse problem as a minimization problem constrained by a partial differential equation that models the forward problem. This framework greatly reduces the computational costs compared with the traditional approach of building the lead-field matrix. It also enables one to flexibly set different discretization resolutions for the source variables and other state variables, a desirable feature for solving ill-posed inverse problems. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.