Identifying Model Inaccuracies and Solution Uncertainties in Noninvasive Activation-Based Imaging of Cardiac Excitation Using Convex Relaxation

Abstract

Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a non-convex, non-linear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second.

Fast uncertainty quantification of activation sequences in patient‐specific cardiac electrophysiology meeting clinical time constraints

“…A single simulation may take several node‐hours on a large cluster, making it unfeasible at clinical scales, albeit things are rapidly improving thanks to massively parallel general purpose graphics processing unit (GPGPU) hardware . Second, more importantly, it is still unclear how to satisfactorily tailor computer models to a given patient, especially when dealing with such a large set of parameters that are difficult to identify from the sparse, heterogeneous, and uncertain data provided by the clinical workflow …”

“…10 Second, more importantly, it is still unclear how to satisfactorily tailor computer models to a given patient, especially when dealing with such a large set of parameters that are difficult to identify from the sparse, heterogeneous, and uncertain data provided by the clinical workflow. 11,12 The de facto standard bidomain model from cardiac electrophysiology is a strongly nonlinear system of equations 13 and is only a mean-field approximation of the electrophysiological behavior of the cardiac tissue. Several of the spatially dependent parameters, such as electric conductivities, are macroscopically approximated and generally not trivially correlated to the cellular and subcellular properties of the substrate.…”

Validation and Opportunities of Electrocardiographic Imaging: From Technical Achievements to Clinical Applications

“…Similarly, recovery times capture the timing of the repolarization phase. Both quantities can be defined either through the 3-dimensional (3D) myocardial wall ( Han et al, 2011 ), or on the heart surface, including both the epicardium and endocardium ( Erem et al, 2014 ). Examples of such methods include the equivalent double layer (EDL) model and the 3D cardiac electrical imaging (3DCEI) model:…”

A Variational Approach to Sparse Model Error Estimation in Cardiac Electrophysiological Imaging

“…Examples of such models include simple step jump functions [9] to describe the activation of action potential, parameterized curve models to describe the spatiotemporal wavefront evolution [5], and biophysical EP models to describe the dynamics of action potential via differential equations arXiv:1905.04813v1 [eess.IV] 13 May 2019 [6,10]. While the use of such a priori models is effective in regularizing the illposed problem, often the inaccuracy and uncertainty of the model itself creates errors and uncertainty in the solution [4]. This issue of model inaccuracy and the resulting solution uncertainty has been studied with convex relaxation of the original problem of EP imaging [4].…”