Bayesian quantitative electrophysiology and its multiple applications in bioengineering

Abstract

Bayesian interpretation of observations began in the early 1700s, and scientific electrophysiology began in the late 1700s. For two centuries these two fields developed mostly separately. In part that was because quantitative Bayesian interpretation, in principle a powerful method of relating measurements to their underlying sources, often required too many steps to be feasible with hand calculation in real applications. As computer power became widespread in the later 1900s, Bayesian models and interpretation moved rapidly but unevenly from the domain of mathematical statistics into applications. Use of Bayesian models now is growing rapidly in electrophysiology. Bayesian models are well suited to the electrophysiological environment, allowing a direct and natural way to express what is known (and unknown) and to evaluate which one of many alternatives is most likely the source of the observations, and the closely related receiver operating characteristic (ROC) curve is a powerful tool in making decisions. Yet, in general, many people would ask what such models are for, in electrophysiology, and what particular advantages such models provide. So to examine this question in particular, this review identifies a number of electrophysiological papers in bioengineering arising from questions in several organ systems to see where Bayesian electrophysiological models or ROC curves were important to the results that were achieved.

Fig. 1

In schematic form, two dipoles (large arrows), having dipole moments p₁ and p₂, represent electrical activity of two segments of cardiac ventricular muscle, drawn as double lines below. At a particular time, these dipoles generate potentials ϕ₁ and ϕ₂ at points S₁ and S₂ on the body surface (represented by the horizontal line at top). Angle θ between each dipole and line from dipole to each body point has a major role in the electrocardiographic forward problem, which is determining potentials on the body from a description of electrical sources in the heart. For inverse electrocardiography, the question is whether, knowing ϕ₁, ϕ₂ the approximate geometry, one can deduce values for p₁, p₂. Although a great deal of knowledge has been developed over time about both forward and inverse problems, there is no comprehensive and satisfactory solution for either forward or inverse problems (small differences between theory and experiment) that has been achieved so far.