Computational transient simulations with varying degree and shape of pulmonic stenosis in models of the bidirectional cavopulmonary anastomosis

Physical and Computer Modelling of Blood Flow in a Systemic-to-pulmonary Shunt

The aim of this work was the application of computer and physical in vitro simulation methods for estimating surgery procedure hemodynamics. The modified Blalock-Taussig (mB-T) palliative surgical procedure is performed to increase the pulmonary blood flow in children with congenital heart defects. Such a systemic-to-pulmonary shunt yields substantial modification in the blood flow within the large blood vessels. The objective of the present study was to investigate basic characteristics of the flow, flow pattern and pressure-flow efficiency, before and after opening of the mB-T graft.

Methods

The model was based on the vessel geometry obtained from the Visible Human Project and included the arch of aorta, the three arteries branching from the arch, the pulmonary trunck, and the left and right pulmonary arteries. The graft was added between the left subclavian artery and the left pulmonary artery. The glass model of the vessels was produced and investigated in a physical model of the cardiovascular system with an artificial ventricular device as the blood pump. Flow rate and hydrostatic pressure were measured at the inlet to and outlets from the glass model and in a few points within the system. Laser flow visualization was also performed. Computer simulations were done using the boundary conditions from the physical model.

Results

The opening of the mB-T graft changed flow distribution in all branches (including inflow). A complex flow pattern with large eddies and channelling of the flow in the vicinity of the graft and within it was observed in flow visualization and in computer simulations. Because of that complexity the local measurements of hydrostatic pressure at the vessel wall could not predict the average flow rate. The reversed flow in the graft was observed during the systole.

Conclusions

The complex flow pattern developed in the physical model of the mB-T graft. The channelling of the flow and the formation of large eddies may yield high shear stress and modify blood properties. The rigid wall model can describe only some flow characteristics observed in vivo. Computer simulation is a very fast and accurate method which permits earlier qualification of cardiac surgeons on how to change cardiac vascular blood flow after operations.

A new multiparameter approach to computational simulation for Fontan assessment and redesign

INTRODUCTION

Despite an abundance of prior Fontan simulation articles, there have been relatively few clinical advances that are a direct result of computational methods. We address a few key limitations of previous Fontan simulations as a step towards increasing clinical relevance. Previous simulations have been limited in scope because they have primarily focused on a single energy loss parameter. We present a multi-parameter approach to Fontan modeling that establishes a platform for clinical decision making and comprehensive evaluation of proposed interventions.

METHODS

Time-dependent, 3-D blood flow simulations were performed on six patient-specific Fontan models. Key modeling advances include detailed pulmonary anatomy, catheterization-derived pressures, and MRI-derived flow with respiration. The following performance parameters were used to rank patients at rest and simulated exercise from best to worst performing: energy efficiency, inferior and superior vena cava (IVC, SVC) pressures, wall shear stress, and IVC flow distribution.

RESULTS

Simulated pressures were well matched to catheterization data, but low Fontan pressure did not correlate with high efficiency. Efficiency varied from 74% to 96% at rest, and from 63% to 91% with exercise. Distribution of IVC flow ranged from 88%/12% (LPA/RPA) to 53%/47%. A "transcatheter" virtual intervention demonstrates the utility of computation in evaluating interventional strategies, and is shown to result in increased energy efficiency.

CONCLUSIONS

A multiparameter approach demonstrates that each parameter results in a different ranking of Fontan performance. Ranking patients using energy efficiency does not correlate with the ranking using other parameters of presumed clinical importance. As such, current simulation methods that evaluate energy dissipation alone are not sufficient for a comprehensive evaluation of new Fontan designs.

Evaluation of a novel Y-shaped extracardiac Fontan baffle using computational fluid dynamics

OBJECTIVES

The objective of this work is to evaluate the hemodynamic performance of a new Y-graft modification of the extracardiac conduit Fontan operation. The performance of the Y-graft design is compared to two designs used in current practice: a t-junction connection of the venae cavae and an offset between the inferior and superior venae cavae.

METHODS

The proposed design replaces the current tube grafts used to connect the inferior vena cava to the pulmonary arteries with a Y-shaped graft. Y-graft hemodynamics were evaluated at rest and during exercise with a patient-specific model from magnetic resonance imaging data together with computational fluid dynamics. Four clinically motivated performance measures were examined: Fontan pressures, energy efficiency, inferior vena cava flow distribution, and wall shear stress. Two variants of the Y-graft were evaluated: an "off-the-shelf" graft with 9-mm branches and an "area-preserving" graft with 12-mm branches.

RESULTS

Energy efficiency of the 12-mm Y-graft was higher than all other models at rest and during exercise, and the reduction in efficiency from rest to exercise was improved by 38%. Both Y-graft designs reduced superior vena cava pressures during exercise by as much as 5 mm Hg. The Y-graft more equally distributed the inferior vena cava flow to both lungs, whereas the offset design skewed 70% of the flow to the left lung. The 12-mm graft resulted in slightly larger regions of low wall shear stress than other models; however, minimum shear stress values were similar.

CONCLUSIONS

The area-preserving 12-mm Y-graft is a promising modification of the Fontan procedure that should be clinically evaluated. Further work is needed to correlate our performance metrics with clinical outcomes, including exercise intolerance, incidence of protein-losing enteropathy, and thrombus formation.

Comparison of Particle Image Velocimetry and Phase Contrast MRI in a Patient-Specific Extracardiac Total Cavopulmonary Connection

Particle image velocimetry (PIV) and phase contrast magnetic resonance imaging (PC-MRI) have not been compared in complex biofluid environments. Such analysis is particularly useful to investigate flow structures in the correction of single ventricle congenital heart defects, where fluid dynamic efficiency is essential. A stereolithographic replica of an extracardiac total cavopulmonary connection (TCPC) is studied using PIV and PC-MRI in a steady flow loop. Volumetric two-component PIV is compared to volumetric three-component PC-MRI at various flow conditions. Similar flow structures are observed in both PIV and PC-MRI, where smooth flow dominates the extracardiac TCPC, and superior vena cava flow is preferential to the right pulmonary artery, while inferior vena cava flow is preferential to the left pulmonary artery. Where three-component velocity is available in PC-MRI studies, some helical flow in the extracardiac TCPC is observed. Vessel cross sections provide an effective means of validation for both experiments, and velocity magnitudes are of the same order. The results highlight similarities to validate flow in a complex patient-specific extracardiac TCPC. Additional information obtained by velocity in three components further describes the complexity of the flow in anatomic structures.

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.

Toward optimal hemodynamics: computer modeling of the Fontan circuit

The construction of efficient designs with minimal energy losses is especially important for cavopulmonary connections. The science of computational fluid dynamics has been increasingly used to study the hemodynamic performance of surgical operations. Three-dimensional computer models can be accurately constructed of typical cavopulmonary connections used in clinical practice based on anatomic data derived from magnetic resonance scans, angiocardiograms, and echocardiograms. Using these methods, the hydraulic performance of the hemi-Fontan, bidirectional Glenn, and a variety of types of completion Fontan operations can be evaluated and compared. This methodology has resulted in improved understanding and design of these surgical operations.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Computational modeling of vascular anastomoses

Recent development of computational technology allows a level of knowledge of biomechanical factors in the healthy or pathological cardiovascular system that was unthinkable a few years ago. In particular, computational fluid dynamics (CFD) and computational structural (CS) analyses have been used to evaluate specific quantities, such as fluid and wall stresses and strains, which are very difficult to measure in vivo. Indeed, CFD and CS offer much more variability and resolution than in vitro and in vivo methods, yet computations must be validated by careful comparison with experimental and clinical data. The enormous parallel development of clinical imaging such as magnetic resonance or computed tomography opens a new way toward a detailed patient-specific description of the actual hemodynamics and structural behavior of living tissues. Coupling of CFD/CS and clinical images is becoming a standard evaluation that is expected to become part of the clinical practice in the diagnosis and in the surgical planning in advanced medical centers. This review focuses on computational studies of fluid and structural dynamics of a number of vascular anastomoses: the coronary bypass graft anastomoses, the arterial peripheral anastomoses, the arterio-venous graft anastomoses and the vascular anastomoses performed in the correction of congenital heart diseases.

Computational fluid dynamics in the evaluation of hemodynamic performance of cavopulmonary connections after the Norwood procedure for hypoplastic left heart syndrome

OBJECTIVE

Computational fluid dynamics have been used to study the hemodynamic performance of surgical operations, resulting in improved design. Efficient designs with minimal energy losses are especially important for cavopulmonary connections. The purpose of this study was to compare hydraulic performance between the hemi-Fontan and bidirectional Glenn procedures, as well as the various types of completion Fontan operations.

METHODS

Three-dimensional models were constructed of typical hemi-Fontan and bidirectional Glenn operations according to anatomic data derived from magnetic resonance scans, angiocardiograms, and echocardiograms. Boundary conditions were imposed, and fluid dynamics were calculated from a mathematic code. Power losses, flow distribution to each lung, and pressures were measured at three predetermined levels of pulmonary arteriolar resistance. Models of the lateral tunnel, total cavopulmonary connection, and extracardiac conduit completion Fontan operations were constructed, and power losses, total flow distribution, vena caval and pulmonary arterial pressures, and flow distribution of inferior vena caval return were calculated.

RESULTS

The hemi-Fontan and bidirectional Glenn procedures performed nearly identically, with similar power losses and nearly equal flow distributions to each lung at all levels of pulmonary arteriolar resistance. However, the lateral tunnel Fontan procedure as performed after the hemi-Fontan operation had lower power losses (6.9 mW, pulmonary arteriolar resistance 3 units) than the total cavopulmonary connection (40.5 mW) or the extracardiac conduit (42.9 mW), although the inclusion of an enlargement patch toward the right in the total cavopulmonary connection was effective in reducing the difference (10.0 mW). Inferior vena caval flow to the right lung was 52% for the lateral tunnel, compared with 19%, 30%, 19%, and 15% for the total cavopulmonary connection, total cavopulmonary connection with right-sided enlargement patch, extracardiac conduit, and extracardiac conduit with a bevel to the left lung, respectively.

CONCLUSIONS

According to these methods, the hemi-Fontan and bidirectional Glenn procedures performed equally well, but important differences in energy losses and flow distribution were found after the completion Fontan procedures. The superior hydraulic performance of the lateral tunnel Fontan operation after the hemi-Fontan procedure relative to any other method may be due to closer to optimal caval offset achieved in the surgical reconstruction.

Computational model of the fluid dynamics in systemic-to-pulmonary shunts

A systemic-to-pulmonary shunt is a connection created between the systemic and pulmonary arterial circulations in order to improve pulmonary perfusion in children with congenital heart diseases. Knowledge of the relationship between pressure and flow in this new, surgically created, cardiovascular district may be helpful in the clinical management of these patients, whose survival is critically dependent on the blood flow distribution between the pulmonary and systemic circulations. In this study a group of three-dimensional computational models of the shunt have been investigated under steady-state and pulsatile conditions by means of a finite element analysis. The model is used to quantify the effects of shunt diameter (D), curvature, angle, and pulsatility on the pressure-flow (DeltaP-Q) relationship of the shunt. Size of the shunt is the main regulator of pressure-flow relationship. Innominate arterial diameter and angles of insertion have less influence. Curvature of the shunt results in lower pressure drops. Inertial effects can be neglected. The following simplified formulae are derived: DeltaP=(0. 097Q+0.521Q(2))/D(4) and DeltaP=(0.096Q+0.393Q(2))/D(4) for the different shunt geometries investigated (straight and curved shunts, respectively).

Use of mathematical model to predict hemodynamics in cavopulmonary anastomosis with persistent forward flow

BACKGROUND

The bidirectional cavopulmonary anastomosis with additional pulmonary blood flow is used as a staged procedure or a definitive palliation of univentricular hearts. In this paper the flow competition occurring between the caval and the pulmonary flows is investigated. The hemodynamics in the superior vena cava and the blood flow distribution into the lungs, as well as the systemic arterial oxygen availability, are correlated with the severity of the right ventricle outflow tract obstruction and the pulmonary arteriolar resistance.

MATERIALS AND METHODS

Computer models of the pre- and postoperative hemodynamics of univentricular hearts were developed. The effects of increasing severity of the right ventricle outflow tract obstruction, with a pulmonary arteriolar resistance ranging from 0.8 to 7.9 nonindexed Woods units, were simulated.

RESULTS

The study indicates that the presence of an additional pulmonary blood flow from the native pulmonary artery may be beneficial. Since an excessive additional blood flow may cause central venous hypertension, its optimal value should be chosen according to the value of pulmonary arteriolar resistance. The model was utilized to simulate four clinical cases.

CONCLUSIONS

The simulations show that the model can predict the postoperative hemodynamics and could therefore be usefully applied to predict quantitatively the effect of the native pulmonary blood flow following bidirectional cavopulmonary anastomosis.

Calculating blood flow from Doppler measurements in the systemic-to-pulmonary artery shunt after the Norwood operation: a method based on computational fluid dynamics

Hypoplastic left heart syndrome is currently the most lethal cardiac malformation of the newborn infant. Survival following a Norwood operation depends on the balance between systemic and pulmonary blood flow, which is highly dependent on the fluid dynamics through the interposition shunt between the two circulations. We used computational fluid dynamic (CFD) models to determine the velocity profile in a systemic-to-pulmonary artery shunt and suggested a simplified method of calculating the blood flow in the shunt based on Doppler measurements. CFD models of systemic-to-pulmonary shunts based on the finite element method were studied. The size of the shunt has been varied from 3 to 5 mm. Velocity profiles at proximal and distal positions were evaluated and correlations between maximum and mean spatial velocity were found. Twenty-one Doppler measurements in the proximal and distal part of the shunt were obtained from six patients with hypoplastic left heart syndrome. Combining Doppler velocities and CFD velocity profiles, blood flow rate in the shunt was calculated. Flow rate evaluated from aortic Doppler and oxygen saturation measurements were performed for comparison. Results showed that proximal shunt Doppler velocities were always greater than the correspondent distal ones (ratio equal to 1.15 +/- 0.11). CFD models showed a similar behaviour (ratio equal to 1.21 +/- 0.03). CFD models gave a V(mean)/V(max) ratio of 0. 480 at the proximal junction and of 0.579 at the distal one. The agreement between the flow evaluated in the proximal and distal areas of the shunt was good (0.576 +/- 0.150 vs. 0.610 +/- 0.166 l/min). Comparison of these data with saturation data and aortic Doppler measurements correlate less well (0.593 +/- 0.156 vs. 1.023 +/- 0.493 l/min). A formula easily to quantify shunt flow rate is proposed. This could be used to evaluate the effects of different therapeutic and pharmacological manoeuvres in this unique circulation.

Surgical variations and flow dynamics in cavopulmonary connections: A historical review

Cavopulmonary connections (CPC) have been extensively used in the palliation of complex forms of congenital heart disease requiring some form of right heart bypass. The concept has evolved from unilateral CPC to total CPC (TCPC) in an attempt to prolong the palliated state, but the physiological implications remain only partially understood. We summarize some of the modifications and experimental data and their impact on flow distribution after the Fontan procedure. Copyright 1998 by W.B. Saunders Company