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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., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

One-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 in in vivo imaging 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. KEY POINTS: This 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., (© 2024 The Author(s). The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.)

The Fontan physiology is a surgically created circulation for patients with a single functioning ventricle. Patients with this circulation tend to have lower exercise tolerance compared to those with a normal circulation. Important computational and experimental work has been done to investigate this reduction in exercise tolerance. However, there are few systematic modeling studies that focus on the effect of several surgically determined parameters within the same framework. We propose a mathematical model to describe the Fontan circulation under exercise. We then formulate a heuristic based on clinical data from Fontan patients to estimate exercise tolerance. The model is used to investigate the effect of three important surgically determined parameters on exercise tolerance: the systemic arterial compliance, the systemic-venous to pulmonary-venous fenestration, and the resistance of the total cavopulmonary connection., Competing Interests: Declaration of Competing Interest None., (Copyright © 2024 IPEM. Published by Elsevier Ltd. All rights reserved.)

This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.)

Patients with hypoplastic left heart syndrome (HLHS) are born with an underdeveloped left heart. They typically receive a sequence of surgeries that result in a single ventricle physiology called the Fontan circulation. While these patients usually survive into early adulthood, they are at risk for medical complications, partially due to their lower than normal cardiac output, which leads to insufficient cerebral and gut perfusion. While clinical imaging data can provide detailed insight into cardiovascular function within the imaged region, it is difficult to use these data for assessing deficiencies in the rest of the body and for deriving blood pressure dynamics. Data from patients used in this paper include three-dimensional, magnetic resonance angiograms (MRA), time-resolved phase contrast cardiac magnetic resonance images (4D-MRI) and sphygmomanometer blood pressure measurements. The 4D-MRI images provide detailed insight into velocity and flow in vessels within the imaged region, but they cannot predict flow in the rest of the body, nor do they provide values of blood pressure. To remedy these limitations, this study combines the MRA, 4D-MRI, and pressure data with 1D fluid dynamics models to predict hemodynamics in the major systemic arteries, including the cerebral and gut vasculature. A specific focus is placed on studying the impact of aortic reconstruction occurring during the first surgery that results in abnormal vessel morphology. To study these effects, we compare simulations for an HLHS patient with simulations for a matched control patient that has double outlet right ventricle (DORV) physiology with a native aorta. Our results show that the HLHS patient has hypertensive pressures in the brain as well as reduced flow to the gut. Wave intensity analysis suggests that the HLHS patient has irregular circulatory function during light upright exercise conditions and that predicted wall shear stresses are lower than normal, suggesting the HLHS patient may have hypertension., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

This paper presents a semi-automatic method for the construction of volumetric models of the aortic valve using computed tomography angiography images. Although the aortic valve typically cannot be segmented directly from a computed tomography angiography image, the method described herein uses manually selected samples of an aortic segmentation derived from this image to inform the construction. These samples capture certain physiologic landmarks and are used to construct a volumetric valve model. As a demonstration of the capabilities of this method, valve models for 25 pediatric patients are created. A selected valve anatomy is used to perform fluid-structure interaction simulations using the immersed finite element/difference method with physiologic driving and loading conditions. Simulation results demonstrate this method creates a functional valve that opens and closes normally and generates pressure and flow waveforms that are similar to those observed clinically., (© 2022. The Author(s) under exclusive licence to Biomedical Engineering Society.)

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., (© 2022. The Author(s).)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Ahmad, Jin, Penny, Rusin, Peskin and Puelz.)

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., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.)

Key Points: Inflammation in response to bacterial endotoxin challenge impacts physiological functions, including cardiovascular, thermal and pain dynamics, although the mechanisms are poorly understood. We develop an innovative mathematical model incorporating interaction pathways between inflammation and physiological processes observed in response to an endotoxin challenge. We calibrate the model to individual data from 20 subjects in an experimental study of the human inflammatory and physiological responses to endotoxin, and we validate the model against human data from an independent study. Using the model to simulate patient responses to different treatment modalities reveals that a multimodal treatment combining several therapeutic strategies gives the best recovery outcome., Abstract: Uncontrolled, excessive production of pro-inflammatory mediators from immune cells and traumatized tissues can cause systemic inflammatory conditions such as sepsis, one of the ten leading causes of death in the USA, and one of the three leading causes of death in the intensive care unit. Understanding how inflammation affects physiological processes, including cardiovascular, thermal and pain dynamics, can improve a patient's chance of recovery after an inflammatory event caused by surgery or a severe infection. Although the effects of the autonomic response on the inflammatory system are well-known, knowledge about the reverse interaction is lacking. The present study develops a mathematical model analyzing the inflammatory system's interactions with thermal, pain and cardiovascular dynamics in response to a bacterial endotoxin challenge. We calibrate the model with individual data from an experimental study of the inflammatory and physiological responses to a one-time administration of endotoxin in 20 healthy young men and validate it against data from an independent endotoxin study. We use simulation to explore how various treatments help patients exposed to a sustained pathological input. The treatments explored include bacterial endotoxin adsorption, antipyretics and vasopressors, as well as combinations of these. Our findings suggest that the most favourable recovery outcome is achieved by a multimodal strategy, combining all three interventions to simultaneously remove endotoxin from the body and alleviate symptoms caused by the immune system as it fights the infection., (© 2021 The Authors. The Journal of Physiology © 2021 The Physiological Society.)

Vascular access connection configurations during tandem extracorporeal membrane oxygenation (ECMO) and therapeutic plasma exchange (TPE) may impact exchange kinetics. In these tandem procedures, typically the TPE inlet line is proximal to the TPE return line with respect to blood flow in the ECMO device, maximizing the opportunity for replacement fluid homogenization within the ECMO circuit. However, if TPE inlet and return line connections are switched, recirculation-a phenomenon in which replacement fluid leaving the TPE return line is prematurely drawn into the TPE inlet line prior to satisfactory homogenization within the ECMO circuit-will occur. Such recirculation could diminish TPE efficacy in patients on ECMO and mitigate therapeutic benefits. Using a mathematical model of recirculation in tandem ECMO and TPE, we demonstrate that the predicted impact of recirculation is negligible and vascular access connection positioning does not appear to be a point of clinical concern with regard to TPE kinetics., (© 2020 Wiley Periodicals LLC.)

We formulate and study a new mathematical model of pulmonary hypertension. Based on principles of fluid and elastic dynamics, we introduce a model that quantifies the stiffening of pulmonary vasculature (arteries and arterioles) to reproduce the hemodynamics of the pulmonary system, including physiologically consistent dependence between compliance and resistance. This pulmonary model is embedded in a closed-loop network of the major vessels in the body, approximated as one-dimensional elastic tubes, and zero-dimensional models for the heart and other organs. Increasingly severe pulmonary hypertension is modeled in the context of two extreme scenarios: (1) no cardiac compensation and (2) compensation to achieve constant cardiac output. Simulations from the computational model are used to estimate cardiac workload, as well as pressure and flow traces at several locations. We also quantify the sensitivity of several diagnostic indicators to the progression of pulmonary arterial stiffening. Simulation results indicate that pulmonary pulse pressure, pulmonary vascular compliance, pulmonary RC time, luminal distensibility of the pulmonary artery, and pulmonary vascular impedance are much better suited to detect the early stages of pulmonary hypertension than mean pulmonary arterial pressure and pulmonary vascular resistance, which are conventionally employed as diagnostic indicators for this disease.

Fontan patients may undergo additional surgical modifications to mitigate complications like protein-losing enteropathy, liver cirrhosis, and other issues in their splanchnic circulation. Recent case reports show promise for several types of modifications, but the subtle effects of these surgeries on the circulation are not well understood. In this paper, we employ mathematical modeling of blood flow to systematically quantify the impact of these surgical changes on extracardiac Fontan hemodynamics. We investigate two modifications: (1) the fenestrated Fontan and (2) the Fontan with hepatic vein exclusion. Closed-loop hemodynamic models are used, which consist of one-dimensional networks for the major vessels and zero-dimensional models for the heart and organ beds. Numerical results suggest the hepatic vein exclusion has the greatest overall impact on the hemodynamics, followed by the largest sized fenestration. In particular, the hepatic vein exclusion drastically lowers portal venous pressure while the fenestration decreases pulmonary artery pressure. Both modifications increase flow to the intestines, a finding consistent with their utility in clinical practice for combating complications in the splanchnic circulation., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.