Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees.

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary anatomies combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. We propose an optimization-based method to personalize multiscale coronary flow simulations by assimilating clinical CT myocardial perfusion imaging and cardiac function measurements to yield patient-specific flow distributions and model parameters. Using this proof-of-concept study on a cohort of six patients, we reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based purely on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

Hemodynamics and Wall Mechanics of Vascular Graft Failure.

Blood vessels are subjected to complex biomechanical loads, primarily from pressure-driven blood flow. Abnormal loading associated with vascular grafts, arising from altered hemodynamics or wall mechanics, can cause acute and progressive vascular failure and end-organ dysfunction. Perturbations to mechanobiological stimuli experienced by vascular cells contribute to remodeling of the vascular wall via activation of mechanosensitive signaling pathways and subsequent changes in gene expression and associated turnover of cells and extracellular matrix. In this review, we outline experimental and computational tools used to quantify metrics of biomechanical loading in vascular grafts and highlight those that show potential in predicting graft failure for diverse disease contexts. We include metrics derived from both fluid and solid mechanics that drive feedback loops between mechanobiological processes and changes in the biomechanical state that govern the natural history of vascular grafts. As illustrative examples, we consider application-specific coronary artery bypass grafts, peripheral vascular grafts, and tissue-engineered vascular grafts for congenital heart surgery as each of these involves unique circulatory environments, loading magnitudes, and graft materials.

A probabilistic neural twin for treatment planning in peripheral pulmonary artery stenosis.

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilistic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

Tissue engineered vascular grafts are resistant to the formation of dystrophic calcification.

Advancements in congenital heart surgery have heightened the importance of durable biomaterials for adult survivors. Dystrophic calcification poses a significant risk to the long-term viability of prosthetic biomaterials in these procedures. Herein, we describe the natural history of calcification in the most frequently used vascular conduits, expanded polytetrafluoroethylene grafts. Through a retrospective clinical study and an ovine model, we compare the degree of calcification between tissue-engineered vascular grafts and polytetrafluoroethylene grafts. Results indicate superior durability in tissue-engineered vascular grafts, displaying reduced late-term calcification in both clinical studies (p < 0.001) and animal models (p < 0.0001). Further assessments of graft compliance reveal that tissue-engineered vascular grafts maintain greater compliance (p < 0.0001) and distensibility (p < 0.001) than polytetrafluoroethylene grafts. These properties improve graft hemodynamic performance, as validated through computational fluid dynamics simulations. We demonstrate the promise of tissue engineered vascular grafts, remaining compliant and distensible while resisting long-term calcification, to enhance the long-term success of congenital heart surgeries.

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics.

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.

Computational approaches for mechanobiology in cardiovascular development and diseases.

The cardiovascular development in vertebrates evolves in response to genetic and mechanical cues. The dynamic interplay among mechanics, cell biology, and anatomy continually shapes the hydraulic networks, characterized by complex, non-linear changes in anatomical structure and blood flow dynamics. To better understand this interplay, a diverse set of molecular and computational tools has been used to comprehensively study cardiovascular mechanobiology. With the continual advancement of computational capacity and numerical techniques, cardiovascular simulation is increasingly vital in both basic science research for understanding developmental mechanisms and disease etiologies, as well as in clinical studies aimed at enhancing treatment outcomes. This review provides an overview of computational cardiovascular modeling. Beginning with the fundamental concepts of computational cardiovascular modeling, it navigates through the applications of computational modeling in investigating mechanobiology during cardiac development. Second, the article illustrates the utility of computational hemodynamic modeling in the context of treatment planning for congenital heart diseases. It then delves into the predictive potential of computational models for elucidating tissue growth and remodeling processes. In closing, we outline prevailing challenges and future prospects, underscoring the transformative impact of computational cardiovascular modeling in reshaping cardiovascular science and clinical practice.

Non-invasive Estimation of Pressure Drop Across Aortic Coarctations: Validation of 0D and 3D Computational Models with In Vivo Measurements.

Blood pressure gradient ( Δ P ) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of Δ P estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations. Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N = 17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. Δ P across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation. The 0D simulations were extremely efficient ( ∼ 15 s computation time) compared to 3D simulations ( ∼ 30 h computation time on a cluster). However, the 0D Δ P estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as Δ P ≥ 20 mmHg) with 76% accuracy and 3D simulations improved this to 88%. Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.

Virtual shape-editing of patient-specific vascular models using Regularized Kelvinlets.

OBJECTIVE: Cardiovascular diseases, and the interventions performed to treat them, can lead to changes in the shape of patient vasculatures and their hemodynamics. Computational modeling and simulations of patient-specific vascular networks are increasingly used to quantify these hemodynamic changes, but they require modifying the shapes of the models. Existing methods to modify these shapes include editing 2D lumen contours prescribed along vessel centerlines and deforming meshes with geometry-based approaches. However, these methods can require extensive by-hand prescription of the desired shapes and often do not work robustly across a range of vascular anatomies. To overcome these limitations, we develop techniques to modify vascular models using physics-based principles that can automatically generate smooth deformations and readily apply them across different vascular anatomies. METHODS: We adapt Regularized Kelvinlets, analytical solutions to linear elastostatics, to perform elastic shape-editing of vascular models. The Kelvinlets are packaged into three methods that allow us to artificially create aneurysms, stenoses, and tortuosity. RESULTS: Our methods are able to generate such geometric changes across a wide range of vascular anatomies. We demonstrate their capabilities by creating sets of aneurysms, stenoses, and tortuosities with varying shapes and sizes on multiple patient-specific models. CONCLUSION: Our Kelvinlet-based deformers allow us to edit the shape of vascular models, regardless of their anatomical locations, and parametrically vary the size of the geometric changes. SIGNIFICANCE: These methods will enable researchers to more easily perform virtual-surgery-like deformations, computationally explore the impact of vascular shape on patient hemodynamics, and generate synthetic geometries for data-driven research.

Patient-specific computational flow simulation reveals significant differences in paravisceral aortic hemodynamics between fenestrated and branched endovascular aneurysm repair.

Background: Endovascular aneurysm repair with four-vessel fenestrated endovascular aneurysm repair (fEVAR) or branched endovascular aneurysm repair (bEVAR) currently represent the forefront of minimally invasive complex aortic aneurysm repair. This study sought to use patient-specific computational flow simulation (CFS) to assess differences in postoperative hemodynamic effects associated with fEVAR vs bEVAR. Methods: Patients from two institutions who underwent four-vessel fEVAR with the Cook Zenith Fenestrated platform and bEVAR with the Jotec E-xtra Design platform were retrospectively selected. Patients in both cohorts were treated for paravisceral and extent II, II, and V thoracoabdominal aortic aneurysms. Three-dimensional finite element volume meshes were created from preoperative and postoperative computed tomography scans. Boundary conditions were adjusted for body surface area, heart rate, and blood pressure. Pulsatile flow simulations were performed with equivalent boundary conditions between preoperative and postoperative states. Postoperative changes in hemodynamic parameters were compared between the fEVAR and bEVAR groups. Results: Patient-specific CFS was performed on 20 patients (10 bEVAR, 10 fEVAR) with a total of 80 target vessels (40 renal, 20 celiac, 20 superior mesenteric artery stents). bEVAR was associated with a decrease in renal artery peak flow rate (-5.2% vs +2.0%; P < .0001) and peak pressure (-3.4 vs +0.1%; P < .0001) compared with fEVAR. Almost all renal arteries treated with bEVAR had a reduction in renal artery perfusion (n = 19 [95%]), compared with 35% (n = 7) treated with fEVAR. There were no significant differences in celiac or superior mesenteric artery perfusion metrics (P = .10-.27) between groups. Time-averaged wall shear stress in the paravisceral aorta and branches also varied significantly depending on endograft configuration, with bEVAR associated with large postoperative increases in renal artery (+47.5 vs +13.5%; P = .002) and aortic time-averaged wall shear stress (+200.1% vs -31.3%; P = .001) compared with fEVAR. Streamline analysis revealed areas of hemodynamic abnormalities associated with branched renal grafts which adopt a U-shaped geometry, which may explain the observed differences in postoperative changes in renal perfusion between bEVAR and fEVAR. Conclusions: bEVAR may be associated with subtle decreases in renal perfusion and a large increase in aortic wall shear stress compared with fEVAR. CFS is a novel tool for quantifying and visualizing the unique patient-specific hemodynamic effect of different complex EVAR strategies. Clinical Relevance: This study used patient-specific CFS to compare postoperative hemodynamic effects of four-vessel fenestrated endovascular aneurysm repair (fEVAR) and branched endovascular aneurysm repair (bEVAR) in patients with complex aortic aneurysms. The findings indicate that bEVAR may result in subtle reductions in renal artery perfusion and a significant increase in aortic wall shear stress compared with fEVAR. These differences are clinically relevant, providing insights for clinicians choosing between these approaches. Understanding the patient-specific hemodynamic effects of complex EVAR strategies, as revealed by CFS, can aid in future personalized treatment decisions, and potentially reduce postoperative complications in aortic aneurysm repair.

High Shear Stress Reduces ERG Causing Endothelial-Mesenchymal Transition and Pulmonary Arterial Hypertension.

Pathological high shear stress (HSS, 100 dyn/cm 2 ) is generated in distal pulmonary arteries (PA) (100-500 µm) in congenital heart defects and in progressive PA hypertension (PAH) with inward remodeling and luminal narrowing. Human PA endothelial cells (PAEC) were subjected to HSS versus physiologic laminar shear stress (LSS, 15 dyn/cm 2 ). Endothelial-mesenchymal transition (EndMT), a feature of PAH not previously attributed to HSS, was observed. H3K27ac peaks containing motifs for an ETS-family transcription factor (ERG) were reduced, as was ERG-Krüppel-like factors (KLF)2/4 interaction and ERG expression. Reducing ERG by siRNA in PAEC during LSS caused EndMT; transfection of ERG in PAEC under HSS prevented EndMT. An aorto-caval shunt was preformed in mice to induce HSS and progressive PAH. Elevated PA pressure, EndMT and vascular remodeling were reduced by an adeno-associated vector that selectively replenished ERG in PAEC. Agents maintaining ERG in PAEC should overcome the adverse effect of HSS on progressive PAH.

Simulation-based design of bicuspidization of the aortic valve.

OBJECTIVE: Severe congenital aortic valve pathology in the growing patient remains a challenging clinical scenario. Bicuspidization of the diseased aortic valve has proven to be a promising repair technique with acceptable durability. However, most understanding of the procedure is empirical and retrospective. This work seeks to design the optimal gross morphology associated with surgical bicuspidization with simulations based on the hypothesis that modifications to the free edge length cause or relieve stenosis. METHODS: Model bicuspid valves were constructed with varying free edge lengths and gross morphology. Fluid-structure interaction simulations were conducted in a single patient-specific model geometry. The models were evaluated for primary targets of stenosis and regurgitation. Secondary targets were assessed and included qualitative hemodynamics, geometric height, effective height, orifice area, and billow. RESULTS: Stenosis decreased with increasing free edge length and was pronounced with free edge length less than or equal to 1.3 times the annular diameter d. With free edge length 1.5d or greater, no stenosis occurred. All models were free of regurgitation. Substantial billow occurred with free edge length 1.7d or greater. CONCLUSIONS: Free edge length 1.5d or greater was required to avoid aortic stenosis in simulations. Cases with free edge length 1.7d or greater showed excessive billow and other changes in gross morphology. Cases with free edge length 1.5d to 1.6d have a total free edge length approximately equal to the annular circumference and appeared optimal. These effects should be studied in vitro and in animal studies.

Learning reduced-order models for cardiovascular simulations with graph neural networks.

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.

A Fluid-Solid-Growth Solver for Cardiovascular Modeling.

We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains.

Hemodynamic effects of entry and exit tear size in aortic dissection evaluated with in vitro magnetic resonance imaging and fluid-structure interaction simulation.

Understanding the complex interplay between morphologic and hemodynamic features in aortic dissection is critical for risk stratification and for the development of individualized therapy. This work evaluates the effects of entry and exit tear size on the hemodynamics in type B aortic dissection by comparing fluid-structure interaction (FSI) simulations with in vitro 4D-flow magnetic resonance imaging (MRI). A baseline patient-specific 3D-printed model and two variants with modified tear size (smaller entry tear, smaller exit tear) were embedded into a flow- and pressure-controlled setup to perform MRI as well as 12-point catheter-based pressure measurements. The same models defined the wall and fluid domains for FSI simulations, for which boundary conditions were matched with measured data. Results showed exceptionally well matched complex flow patterns between 4D-flow MRI and FSI simulations. Compared to the baseline model, false lumen flow volume decreased with either a smaller entry tear (- 17.8 and - 18.5%, for FSI simulation and 4D-flow MRI, respectively) or smaller exit tear (- 16.0 and - 17.3%). True to false lumen pressure difference (initially 11.0 and 7.9 mmHg, for FSI simulation and catheter-based pressure measurements, respectively) increased with a smaller entry tear (28.9 and 14.6 mmHg), and became negative with a smaller exit tear (- 20.6 and - 13.2 mmHg). This work establishes quantitative and qualitative effects of entry or exit tear size on hemodynamics in aortic dissection, with particularly notable impact observed on FL pressurization. FSI simulations demonstrate acceptable qualitative and quantitative agreement with flow imaging, supporting its deployment in clinical studies.

Longitudinal investigation of aortic dissection in mice with computational fluid dynamics.

Predicting late adverse events in aortic dissections is challenging. One commonly observed risk factor is partial thrombosis of the false lumen. In this study we investigated false lumen thrombus progression over 7 days in four mice with angiotensin II-induced aortic dissection. We performed computational fluid dynamic simulations with subject-specific boundary conditions from velocity and pressure measurements. We investigated endothelial cell activation potential, mean velocity, thrombus formation potential, and other hemodynamic factors. Our findings support the hypothesis that flow stagnation is the predominant hemodynamic factor driving a large thrombus ratio in false lumina, particularly those with a single fenestration.

Simulation-Based Design of Bicuspidization of the Aortic Valve.

OBJECTIVE: Severe congenital aortic valve pathology in the growing patient remains a challenging clinical scenario. Bicuspidization of the diseased aortic valve has proven to be a promising repair technique with acceptable durability. However, most understanding of the procedure is empirical and retrospective. This work seeks to design the optimal gross morphology associated with surgical bicuspidization with simulations, based on the hypothesis that modifications to the free edge length cause or relieve stenosis. METHODS: Model bicuspid valves were constructed with varying free edge lengths and gross morphology. Fluid-structure interaction simulations were conducted in a single patient-specific model geometry. The models were evaluated for primary targets of stenosis and regurgitation. Secondary targets were assessed and included qualitative hemodynamics, geometric height, effective height, orifice area and prolapse. RESULTS: Stenosis decreased with increasing free edge length and was pronounced with free edge length less than or equal to 1.3 times the annular diameter d. With free edge length 1.5d or greater, no stenosis occurred. All models were free of regurgitation. Substantial prolapse occurred with free edge length greater than or equal to 1.7d. CONCLUSIONS: Free edge length greater than or equal to 1.5d was required to avoid aortic stenosis in simulations. Cases with free edge length greater than or equal to 1.7d showed excessive prolapse and other changes in gross morphology. Cases with free edge length 1.5-1.6d have a total free edge length approximately equal to the annular circumference and appeared optimal. These effects should be studied in vitro and in animal studies.

Non-invasive estimation of pressure drop across aortic coarctations: validation of 0D and 3D computational models with in vivo measurements.

Purpose: Blood pressure gradient (ΔP) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of ΔP estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations. Methods: Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N=17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. ΔP across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation. Results: The 0D simulations were extremely efficient (~15 secs computation time) compared to 3D simulations (~30 hrs computation time on a cluster). However, the 0D ΔP estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as ΔP≥20 mmHg) with 76% accuracy and 3D simulations improved this to 88%. Conclusion: Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.

A computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics.

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

Passive performance evaluation and validation of a viscous impeller pump for subpulmonary fontan circulatory support.

Patients with single ventricle defects undergoing the Fontan procedure eventually face Fontan failure. Long-term cavopulmonary assist devices using rotary pump technologies are currently being developed as a subpulmonary power source to prevent and treat Fontan failure. Low hydraulic resistance is a critical safety requirement in the event of pump failure (0 RPM) as a modest 2 mmHg cavopulmonary pressure drop can compromise patient hemodynamics. The goal of this study is therefore to assess the passive performance of a viscous impeller pump (VIP) we are developing for Fontan patients, and validate flow simulations against in-vitro data. Two different blade heights (1.09 mm vs 1.62 mm) and a blank housing model were tested using a mock circulatory loop (MCL) with cardiac output ranging from 3 to 11 L/min. Three-dimensional flow simulations were performed and compared against MCL data. In-silico and MCL results demonstrated a pressure drop of < 2 mmHg at a cardiac output of 7 L/min for both blade heights. There was good agreement between simulation and MCL results for pressure loss (mean difference - 0.23 mmHg 95% CI [0.24-0.71]). Compared to the blank housing model, low wall shear stress area and oscillatory shear index on the pump surface were low, and mean washout times were within 2 s. This study demonstrated the low resistance characteristic of current VIP designs in the failed condition that results in clinically acceptable minimal pressure loss without increased washout time as compared to a blank housing model under normal cardiac output in Fontan patients.