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

Mathematical Analysis and Physical Profile of Blalock-Taussig Shunt and Sano Modification Procedure in Hypoplastic Left Heart Syndrome: Review of the Literature and Implications for the Anesthesiologist

The first stage of surgical treatment for hypoplastic left heart syndrome (HLHS) includes the creation of artificial systemic-to-pulmonary connections to provide pulmonary blood flow. The modified Blalock-Taussig (mBT) shunt has been the technique of choice for this procedure; however, a right ventricle-pulmonary artery (RV-PA) shunt has been introduced into clinical practice with encouraging but still conflicting outcomes when compared with the mBT shunt. The aim of this study is to explore mathematical modeling as a tool for describing physical profiles that could assist the surgical team in predicting complications related to stenosis and malfunction of grafts in an attempt to find correlations with clinical outcomes from clinical studies that compared both surgical techniques and to assist the anesthesiologist in making decisions to manage patients with this complex cardiac anatomy. Mathematical modeling to display the physical characteristics of the chosen surgical shunt is a valuable tool to predict flow patterns, shear stress, and rate distribution as well as energetic performance at the graft level and relative to ventricular efficiency. Such predictions will enable the surgical team to refine the technique so that hemodynamic complications be anticipated and prevented, and are also important for perioperative management by the anesthesia team.

UNSTEADY MAGNETOHYDRODYNAMIC BLOOD FLOW IN A POROUS-SATURATED OVERLAPPING STENOTIC ARTERY — NUMERICAL MODELING

Unsteady pulsatile flow of blood through a porous-saturated, tapered and overlapping stenotic artery in the presence of magnetic field is examined theoretically and computationally. The power law constitutive model is employed to simulate hameo-rheological characteristics. The governing equation is derived assuming the flow to be unsteady, laminar, uni-directional and one-dimensional (1D). A robust, finite difference method is employed for the solution of the governing equation, subject to appropriate boundary conditions. Based on this solution, an extensive quantitative analysis is performed to analyze the effects of blood rheology, body acceleration, magnetohydrodynamic parameter, permeability parameter and arterial geometrical parameters of stenosis on various quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress. The computations demonstrate that velocity, flow rate and shear stress increase while resistance to flow decreases with greater permeability parameter. Additionally, the effects of magnetic field are observed to be converse to those of permeability i.e., flow is decelerated and resistance is increased, demonstrating the powerful utility of exploiting magnetic fields in hemodynamic flow control (e.g., intra-corporeal surgical procedures). Furthermore, the size of trapped bolus of fluid is also found to be reduced for large values of the permeability parameter indicating that progressively more porous media circumvent bolus growth.

Computational modelling to optimize the hybrid configuration for hypoplastic left heart syndrome

OBJECTIVES

Hybrid palliation for hypoplastic left heart syndrome (HLHS) is associated with mortality and late ventricular dysfunction. Increased ventricular workload and coronary perfusion limitation may be the important factors. Using mathematical modelling, this study investigated the effects of differing hybrid configurations on the demands on this single ventricle circulation.

METHODS

A multicompartmental Windkessel model of hybrid HLH-aortic atresia circulation was adopted, with a time-varying elastance representing ventricular functionality. The effects of diameter increases in bilateral pulmonary artery bandings (PABs) (+0.5, 2.5-4 mm) and ductal stent (+1, 4-10 mm) on cardiovascular haemodynamics, systemic oxygenation and ventricular energetics were assessed.

RESULTS

Simulations showed that an increase in PAB diameter of 2.5-4 mm resulted in an increased Q (0.61-2.66), and diastolic stent backflow (-0.2 to -0.78 l/min) with reduced systemic perfusion (0.82-0.77 l/min) and diastolic pressures (48.3-41.2 mmHg). Arterial and venous saturations increased, SaO2 (%) was 62-88 and SvO(2) 41-65. To maintain mean systemic pressures, substantial increases in cardiac output (1.3-2.8 l/min) and ventricular stroke work (576-1360 mmHg ml) were required. A decrease in the ductal stent diameter over the range 10-7 mm had a negligible haemodynamic effect: reduced systemic systolic pressure (77-72 mmHg) and increase in ventricular stroke work (781-790 mmHg ml). When the ductal diameter was restricted to <7 mm, it resulted in a significant reduced systemic flow and increased stroke work. Optimal hybrid configuration was defined at PAB 3 mm and ductal stent ≥7 mm.

CONCLUSIONS

In this model, increasing the PAB diameter, or a stent diameter <7 mm, substantially increased single ventricle workload and reduced systemic perfusion and diastolic pressure. This may compromise myocardial oxygen demand-supply, particularly in the setting of retrograde-dependent coronary perfusion.

Computational fluid dynamics models and congenital heart diseases

Mathematical modeling is a powerful tool to investigate hemodynamics of the circulatory system. With improving imaging techniques and detailed clinical investigations, it is now possible to construct patient-specific models of reconstructive surgeries for the treatment of congenital heart diseases. These models can help clinicians to better understand the hemodynamic behavior of different surgical options for a treated patient. This review outlines recent advances in mathematical modeling in congenital heart diseases, the discoveries and limitations these models present, and future directions that are on the horizon.

Computational fluid dynamics in congenital heart disease

Computational fluid dynamics has been applied to the design, refinement, and assessment of surgical procedures and medical devices. This tool calculates flow patterns and pressure changes within a virtual model of the cardiovascular system. In the field of paediatric cardiac surgery, computational fluid dynamics is being used to elucidate the optimal approach to staged reconstruction of specific defects and study the haemodynamics of the resulting anatomical configurations after reconstructive or palliative surgery. In this paper, we review the techniques and principal findings of computational fluid dynamics studies as applied to a few representative forms of congenital heart disease.

Use of mathematical modeling to compare and predict hemodynamic effects between hybrid and surgical Norwood palliations for hypoplastic left heart syndrome

BACKGROUND

Combining bilateral pulmonary artery banding with arterial duct stenting, the hybrid approach achieves stage 1 palliation for hypoplastic left heart syndrome with different flow characteristics than those after the surgical Norwood procedures. Accordingly, we used computational modeling to assess some of these differences, including influence on systemic and cerebral oxygen deliveries.

METHODS AND RESULTS

A 3-dimensional computational model of hybrid palliation was developed by the finite volume method, along with models of the Norwood operation with a modified Blalock-Tausig or right ventricle-to-pulmonary artery shunt. Hybrid circulation was modeled with a 7-mm ductal stent and bilateral pulmonary artery banding to a 2-mm diameter. A 3.5-mm conduit was used in the Blalock-Tausig shunt model, whereas a 5-mm conduit was used in the right ventricle-to-pulmonary artery shunt model. Coupled to all the models was an identical hydraulic network that described the entire circulatory system based on pre-stage 2 hemodynamics. This clinically validated multiscale approach predicts flow dynamics, as well as global cardiac output, mixed venous oxygen saturation, and systemic and cerebral oxygen delivery. Compared with either of the Norwood models, the hybrid palliation had higher pulmonary-to-systemic flow ratio and lower cardiac output. Total systemic oxygen delivery was markedly reduced in the hybrid palliation (Blalock-Tausig shunt 591, right ventricle-to-pulmonary artery shunt 640, and hybrid 475 mL · min(-1) · m(-2)). Cerebral oxygen delivery was similarly lower in the hybrid palliation.

CONCLUSIONS

These computational results suggest that the hybrid approach may provide inferior systemic and cerebral oxygen deliveries compared with either of the 2 surgical Norwood procedures before stage 2 palliation.

Computational patient-specific models based on 3-D ultrasound data to quantify uterine arterial flow during pregnancy

Information on uterine blood flow rate during pregnancy would widely improve our knowledge on feto-placental patho-physiology. Ultrasonographic flow rate evaluation requires the knowledge of the spatial velocity profiles throughout the investigated vessel; these data may be obtained from hemodynamic simulations with accurate computational models. Recently, computational models of superficial vessels have been created using 3-D ultrasound data; unfortunately, common reconstruction methods are unsuitable for the uterine arteries due to the low quality achievable of imaged deep vessels. In this paper a simplified spline-based technique was applied to create computational models for patient-specific simulations of uterine arterial heamodynamics. Moreover, a novel method to quantify the uterine flow rates was developed based on echo-Doppler measurements and computational data. Preliminary results obtained for four patients indicated a quite narrow range for the blood flow rate through the main uterine artery with large variability in the flow split between corporal and cervical branches. Furthermore, parabolic-like velocity profiles were obtained in the branching region of the different patients, suggesting a clinical use of averaged, not patient-specific, spatial velocity distribution coefficients for the blood flow rate calculation. The developed reconstruction method based on 3-D ultrasound imaging is efficient for creating realistic custom models of the uterine arteries. The results of the fluid dynamic simulations allowed us to quantify the uterine arterial flow and its repartition in normal pregnancies.

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.

Multiscale modelling in biofluidynamics: Application to reconstructive paediatric cardiac surgery

Multiscale computing is a challenging area even in biomechanics. Application of such a methodology to quantitatively compare postoperative hemodynamics in congenital heart diseases is very promising. In the treatment of hypoplastic left heart syndrome, which is a congenital heart disease where the left ventricle is missing or very small, the necessity to feed the pulmonary and systemic circulations is obtained with an interposition shunt. Two main options are available and differ from the sites of anastomoses: (i) the systemic-to-pulmonary conduit (Blalock-Taussig shunt known as the Norwood Operation (NO)) connecting the innominate artery (NO-BT) or the aorta (NO-CS) to the right pulmonary artery and (ii) the right ventricle to pulmonary artery shunt (known as Sano operation (SO)). The proposition that the SO is superior to the NO remains controversial. 3-D computer models of the NO (NO-BT and NO-CS) and SO were developed and investigated using the finite volume method. Conduits of 3, 3.5 and 4 mm were used in the NO models, whereas conduits of 4, 5 and 6 mm were used in the SO model. The hydraulic nets (lumped resistances, compliances, inertances and elastances) which represent the systemic, coronary and pulmonary circulations and the heart were identical in the two models. A multiscale approach was adopted to couple the 3-D models with the circulation net. Computer simulation results were compared with post-operative catheterization data. Results showed that (i) there is a good correlation between predicted and observed data: higher aortic diastolic pressure, decreased pulmonary arterial pressure, lower pulmonary-to-systemic flow ratio and higher coronary perfusion pressure in SO; (ii) there is a minimal regurgitant flow in the SO conduit. The close correlation between predicted and observed clinical data supports the use of mathematical modelling, with a mandatory multiscale approach, in the design and assessment of surgical procedures.

Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation

The objective of this study is to compare the coronary and pulmonary blood flow dynamics resulting from two configurations of systemic-to-pulmonary artery shunts currently utilized during the Norwood procedure: the central (CS) and modified Blalock Taussig (MBTS) shunts. A lumped parameter model of the neonatal cardiovascular circulation and detailed 3-D models of the shunt based on the finite volume method were constructed. Shunt sizes of 3, 3.5 and 4 mm were considered. A multiscale approach was adopted to prescribe appropriate and realistic boundary conditions for the 3-D models of the Norwood circulation. Results showed that the average shunt flow rate is higher for the CS option than for the MBTS and that pulmonary flow increases with shunt size for both options. Cardiac output is higher for the CS option for all shunt sizes. Flow distribution between the left and the right pulmonary arteries is not completely balanced, although for the CS option the discrepancy is low (50-51% of the pulmonary flow to the right lung) while for the MBTS it is more pronounced with larger shunt sizes (51-54% to the left lung). The CS option favors perfusion to the right lung while the MBTS favors the left. In the CS option, a smaller percentage of aortic flow is distributed to the coronary circulation, while that percentage rises for the MBTS. These findings may have important implications for coronary blood flow and ventricular function.

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.

Pressure drops in a distensible model of end-to-side anastomosis in systemic-to-pulmonary shunts

The modified Blalock-Taussig shunt is a surgical procedure used as a palliation to treat complex congenital heart defects. It consists of an interposing prosthetic tube between the innominate/subclavian artery and the right pulmonary artery. Previous experience indicates that the pressure drop across the shunt is affected by the pulmonary pressure at the distal anastomosis combined with the distensibility of the anastomosis. In this study, a computational fluid-structure interaction approach is presented to investigate the haemodynamic behaviour. Steady-state fluid dynamics and structural analyses were carried out using commercial codes based on the finite element method (FIDAP and ABAQUS) coupled by means of a purposely-developed procedure to transfer boundary conditions. Both prosthetic tube and artery walls were characterised by non-linear material properties. Three different pulmonary pressures (2, 5 and 15 mmHg) and two volume flow rates (0.4 and 0.8 l/min) were investigated. Results indicate that the effects of distensibility at the distal anastomosis on the shunt pressure drop are relevant only when the distal anastomosis on the shunt pressure drop are relevant only when the distal anastomosis is not fully distended, which occurs when the pulmonary pressure is lower than 5 mmHg.

First-stage palliation for hypoplastic left heart syndrome in the twenty-first century

Improved understanding of the postoperative physiology and experience with the surgical techniques and perioperative care of patients with hypoplastic left heart syndrome have resulted in improved outcomes. Over the past few years, numerous modifications to the intraoperative and postoperative management of these patients have been described. It is likely that in combination, these modifications and better understanding of the unique physiology after the Norwood procedure are responsible for decreasing early mortality. This review describes and discusses the current surgical and medical management of patients undergoing first-stage palliation for hypoplastic left heart syndrome and its variants.

Neonates with congenital heart disease

Early reparative surgery in neonates and infants with congenital heart disease, as opposed to initial palliation and later repair, is now commonplace. Changes to the conduct of cardiopulmonary bypass, timing of surgery and surgical techniques, and perioperative management substantially have reduced the postoperative mortality and morbidity for these patients. The success of this strategy of early reparative surgery now has been extended to the premature and low-birth-weight newborn, and, along with this, new challenges to postoperative care in the intensive care unit. However, the low mortality associated with two-ventricle repairs has not been the experience in newborns undergoing palliation for single-ventricle defects, in particular, hypoplastic left heart syndrome. A number of articles regarding management of newborns with single-ventricle defects have been published during the past 12 months, ranging from classification, prenatal diagnosis, treatment options, and predictors of both early and late outcome, which may provide a guide for patient management. As mortality has declined, there has been an increased emphasis on identifying indices that may predict outcome or morbidity both before and after surgery, along with possible strategies to attenuate adverse clinical responses. The inflammatory response to bypass is heightened in neonates and infants, and several reports have addressed possible techniques for attenuating the response. In addition, reports regarding the risk for necrotizing enterocolitis, the utility of lactate as an index of systemic perfusion, potential markers of myocardial and neurologic injury, and the use of mechanical support of the circulation in newborns with congenital heart disease are summarized.

Requirements for mesh resolution in 3D computational hemodynamics

Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.

In vitro steady-flow analysis of systemic-to-pulmonary shunt haemodynamics

A modified Blalock-Taussig shunt is a connection created between the systemic and pulmonary arterial circulations to improve pulmonary perfusion in children with congenital heart diseases. Survival of these patients is critically dependent on blood flow distribution between the pulmonary and systemic circulations which in turn depends upon the flow resistance of the shunt. Previously, we investigated the pressure-flow relationship in rigid shunts with a computational approach. to estimate the pulmonary blood flow rate on the basis of the in vivo measured pressure drop. The present study aims at evaluating, in vitro how the anastomotic distensibility and restrictions due to suture presence affect the shunt pressure-flow relationship. Two actual Gore-Tex shunts (3 and 4 mm diameters) were sutured to compliant conduits by a surgeon and tested at different steady flow rates (0.25-11 min(-1)) and pulmonary pressures (3-34 mmHg). Corresponding computational models were also created to investigate the role of the anastomotic restrictions due to sutures. In vitro experiments showed that pulmonary artery pressure affects the pressure-flow relationship of the anastomoses. particularly at the distal site. However, this occurrence scarcely influences the total shunt pressure drop. Comparisons between in vitro and computational models without anastomotic restrictions show that the latter underestimates the in vitro pressure drops at any flow rate. The addition of the anastomotic restrictions (31 and 47% of the original area of 3 and 4 mm shunts, respectively) to the computational models reduces the gap, especially at high shunt flow rate and high pulmonary pressure.