Efficiency differences in computational simulations of the total cavo-pulmonary circulation with and without compliant vessel walls

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

Simple Summary

A fluid-structure interaction (FSI) simulation of an intra-atrial Fontan connection was performed. Power loss and pressure drop results fluctuated less during the FSI simulation than during the simulation run with rigid walls, but there were no observable differences in time-averaged pressure drop, connection power loss or hepatic flow distribution. These results suggested that employing a rigid wall is a reasonable assumption when evaluating time-averaged hemodynamic quantities of the Fontan connection under resting breath-held flow conditions.

Abstract

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.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Fontan Surgical Planning: Previous Accomplishments, Current Challenges, and Future Directions

The ultimate goal of Fontan surgical planning is to provide additional insights into the clinical decision-making process. In its current state, surgical planning offers an accurate hemodynamic assessment of the pre-operative condition, provides anatomical constraints for potential surgical options, and produces decent post-operative predictions if boundary conditions are similar enough between the pre-operative and post-operative states. Moving forward, validation with post-operative data is a necessary step in order to assess the accuracy of surgical planning and determine which methodological improvements are needed. Future efforts to automate the surgical planning process will reduce the individual expertise needed and encourage use in the clinic by clinicians. As post-operative physiologic predictions improve, Fontan surgical planning will become an more effective tool to accurately model patient-specific hemodynamics.

Respiratory Effects on Fontan Circulation During Rest and Exercise Using Real-Time Cardiac Magnetic Resonance Imaging

BACKGROUND

It is known that respiration modulates cavopulmonary flows, but little data compare mean flows under breath-holding and free-breathing conditions to isolate the respiratory effects and effects of exercise on the respiratory modulation.

METHODS

Real-time phase-contrast magnetic resonance combined with a novel method to track respiration on the same image acquisition was used to investigate respiratory effects on Fontan caval and aortic flows under breath-holding, free-breathing, and exercise conditions. Respiratory phasicity indices that were based on beat-averaged flow were used to quantify the respiratory effect.

RESULTS

Flow during inspiration was substantially higher than expiration under the free-breathing and exercise conditions for both inferior vena cava (inspiration/expiration: 1.6 ± 0.5 and 1.8 ± 0.5, respectively) and superior vena cava (inspiration/expiration: 1.9 ± 0.6 and 2.6 ± 2.0, respectively). Changes from rest to exercise in the respiratory phasicity index for these vessels further showed the impact of respiration. Total systemic venous flow showed no significant statistical difference between the breath-holding and free-breathing conditions. In addition, no substantial difference was found between the descending aorta and inferior vena cava mean flows under either resting or exercise conditions.

CONCLUSIONS

This study demonstrated that inferior vena cava and superior vena cava flow time variance is dominated by respiratory effects, which can be detected by the respiratory phasicity index. However, the minimal respiration influence on net flow validates the routine use of breath-holding techniques to measure mean flows in Fontan patients. Moreover, the mean flows in the inferior vena cava and descending aorta are interchangeable.

Use of computational fluid dynamics to estimate hemodynamic effects of respiration on hypoplastic left heart syndrome surgery: total cavopulmonary connection treatments

Total cavopulmonary connection (TCPC), a typical kind of Fontan procedure, is commonly used in the treatment of a functional single ventricle. The palliative cardiothoracic procedure is performed by connecting the superior vena cava and the inferior vena cava to the pulmonary arteries. Due to the difficulty of direct study in vivo, in this paper, computational fluid dynamics (CFD) was introduced to estimate the outcomes of patient-specific TCPC configuration. We mainly focused on the influence of blood pulsation and respiration. Fast Fourier transforms method was employed to separate the measured flow conditions into the rate of breath and heart beat. Blood flow performance around the TCPC connection was investigated by analyzing the results of time-varying energy losses, blood flow distribution rate, local pressure, and wall shear stress distributions. It was found that the value of energy loss including the influence of respiration was 1.5 times higher than the value of energy loss disregarding respiratory influences. The results indicated that the hemodynamic outcomes of TCPC treatment are obviously influenced by respiration. The influence of respiration plays an important role in estimating the results of TCPC treatment and thus should be included as one of the important conditions of computational haemodynamic analysis.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

Lagrangian analysis of hemodynamics data from FSI simulation

We present the computation of lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid-structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in lagrangian measures of the flow between deformable and rigid-vessel models was observed.

Treatment planning for a TCPC test case: a numerical investigation under rigid and moving wall assumptions

The hemodynamics in patients with total cavopulmonary connections (TCPC) is generally very complex and characterized by patient-to-patient variability. To better understand its effect on patients' outcome, CFD models are widely used, also to test and optimize surgical options before their implementation. These models often assume rigid geometries, despite the motion experienced by thoracic vessels that could influence the hemodynamics predictions. By improving their accuracy and expanding the range of simulated interventions, the benefit of treatment planning for patients is expected to increase. We simulate three types of intervention on a patient-specific 3D model, and compare their predicted outcome with baseline condition: a decrease in pulmonary vascular resistance obtainable with medications; a surgical revision of the connection design; the introduction of a fenestration in the TCPC wall. The simulations are performed both with rigid wall assumption and including patient-specific TCPC wall motion, reconstructed from a 4DMRI dataset. The results show the effect of each option on clinically important metrics and highlight the impact of patient-specific wall motion. The largest differences between rigid and moving wall models are observed in measures of energetic efficiency of TCPC as well as in hepatic flow distribution and transit time of seeded particles through the connection.

Fluid-structure interaction simulations of the Fontan procedure using variable wall properties

Children born with single ventricle heart defects typically undergo a staged surgical procedure culminating in a total cavopulmonary connection (TCPC) or Fontan surgery. The goal of this work was to perform physiologic, patient-specific hemodynamic simulations of two post-operative TCPC patients by using fluid-structure interaction (FSI) simulations. Data from two patients are presented, and post-op anatomy is reconstructed from MRI data. Respiration rate, heart rate, and venous pressures are obtained from catheterization data, and inflow rates are obtained from phase contrast MRI data and are used together with a respiratory model. Lumped parameter (Windkessel) boundary conditions are used at the outlets. We perform FSI simulations by using an arbitrary Lagrangian-Eulerian finite element framework to account for motion of the blood vessel walls in the TCPC. This study is the first to introduce variable elastic properties for the different areas of the TCPC, including a Gore-Tex conduit. Quantities such as wall shear stresses and pressures at critical locations are extracted from the simulation and are compared with pressure tracings from clinical data as well as with rigid wall simulations. Hepatic flow distribution and energy efficiency are also calculated and compared for all cases. There is little effect of FSI on pressure tracings, hepatic flow distribution, and time-averaged energy efficiency. However, the effect of FSI on wall shear stress, instantaneous energy efficiency, and wall motion is significant and should be considered in future work, particularly for accurate prediction of thrombus formation.

Optimization of inflow waveform phase-difference for minimized total cavopulmonary power loss

The Fontan operation is a palliative surgical procedure performed on children, born with congenital heart defects that have yielded only a single functioning ventricle. The total cavo-pulmonary connection (TCPC) is a common variant of the Fontan procedure, where the superior vena cava (SVC) and inferior vena cava (IVC) are routed directly into the pulmonary arteries (PA). Due to the limited pumping energy available, optimized hemodynamics, in turn, minimized power loss, inside the TCPC pathway is required for the best optimal surgical outcomes. To complement ongoing efforts to optimize the anatomical geometric design of the surgical Fontan templates, here, we focused on the characterization of power loss changes due to the temporal variations in between SVC and IVC flow waveforms. An experimentally validated pulsatile computational fluid dynamics solver is used to quantify the effect of phase-shift between SVC and IVC inflow waveforms and amplitudes on internal energy dissipation. The unsteady hemodynamics of two standard idealized TCPC geometries are presented, incorporating patient-specific real-time PC-MRI flow waveforms of "functional" Fontan patients. The effects of respiration and pulsatility on the internal energy dissipation of the TCPC pathway are analyzed. Optimization of phase-shift between caval flows is shown to lead to lower energy dissipation up to 30% in these idealized models. For physiological patient-specific caval waveforms, the power loss is reduced significantly (up to 11%) by the optimization of all three major harmonics at the same mean pathway flow (3 L/min). Thus, the hemodynamic efficiency of single ventricle circuits is influenced strongly by the caval flow waveform quality, which is regulated through respiratory dependent physiological pathways. The proposed patient-specific waveform optimization protocol may potentially inspire new therapeutic applications to aid postoperative hemodynamics and improve the well being of the Fontan patients.

Three-dimensional hemodynamics in the human pulmonary arteries under resting and exercise conditions

The biomechanical forces associated with blood flow have been shown to play a role in pulmonary vascular cell health and disease. Therefore, the quantification of human pulmonary artery hemodynamic conditions under resting and exercise states can be useful in investigating the physiology of disease development and treatment outcomes. In this study, a combined magnetic resonance imaging and computational fluid dynamics approach was used to quantify pulsatile flow fields, wall shear stress (WSS), oscillations in WSS (OSI), and energy efficiency in six subject-specific models of the human pulmonary vasculature with high spatial and temporal resolution. Averaging over all subjects, WSS was found to increase from 19.8±4.0 to 51.8±6.7 dynes/cm2, and OSI was found to decrease from 0.094±0.016 to 0.081±0.015 in the proximal pulmonary arteries between rest and exercise conditions (p<0.05). These findings demonstrate the localized, biomechanical effects of exercise. Furthermore, an average decrease of 10% in energy efficiency was noted between rest and exercise. These data indicate the amount of energy dissipation that typically occurs with exercise and may be useful in future surgical planning applications.

Hemodynamic performance of stage-2 univentricular reconstruction: Glenn vs. hemi-Fontan templates

Flow structures, hemodynamics and the hydrodynamic surgical pathway resistances of the final stage functional single ventricle reconstruction, namely the total cavopulmonary connection (TCPC) anatomy, have been investigated extensively. However, the second stage surgical anatomy (i.e., bi-directional Glenn or hemi-Fontan template) has received little attention. We thus initiated a multi-faceted study, involving magnetic resonance imaging (MRI), phase contrast MRI, computational and experimental fluid dynamics methodologies, focused on the second stage of the procedure. Twenty three-dimensional computer and rapid prototype models of 2nd stage TCPC anatomies were created, including idealized parametric geometries (n = 6), patient-specific anatomies (n = 7), and their virtual surgery variant (n = 7). Results in patient-specific and idealized models showed that the Glenn connection template is hemodynamically more efficient with (83% p = 0.08 in patient-specific models and 66% in idealized models) lower power losses compared to hemi-Fontan template, respectively, due to its direct end-to-side anastomosis. Among the several secondary surgical geometrical features, stenosis at the SVC anastomosis or in pulmonary branches was found to be the most critical parameter in increasing the power loss. The pouch size and flare shape were found to be less significant. Compared to the third stage surgery the hydrodynamic resistance of the 2nd stage is considerably lower (both in idealized models and in anatomical models at MRI resting conditions) for both hemi- and Glenn templates. These results can impact the surgical design and planning of the staged TCPC reconstruction.

Modeling the Fontan circulation: where we are and where we need to go

The Fontan procedure and its subsequent modifications over the past 30 years can be described as a class of surgical procedures for patients born with complex congenital heart disease exhibiting a single-ventricle physiology. The long-term outcome for children currently undergoing a Fontan procedure remains worrisome because of multiple late morbidities observed. Despite significant modeling efforts spanning three decades, improvements to the Fontan procedure have occurred without comprehensive validation from these modeling studies. Careful examination shows that modeling studies to date offer only a "glimpse through a keyhole" into understanding and modeling a representative range of the variations in anatomy and physiology that exist in Fontan patients. Suggestions for future investigations are provided.

Nonlinear power loss during exercise in single-ventricle patients after the Fontan: insights from computational fluid dynamics

BACKGROUND

We previously demonstrated that power loss (PL) through the total cavopulmonary connection (TCPC) in single-ventricle patients undergoing Fontan can be calculated by computational fluid dynamic analysis using 3-dimensional MRI anatomic reconstructions. PL through the TCPC may play a role in single-ventricle physiology and is a function of cardiac output. We hypothesized that PL through the TCPC increases significantly under exercise flow conditions.

METHODS AND RESULTS

MRI data of 10 patients with a TCPC were analyzed to obtain 3-dimensional geometry and flow rates through the superior vena cava, inferior vena cava, left pulmonary artery, and right pulmonary artery. Steady computational fluid dynamic simulations were performed at baseline conditions using MRI-derived flows. Simulated exercise conditions of twice (2x) and three times (3x) baseline flow were performed by increasing inferior vena cava flow. PL, head loss, and effective resistance through the TCPC were calculated for each condition. Each condition was repeated at left pulmonary artery/right pulmonary artery ratios of 30/70 and 70/30 to determine the effects of pulmonary flow splits on exercise PL. For each patient, PL increases dramatically in a nonlinear fashion with increasing cardiac output, even when normalized to calculate head loss or resistance. Flow splits had a significant effect on PL at exercise, with most geometries favoring right pulmonary artery flow.

CONCLUSIONS

The relationship between cardiac output and PL is nonlinear and highly dependent on TCPC geometry and pulmonary flow splits. This study demonstrates the importance of studying the TCPC under exercise conditions, because baseline conditions may not adequately characterize TCPC efficiency.