Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

Branched Latent Neural Maps

We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input-output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent in-distribution generalization properties with small training datasets and short training times on a single processor. Indeed, their in-distribution generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections, in place of a fully-connected structure, significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving biophysically detailed electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale, organ-level and electrical dyssynchrony. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 hours on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of 10 - 4 on an independent test dataset comprised of 50 additional electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be employed to solve inverse problems via global optimization in a few seconds of computational time. This paper provides a novel computational tool to build reliable and efficient reduced-order models for digital twinning in engineering applications. The Julia implementation is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.jl.