Parametric Uncertainty Quantification in Electrocardiographic Forward and Inverse Problems

Jake Bergquist1, Lindsay Rupp1, Dana Brooks2, Jess Tate1, Rob MacLeod1, Akil Narayan1
1University of Utah, 2Northeastern University


Parametric uncertainty quantification (UQ) allows for the efficient exploration of model response to inevitable and often poorly understood variability in the model inputs. UQ approaches and implementations have seen increasing development and interest supporting its application to cardiac bioelectrical modeling. Traditionally UQ has targeted forward modeling problems, which implement generally well-posed models and mathematical systems to related parameter inputs to model outputs. However, inverse problems are often more appealing targets for UQ analysis due to their clinical utility in reconstructing source phenomena from measured data. However the ill-posed and generally more complex mathematical formulations of inverse problems has hindered applications of UQ to explore them. One example of such a cardiac bioelectric inverse problem is electrocardiographic imaging (ECGI), which seeks to reconstruct cardiac bioelectric activity from body surface potential (BSP) measurements. Until recently, most attempts to address UQ in the context of ECGI have either explicitly targeted the forward problem (predicting BSP from known cardiac sources) or treated the ECGI inverse problem as if it were a forward problem. These approaches are limited in what useful UQ results they can provide, and the relationship between forward UQ approaches and inverse UQ approaches is poorly understood. In this study, we examine how UQ has been approached in the context of ECGI from both the forward and inverse problem perspective. We address some of the challenges facing UQ in ECGI and explore the interpretation of different UQ approaches for ECGI. Finally, we compare forward problem-based UQ approaches to recently developed inverse problem-based UQ using our novel ECGI formulation.