Multiscale Modeling of Cardiovascular Flows

Simulations of blood flow in the cardiovascular system offer investigative and predictive capabilities to augment current clinical tools. Using image-based modeling, the Navier-Stokes equations can be solved to obtain detailed 3-dimensional hemodynamics in patient-specific anatomical models. Relevant parameters such as wall shear stress and particle residence times can then be calculated from the 3D results and correlated with clinical data for treatment planning and device evaluation. Reduced-order models such as open or closed loop 0D lumped-parameter models can simulate the dynamic behavior of the circulatory system using an analogy to electrical circuits. When coupled to 3D simulations as boundary conditions, they produce physiologically realistic pressure and flow conditions in the 3D domain. We describe fundamentals and current state of the art of patient-specific, multi-scale computational modeling approaches applied to cardiovascular disease. These tools enable investigations of hemodynamics reflecting individual patients physiology, and we provide several illustrative case studies. These methods can supplement current clinical measurement and imaging capabilities and provide predictions of patient outcomes for surgical planning and risk stratification

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 generalization properties with small training datasets and short training times on a single processor. Indeed, their generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving 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 and organ-level. 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 a test dataset comprised of 50 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 used to solve inverse problems via global optimization in a few seconds of computational time

Identification of Hemodynamically Optimal Coronary Stent Designs Based on Vessel Caliber

Coronary stent design influences local patterns of wall shear stress (WSS) that are associated with neointimal growth, restenosis, and the endothelialization of stent struts. The number of circumferentially repeating crowns NC for a given stent de- sign is often modified depending on the target vessel caliber, but the hemodynamic implications of altering NC have not previously been studied. In this investigation, we analyzed the relationship between vessel diameter and the hemodynamically optimal NC using a derivative-free optimization algorithm coupled with computational fluid dynamics. The algorithm computed the optimal vessel diameter, defined as minimizing the area of stent-induced low WSS, for various configurations (i.e., NC) of a generic slotted-tube design and designs that resemble commercially available stents. Stents were modeled in idealized coronary arteries with a vessel diameter that was allowed to vary between 2 and 5 mm. The results indicate that the optimal vessel diameter increases for stent configurations with greater NC, and the designs of current commercial stents incorporate a greater NC than hemodynamically optimal stent designs. This finding suggests that reducing the NC of current stents may improve the hemodynamic environment within stented arteries and reduce the likelihood of excessive neointimal growth and thrombus formation