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

Characterization of the Ejector Pump Performance for the Assisted Bidirectional Glenn Procedure

This study introduces an algebraic model informed by computational fluid dynamics (CFD) simulations to investigate the performance of the assisted bidirectional Glenn (ABG) operation on a broad range of conditions. The performance of this operation, as measured by the superior vena cava (SVC) pressure, depends on the nozzle area in its ejector pump and the patient’s pulmonary vascular resistance (PVR). Using the developed algebraic model to explore this two-dimensional parameter space shows that the ejector pump can create a pressure difference between the pulmonary artery and the SVC as high as 5 mmHg. The lowest SVC pressure is produced at a nozzle area that decreases linearly with the PVR such that, at PVR =4.2 (Wood units-m2), there is no added benefit in utilizing the ejector pump effect (optimal nozzle area is zero, corresponding to the bidirectional Glenn circulation). At PVR =2 (Wood units-m2), the SVC pressure can be lowered to less than 4 mmHg by using an optimal nozzle area of ≈2.5 mm2. Regardless of the PVR, adding a 2 mm2 nozzle to the baseline bidirectional Glenn boosts the oxygen saturation and delivery by at least 15%. The SVC pressure for that 2 mm2 nozzle remains below 14 mmHg for all PVRs less than 7 Wood units-m2. The mechanical efficiency of the optimal designs consistently remains below 30%, indicating the potential for improvement in the future. A good agreement is observed between the algebraic model and high-fidelity CFD simulations.

Multiscale modelling of Potts shunt as a potential palliative treatment for suprasystemic idiopathic pulmonary artery hypertension: a paediatric case study

Potts shunt (PS) was suggested as palliation for patients with suprasystemic pulmonary arterial hypertension (PAH) and right ventricular (RV) failure. PS, however, can result in poorly understood mortality. Here, a patient-specific geometrical multiscale model of PAH physiology and PS is developed for a paediatric PAH patient with stent-based PS. In the model, 7.6mm-diameter PS produces near-equalisation of the aortic and PA pressures and [Formula: see text] (oxygenated vs deoxygenated blood flow) ratio of 0.72 associated with a 16% decrease of left ventricular (LV) output and 18% increase of RV output. The flow from LV to aortic arch branches increases by 16%, while LV contribution to the lower body flow decreases by 29%. Total flow in the descending aorta (DAo) increases by 18% due to RV contribution through the PS with flow into the distal PA branches decreasing. PS induces 18% increase of RV work due to its larger stroke volume pumped against lower afterload. Nonetheless, larger RV work does not lead to increased RV end-diastolic volume. Three-dimensional flow assessment demonstrates the PS jet impinging with a high velocity and wall shear stress on the opposite DAo wall with the most of the shunt flow being diverted to the DAo. Increasing the PS diameter from 5mm up to 10mm results in a nearly linear increase in post-operative shunt flow and a nearly linear decrease in shunt pressure-drop. In conclusion, this model reasonably represents patient-specific haemodynamics pre- and post-creation of the PS, providing insights into physiology of this complex condition, and presents a predictive tool that could be useful for clinical decision-making regarding suitability for PS in PAH patients with drug-resistant suprasystemic PAH.

An Efficient Assisted Bidirectional Glenn Design With Lowered Superior Vena Cava Pressure for Stage-One Single Ventricle Patients

Recently, the assisted bidirectional Glenn (ABG) procedure has been proposed as an alternative to the modified Blalock-Taussig shunt (mBTS) operation for neonates with single-ventricle physiology. Despite success in reducing heart workload and maintaining sufficient pulmonary flow, the ABG also raised the superior vena cava (SVC) pressure to a level that may not be tolerated by infants. To lower the SVC pressure, we propose a modified version of the ABG (mABG), in which a shunt with a slit-shaped nozzle exit is inserted at the junction of the right and left brachiocephalic veins. The proposed operation is compared against the ABG, the mBTS, and the bidirectional Glenn (BDG) operations using closed-loop multiscale simulations. Both normal (2.3 Wood units-m2) and high (7 Wood units-m2) pulmonary vascular resistance (PVR) values are simulated. The mABG provides the highest oxygen saturation, oxygen delivery, and pulmonary flow rate in comparison to the BDG and the ABG. At normal PVR, the SVC pressure is significantly reduced below that of the ABG and the BDG (mABG: 4; ABG: 8; BDG: 6; mBTS: 3 mmHg). However, the SVC pressure remains high at high PVR (mABG: 15; ABG: 16; BDG: 12; mBTS: 3 mmHg), motivating an optimization study to improve the ABG hemodynamics efficiency for a broader range of conditions in the future. Overall, the mABG preserves all advantages of the original ABG procedure while reducing the SVC pressure at normal PVR.

Multiscale modeling of a modified Blalock-Taussig surgery in a patient-specific tetralogy of Fallot

Tetralogy of Fallot (TOF) is a congenital heart anomaly that causes a drastic reduction in the oxygen level. In this study, we coupled a lumped-parameter model with a patient-specific three-dimensional (3D) model which included a modified Blalock-Taussig (MBT) shunt. By forming a closed loop, we investigated the effects of certain parameters on the flow rates and the pressures at different locations of the developed network. A local sensitivity analysis on an initial zero-dimensional (0D) closed-loop model was conducted. The 0D lumped parameter (LP) model was then refined based on the results of the multiscale 0D-3D model and the local sensitivity analysis was repeated for the refined 0D model. It was shown that the maximum pressure of the pulmonary bed had the highest sensitivity of 94% to the diameter of MBT shunt. We observed that the existence of the flow in the shunt during the diastole caused an elevated wall shear stress (WSS) in the pulmonary artery. In this work, we calculated the flow velocity and pressure field in a 3D patient-specific aorta with an MBT shunt, and then we used the results to increase the accuracy of our LP model to simulate numerous 0D simulations in a significantly shorter time, which is potentially applicable for medical decision-making.

Computational Fluid Dynamics Characterization of Two Patient-Specific Systemic-to-Pulmonary Shunts before and after Operation

Studying the haemodynamics of the central shunt (CS) and modified Blalock–Taussig shunt (MBTS) benefits the improvement of postoperative recovery for patients with an aorta-pulmonary shunt. Shunt configurations, including CS and MBTS, are virtually reconstructed for infants A and B based on preoperative CT data, and three-dimensional models of A, 11 months after CS, and B, 8 months after MBTS, are reconstructed based on postoperative CT data. A series of parameters including energy loss, wall shear stress, and shunt ratio are computed from simulation to analyse the haemodynamics of CS and MBTS. Our results showed that the shunt ratio of the CS is approximately 30% higher than the MBTS and velocity distribution in the left pulmonary artery (LPA) and right pulmonary artery (RPA) was closer to a natural development in the CS than the MBTS. However, energy loss of the MBTS is lower, and the MBTS can provide more symmetric pulmonary artery (PA) flow than the CS. With the growth of infants A and B, the shunt ratio of infants was decreased, but maximum wall shear stress and the distribution region of high wall shear stress (WSS) were increased, which raises the probability of thrombosis. For infant A, the preoperative abnormal PA structure directly resulted in asymmetric growth of PA after operation, and the LPA/RPA ratio decreased from 0.49 to 0.25. Insufficient reserved length of the MBTS led to traction phenomena with the growth of infant B; on the one hand, it increased the eddy current, and on the other hand, it increased the flow resistance of anastomosis, promoting asymmetric PA flow.

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.

Computer and Physical Modeling of Blood Circulation Pump Support for a New Field of Application in Palliative Surgery

Objectives

One of the most popular palliative procedures performed to increase pulmonary blood flow in children with congenital heart defects is a shunt operation (Blalock-Taussig graft or Glenn procedure), which creates the new blood channel to the pulmonary artery. The main problem with this kind of surgery is poor shunt effectiveness and the lack of possibility to regulate the flow. The aim of this work is to use advanced computer simulation methods to study the effectiveness of a new idea to introduce a small axial blood pump into a Blalock-Taussig (B-T) or Glenn shunt in order to control the blood flow and prevent any increase in the graft stenosis.

Methods

Physical and computer 3-D simulation based on a finite element mesh (FEM) model was applied. Studies for optimization of the shunt and hybrid shunt with pump were performed for different stages of the disease.

Results and Conclusion

The graft with the axial pump creates good conditions for the vascular system and pulmonary artery blood flow as well as regulating blood pressure under variable conditions caused by palliative procedures. Its use permits the afterload of the left heart ventricle to be decreased. A palliative procedure is only a temporary solution. When a child grows, while the graft size is fixed, the blood flow through this graft may be not sufficient under changing hemodynamic conditions. The use of an axial pump for regulating the blood flow volume, during palliative procedures, allows to obtain the optimal flow conditions in pulmonary artery and safely wait on the final cardiac surgery correction later. However, the use of a pump mounted inside the graft increased hemodynamic resistance, which caused the flow to decrease up to 70% in the graft when the axial pump was not working.

Tetralogy of Fallot Surgical Repair: Shunt Configurations, Ductus Arteriosus and the Circle of Willis

In this study, hemodynamic performance of three novel shunt configurations that are considered for the surgical repair of tetralogy of Fallot (TOF) disease are investigated in detail. Clinical experience suggests that the shunt location, connecting angle, and its diameter can influence the post-operative physiology and the neurodevelopment of the neonatal patient. An experimentally validated second order computational fluid dynamics (CFD) solver and a parametric neonatal diseased great artery model that incorporates the ductus arteriosus (DA) and the full patient-specific circle of Willis (CoW) are employed. Standard truncated resistance CFD boundary conditions are compared with the full cerebral arterial system, which resulted 21, -13, and 37% difference in flow rate at the brachiocephalic, left carotid, and subclavian arteries, respectively. Flow splits at the aortic arch and cerebral arteries are calculated and found to change with shunt configuration significantly for TOF disease. The central direct shunt (direct shunt) has pulmonary flow 5% higher than central oblique shunt (oblique shunt) and 23% higher than modified Blalock Taussig shunt (RPA shunt) while the DA is closed. Maximum wall shear stress (WSS) in the direct shunt configuration is 9 and 60% higher than that of the oblique and RPA shunts, respectively. Patent DA, significantly eliminated the pulmonary flow control function of the shunt repair. These results suggests that, due to the higher flow rates at the pulmonary arteries, the direct shunt, rather than the central oblique, or right pulmonary artery shunts could be preferred by the surgeon. This extended model introduced new hemodynamic performance indices for the cerebral circulation that can correlate with the post-operative neurodevelopment quality of the patient.

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.

Simulation of Acute Haemodynamic Outcomes of the Surgical Strategies for the Right Ventricular Failure Treatment in Pediatric LVAD

Background

Right ventricular failure (RVF) is one of the major complications during LVAD. Apart from drug therapy, the most reliable option is the implantation of RVAD. However, BIVAD have a poor prognosis and increased complications. Experiments have been conducted on alternative approaches, such as the creation of an atrial septal defect (ASD), a cavo-aortic shunt (CAS) including the LVAD and a cavo-pulmonary connection (CPC). This work aims at realizing a lumped parameter model (LPM) to compare the acute hemodynamic effects of ASD, CPC, CAS, RVAD in LVAD pediatric patients with RVF.

Methods

Data of 5 pediatric patients undergoing LVAD were retrospectively collected to reproduce patients baseline hemodynamics with the LPM. The effects of continuous flow LVAD implantation complicated by RVF was simulated and then the effects of ASD, CPC, CAS and RVAD treatments were simulated for each patient.

Results

The model successfully reproduced patients' baseline and the hemodynamic effects of the surgical strategies. Simulating the different surgical strategies, an unloading of the right ventricle and an increment of left ventricular preload were observed with an improvement of the hemodynamics (total cardiac output: ASD +15%, CPC +10%, CAS +70% RVAD +20%; right ventricular external work: ASD -19%, CPC -46%, CAS -76%, RVAD -32%; left ventricular external work: ASD +12%, CPC +28%, RVAD +64%).

Conclusions

The use of numerical model could offer an additional support for clinical decision-making, also potentially reducing animal experiments, to compare the outcome of different surgical strategies to treat RVF in LVAD.

Data assimilation and modelling of patient-specific single-ventricle physiology with and without valve regurgitation

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

Hemodynamic Effects of Ventricular Assist Device Implantation on Norwood, Glenn, and Fontan Circulation: A Simulation Study

The growing population of failing single-ventricle (SV) patients might benefit from ventricular assist device (VAD) support as a bridge to heart transplantation. However, the documented experience is limited to isolated case reports. Considering the complex and different physiopathology of Norwood, Glenn, and Fontan patients and the lack of established experience, the aim of this work is to realize and test a lumped parameter model of the cardiovascular system able to simulate SV hemodynamics and VAD implantation effects to support clinical decision. Hemodynamic and echocardiographic data of 30 SV patients (10 Norwood, 10 Glenn, and 10 Fontan) were retrospectively collected and used to simulate patients' baseline. Then, the effects of VAD implantation were simulated. Simulation results suggest that the implantation of VAD: (i) increases the cardiac output and the mean arterial systemic pressure in all the three palliation conditions (Norwood 77.2 and 19.7%, Glenn 38.6 and 32.2%, and Fontan 17.2 and 14.2%); (ii) decreases the SV external work (Norwood 55%, Glenn 35.6%, and Fontan 41%); (iii) decreases the pressure pulsatility index (Norwood 65.2%, Glenn 81.3%, and Fontan 64.8%); (iv) increases the pulmonary arterial pressure in particular in the Norwood circulation (Norwood 39.7%, Glenn 12.1% and Fontan 3%); and (v) decreases the atrial pressure (Norwood 2%, Glenn 10.6%, and Fontan 8.6%). Finally, the VAD work is lower in the Norwood circulation (30.4 mL·mm Hg) in comparison with Fontan (40.3 mL·mm Hg) and to Glenn (64.5 mL·mm Hg) circulations. The use of VAD in SV physiology could be helpful to bridge patients to heart transplantations by increasing the CO and unloading the SV with a decrement of the atrial pressure and the SV external work. The regulation of the pulmonary flow is challenging because the Pap is increased by the presence of VAD. The hemodynamic changes are different in the different SV palliation step. The use of numerical models could be helpful to support patient and VAD selection to optimize the clinical outcome.

Use of Ventricular Assist Device in Univentricular Physiology: The Role of Lumped Parameter Models

Failing single-ventricle (SV) patients might benefit from ventricular assist devices (VADs) as a bridge to heart transplantation. Considering the complex physiopathology of SV patients and the lack of established experience, the aim of this work was to realize and test a lumped parameter model of the cardiovascular system, able to simulate SV hemodynamics and VAD implantation effects. Data of 30 SV patients (10 Norwood, 10 Glenn, and 10 Fontan) were retrospectively collected and used to simulate patients' baseline. Then, the effects of VAD implantation were simulated. Additionally, both the effects of ventricular assistance and cavopulmonary assistance were simulated in different pathologic conditions on Fontan patients, including systolic dysfunction, diastolic dysfunction, and pulmonary vascular resistance increment. The model can reproduce patients' baseline well. Simulation results suggest that the implantation of VAD: (i) increases the cardiac output (CO) in all the three palliation conditions (Norwood 77.2%, Glenn 38.6%, and Fontan 17.2%); (ii) decreases the SV external work (SVEW) (Norwood 55%, Glenn 35.6%, and Fontan 41%); (iii) increases the mean pulmonary arterial pressure (Pap) (Norwood 39.7%, Glenn 12.1%, and Fontan 3%). In Fontan circulation, with systolic dysfunction, the left VAD (LVAD) increases CO (35%), while the right VAD (RVAD) determines a decrement of inferior vena cava pressure (Pvci) (39%) with 34% increment of CO. With diastolic dysfunction, the LVAD increases CO (42%) and the RVAD decreases the Pvci. With pulmonary vascular resistance increment, the RVAD allows the highest CO (50%) increment with the highest decrement of Pvci (53%). The single ventricular external work (SVEW) increases (decreases) increasing the VAD speed in cavopulmonary (ventricular) assistance. Numeric models could be helpful in this challenging and innovative field to support patients and VAD selection to optimize the clinical outcome and personalize the therapy.

Computational fluid dynamics characterization of blood flow in central aorta to pulmonary artery connections: importance of shunt angulation as a determinant of shear stress-induced thrombosis

The central aortic shunt, consisting of a Gore-Tex (polytetrafluoroethylene) tube (graft) connecting the ascending aorta to the pulmonary artery, is a palliative operation for neonates with cyanotic congenital heart disease. These tubes often have an extended length, and therefore must be angulated to complete the connection to the posterior pulmonary arteries. Thrombosis of the graft is not uncommon and can be life-threatening. We have shown that a viscous fluid (such as blood) traversing a curve or bend in a small-caliber vessel or conduit can give rise to marked increases in wall shear stress, which is the major mechanical factor responsible for vascular thrombosis. Thus, the objective of this study was to use computational fluid dynamics to investigate whether wall shear stress (and shear rate) generated in angulated central aorta-to-pulmonary artery connections, in vivo, can be of magnitude and distribution to initiate platelet activation/aggregation, ultimately leading to thrombus formation. Anatomical features required to construct the computer-simulated blood flow pathways were verified from angiograms of central aortic shunts in patients. For the modeled central aortic shunts, we found wall shear stresses of (80-200 N/m(2)), with shear rates of (16,000-40,000/s), at sites of even modest curvature, to be high enough to cause platelet-mediated shunt thrombosis. The corresponding energy losses for the fluid transitions through the aorta-to-pulmonary connections constituted (70 %) of the incoming flow's mechanical energy. The associated velocity fields within these shunts exhibited vortices, eddies, and flow stagnation/recirculation, which are thrombogenic in nature and conducive to energy dissipation. Angulation-induced, shear stress-mediated shunt thrombosis is insensitive to aspirin therapy alone. Thus, for patients with central aortic shunts of longer length and with angulation, aspirin alone will provide insufficient protection against clotting. These patients are at risk for shunt thrombosis and significant morbidity and mortality, unless their anticoagulation regimen includes additional antiplatelet medications.

HEMODYNAMIC EFFECTS OF THE ANASTOMOSES IN THE MODIFIED BLALOCK–TAUSSIG SHUNT: A NUMERICAL STUDY USING A 0D/3D COUPLING METHOD

The modified Blalock–Taussig (BT) shunt is a palliative surgery which can help the tetralogy of Fallot (TOF) patient increase the blood oxygen saturation by interposing a systemic-to-pulmonary artery shunt. Two typical anastomotic shapes are frequently used in clinical practice: the end-to-side (ETS) and the side-to-side (STS) anastomosis. This paper examines the hemodynamic influence of the anastomotic shape in the modified BT shunt. Three models with different anastomotic shapes were reconstructed. The ETS anastomoses were applied in the first model. For the innominate artery (IA) and the pulmonary artery (PA) in the second model, the ETS and the STS anastomosis were applied, respectively. Finally, the STS anastomoses were applied in the third model. The 0D/3D coupling method was used to perform a numerical simulation by coupling the three-dimensional (3D) artery model with a zero-dimensional (0D) lumped parameter model for the cardiovascular system. The simulation results showed that the perfusion into the left and right PA in Model 1 was unbalanced. Swirling flow appeared in the shunt in Model 3, but the shunt flow rate in Model 3 was lower. The ETS anastomosis at the PA may cause unbalanced blood perfusion into the left and right PA. Conversely, the STS anastomosis can make the blood perfusion more balanced. Otherwise, the STS anastomosis at the IA could generate a swirling flow in the shunt which may provide a better hemodynamic environment while decreasing the pulmonary perfusion.

Computational Models of Aortic Coarctation in Hypoplastic Left Heart Syndrome: Considerations on Validation of a Detailed 3D model

Background

Reliability of computational models for cardiovascular investigations strongly depends on their validation against physical data. This study aims to experimentally validate a computational model of complex congenital heart disease (i.e., surgically palliated hypoplastic left heart syndrome with aortic coarctation) thus demonstrating that hemodynamic information can be reliably extrapolated from the model for clinically meaningful investigations.

Materials and methods

A patient-specific aortic arch model was tested in a mock circulatory system and the same flow conditions were re-created in silico, by setting an appropriate lumped parameter network (LPN) attached to the same three-dimensional (3D) aortic model (i.e., multi-scale approach). The model included a modified Blalock-Taussig shunt and coarctation of the aorta. Different flow regimes were tested as well as the impact of uncertainty in viscosity.

Results

Computational flow and pressure results were in good agreement with the experimental signals, both qualitatively, in terms of the shape of the waveforms, and quantitatively (mean aortic pressure 62.3 vs. 65.1 mmHg, 4.8% difference; mean aortic flow 28.0 vs. 28.4% inlet flow, 1.4% difference; coarctation pressure drop 30.0 vs. 33.5 mmHg, 10.4% difference), proving the reliability of the numerical approach. It was observed that substantial changes in fluid viscosity or using a turbulent model in the numerical simulations did not significantly affect flows and pressures of the investigated physiology. Results highlighted how the non-linear fluid dynamic phenomena occurring in vitro must be properly described to ensure satisfactory agreement.

Conclusions

This study presents methodological considerations for using experimental data to preliminarily set up a computational model, and then simulate a complex congenital physiology using a multi-scale approach.

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 OF TWO PATIENT-SPECIFIC SYSTEMIC TO PULMONARY SHUNTS

Tetralogy of Fallot is the most common cyanotic congenital heart defect. For severe cases, inserting a systemic to pulmonary shunt, which distributes part of systemic artery blood into the pulmonary artery, is the preferable palliative surgery. Based on the computed tomography images and three-dimensional geometry technologies, two patient-specific anatomical options of systemic to pulmonary shunts including the aorta to pulmonary shunt (APS) and innominate artery to pulmonary shunt (IPS) have been simulated for computational fluid dynamics. The objective of this study was to predict the hemodynamics within the shunts and confirm, through patient-specific simulations, the shunt with the optimal performance. Results indicated that both options created high velocity gradients and pressure gradients at the proximal end of the shunts. Obvious flow recirculation appeared at the inner region near the proximal end of the shunts. Part of the reverse flow from the descending aorta, left subclavian artery, left carotid artery and innominate artery was driven into the shunts during the diastolic period. The IPS provided better balanced and more adequate blood flow distributions between the systemic and pulmonary circulations. The APS provided slightly excessive pulmonary blood flow which can ultimately result in cardiac failure and pulmonary hypertension.

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.

Optimization of Shunt Placement for the Norwood Surgery Using Multi-Domain Modeling

An idealized systemic-to-pulmonary shunt anatomy is parameterized and coupled to a closed loop, lumped parameter network (LPN) in a multidomain model of the Norwood surgical anatomy. The LPN approach is essential for obtaining information on global changes in cardiac output and oxygen delivery resulting from changes in local geometry and physiology. The LPN is fully coupled to a custom 3D finite element solver using a semi-implicit approach to model the heart and downstream circulation. This closed loop multidomain model is then integrated with a fully automated derivative-free optimization algorithm to obtain optimal shunt geometries with variable parameters of shunt diameter, anastomosis location, and angles. Three objective functions: (1) systemic; (2) coronary; and (3) combined systemic and coronary oxygen deliveries are maximized. Results show that a smaller shunt diameter with a distal shunt-brachiocephalic anastomosis is optimal for systemic oxygen delivery, whereas a more proximal anastomosis is optimal for coronary oxygen delivery and a shunt between these two anatomies is optimal for both systemic and coronary oxygen deliveries. Results are used to quantify the origin of blood flow going through the shunt and its relationship with shunt geometry. Results show that coronary artery flow is directly related to shunt position.

Norwood procedure with non-valved right ventricle to pulmonary artery shunt improves ventricular energetics despite the presence of diastolic regurgitation: a theoretical analysis

When the Norwood procedure is conducted for the hypoplastic left heart syndrome using a non-valved right ventricle (RV) to pulmonary artery (PA) shunt, diastolic regurgitation from PA to RV may have an adverse effect on postoperative hemodynamics. In this study, we examined the impact of the diastolic regurgitation on ventricular energetics by computational analysis using a combination of a time-varying elastance chamber model and a modified three-element Windkessel vascular model. This study revealed that use of the valved or non-valved RV-PA shunt eliminated pulmonary over-circulation which was observed when using the systemic to pulmonary artery shunt (modified Blalock-Taussig shunt). Although the valved RV-PA shunt improved pulmonary blood supply and consequently increased pulmonary artery flow and oxygen saturation compared to the non-valved RV-PA shunt, the non-valved RV-PA shunt improved ventricular energetics in spite of the presence of PA to RV regurgitation.

A cycle-averaged model of hypoplastic left heart syndrome (HLHS)

This paper is concerned with computational modeling of a severe congenital defect called Hypoplastic left heart syndrome (HLHS) that is the most common cardiac malformation with the highest likelihood of deaths in newborns. A lumped parameter model of the HLHS circulation has been developed to study the hemodynamic variables in the various sections of the cardio-pulmonary circulation system. We applied a short-term, cycle-averaging operation to the differential equations of the HLHS model to obtain the cycle-averaged model. Study has been carried out to analyze the variation of blood flow rate in different parts due to parameter changes. Results show that the developed model, could bring a good insight into understanding of the HLHS disease.

A model for educational simulation of hemodynamic transitions at birth

Birth is characterized by swift and complex transitions in hemodynamic and respiratory variables. Unrecognized pathologies or incidents may quickly become fatal or cause permanent damage. This article introduces an essential component of an acute perinatal care simulator, namely a model for educational simulation of normal hemodynamic transitions seen during and shortly after birth. We explicitly formulate educational objectives and adapt a preexisting model for the simulation of neonatal cardiovascular physiology to include essential aspects of fetal hemodynamics. From the scientific literature, we obtain model parameters that characterize these aspects quantitatively. The fetal model is controlled by a time- and event-based script of changes occurring at birth, such as onset of breathing and cord clamping, and the transitory phase up to 24 h after birth. Comparison of simulation results with published target data confirms that realistic simulated hemodynamic vital signs are achieved.

Numerical investigation of regurgitation phenomena in pulmonary arteries of Tetralogy of Fallot patients after repair

Pulmonary regurgitation is a very common phenomenon in pulmonary arteries after repair of patients of Tetralogy of Fallot (TOF) which is the most common complex congenital heart diseases. The aim of this study is to use numerical approaches to simulate flow variations in pulmonary artery after repair of patients of TOF. We analyze the flow patterns in an in-vitro bifurcation pulmonary artery and consider effects of various regurgitation fractions (RF or b/f) in left pulmonary artery (LPA) and right pulmonary artery (RPA). We not only observe the variation of flow patterns, but also analyze the results of b/f and net volumetric flow rates in LPA and RPA. In general, the b/f of LPA is higher than RPA in the measured data provided by phase-contrast magnetic resonance imaging (PC-MRI). We validate the result using numerical approaches to analyze the flow patterns in pulmonary artery in this study. The results will be useful for medical doctors when they perform operations for TOF patients.

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.

In vitro set-up of modified Blalock Taussig shunt: vascular resistance-flow relationship

BACKGROUND

A modified Blalock-Taussig (mBT) shunt is an anastomosis created between the systemic and pulmonary arterial tree in order to improve pulmonary blood flow in neonates and children with congenital heart disease. The aim of this study was to assess vascular resistance-flow relationship in an in vitro set-up of a modified Blalock Taussig shunt.

METHODS

A shunt set-up was constructed with the vessels of a sheep. A modified BT shunt was anastomosed between an innominate (brachiocephalic) and a right pulmonary artery. A Medos pump (ventricular assist device) was used to create pulsatile flow. Three different mean pulmonary artery flow rates (Q PA ) were applied. Once mean pulmonary and mean aortic flows (Q AO ) were fixed, shunt flow rates for twelve different pulmonary vascular resistances (R p ) were investigated.

RESULTS

For all three pulmonary flow rates, the shunt flow decreased with increasing pulmonary resistance. In addition, systemic flow decreased compared to pulmonary flow. When pulmonary flow rate was set at 800 ml/min and aorta flow rate at 900 ml/min, the distribution of flow between pulmonary and systemic organs flow rates ranged between 69% - 70% and 30% - 31% respectively. Similarly, when both pulmonary and aorta flow rates were set at 900 ml/min, pulmonary and systemic organ flows ranged between 73% - 77% and 23% - 27% respectively. For pulmonary and aorta flow rates of 1000 ml/min and 900 ml/min, respectively, the distribution of flow between pulmonary and systemic organ flow rates varied between 79% - 83% and 17% - 21% respectively.

CONCLUSION

Knowledge of the relationship between vascular resistances and flow in this surgically created in vitro mBT shunt set-up may be helpful in the clinical management of the patients whose survival is crucially dependent on the blood flow distribution between the pulmonary and systemic circulation.

The Effects of Graft Geometry on the Patency of a Systemic-to-Pulmonary Shunt: A Computational Fluid Dynamics Study

The modified Blalock-Taussig shunt is a palliative operation for some congenital heart diseases. An artificial conduit with antithrombotic surface placed between the subclavian (or innominate) and the pulmonary artery supplies blood to the lungs in defects with decreased pulmonary flow. Clotting of the graft is the main cause of its failure. Stenosis of the arteries is also observed. The objective of the present study was to investigate the flow pattern in the graft to investigate the possibility that clotting is initiated by the stimulation of platelets by high shear stress, and the possible effect of the pathological wall shear stress on the stenosis formation. The model included the left subclavian artery (LSA), the left pulmonary artery (LPA), and the graft. The three-dimensional relative position and size of the arteries was obtained from a CT scan of real anatomy. Four different types of the graft with two different diameters (3 and 4 mm) and two different shapes (straight and curved) of the pipe, and one variable diameter pipe were inserted in the model. A pulsatile flow of 0.81 L/min on average was assumed at the inlet to LSA, and 80% of the flow was directed through the graft. Computer simulations demonstrated a complex flow pattern with eddies and low velocity regions in the arteries at the anastomoses with the graft in all five models. An eddy was also found inside the straight 4 mm graft. A high pathological shear rate was present within the graft, with higher values in the 3 mm grafts. The fractional volume with a high (>2500 L/s) shear rate was between 2.5% and 4.5%, and that with a very high (>7500 L/s) shear rate between 0 and 1.5% of the model volume, and depended on the graft geometry and the phase of the cardiac cycle. Pathologically high (>3.5 Pa) and pathologically low (<1.0 Pa) wall shear stress, which may induce neointimal growth, was found in LSA and LPA. We conclude that the activation of platelets by high shear rate is possible within the graft, followed by their subsequent aggregation in the eddies with a low flow rate. Flow-induced changes of the vessel wall thickness (stenosis) can also appear, especially in the pulmonary artery.

Three-dimensional velocity field reconstruction

The problem of inter-slice magnetic resonance (MR) image reconstruction is encountered often in medical imaging applications, in such scenarios, there is a need to approximate information not captured in contiguously acquired MR images due to hardware sampling limitations. In the context of velocity field reconstruction, these data are required for visualization and computational analyses of flow fields to be effective. To provide more complete velocity information, a method has been developed for the reconstruction of flow fields based on adaptive control grid interpolation (ACGI). In this study, data for reconstruction were acquired via MRJ from in vitro models of surgically corrected pediatric cardiac vasculatures. Reconstructed velocity fields showed strong qualitative agreement with those obtained via other acquisition techniques. Quantitatively reconstruction was shown to produce data of comparable quality to accepted velocity data acquisition methods. Results indicate that ACGI-based velocity field reconstruction is capable of producing information suitable for a variety of applications demanding three-dimensional in vivo velocity data.

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.

Application of an adaptive control grid interpolation technique to morphological vascular reconstruction

The problem of interslice magnetic resonance (MR) image reconstruction arises in a broad range of medical applications. In such cases, there is a need to approximate information present in the original subject that is not reflected in contiguously acquired MR images because of hardware sampling limitations. In the context of vascular morphology reconstruction, this information is required in order for subsequent visualization and computational analysis of blood vessels to be most effective. Toward that end we have developed a method of vascular morphology reconstruction based on adaptive control grid interpolation (ACGI) to function as a precursor to visualization and computational analysis. ACGI has previously been implemented in addressing various problems including video coding and tracking. This paper focuses on the novel application of the technique to medical image processing. ACGI combines features of optical flow-based and block-based motion estimation algorithms to enhance insufficiently dense MR data sets accurately with a minimal degree of computational complexity. The resulting enhanced data sets describe vascular geometries. These reconstructions can then be used as visualization tools and in conjunction with computational fluid dynamics (CFD) simulations to offer the pressure and velocity information necessary to quantify power loss. The proposed ACGI methodology is envisioned ultimately to play a role in surgical planning aimed at producing optimal vascular configurations for successful surgical outcomes.

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.

Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate

Hypoplastic left heart syndrome is the most common lethal cardiac malformation of the newborn. Its treatment, apart from heart transplantation, is the Norwood operation. The initial procedure for this staged repair consists of reconstructing a circulation where a single outlet from the heart provides systemic perfusion and an interpositioning shunt contributes blood flow to the lungs. To better understand this unique physiology, a computational model of the Norwood circulation was constructed on the basis of compartmental analysis. Influences of shunt diameter, systemic and pulmonary vascular resistance, and heart rate on the cardiovascular dynamics and oxygenation were studied. Simulations showed that 1) larger shunts diverted an increased proportion of cardiac output to the lungs, away from systemic perfusion, resulting in poorer O2 delivery, 2) systemic vascular resistance exerted more effect on hemodynamics than pulmonary vascular resistance, 3) systemic arterial oxygenation was minimally influenced by heart rate changes, 4) there was a better correlation between venous O2 saturation and O2 delivery than between arterial O2 saturation and O2 delivery, and 5) a pulmonary-to-systemic blood flow ratio of 1 resulted in optimal O2 delivery in all physiological states and shunt sizes.

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.