Global Sensitivity Analysis for Patient-Specific Aortic Simulations: The Role of Geometry, Boundary Condition and Large Eddy Simulation Modeling Parameters.

Numerical simulations for computational hemodynamics in clinical settings require a combination of many ingredients, mathematical models, solvers and patient-specific data. The sensitivity of the solutions to these factors may be critical, particularly when we have a partial or noisy knowledge of data. Uncertainty quantification is crucial to assess the reliability of the results. We present here an extensive sensitivity analysis in aortic flow simulations, to quantify the dependence of clinically relevant quantities to the patient-specific geometry and the inflow boundary conditions. Geometry and inflow conditions are generally believed to have a major impact on numerical simulations. We resort to a global sensitivity analysis, (i.e., not restricted to a linearization around a working point), based on polynomial chaos expansion (PCE) and the associated Sobol' indices. We regard the geometry and the inflow conditions as the realization of a parametric stochastic process. To construct a physically consistent stochastic process for the geometry, we use a set of longitudinal-in-time images of a patient with an abdominal aortic aneurysm (AAA) to parametrize geometrical variations. Aortic flow is highly disturbed during systole. This leads to high computational costs, even amplified in a sensitivity analysis -when many simulations are needed. To mitigate this, we consider here a large Eddy simulation (LES) model. Our model depends in particular on a user-defined parameter called filter radius. We borrowed the tools of the global sensitivity analysis to assess the sensitivity of the solution to this parameter too. The targeted quantities of interest (QoI) include: the total kinetic energy (TKE), the time-average wall shear stress (TAWSS), and the oscillatory shear index (OSI). The results show that these indexes are mostly sensitive to the geometry. Also, we find that the sensitivity may be different during different instants of the heartbeat and in different regions of the domain of interest. This analysis helps to assess the reliability of in silico tools for clinical applications.

Simulating the spread of COVID-19 via a spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion.

We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

Numerical sensitivity analysis of a variational data assimilation procedure for cardiac conductivities.

An accurate estimation of cardiac conductivities is critical in computational electro-cardiology, yet experimental results in the literature significantly disagree on the values and ratios between longitudinal and tangential coefficients. These are known to have a strong impact on the propagation of potential particularly during defibrillation shocks. Data assimilation is a procedure for merging experimental data and numerical simulations in a rigorous way. In particular, variational data assimilation relies on the least-square minimization of the misfit between simulations and experiments, constrained by the underlying mathematical model, which in this study is represented by the classical Bidomain system, or its common simplification given by the Monodomain problem. Operating on the conductivity tensors as control variables of the minimization, we obtain a parameter estimation procedure. As the theory of this approach currently provides only an existence proof and it is not informative for practical experiments, we present here an extensive numerical simulation campaign to assess practical critical issues such as the size and the location of the measurement sites needed for in silico test cases of potential experimental and realistic settings. This will be finalized with a real validation of the variational data assimilation procedure. Results indicate the presence of lower and upper bounds for the number of sites which guarantee an accurate and minimally redundant parameter estimation, the location of sites being generally non critical for properly designed experiments. An effective combination of parameter estimation based on the Monodomain and Bidomain models is tested for the sake of computational efficiency. Parameter estimation based on the Monodomain equation potentially leads to the accurate computation of the transmembrane potential in real settings.

SEX AND VASCULAR BIOMECHANICS: A HYPOTHESIS FOR THE MECHANISM UNDERLYING DIFFERENCES IN THE PREVALENCE OF ABDOMINAL AORTIC ANEURYSMS IN MEN AND WOMEN.

The prevalence of abdominal aortic aneurysms differs greatly between men and women across the spectrum of ages. The reason for this discrepancy is not clear and likely involves several factors including the impact of sex hormones. We hypothesize that the unique spatial localization of abdominal aortic aneurysms is dictated in part by local hemodynamic forces on the vascular wall. Specifically, we propose that oscillatory shear stress is a specific signal to the endothelium that initiates the events ultimately leading to abdominal aortic aneurysm formation. We are proposing that sex-dependent differences in oscillatory shear stress in the infra-renal aorta may explain the observed differences between men and women. Initial observations suggest that, indeed, men and women have different degrees of oscillatory blood flow in the infra-renal abdominal aorta. The challenge is to extend these observations to show a causal relationship between oscillatory flow and aneurysm formation.

Aortic hemodynamics after thoracic endovascular aortic repair, with particular attention to the bird-beak configuration.

PURPOSE: To quantitatively evaluate the impact of thoracic endovascular aortic repair (TEVAR) on aortic hemodynamics, focusing on the implications of a bird-beak configuration. METHODS: Pre- and postoperative CTA images from a patient treated with TEVAR for post-dissecting thoracic aortic aneurysm were used to evaluate the anatomical changes induced by the stent-graft and to generate the computational network essential for computational fluid dynamics (CFD) analysis. These analyses focused on the bird-beak configuration, flow distribution into the supra-aortic branches, and narrowing of the distal descending thoracic aorta. Three different CFD analyses (A: preoperative lumen, B: postoperative lumen, and C: postoperative lumen computed without stenosis) were compared at 3 time points during the cardiac cycle (maximum acceleration of blood flow, systolic peak, and maximum deceleration of blood flow). RESULTS: Postoperatively, disturbance of flow was reduced at the bird-beak location due to boundary conditions and change of geometry after TEVAR. Stent-graft protrusion with partial coverage of the origin of the left subclavian artery produced a disturbance of flow in this vessel. Strong velocity increase and flow disturbance were found at the aortic narrowing in the descending thoracic aorta when comparing B and C, while no effect was seen on aortic arch hemodynamics. CONCLUSION: CFD may help physicians to understand aortic hemodynamic changes after TEVAR, including the change in aortic arch geometry, the effects of a bird-beak configuration, the supra-aortic flow distribution, and the aortic true lumen dynamics. This study is the first step in establishing a computational framework that, when completed with patient-specific data, will allow us to study thoracic aortic pathologies and their endovascular management.

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries.

PURPOSE: The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements. METHODS: Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS. RESULTS: Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15 mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods. CONCLUSION: The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

Reduced Order Modeling for Real-Time Stent Deformation Simulations of Transcatheter Aortic Valve Prostheses.

Computational modeling can be a critical tool to predict deployment behavior for transcatheter aortic valve replacement (TAVR) in patients with aortic stenosis. However, due to the mechanical complexity of the aortic valve and the multiphysics nature of the problem, described by partial differential equations (PDEs), traditional finite element (FE) modeling of TAVR deployment is computationally expensive. In this preliminary study, a PDEs-based reduced order modeling (ROM) framework is introduced for rapidly simulating structural deformation of the Medtronic Evolut R valve stent frame. Using fifteen probing points from an Evolut model with parametrized loads enforced, 105 FE simulations were performed in the so-called offline phase, creating a snapshot library. The library was used in the online phase of the ROM for a new set of applied loads via the proper orthogonal decomposition-Galerkin (POD-Galerkin) approach. Simulations of small radial deformations of the Evolut stent frame were performed and compared to full order model (FOM) solutions. Linear elastic and hyperelastic constitutive models in steady and unsteady regimes were implemented within the ROM. Since the original POD-Galerkin method is formulated for linear problems, specific methods for the nonlinear terms in the hyperelastic case were employed, namely, the Discrete Empirical Interpolation Method. The ROM solutions were in strong agreement with the FOM in all numerical experiments, with a speed-up of at least 92% in CPU Time. This framework serves as a first step toward real-time predictive models for TAVR deployment simulations.

Dynamic Coronary Blood Flow Velocity and Wall Shear Stress Estimation Using Ultrasound in an Ex Vivo Porcine Heart.

PURPOSE: Wall shear stress (WSS) is a critically important physical factor contributing to atherosclerosis. Mapping the spatial distribution of local, oscillatory WSS can identify important mechanisms underlying the progression of coronary artery disease. METHODS: In this study, blood flow velocity and time-varying WSS were estimated in the left anterior descending (LAD) coronary artery of an ex vivo beating porcine heart using ultrasound with an 18 MHz linear array transducer aligned with the LAD in a forward-viewing orientation. A pulsatile heart loop with physiologically-accurate flow was created using a pulsatile pump. The coronary artery wall motion was compensated using a local block matching technique. Next, 2D and 3D velocity magnitude and WSS maps in the LAD coronary artery were estimated at different time points in the cardiac cycle using an ultrafast Doppler approach. The blood flow velocity estimated using the presented approach was compared with a commercially-available, calibrated single element blood flow velocity measurement system. RESULTS: The resulting root mean square error (RMSE) of 2D velocity magnitude acquired from a high frequency, linear array transducer was less than 8% of the maximum velocity estimated by the commercial system. CONCLUSION: When implemented in a forward-viewing intravascular ultrasound device, the presented approach will enable dynamic estimation of WSS, an indicator of plaque vulnerability in coronary arteries.

Biomechanical modeling and morphology analysis indicates plaque rupture due to mechanical failure unlikely in atherosclerosis-prone mice.

Spontaneous plaque rupture in mouse models of atherosclerosis is controversial, although numerous studies have discussed so-called "vulnerable plaque" phenotypes in mice. We compared the morphology and biomechanics of two acute and one chronic murine model of atherosclerosis to human coronaries of the thin-cap fibroatheroma (TCFA) phenotype. Our acute models were apolipoprotein E-deficient (ApoE(-/-)) and LDL receptor-deficient (LDLr(-/-)) mice, both fed a high-fat diet for 8 wk with simultaneous infusion of angiotensin II (ANG II), and our chronic mouse model was the apolipoprotein E-deficient strain fed a regular chow diet for 1 yr. We found that the mouse plaques from all three models exhibited significant morphological differences from human TCFA plaques, including the plaque burden, plaque thickness, eccentricity, and amount of the vessel wall covered by lesion as well as significant differences in the relative composition of plaques. These morphological differences suggested that the distribution of solid mechanical stresses in the walls may differ as well. Using a finite-element analysis computational solid mechanics model, we computed the relative distribution of stresses in the walls of murine and human plaques and found that although human TCFA plaques have the highest stresses in the thin fibrous cap, murine lesions do not have such stress distributions. Instead, local maxima of stresses were on the media and adventitia, away from the plaque. Our results suggest that if plaque rupture is possible in mice, it may be driven by a different mechanism than mechanics.

Stent underexpansion is associated with high wall shear stress: a biomechanical analysis of the shear stent study.

Coronary stent underexpansion is associated with restenosis and stent thrombosis. In clinical studies of atherosclerosis, high wall shear stress (WSS) has been associated with activation of prothrombotic pathways, upregulation of matrix metalloproteinases, and future myocardial infarction. We hypothesized that stent underexpansion is predictive of high WSS. WSS distribution was investigated in patients enrolled in the prospective randomized controlled study of angulated coronary arteries randomized to undergo percutaneous coronary intervention with R-ZES or X-EES. WSS was calculated from 3D reconstructions of arteries from intravascular ultrasound (IVUS) and angiography using computational fluid dynamics. A logistic regression model investigated the relationship between WSS and underexpansion and the relationship between underexpansion and stent platform. Mean age was 63±11, 78% were male, 35% had diabetes, mean pre-stent angulation was 36.7°±14.7°. Underexpansion was assessed in 83 patients (6,181 IVUS frames). Frames with stent underexpansion were significantly more likely to exhibit high WSS (> 2.5 Pa) compared to those without underexpansion with an OR of 2.197 (95% CI = [1.233-3.913], p = 0.008). There was no significant association between underexpansion and low WSS (< 1.0 Pa) and no significant differences in underexpansion between R-ZES and X-EES. In the Shear Stent randomized controlled study, underexpanded IVUS frames were more than twice as likely to be associated with high WSS than frames without underexpansion.

Semi-Automatic Reconstruction of Patient-Specific Stented Coronaries based on Data Assimilation and Computer Aided Design.

PURPOSE: The interplay between geometry and hemodynamics is a significant factor in the development of cardiovascular diseases. This is particularly true for stented coronary arteries. To elucidate this factor, an accurate patient-specific analysis requires the reconstruction of the geometry following the stent deployment for a computational fluid dynamics (CFD) investigation. The image-based reconstruction is troublesome for the different possible positions of the stent struts in the lumen and the coronary wall. However, the accurate inclusion of the stent footprint in the hemodynamic analysis is critical for detecting abnormal stress conditions and flow disturbances, particularly for thick struts like in bioresorbable scaffolds. Here, we present a novel reconstruction methodology that relies on Data Assimilation and Computer Aided Design. METHODS: The combination of the geometrical model of the undeployed stent and image-based data assimilated by a variational approach allows the highly automated reconstruction of the skeleton of the stent. A novel approach based on computational mechanics defines the map between the intravascular frame of reference (called L-view) and the 3D geometry retrieved from angiographies. Finally, the volumetric expansion of the stent skeleton needs to be self-intersection free for the successive CFD studies; this is obtained by using implicit representations based on the definition of Nef-polyhedra. RESULTS: We assessed our approach on a vessel phantom, with less than 10% difference (properly measured) vs. a customized manual (and longer) procedure previously published, yet with a significant higher level of automation and a shorter turnaround time. Computational hemodynamics results were even closer. We tested the approach on two patient-specific cases as well. CONCLUSIONS: The method presented here has a high level of automation and excellent accuracy performances, so it can be used for larger studies involving patient-specific geometries.

Biomechanics of Transcatheter Aortic Valve Replacement Complications and Computational Predictive Modeling.

Transcatheter aortic valve replacement (TAVR) is a rapidly growing field enabling replacement of diseased aortic valves without the need for open heart surgery. However, due to the nature of the procedure and nonremoval of the diseased tissue, there are rates of complications ranging from tissue rupture and coronary obstruction to paravalvular leak, valve thrombosis, and permanent pacemaker implantation. In recent years, computational modeling has shown a great deal of promise in its capabilities to understand the biomechanical implications of TAVR as well as help preoperatively predict risks inherent to device-patient-specific anatomy biomechanical interaction. This includes intricate replication of stent and leaflet designs and tested and validated simulated deployments with structural and fluid mechanical simulations. This review outlines current biomechanical understanding of device-related complications from TAVR and related predictive strategies using computational modeling. An outlook on future modeling strategies highlighting reduced order modeling which could significantly reduce the high time and cost that are required for computational prediction of TAVR outcomes is presented in this review paper. A summary of current commercial/in-development software is presented in the final section.

Trends in biomedical engineering: focus on Patient Specific Modeling and Life Support Systems.

Over the last twenty years major advancements have taken place in the design of medical devices and personalized therapies. They have paralleled the impressive evolution of three-dimensional, non invasive, medical imaging techniques and have been continuously fuelled by increasing computing power and the emergence of novel and sophisticated software tools. This paper aims to showcase a number of major contributions to the advancements of modeling of surgical and interventional procedures and to the design of life support systems. The selected examples will span from pediatric cardiac surgery procedures to valve and ventricle repair techniques, from stent design and endovascular procedures to life support systems and innovative ventilation techniques.

A multi-domain shear-stress dependent diffusive model of cell transport-aided dialysis: analysis and simulation.

Kidney dialysis is the most widespread treatment method for end-stage renal disease, a debilitating health condition common in industrialized societies. While ubiquitous, kidney dialysis suffers from an inability to remove larger toxins, resulting in a gradual buildup of these toxins in dialysis patients, ultimately leading to further health complications. To improve dialysis, hollow fibers incorporating a cell-monolayer with cultured kidney cells have been proposed; however, the design of such a fiber is nontrivial. In particular, the effects of fluid wall-shear stress have an important influence on the ability of the cell layer to transport toxins. In the present work, we introduce a model for cell-transport aided dialysis, incorporating the effects of the shear stress. We analyze the model mathematically and establish its well-posedness. We then present a series of numerical results, which suggest that a hollow-fiber design with a wavy profile may increase the efficiency of the dialysis treatment. We investigate numerically the shape of the wavy channel to maximize the toxin clearance. These results demonstrate the potential for the use of computational models in the study and advancement of renal therapies.

Comparative finite element model analysis of ascending aortic flow in bicuspid and tricuspid aortic valve.

In bicuspid aortic valve (BAV) disease, the role of genetic and hemodynamic factors influencing ascending aortic pathology is controversial. To test the effect of BAV geometry on ascending aortic flow, a finite element analysis was undertaken. A surface model of aortic root and ascending aorta was obtained from magnetic resonance images of patients with BAV and tricuspid aortic valve using segmentation facilities of the image processing code Vascular Modeling Toolkit (developed at the Mario Negri Institute). Analytical models of bicuspid (antero-posterior [AP], type 1 and latero-lateral, type 2 commissures) and tricuspid orifices were mathematically defined and turned into a volumetric mesh of linear tetrahedra for computational fluid dynamics simulations. Numerical simulations were performed with the finite element code LifeV. Flow velocity fields were assessed for four levels: aortic annulus, sinus of Valsalva, sinotubular junction, and ascending aorta. Comparison of finite element analysis of bicuspid and tricuspid aortic valve showed different blood flow velocity pattern. Flow in bicuspid configurations showed asymmetrical distribution of velocity field toward the convexity of mid-ascending aorta returning symmetrical in distal ascending aorta. On the contrary, tricuspid flow was symmetrical in each aortic segment. Comparing type 1 BAV with type 2 BAV, more pronounced recirculation zones were noticed in the latter. Finally, we found that in both BAV configurations, maximum wall shear stress is highly localized at the convex portion of the mid-ascending aorta level. Comparison between models showed asymmetrical and higher flow velocity in bicuspid models, in particular in the AP configuration. Asymmetry was more pronounced at the aortic level known to be more exposed to aneurysm formation in bicuspid patients. This supports the hypothesis that hemodynamic factors may contribute to ascending aortic pathology in this subset of patients.

Fluid-Structure Interaction Simulation of an Intra-Atrial Fontan Connection.

Total cavopulmonary connection (TCPC) hemodynamics has been hypothesized to be associated with long-term complications in single ventricle heart defect patients. Rigid wall assumption has been commonly used when evaluating TCPC hemodynamics using computational fluid dynamics (CFD) simulation. Previous study has evaluated impact of wall compliance on extra-cardiac TCPC hemodynamics using fluid-structure interaction (FSI) simulation. However, the impact of ignoring wall compliance on the presumably more compliant intra-atrial TCPC hemodynamics is not fully understood. To narrow this knowledge gap, this study aims to investigate impact of wall compliance on an intra-atrial TCPC hemodynamics. A patient-specific model of an intra-atrial TCPC is simulated with an FSI model. Patient-specific 3D TCPC anatomies were reconstructed from transverse cardiovascular magnetic resonance images. Patient-specific vessel flow rate from phase-contrast magnetic resonance imaging (MRI) at the Fontan pathway and the superior vena cava under resting condition were prescribed at the inlets. From the FSI simulation, the degree of wall deformation was compared with in vivo wall deformation from phase-contrast MRI data as validation of the FSI model. Then, TCPC flow structure, power loss and hepatic flow distribution (HFD) were compared between rigid wall and FSI simulation. There were differences in instantaneous pressure drop, power loss and HFD between rigid wall and FSI simulations, but no difference in the time-averaged quantities. The findings of this study support the use of a rigid wall assumption on evaluation of time-averaged intra-atrial TCPC hemodynamic metric under resting breath-held condition.

Non-Newtonian Effects on Patient-Specific Modeling of Fontan Hemodynamics.

The Fontan procedure is a common palliative surgery for congenital single ventricle patients. In silico and in vitro patient-specific modeling approaches are widely utilized to investigate potential improvements of Fontan hemodynamics that are related to long-term complications. However, there is a lack of consensus regarding the use of non-Newtonian rheology, warranting a systematic investigation. This study conducted in silico patient-specific modeling for twelve Fontan patients, using a Newtonian and a non-Newtonian model for each patient. Differences were quantified by examining clinically relevant metrics: indexed power loss (iPL), indexed viscous dissipation rate (iVDR), hepatic flow distribution (HFD), and regions of low wall shear stress (AWSS). Four sets of "non-Newtonian importance factors" were calculated to explore their effectiveness in identifying the non-Newtonian effect. No statistical differences were observed in iPL, iVDR, and HFD between the two models at the population-level, but large inter-patient variations exist. Significant differences were detected regarding AWSS, and its correlations with non-Newtonian importance factors were discussed. Additionally, simulations using the non-Newtonian model were computationally faster than those using the Newtonian model. These findings distinguish good importance factors for identifying non-Newtonian rheology and encourage the use of a non-Newtonian model to assess Fontan hemodynamics.

Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study.

The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics.

Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.

The effect of respiration-driven flow waveforms on hemodynamic metrics used in Fontan surgical planning.

OBJECTIVE: Poor total cavopulmonary connection (TCPC) hemodynamics have been hypothesized to be associated with long-term complications in Fontan patients. Image-based Fontan surgical planning has shown great potential as a clinical tool because it can pre-operatively evaluate patient-specific hemodynamics. Current surgical planning paradigms commonly utilize cardiac-gated phase contrast magnetic resonance (MR) imaging to acquire vessel flows. These acquisitions are often taken under breath-held (BH) conditions and ignore the effect of respiration on blood flow waveforms. This study investigates the effect of respiration-driven flow waveforms on patient-specific hemodynamics using real-time MR acquisitions. METHODS: Patient-specific TCPCs were reconstructed from cardiovascular MR images. Real-time phase contrast MR images were acquired under both free-breathing (FB) and breath-held conditions for 9 patients. Numerical simulations were employed to assess flow structures and hemodynamics used in Fontan surgical planning including hepatic flow distribution (HFD) and indexed power loss (iPL), which were then compared between FB and BH conditions. RESULTS: Differences in TCPC flow structures between FB and BH conditions were observed throughout the respiratory cycle. However, the average differences (BH - FB values for each patient, which are then averaged) in iPL and HFD between these conditions were 0.002 ±â€¯0.011 (p = 0.40) and 1 ±â€¯3% (p = 0.28), respectively, indicating no significant difference in clinically important hemodynamic metrics. CONCLUSIONS: Respiration affects blood flow waveforms and flow structures, but might not significantly influence the values of iPL or HFD. Therefore, breath-held MR acquisition can be adequate for Fontan surgical planning when focusing on iPL and HFD.