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Abstract Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid–structure interactions (FSIs). However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the valves are limited in their abilities to predict valve performance, capture fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac FSI in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart’s microstructure. Further, it is the first FSI model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure–volume loops that automatically capture isovolumetric contraction and relaxation, and that its responses to changes in loading conditions are consistent with the Frank–Starling mechanism. These complex relationships emerge intrinsically from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical interventions. They also can provide platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients. 

In this work, we use the immersed boundary method with four extensions to simulate a moving liquid–gas interface on a solid surface. We first define a moving contact line model and implements a static-dynamic friction condition at the immersed solid boundary. The dynamic contact angle is endogenous instead of prescribed, and the solid boundary can be non-stationary with respect to time. Second, we simulate both a surface tension force and a Young's force with one general equation that does not involve estimating local curvature. In the third extension, we splice liquid–gas interfaces to handle topological changes, such as the coalescence and separation of liquid droplets or gas bubbles. Finally, we re-sample liquid–gas interface markers to ensure a near-uniform distribution without exerting artificial forces. We demonstrate empirical convergence of our methods on non-trivial examples and apply them to several benchmark cases, including a slipping droplet on a wall and a rising bubble. 

Abstract Transcatheter aortic valve replacement (TAVR) first received FDA approval for high-risk surgical patients in 2011 and has been approved for low-risk surgical patients since 2019. It is now the most common type of aortic valve replacement, and its use continues to accelerate. Computer modeling and simulation (CM&S) is a tool to aid in TAVR device design, regulatory approval, and indication in patient-specific care. This study introduces a computational fluid-structure interaction (FSI) model of TAVR with Medtronic’s CoreValve Evolut R device using the immersed finite element-difference (IFED) method. We perform dynamic simulations of crimping and deployment of the Evolut R, as well as device behavior across the cardiac cycle in a patient-specific aortic root anatomy reconstructed from computed tomography (CT) image data. These IFED simulations, which incorporate biomechanics models fit to experimental tensile test data, automatically capture the contact within the device and between the self-expanding stent and native anatomy. Further, we apply realistic driving and loading conditions based on clinical measurements of human ventricular and aortic pressures and flow rates to demonstrate that our Evolut R model supports a physiological diastolic pressure load and provides informative clinical performance predictions. 

In this paper, we develop a pulsatile compartmental model of the Fontan circulation and use it to explore the effects of a fenestration added to this physiology. A fenestration is a shunt between the systemic and pulmonary veins that is added either at the time of Fontan conversion or at a later time for the treatment of complications. This shunt increases cardiac output and decreases systemic venous pressure. However, these hemodynamic benefits are achieved at the expense of a decrease in the arterial oxygen saturation. The model developed in this paper incorporates fenestration size as a parameter and describes both blood flow and oxygen transport. It is calibrated to clinical data from Fontan patients, and we use it to study the impact of a fenestration on several hemodynamic variables, including systemic oxygen availability, effective oxygen availability, and systemic venous pressure. In certain scenarios corresponding to high-risk Fontan physiology, we demonstrate the existence of a range of fenestration sizes in which the systemic oxygen availability remains relatively constant while the systemic venous pressure decreases. 

Abstract This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data (Randerson et al., 1982, Artif. Organs, 6, 43–49). We also show that the algebraic differential equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters. 

AbstractOne‐dimensional (1D) cardiovascular models offer a non‐invasive method to answer medical questions, including predictions of wave‐reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient‐specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty inin vivoimaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image‐derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three‐dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high‐fidelity patient‐specific haemodynamics models.image Key pointsThis study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error.Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks.Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty.Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.