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Dynamic contrast-enhanced (DCE) perfusion imaging has shown great potential to non-invasively assess cancer development and its treatment by their characteristic tissue signatures. Different tracer kinetics models are being applied to estimate tissue and tumor perfusion parameters from DCE perfusion imaging. The goal of this work is to provide an in silico model-based pipeline to evaluate how these DCE imaging parameters may relate to the true tissue parameters. As histology data provides detailed microstructural but not functional parameters, this work can also help to better interpret such data. To this aim in silico vasculatures are constructed and the spread of contrast agent in the tissue is simulated. As a proof of principle we show the evaluation procedure of two tracer kinetic models from in silico contrast-agent perfusion data after a bolus injection. Representative microvascular arterial and venous trees are constructed in silico . Blood flow is computed in the different vessels. Contrast-agent input in the feeding artery, intra-vascular transport, intra-extravascular exchange and diffusion within the interstitial space are modeled. From this spatiotemporal model, intensity maps are computed leading to in silico dynamic perfusion images. Various tumor vascularizations (architecture and function) are studied and show spatiotemporal contrast imaging dynamics characteristic of in vivo tumor morphotypes. The Brix II also called 2CXM, and extended Tofts tracer-kinetics models common in DCE imaging are then applied to recover perfusion parameters that are compared with the ground truth parameters of the in silico spatiotemporal models. The results show that tumor features can be well identified for a certain permeability range. The simulation results in this work indicate that taking into account space explicitly to estimate perfusion parameters may lead to significant improvements in the perfusion interpretation of the current tracer-kinetics models., 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 © 2023 Vignon-Clementel, Jagiella, Dichamp, Kowalski, Lederle, Laue, Kiessling, Sedlaczek and Drasdo.)

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.)

Anatomical and physiological changes alter airflow characteristics and aerosol distribution in the developing lung. Correlation between age and aerosol dosimetry is needed, specifically because youth are more susceptible to medication side effects. In this study, we estimate aerosol dosages (particle diameters of 1, 3, and 5 [Formula: see text]m) in a 3 month-old infant, a 6 year-old child, and a 36 year-old adult by performing whole lung subject-specific particle simulations throughout respiration. For 3 [Formula: see text]m diameter particles we estimate total deposition as 88, 73, and [Formula: see text] and the conducting versus respiratory deposition ratios as 4.0, 0.5, and 0.4 for the infant, child, and adult, respectively. Due to their lower tidal volumes and functional residual capacities the deposited mass is smaller while the tissue concentrations are larger in the infant and child subjects, compared to the adult. Furthermore, we find that dose cannot be predicted by simply scaling by tidal volumes. These results highlight the need for additional clinical and computational studies that investigate the efficiency of treatment, while optimizing dosage levels in order to alleviate side effects, in youth.

Background & Aims: Despite improvements in medical and surgical techniques, post-hepatectomy liver failure (PHLF) remains the leading cause of postoperative death. High postoperative portal vein pressure (P PV ) and portocaval gradient (PCG), which cannot be predicted by current tools, are the most important determinants of PHLF. Therefore, we aimed to evaluate a digital twin to predict the risk of postoperative portal hypertension (PHT)., Methods: We prospectively included 47 patients undergoing major hepatectomy. A mathematical (0D) model of the entire blood circulation was assessed and automatically calibrated from patient characteristics. Hepatic flows were obtained from preoperative flow MRI (n = 9), intraoperative flowmetry (n = 16), or estimated from cardiac output (n = 47). Resection was then simulated in these 3 groups and the computed P PV and PCG were compared to intraoperative data., Results: Simulated post-hepatectomy pressures did not differ between the 3 groups, comparing well with collected data (no significant differences). In the entire cohort, the correlation between measured and simulated P PV values was good (r = 0.66, no adjustment to intraoperative events) or excellent (r = 0.75) after adjustment, as well as for PCG (respectively r = 0.59 and r = 0.80). The difference between simulated and measured post-hepatectomy PCG was ≤3 mmHg in 96% of cases. Four patients suffered from lethal PHLF for whom the model satisfactorily predicted their postoperative pressures., Conclusions: We demonstrated that a 0D model could correctly anticipate postoperative PHT, even using estimated hepatic flow rates as input data. If this major conceptual step is confirmed, this algorithm could change our practice toward more tailor-made procedures, while ensuring satisfactory outcomes., Lay Summary: Post-hepatectomy portal hypertension is a major cause of liver failure and death, but no tool is available to accurately anticipate this potentially lethal complication for a given patient. Herein, we propose using a mathematical model to predict the portocaval gradient at the end of liver resection. We tested this model on a cohort of 47 patients undergoing major hepatectomy and demonstrated that it could modify current surgical decision-making algorithms., Competing Interests: Conflict of interest The authors declare no conflicts of interest that pertain to this work. Please refer to the accompanying ICMJE disclosure forms for further details., (Copyright © 2020 European Association for the Study of the Liver. Published by Elsevier B.V. All rights reserved.)

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.)

In this paper, we perform a verification study of the Coupled-Momentum Method (CMM), a 3D fluid-structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi-infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection-free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi-infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space-time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory., (© 2019 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.

Growth and remodeling of the primitive pharyngeal arch artery (PAA) network into the extracardiac great vessels is poorly understood but a major source of clinically serious malformations. Undisrupted blood flow is required for normal PAA development, yet specific relationships between hemodynamics and remodeling remain largely unknown. Meeting this challenge is hindered by the common reductionist analysis of morphology to single idealized models, where in fact structural morphology varies substantially. Quantitative technical tools that allow tracking of morphological and hemodynamic changes in a population-based setting are essential to advancing our understanding of morphogenesis. Here, we have developed a methodological pipeline from high-resolution nano-computed tomography imaging and live-imaging flow measurements to multiscale pulsatile computational models. We combine experimental-based computational models of multiple PAAs to quantify hemodynamic forces in the rapidly morphing Hamburger Hamilton (HH) stage HH18, HH24 and HH26 embryos. We identify local morphological variation along the PAAs and their association with specific hemodynamic changes. Population-level mechano-morphogenic variability analysis is a powerful strategy for identifying stage-specific regions of well and poorly tolerated morphological and/or hemodynamic variation that may protect or initiate cardiovascular malformations., Competing Interests: Competing interestsThe authors declare no competing or financial interests., (© 2018. Published by The Company of Biologists Ltd.)

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.

Objective: To investigate safety and efficacy of temporary portal hemodynamics modulation with a novel percutaneously adjustable vascular ring (MID-AVR) onto a porcine model of 75% hepatectomy., Background: Postoperative liver failure is a leading cause of mortality after major hepatectomy. Portal flow modulation is an increasingly accepted concept to prevent postoperative liver failure. Nonetheless, the current strategies have shortcomings., Methods: Resection was performed under hemodynamic monitoring in 17 large, white pigs allocated into 2 groups. Eight pigs had ring around the portal vein for 3 days with the aim of reducing changes in hemodynamics due to hepatectomy. Analysis of hemodynamics, laboratory, and histopathological parameters was performed., Results: Percutaneous inflation, deflation, and removal of the MID-AVR were safe. Two (25%) pigs in the MID-AVR group and 4 (45%) controls died before day 3 (P = NS). A moderate increase of portal flow rate per liver mass after resection was associated with better survival (P = 0.017). The portocaval pressure gradient was lower after hepatectomy in the MID-AVR group (P = 0.001). Postoperative serum bilirubin levels were lower in the MID-AVR group (P = 0.007 at day 5). In the MID-AVR group, the Ki67 index was significantly higher on day 3 (P = 0.043) and the architectural derangement was lower (P < 0.05). Morphometric quantification of the bile canaliculi revealed a significantly lower number of intersection branches (P < 0.05) and intersection nodes (P < 0.001) on day 7 compared with the preoperative specimen, in the control group. These differences were not found in the ring group., Conclusions: MID-AVR is safe for portal hemodynamics modulation. It might improve liver regeneration by protecting liver microarchitecture.

The indocyanine green (ICG) clearance, presented as plasma disappearance rate is, presently, a reliable method to estimate the hepatic "function". However, this technique is not instantaneously available and thus cannot been used intra-operatively (during liver surgery). Near-infrared spectroscopy enables to assess hepatic ICG concentration over time in the liver tissue. This article proposes to extract more information from the liver intensity dynamics by interpreting it through a dedicated pharmacokinetics model. In order to account for the different exchanges between the liver tissues, the proposed model includes three compartments for the liver model (sinusoids, hepatocytes and bile canaliculi). The model output dependency to parameters is studied with sensitivity analysis and solving an inverse problem on synthetic data. The estimation of model parameters is then performed with in-vivo measurements in rabbits (El-Desoky et al. 1999). Parameters for different liver states are estimated, and their link with liver function is investigated. A non-linear (Michaelis-Menten type) excretion rate from the hepatocytes to the bile canaliculi was necessary to reproduce the measurements for different liver conditions. In case of bile duct ligation, the model suggests that this rate is reduced, and that the ICG is stored in the hepatocytes. Moreover, the level of ICG remains high in the blood following the ligation of the bile duct. The percentage of retention of indocyanine green in blood, which is a common test for hepatic function estimation, is also investigated with the model. The impact of bile duct ligation and reduced liver inflow on the percentage of ICG retention in blood is studied. The estimation of the pharmacokinetics model parameters may lead to an evaluation of different liver functions., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Background: Up to 90% of individuals with Alagille syndrome have congenital heart diseases. Peripheral pulmonary artery stenosis (PPS), resulting in right ventricular hypertension and pulmonary flow disparity, is one of the most common abnormalities, yet the hemodynamic effects are ill-defined, and optimal patient management and treatment strategies are not well established. The purpose of this pilot study is to use recently refined computational simulation in the setting of multiple surgical strategies, to examine the influence of pulmonary artery reconstruction on hemodynamics in this population., Materials and Methods: Based on computed tomography angiography and cardiac catheterization data, preoperative pulmonary artery models were constructed for 4 patients with Alagille syndrome with PPS (all male, age range: 0.6-2.9 years), and flow simulations with deformable walls were performed. Surgeon directed virtual surgery, mimicking the surgical procedure, was then performed to derive postoperative models. Postoperative simulation-derived hemodynamics and blood flow distribution were then compared with the clinical results., Results: Simulations confirmed substantial resistance, resulting from preoperative severe ostial stenoses, and the use of newly developed adaptive outflow boundary conditions led to excellent agreement with in vivo measurements. Relief of PPS decreased pulmonary artery pressures and improved pulmonary flow distribution both in vivo and in silico with good correlation., Conclusions: Using adaptive outflow boundary conditions, computational simulations can estimate postoperative overall pulmonary flow distribution in patients with Alagille syndrome after pulmonary artery reconstruction. Obstruction relief along with pulmonary artery vasodilation determines postoperative pulmonary flow distribution and newer methods can incorporate these physiologic changes. Evolving blood flow simulations may be useful in surgical or transcatheter planning and in understanding the complex interplay among various obstructions in patients with peripheral pulmonary stenosis., (© 2017 Wiley Periodicals, Inc.)

Diffusion-weighted magnetic resonance imaging (DWI) is a key non-invasive imaging technique for cancer diagnosis and tumor treatment assessment, reflecting Brownian movement of water molecules in tissues. Since densely packed cells restrict molecule mobility, tumor tissues produce usually higher signal (a.k.a. less attenuated signal) on isotropic maps compared with normal tissues. However, no general quantitative relation between DWI data and the cell density has been established. In order to link low-resolution clinical cross-sectional data with high-resolution histological information, we developed an image processing and analysis chain, which was used to study the correlation between the diffusion coefficient (D value) estimated from DWI and tumor cellularity from serial histological slides of a resected non-small cell lung cancer tumor. Color deconvolution followed by cell nuclei segmentation was performed on digitized histological images to determine local and cell-type specific 2d (two-dimensional) densities. From these, the 3d cell density was inferred by a model-based sampling technique, which is necessary for the calculation of local and global 3d tumor cell count. Next, DWI sequence information was overlaid with high-resolution CT data and the resected histology using prominent anatomical hallmarks for co-registration of histology tissue blocks and non-invasive imaging modalities' data. The integration of cell numbers information and DWI data derived from different tumor areas revealed a clear negative correlation between cell density and D value. Importantly, spatial tumor cell density can be calculated based on DWI data. In summary, our results demonstrate that tumor cell count and heterogeneity can be predicted from DWI data, which may open new opportunities for personalized diagnosis and therapy optimization.

Little is known about transport throughout the respiration cycle in the conducting airways. It is challenging to appropriately describe the time-dependent number of particles entering back into the model during exhalation. Modeling the entire lung is not feasible; therefore, multidomain methods must be used. Here, we present a new framework that is designed to simulate particles throughout the respiration cycle, incorporating realistic airway geometry and respiration. This framework is applied for a healthy rat lung exposed to  ∼ 1μm diameter particles, chosen to facilitate parameterization and validation. The flow field is calculated in the conducting airways (3D domain) by solving the incompressible Navier-Stokes equations with experimentally derived boundary conditions. Particles are tracked throughout inspiration by solving a modified Maxey-Riley equation. Next, we pass the time-dependent particle concentrations exiting the 3D model to the 1D volume conservation and advection-diffusion models (1D domain). Once the 1D models are solved, we prescribe the time-dependent number of particles entering back into the 3D airways to again solve for 3D transport. The coupled simulations highlight that about twice as many particles deposit during inhalation compared to exhalation for the entire lung. In contrast to inhalation, where most particles deposit at the bifurcation zones, particles deposit relatively uniformly on the gravitationally dependent side of the 3D airways during exhalation. Strong agreement to previously collected regional experimental data is shown, as the 1D models account for lobe-dependent morphology. This framework may be applied to investigate dosimetry in other species and pathological lungs., (Copyright © 2016 John Wiley & Sons, Ltd.)

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).)

Peripheral pulmonary artery stenosis (PPS) is a congenital abnormality resulting in pulmonary blood flow disparity and right ventricular hypertension. Despite recent advance in catheter-based interventions, surgical reconstruction is still preferred to treat complex PPS. However optimal surgical strategies remain unclear. It would be of great benefit to be able to predict post-operative hemodynamics to assist with surgical planning toward optimizing outcomes. While image-based computational fluid dynamics has been used in cardiovascular surgical planning, most studies have focused on the impact of local geometric changes on hemodynamic performance. Previous experimental studies suggest morphological changes in the pulmonary arteries not only alter local hemodynamics but also lead to distal pulmonary adaptation. In this proof of concept study, a constant shear stress hypothesis and structured pulmonary trees are used to derive adaptive outflow boundary conditions for post-operative simulations. Patient-specific simulations showed the adaptive outflow boundary conditions by the constant shear stress model to provide better predictions of pulmonary flow distribution than the conventional strategy of maintaining outflow boundary conditions. On average, the relative difference, when compared to the gold standard clinical test, in blood flow distribution to the right lung is reduced from 20 to 4 %. This suggests adaptive outflow boundary conditions should be incorporated into post-operative modeling in patients with complex PPS.

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.

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

There has been relatively little attention given on predicting particle deposition in the respiratory zone of the diseased lungs despite the high prevalence of chronic obstructive pulmonary disease (COPD). Increased alveolar volume and deterioration of alveolar septum, characteristic of emphysema, may alter the amount and location of particle deposition compared to healthy lungs, which is particularly important for toxic or therapeutic aerosols. In an attempt to shed new light on aerosol transport and deposition in emphysematous lungs, we performed numerical simulations in models of healthy and emphysematous acini motivated by recent experimental lobar-level data in rats (Oakes et al., 2014a). Compared to healthy acinar structures, models of emphysematous subacini were created by removing inter-septal alveolar walls and enhancing the alveolar volume in either a homogeneous or heterogeneous fashion. Flow waveforms and particle properties were implemented to match the experimental data. The occurrence of flow separation and recirculation within alveolar cavities was found in proximal generations of the healthy zones, in contrast to the radial-like airflows observed in the diseased regions. In agreement with experimental data, simulations point to particle deposition concentrations that are more heterogeneously distributed in the diseased models compared with the healthy one. Yet, simulations predicted less deposition in the emphysematous models in contrast to some experimental studies, a likely consequence due to the shallower penetration depths and modified flow topologies in disease compared to health. These spatial-temporal particle transport simulations provide new insight on deposition in the emphysematous acini and shed light on experimental observations., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

The adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions. We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero-dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs., (Copyright © 2015 John Wiley & Sons, Ltd.)

We develop a quantitative single cell-based mathematical model for multi-cellular tumor spheroids (MCTS) of SK-MES-1 cells, a non-small cell lung cancer (NSCLC) cell line, growing under various nutrient conditions: we confront the simulations performed with this model with data on the growth kinetics and spatial labeling patterns for cell proliferation, extracellular matrix (ECM), cell distribution and cell death. We start with a simple model capturing part of the experimental observations. We then show, by performing a sensitivity analysis at each development stage of the model that its complexity needs to be stepwise increased to account for further experimental growth conditions. We thus ultimately arrive at a model that mimics the MCTS growth under multiple conditions to a great extent. Interestingly, the final model, is a minimal model capable of explaining all data simultaneously in the sense, that the number of mechanisms it contains is sufficient to explain the data and missing out any of its mechanisms did not permit fit between all data and the model within physiological parameter ranges. Nevertheless, compared to earlier models it is quite complex i.e., it includes a wide range of mechanisms discussed in biological literature. In this model, the cells lacking oxygen switch from aerobe to anaerobe glycolysis and produce lactate. Too high concentrations of lactate or too low concentrations of ATP promote cell death. Only if the extracellular matrix density overcomes a certain threshold, cells are able to enter the cell cycle. Dying cells produce a diffusive growth inhibitor. Missing out the spatial information would not permit to infer the mechanisms at work. Our findings suggest that this iterative data integration together with intermediate model sensitivity analysis at each model development stage, provide a promising strategy to infer predictive yet minimal (in the above sense) quantitative models of tumor growth, as prospectively of other tissue organization processes. Importantly, calibrating the model with two nutriment-rich growth conditions, the outcome for two nutriment-poor growth conditions could be predicted. As the final model is however quite complex, incorporating many mechanisms, space, time, and stochastic processes, parameter identification is a challenge. This calls for more efficient strategies of imaging and image analysis, as well as of parameter identification in stochastic agent-based simulations.

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.

In silico models of airflow and particle deposition in the lungs are increasingly used to determine the therapeutic or toxic effects of inhaled aerosols. While computational methods have advanced significantly, relatively few studies have directly compared model predictions to experimental data. Furthermore, few prior studies have examined the influence of emphysema on particle deposition. In this work we performed airflow and particle simulations to compare numerical predictions to data from our previous aerosol exposure experiments. Employing an image-based 3D rat airway geometry, we first compared steady flow simulations to coupled 3D-0D unsteady simulations in the healthy rat lung. Then, in 3D-0D simulations, the influence of emphysema was investigated by matching disease location to the experimental study. In both the healthy unsteady and steady simulations, good agreement was found between numerical predictions of aerosol delivery and experimental deposition data. However, deposition patterns in the 3D geometry differed between the unsteady and steady cases. On the contrary, satisfactory agreement was not found between the numerical predictions and experimental data for the emphysematous lungs. This indicates that the deposition rate downstream of the 3D geometry is likely proportional to airflow delivery in the healthy lungs, but not in the emphysematous lungs. Including small airway collapse, variations in downstream airway size and tissue properties, and tracking particles throughout expiration may result in a more favorable agreement in future studies., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

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.)

Image-based in silico modeling tools provide detailed velocity and particle deposition data. However, care must be taken when prescribing boundary conditions to model lung physiology in health or disease, such as in emphysema. In this study, the respiratory resistance and compliance were obtained by solving an inverse problem; a 0D global model based on healthy and emphysematous rat experimental data. Multi-scale CFD simulations were performed by solving the 3D Navier-Stokes equations in an MRI-derived rat geometry coupled to a 0D model. Particles with 0.95 μm diameter were tracked and their distribution in the lung was assessed. Seven 3D-0D simulations were performed: healthy, homogeneous, and five heterogeneous emphysema cases. Compliance (C) was significantly higher (p = 0.04) in the emphysematous rats (C = 0.37 ± 0.14 cm(3)/cmH2O) compared to the healthy rats (C = 0.25 ± 0.04 cm(3)/cmH2O), while the resistance remained unchanged (p = 0.83). There were increases in airflow, particle deposition in the 3D model, and particle delivery to the diseased regions for the heterogeneous cases compared to the homogeneous cases. The results highlight the importance of multi-scale numerical simulations to study airflow and particle distribution in healthy and diseased lungs. The effect of particle size and gravity were studied. Once available, these in silico predictions may be compared to experimental deposition data.

Background: Computational fluid dynamics has been increasingly used in congenital heart surgery to simulate pathophysiological blood flow, investigate surgical options, or design medical devices. Several commercial and research computational or numerical codes have been developed. They present different approaches to numerically solve the blood flow equations, raising the question whether these numerical codes are equally reliable to achieve accurate simulation results. Accordingly, we sought to examine the influence of numerical code selection in several complex congenital cardiac operations., Material and Methods: The main steps of blood flow simulations are detailed (geometrical mesh, boundary conditions, and solver numerical methods) for congenital cardiac operations of increasing complexity. The first case tests different numerical solutions against an analytical, or exact, solution. In the second case, the three-dimensional domain is a patient-specific superior cavopulmonary anastomosis. As an analytical solution does not exist in such a complex geometry, different numerical solutions are compared. Finally, a realistic case of a systemic-to-pulmonary shunt is presented with both geometrically and physiologically challenging conditions. For all, solutions from a commercially available code and an open-source research code are compared., Results: In the first case, as the mesh or solver numerical method is refined, the simulation results for both codes converged to the analytical solution. In the second example, velocity differences between the two codes are greater when the resolution of the mesh were lower and less refined. The third case with realistic anatomy reveals that the pulsatile complex flow is very similar for both codes., Conclusions: The precise setup of the numerical cases has more influence on the results than the choice of numerical codes. The need for detailed construction of the numerical model that requires high computational cost depends on the precision needed to answer the biomedical question at hand and should be assessed for each problem on a combination of clinically relevant patient-specific geometry and physiological conditions., (Copyright © 2014 Elsevier Inc. All rights reserved.)

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.)

Single ventricle heart defects are among the most serious congenital heart diseases, and are uniformly fatal if left untreated. Typically, a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed, after which the superior vena cava (SVC) and inferior vena cava (IVC) are directly connected to the pulmonary arteries (PA). In an attempt to improve hemodynamic performance and hepatic flow distribution (HFD) of Fontan patients, a novel Y-shaped graft has recently been proposed to replace the traditional tube-shaped extracardiac grafts. Previous studies have demonstrated that the Y-graft is a promising design with the potential to reduce energy loss and improve HFD. However these studies also found suboptimal Y-graft performance in some patient models. The goal of this work is to determine whether performance can be improved in these models through further design optimization. Geometric and hemodynamic factors that influence the HFD have not been sufficiently investigated in previous work, particularly for the Y-graft. In this work, we couple Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Specifically, we investigate the potential of using a Y-graft design with unequal branch diameters to improve hepatic distribution under a highly uneven RPA/LPA flow split. As expected, the resulting optimal Y-graft geometry largely depends on the pulmonary flow split for a particular patient. The unequal branch design is demonstrated to be unnecessary under most conditions, as it is possible to achieve the same or better performance with equal-sized branches. Two patient-specific examples show that optimization-derived Y-grafts effectively improve the HFD, compared to initial nonoptimized designs using equal branch diameters. An instance of constrained optimization shows that energy efficiency slightly increases with increasing branch size for the Y-graft, but that a smaller branch size is preferred when a proximal anastomosis is needed to achieve optimal HFD.

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.)

An idealized systemic-to-pulmonary shunt anatomy is parameterized and coupled to a closed loop, lumped parameter network (LPN) in a multidomain model of the Norwood surgical anatomy. The LPN approach is essential for obtaining information on global changes in cardiac output and oxygen delivery resulting from changes in local geometry and physiology. The LPN is fully coupled to a custom 3D finite element solver using a semi-implicit approach to model the heart and downstream circulation. This closed loop multidomain model is then integrated with a fully automated derivative-free optimization algorithm to obtain optimal shunt geometries with variable parameters of shunt diameter, anastomosis location, and angles. Three objective functions: (1) systemic; (2) coronary; and (3) combined systemic and coronary oxygen deliveries are maximized. Results show that a smaller shunt diameter with a distal shunt-brachiocephalic anastomosis is optimal for systemic oxygen delivery, whereas a more proximal anastomosis is optimal for coronary oxygen delivery and a shunt between these two anatomies is optimal for both systemic and coronary oxygen deliveries. Results are used to quantify the origin of blood flow going through the shunt and its relationship with shunt geometry. Results show that coronary artery flow is directly related to shunt position.

The objective of this work is to perform a virtual planning of surgical repairs in patients with congenital heart diseases--to test the predictive capability of a closed-loop multi-scale model. As a first step, we reproduced the pre-operative state of a specific patient with a univentricular circulation and a bidirectional cavopulmonary anastomosis (BCPA), starting from the patient's clinical data. Namely, by adopting a closed-loop multi-scale approach, the boundary conditions at the inlet and outlet sections of the three-dimensional model were automatically calculated by a lumped parameter network. Successively, we simulated three alternative surgical designs of the total cavopulmonary connection (TCPC). In particular, a T-junction of the venae cavae to the pulmonary arteries (T-TCPC), a design with an offset between the venae cavae (O-TCPC) and a Y-graft design (Y-TCPC) were compared. A multi-scale closed-loop model consisting of a lumped parameter network representing the whole circulation and a patient-specific three-dimensional finite volume model of the BCPA with detailed pulmonary anatomy was built. The three TCPC alternatives were investigated in terms of energetics and haemodynamics. Effects of exercise were also investigated. Results showed that the pre-operative caval flows should not be used as boundary conditions in post-operative simulations owing to changes in the flow waveforms post-operatively. The multi-scale approach is a possible solution to overcome this incongruence. Power losses of the Y-TCPC were lower than all other TCPC models both at rest and under exercise conditions and it distributed the inferior vena cava flow evenly to both lungs. Further work is needed to correlate results from these simulations with clinical outcomes.

While many congenital heart defects can be treated without significant long term sequelae, some achieve successful palliation as their definitive endpoints. The single-ventricle defect is one such defect and leaves the child with only one operational ventricle, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during early childhood. Numerical simulations may be used to investigate these hemodynamic conditions and their relation to post-operative sequelae; however, they rely heavily on boundary condition prescription. In this study, we investigate the impact of hemodynamic input data uncertainties on simulation results. Imaged-based patient-specific models of the multi-branched pulmonary arteries and superior vena cava were built for five cavopulmonary connection (i.e. Glenn) patients. Magnetic resonance imaging and catheterization data were acquired for each patient prior to their Fontan surgery. Inflow and outflow boundary conditions were constructed to match available clinical data and resulted in the development of a framework to incorporate these types of clinical data into patient-specific simulations. Three-dimensional computational fluid dynamics simulations were run and hemodynamic indicators were computed. Power loss was low (and efficiency very high) and a linear correlation was found between power loss and cardiac index among the five patients. Other indicators such as low wall shear stress were considered to better characterize these patients. Flow was complex and oscillatory near the anastomosis, and laminar in the smaller branches. While common trends were seen among patients, results showed differences among patients, especially in the 3D maps, strengthening the importance of patient-specific simulations. A sensitivity analysis was performed to investigate the impact of input data (clinical and modeling) to construct boundary conditions on several indicators. Overall, the sensitivity of the output indicators to the input data was small but non-negligible. The sensitivity of commonly used hemodynamic indicators to compare patients is discussed in this context. Power efficiency was much more sensitive to pressure variation than power loss. To increase the precision of such indicators, mean flow split between right and left lungs needs to be measured with more accuracy with higher priority than refining the model of how the flow is distributed on average among the smaller branches. Although ± 10% flow split imprecision seemed reasonable in terms of patient comparison, this study suggests that the common practice of imposing a right pulmonary artery/left pulmonary artery flow split of 55%/45% when performing patient specific simulations should be avoided. This study constitutes a first step towards understanding the hemodynamic differences between pre- and post Fontan surgery, predicting these differences, and evaluating surgical outcomes based on preoperative data.

Treatments for coarctation of the aorta (CoA) can alleviate blood pressure (BP) gradients (Δ), but long-term morbidity still exists that can be explained by altered indices of hemodynamics and biomechanics. We introduce a technique to increase our understanding of these indices for CoA under resting and nonresting conditions, quantify their contribution to morbidity, and evaluate treatment options. Patient-specific computational fluid dynamics (CFD) models were created from imaging and BP data for one normal and four CoA patients (moderate native CoA: Δ12 mmHg, severe native CoA: Δ25 mmHg and postoperative end-to-end and end-to-side patients: Δ0 mmHg). Simulations incorporated vessel deformation, downstream vascular resistance and compliance. Indices including cyclic strain, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were quantified. Simulations replicated resting BP and blood flow data. BP during simulated exercise for the normal patient matched reported values. Greatest exercise-induced increases in systolic BP and mean and peak ΔBP occurred for the moderate native CoA patient (SBP: 115 to 154 mmHg; mean and peak ΔBP: 31 and 73 mmHg). Cyclic strain was elevated proximal to the coarctation for native CoA patients, but reduced throughout the aorta after treatment. A greater percentage of vessels was exposed to subnormal TAWSS or elevated OSI for CoA patients. Local patterns of these indices reported to correlate with atherosclerosis in normal patients were accentuated by CoA. These results apply CFD to a range of CoA patients for the first time and provide the foundation for future progress in this area.

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.)

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.

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.

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed.

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.

Background: Reduced lower limb blood flow and resistive hemodynamic conditions potentially promote aortic inflammation and aneurysmal degeneration. We used abdominal ultrasonography, magnetic resonance imaging, and computational flow modeling to determine the relationship between reduced infrarenal aortic blood flow in chronic spinal cord injury (SCI) subjects and risk for abdominal aortic aneurysm (AAA) disease., Methods: Aortic diameter in consecutive SCI subjects (n = 123) was determined via transabdominal ultrasonography. Aortic anatomic and physiologic data were acquired via magnetic resonance angiography (MRA; n = 5) and cine phase-contrast magnetic resonance flow imaging (n = 4) from SCI subjects whose aortic diameter was less than 3.0 cm by ultrasonography. Computational flow models were constructed from magnetic resonance data sets. Results were compared with those obtained from ambulatory control subjects (ultrasonography, n = 129; MRA/phase-contrast magnetic resonance flow imaging, n = 6) who were recruited at random from a larger pool of risk factor-matched individuals without known AAA disease., Results: Age, sex distribution, and smoking histories were comparable between the SCI and control groups. In the SCI group, time since injury averaged 26 +/- 13 years (mean +/- SD). Aortic diameter was larger (P < .01), and the prevalence of large (> or = 2.5 cm; P < .01) or aneurysmal (> or = 3.0 cm; P < .05) aortas was greater in SCI subjects. Paradoxically, common iliac artery diameters were reduced in SCI subjects (< 1.0 cm; 48% SCI vs 26% control; P < .0001). Focal preaneurysmal enlargement was noted in four of five SCI subjects by MRA. Flow modeling revealed normal flow volume, biphasic and reduced oscillatory flow, slower pressure decay, and reduced wall shear stress in the SCI infrarenal aorta., Conclusions: Characteristic aortoiliac hemodynamic and morphologic adaptations occur in response to chronic SCI. Slower aortic pressure decay and reduced wall shear stress after SCI may contribute to mural degeneration, enlargement, and an increased prevalence of AAA disease.