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Mechanical forces are essential for proper growth and remodeling of the primitive pharyngeal arch arteries (PAAs) into the great vessels of the heart. Despite general acknowledgement of a hemodynamic-malformation link, the direct correlation between hemodynamics and PAA morphogenesis remains poorly understood. The elusiveness is largely due to difficulty in performing isolated hemodynamic perturbations and quantifying changes in-vivo. Previous in-vivo arch artery occlusion/ablation experiments either did not isolate the effects of hemodynamics, did not analyze the results in a 3D context or did not consider the effects of varying degrees of occlusion. Here, we overcome these limitations by combining minimally invasive occlusion experiments in the avian embryo with 3D anatomical models of development and in-silico testing of experimental phenomenon. We detail morphological and hemodynamic changes 24 hours post vessel occlusion. 3D anatomical models showed that occlusion geometries had more circular cross-sectional areas and more elongated arches than their control counterparts. Computational fluid dynamics revealed a marked change in wall shear stress-morphology trends. Instantaneous (in-silico) occlusion models provided mechanistic insights into the dynamic vessel adaptation process, predicting pressure-area trends for a number of experimental occlusion arches. We follow the propagation of small defects in a single embryo Hamburger Hamilton (HH) Stage 18 embryo to a more serious defect in an HH29 embryo. Results demonstrate that hemodynamic perturbation of the presumptive aortic arch, through varying degrees of vessel occlusion, overrides natural growth mechanisms and prevents it from becoming the dominant arch of the aorta., (© 2021. Biomedical Engineering Society.)

When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs., (© 2020 John Wiley & Sons, Ltd.)

Goal: This manuscript evaluates atrioventric-ular valve regurgitation (AVVR) in babies born with an already very challenging heart condition, i.e., with single ventricle physiology. Although the second surgery that single ventricle patients undergo is thought to decrease AVVR, there is much controversy in the clinical literature about AVVR treatment., Methods: The effect of AVVR on Stage 1 haemodynamics and resulting acute changes from conversion to Stage 2 circulation in single ventricle patients are analyzed through lumped parameter models. Several degrees of AVVR severity are analyzed, for two types of valve regurgitation: incomplete leaflet closure and valve prolapse., Results: The models show that increasing AVVR in Stage 1 induces the following effects: first, higher stroke volume and associated decrease in ventricular end-systolic volume; second, increase in atrial volumes with V-loop enlargement in pressure-volume curves; third, pulmonary venous hypertension. The Stage 2 surgery results in volume unloading of the ventricle, thereby, driving a decrease in AVVR. However, this effect is offset by an increase in ventricular pressures resulting in a net increase in regurgitation fraction (RF) of approximately 0.1 (for example, in severe AVVR, the preoperative RF increases from 60% to 70% postoperatively). Moreover, despite some improvements to sarcomere function early after Stage 2 surgery, it may deteriorate in cases of severe AVVR., Conclusion: In patients with moderate to severe AVVR, restoration of atrioventricular valve competence prior to, or at the time of, Stage 2 surgery would likely lead to improved haemodynamics and clinical outcome as the models suggest that uncorrected AVVR can worsen across Stage 2 surgery. This was found to be independent of the AVVR degree and mechanisms.

Objective: Cirrhosis is the common end stage of any given chronic liver disease, developing after persistent destruction and regeneration of parenchymal liver cells. The associated architectural distortion increases the intrahepatic vascular resistance, leading to portal hypertension and systemic circulatory disorders. This study investigates the impact of the changing vascular resistances on the hepatic and global circulation hemodynamics during cirrhogenesis., Methods: Cirrhogenesis was revisited using the thioacetamide rat model (N = 20). Rats were sacrificed at weeks 0, 6, 12, and 18. For each time-point, three-dimensional vascular geometries were created by combining hepatic vascular corrosion casting with μCT imaging. Morphological quantification of the trees branching topology provided the input for a lobe-specific lumped parameter model of the liver that was coupled to a closed-loop model of the entire circulation of the rat. Hemodynamics was simulated in physiological and pathological circumstances., Results: The simulations showed the effect of the liver vascular resistances (driven by the hepatic venous resistance increase) on liver hemodynamics with portal hypertension observed after 12 weeks. The closed-loop model was further adapted to account for systemic circulatory compensation mechanisms and disorders frequently observed in cirrhosis and simulated their impact on the hepatic, systemic, and pulmonary hemodynamics., Conclusion: The simulations explain how vascular changes due to cirrhosis severely disrupt both hepatic and global hemodynamics., Significance: This study is a priori the first to model the rat's entire blood circulation during cirrhogenesis. Since it is able to simulate cirrhosis main characteristics, the model may be translated to humans for the assessment of liver interventions.

The liver function may be degraded after partial liver ablation surgery. Adverse liver hemodynamics have been shown to be associated to liver failure. The link between these hemodynamics changes and ablation size is however poorly understood. This article proposes to explain with a closed-loop lumped model the hemodynamics changes observed during twelve surgeries in pigs. The portal venous tree is modeled with a pressure-dependent variable resistor. The variables measured, before liver ablation, are used to tune the model parameters. Then, the liver partial ablation is simulated with the model and the simulated pressures and flows are compared with post-operative measurements. Fluid infusion and blood losses occur during the surgery. The closed-loop model presented accounts for these blood volume changes. Moreover, the impact of blood volume changes and the liver lobe mass estimations on the simulated variables is studied. The typical increase of portal pressure, increase of liver pressure loss, slight decrease of portal flow and major decrease in arterial flow are quantitatively captured by the model for a 75% hepatectomy. It appears that the 75% decrease in hepatic arterial flow can be explained by the resistance increase induced by the surgery, and that no hepatic arterial buffer response (HABR) mechanism is needed to account for this change. The different post-operative states, observed in experiments, are reproduced with the proposed model. Thus, an explanation for inter-subjects post-operative variability is proposed. The presented framework can easily be adapted to other species circulations and to different pathologies for clinical hepatic applications., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies)., (© 2017 The Author(s).)

A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition, while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification.

Tetralogy of Fallot is a congenital heart disease characterized over time, after the initial repair, by the absence of a functioning pulmonary valve, which causes regurgitation, and by progressive enlargement of the right ventricle outflow tract (RVOT). Due to this pathological anatomy, available transcatheter valves are usually too small to be deployed there. To avoid surgical valve replacement, an alternative consists in implanting a reducer prior to or in combination with the valve. It has been shown in animal experiments to be promising, but with some limitations. The effect of a percutaneous pulmonary valve reducer on hemodynamics in enlarged RVOT is thus studied by computational modeling. To this aim, blood flow in the RVOT is modeled with CFD coupled to a simplified valve model and 0D downstream models. Simulations are performed in an image-based geometry and boundary conditions tuned to reproduce the pathological flow without the device. Different device designs are built and compared with the initial device-free state, or with the reducer alone. Results suggest that pressure loss is higher for the reducer alone than for the full device, and that the latter successfully restores hemodynamics to a healthy state and induces a more symmetric flow in the pulmonary arteries. Moreover, pressure forces on the reducer and on the valve have the same magnitudes. Migration would occur towards the right ventricle rather than the pulmonary arteries. Results support the thesis that the reducer does not introduce clinically significant pressure gradients, as was found in animal experiments. Such study could help transfer to patients.

Single ventricle heart defects involve pathologies in which the heart has only one functional pumping chamber. In these conditions, treatment consists of three staged procedures. At stage 1 pulmonary flow is provided through an artificial shunt from the systemic circulation. Representative hemodynamics models able to explore different virtual surgical options can be built based on pre-operative imaging and patient data. In this context, the specification of boundary conditions is necessary to compute pressure and flow in the entire domain. However, these boundary conditions are rarely the measured variables. Moreover, to take into account the rest of the circulation outside of the three-dimensional modeled domain, a number of reduced order models exist. A simplified method is presented to iteratively, but automatically, tune reduced model parameters from hemodynamic data clinically measured before stage 2 surgery. Patient-specific local hemodynamics around the distal systemic-to-pulmonary shunt anastomosis and the connected pulmonary arteries are also analyzed. Multi-scale models of pre-stage 2 single ventricle patients are developed, including a 3D model of shunt-pulmonary connection and a number of pulmonary arteries. For each pulmonary outlet a total downstream resistance is identified, consistent with measured flow split and pressures. Target pressures such as minimum, maximum or average over one or both lungs are considered, depending on the clinical measurement. When possible, both steady and pulsatile identifications are performed. The methodology is demonstrated with six patient-specific models: the clinical target data are well-matched, except for one case where clinical data were subsequently found inconsistent. Inhomogeneous pressure, swirling blood flow patterns and very high wall shear stress 3D maps highlight similarities and differences among patients. Steady and pulsatile tuning results are similar. This work demonstrates (1) how to use routine clinical data to define boundary conditions for patient-specific 3D models in pre-stage 2 single ventricle circulations and (2) how simulations can help to check the coherence of clinical data, or provide insights to clinicians that are otherwise difficult to measure, such as in the presence of kinks. Finally, the choice of steady vs. pulsatile tuning, limitations and possible extensions of this work are discussed.

A new framework for estimation of lumped (for instance, Windkessel) model parameters from uncertain clinical measurements is presented. The ultimate aim is to perform patient-specific haemodynamic analysis. This framework is based on sensitivity analysis tools and the sequential estimation approach of the unscented Kalman filter. Sensitivity analysis and parameter estimation are performed in lumped parameter models, which act as reduced order surrogates of the 3D domain for haemodynamic analysis. While the goal of sensitivity analysis is to assess potential identifiability problems, the unscented Kalman filter estimation leads to parameter estimates based on clinical measurements and modelling assumptions. An application of such analysis and parameter estimation methodology is demonstrated for synthetic and real data. Equality constraints on various physiological parameters are enforced. Since the accuracy of the Windkessel parameter estimates depends on the lumped parameter representativeness, the latter is iteratively improved by running few 3D simulations while simultaneously improving the former. Such a method is applied on a patient-specific aortic coarctation case. Less than 3% and 9% errors between the clinically measured quantities and 3D simulation results for rest and stress are obtained, respectively. Knowledge on how these Windkessel parameters change from rest to stress can thus be learned by such an approach. Lastly, it is demonstrated that the proposed approach is capable of dealing with a wide variety of measurements and cases where the pressure and flow clinical measurements are not taken simultaneously., (Copyright © 2014 John Wiley & Sons, Ltd.)

3D computational fluid dynamics (CFD) in patient-specific geometries provides complementary insights to clinical imaging, to better understand how heart disease, and the side effects of treating heart disease, affect and are affected by hemodynamics. This information can be useful in treatment planning for designing artificial devices that are subject to stress and pressure from blood flow. Yet, these simulations remain relatively costly within a clinical context. The aim of this work is to reduce the complexity of patient-specific simulations by combining image analysis, computational fluid dynamics and model order reduction techniques. The proposed method makes use of a reference geometry estimated as an average of the population, within an efficient statistical framework based on the currents representation of shapes. Snapshots of blood flow simulations performed in the reference geometry are used to build a POD (Proper Orthogonal Decomposition) basis, which can then be mapped on new patients to perform reduced order blood flow simulations with patient specific boundary conditions. This approach is applied to a data-set of 17 tetralogy of Fallot patients to simulate blood flow through the pulmonary artery under normal (healthy or synthetic valves with almost no backflow) and pathological (leaky or absent valve with backflow) conditions to better understand the impact of regurgitated blood on pressure and velocity at the outflow tracts. The model reduction approach is further tested by performing patient simulations under exercise and varying degrees of pathophysiological conditions based on reduction of reference solutions (rest and medium backflow conditions respectively)., (Copyright © 2013 Elsevier B.V. All rights reserved.)

Single ventricle hearts are congenital cardiovascular defects in which the heart has only one functional pumping chamber. The treatment for these conditions typically requires a three-staged operative process where Stage 1 is typically achieved by a shunt between the systemic and pulmonary arteries, and Stage 2 by connecting the superior venous return to the pulmonary circulation. Surgically, the Stage 2 circulation can be achieved through a procedure called the Hemi-Fontan, which reconstructs the right atrium and pulmonary artery to allow for an enlarged confluence with the superior vena cava. Based on pre-operative data obtained from two patients prior to Stage 2 surgery, we developed two patient-specific multi-scale computational models, each including the 3D geometrical model of the surgical junction constructed from magnetic resonance imaging, and a closed-loop systemic lumped-parameter network derived from clinical measurements. "Virtual" Hemi-Fontan surgery was performed on the 3D model with guidance from clinical surgeons, and a corresponding multi-scale simulation predicts the patient's post-operative hemodynamic and physiologic conditions. For each patient, a post-operative active scenario with an increase in the heart rate (HR) and a decrease in the pulmonary and systemic vascular resistance (PVR and SVR) was also performed. Results between the baseline and this "active" state were compared to evaluate the hemodynamic and physiologic implications of changing conditions. Simulation results revealed a characteristic swirling vortex in the Hemi-Fontan in both patients, with flow hugging the wall along the SVC to Hemi-Fontan confluence. One patient model had higher levels of swirling, recirculation, and flow stagnation. However, in both models, the power loss within the surgical junction was less than 13% of the total power loss in the pulmonary circulation, and less than 2% of the total ventricular power. This implies little impact of the surgical junction geometry on the SVC pressure, cardiac output, and other systemic parameters. In contrast, varying HR, PVR, and SVR led to significant changes in theses clinically relevant global parameters. Adopting a work-flow of customized virtual planning of the Hemi-Fontan procedure with patient-specific data, this study demonstrates the ability of multi-scale modeling to reproduce patient specific flow conditions under differing physiological states. Results demonstrate that the same operation performed in two different patients can lead to different hemodynamic characteristics, and that modeling can be used to uncover physiologic changes associated with different clinical conditions., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Objectives: A novel Y-shaped baffle has been proposed for the Fontan operation with promising initial results. However, previous studies have relied either on idealized models or a single patient-specific model. The objective of this study is to comprehensively compare the hemodynamic performance and hepatic blood flow distribution of the Y-graft Fontan baffle with 2 current designs using multiple patient-specific models., Methods: Y-shaped and tube-shaped grafts were virtually implanted into 5 patient-specific Glenn models forming 3 types of Fontan geometries: Y-graft, T-junction, and offset. Unsteady flow simulations were performed at rest and at varying exercise conditions. The hepatic flow distribution between the right and left lungs was carefully quantified using a particle tracking method. Other physiologically relevant parameters such as energy dissipation, superior vena cava pressure, and wall shear stress were evaluated., Results: The Fontan geometry significantly influences the hepatic flow distribution. The Y-graft design improves the hepatic flow distribution effectively in 4 of 5 patients, whereas the T-junction and offset designs may skew as much as 97% of hepatic flow to 1 lung in 2 cases. Sensitivity studies show that changes in pulmonary flow split can affect the hepatic flow distribution dramatically but that some Y-graft and T-junction designs are relatively less sensitive than offset designs. The Y-graft design offers moderate improvements over the traditional designs in power loss and superior vena cava pressure in all patients., Conclusions: The Y-graft Fontan design achieves overall superior hemodynamic performance compared with traditional designs. However, the results emphasize that no one-size-fits-all solution is available that will universally benefit all patients and that designs should be customized for individual patients before clinical application., (Copyright © 2012 The American Association for Thoracic Surgery. Published by Mosby, Inc. All rights reserved.)

Background: Atherosclerotic plaque in the descending thoracic aorta (dAo) is related to altered wall shear stress (WSS) for normal patients. Resection with end-to-end anastomosis (RWEA) is the gold standard for coarctation of the aorta (CoA) repair, but may lead to altered WSS indices that contribute to morbidity., Methods: Computational fluid dynamics (CFD) models were created from imaging and blood pressure data for control subjects and age- and gender-matched CoA patients treated by RWEA (four males, two females, 15 ± 8 years). CFD analysis incorporated downstream vascular resistance and compliance to generate blood flow velocity, time-averaged WSS (TAWSS), and oscillatory shear index (OSI) results. These indices were quantified longitudinally and circumferentially in the dAo, and several visualization methods were used to highlight regions of potential hemodynamic susceptibility., Results: The total dAo area exposed to subnormal TAWSS and OSI was similar between groups, but several statistically significant local differences were revealed. Control subjects experienced left-handed rotating patterns of TAWSS and OSI down the dAo. TAWSS was elevated in CoA patients near the site of residual narrowings and OSI was elevated distally, particularly along the left dAo wall. Differences in WSS indices between groups were negligible more than 5 dAo diameters distal to the aortic arch., Conclusions: Localized differences in WSS indices within the dAo of CoA patients treated by RWEA suggest that plaque may form in unique locations influenced by the surgical repair. These regions can be visualized in familiar and intuitive ways allowing clinicians to track their contribution to morbidity in longitudinal studies., (© 2011 Copyright the Authors. Congenital Heart Disease © 2011 Wiley Periodicals, Inc.)

Coronary flow is different from the flow in other parts of the arterial system because it is influenced by the contraction and relaxation of the heart. To model coronary flow realistically, the compressive force of the heart acting on the coronary vessels needs to be included. In this study, we developed a method that predicts coronary flow and pressure of three-dimensional epicardial coronary arteries by considering models of the heart and arterial system and the interactions between the two models. For each coronary outlet, a lumped parameter coronary vascular bed model was assigned to represent the impedance of the downstream coronary vascular networks absent in the computational domain. The intramyocardial pressure was represented with either the left or right ventricular pressure depending on the location of the coronary arteries. The left and right ventricular pressure were solved from the lumped parameter heart models coupled to a closed loop system comprising a three-dimensional model of the aorta, three-element Windkessel models of the rest of the systemic circulation and the pulmonary circulation, and lumped parameter models for the left and right sides of the heart. The computed coronary flow and pressure and the aortic flow and pressure waveforms were realistic as compared to literature data.

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure-volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.

Congenital heart defects with a single functional ventricle, such as hypoplastic left heart syndrome and tricuspid atresia, require a staged surgical approach to separate the systemic and pulmonary circulations. Ultimately, the venous or pulmonary side of the heart is bypassed by directly connecting the vena cava to the pulmonary arteries with a modified t-shaped junction. The Fontan procedure (total cavopulmonary connection, TCPC) completes this process of separation. To date, computational fluid dynamics (CFD) simulations in this low pressure, passive flow, intrathoracic system have neglected the presumed important effects of respiration on physiology and higher "stress" states such as with exercise have never been considered. We hypothesize that incorporating effects of respiration and exercise would provide more realistic estimates of TCPC performance. Time-dependent, 3D blood flow simulations are performed by a custom finite element solver for two patient-specific Fontan models with a novel respiration model, developed to generate physiologic time-varying flow conditions. Blood flow features, pressure, and energy efficiency are analyzed at rest and with increasing flow rates to simulate exercise conditions. The simulations produce realistic pressure and flow data, comparable to that measured by catheterization and echocardiography, and demonstrate substantial increases in energy dissipation (i.e. decreased performance) with exercise and respiration due to increasing intensity of small scale vortices in the flow. As would be expected, these changes are highly dependent on patient-specific anatomy and Fontan geometry. We propose that respiration and exercise should be incorporated into TCPC CFD simulations to provide increasingly realistic evaluations of TCPC performance.