Anomalous hemodynamic effects of a self-expanding intracranial stent: Comparing in-vitro and ex-vivo models using ultra-high resolution MicroCT based CFD

Previous research on the effects of intracranial stents on arterial hemodynamics has involved computational hemodynamics (CHD) simulations applied to artificially generated stent models. In this study, accurate geometric reconstructions of in-vitro (PTFE tube) and ex-vivo (canine artery) deployed stents based on ultra-high resolution MicroCT imaging were used. The primary goal was to compare the hemodynamic effects of deployment in these two different models and to identify flow perturbations due to deployment anomalies such as stent malapposition and strut prolapse, important adverse mechanics occurring in clinical practice, but not considered in studies using idealized stent models.Ultra-high resolution MicroCT data provided detailed visualization of deployment characteristics allowing for accurate in-stent flow simulation. For stent cells that are regularly and symmetrically deployed, the near wall flow velocities and wall shear stresses were similar to previously published results derived from idealized models. In-stent hemodynamics were significantly altered by misaligned or malapposed stent cells, important effects not realistically captured in previous models. This research shows the feasibility and value of an ex-vivo stent model for MicroCT based CHD studies. It validates previous in-vitro studies and further contributes to the understanding of in-stent hemodynamics associated with adverse mechanics of self-expanding intracranial stents.     

Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND: Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH: An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION: CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.     

On the effect of parent-aneurysm angle on flow patterns in basilar tip aneurysms: towards a surrogate geometric marker of intra-aneurismal hemodynamics

As a part of previous computational fluid dynamic (CFD) validation studies, particle image velocimetry (PIV) of two anatomically realistic basilar artery tip aneurysm models revealed two distinct types of flow (one of which has yet to be reported in the literature), characterized by the location and strength of the intra-aneurismal vortex. We hypothesized that these distinct "hemodynamic phenotypes" could be anticipated by a simple geometric parameter: the angle of the aneurysm bulb relative to the parent artery. An idealized basilar tip aneurysm model was constructed to allow independent control of this angle, and CFD simulations were carried out for angles ranging from 2 degrees to 30 degrees , these extremes corresponding to the angles measured from the two anatomically realistic models. The gross hemodynamics predicted by the idealized model for 2 degrees and 30 degrees were consistent with those seen in the corresponding anatomically realistic models. For the idealized model, the flow type switched at an angle between 8 degrees and 12 degrees . Sensitivity studies suggested that, near these angles, the hemodynamic phenotype was sensitive to inflow momentum. Outside this range, however, the parent-bulb angle appeared to be a robust predictor of hemodynamic phenotype. Our findings suggest that blood flow dynamics in basilar artery tip aneurysms fall into one of the two broad phenotypes, each subject to distinct hemodynamic forces. That the general features of these flow types may be anticipated by a relatively simple-to-measure geometric parameter could help ease the introduction of hemodynamic information into routine clinical decision-making.     

Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better (\( R^{2} = 0.942 \)). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.     

Hemodynamic mechanisms of the pulmonary artery pressure and blood flow changes following vasoactive depressor drugs injection

The character and values of changes of the pulmonary hemodynamics and venous return following acetylcholine, histamine and isoproterenol intravenous injection were studied in acute experiments on the anesthetized cats. After depressor drugs injection the character and values of changes of pulmonary artery pressure and flow were different. In 67% cases the pulmonary artery pressure was decreased, and in 33%--it was elevated, meanwhile the pulmonary artery flow was decreased in 48% cases and it was increased in 52%, i.e., in the equal number of observations. Thus, following depressor drugs intravenous injection, hemodynamic mechanisms of the changes of pulmonary artery pressure and flow are different. The character and values of changes of the pulmonary artery pressure are correlated with the changes of pulmonary vascular resistance and are not dependent with the left atrial pressure shifts. The changes of the pulmonary artery blood flow are caused by the changes of the venous return and are not correlated with the changes of the right and left atrial pressure.     

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.     

Circumferential vascular deformation after stent implantation alters wall shear stress evaluated with time-dependent 3D computational fluid dynamics models.

The success of vascular stents in the restoration of blood flow is limited by restenosis. Recent data generated from computational fluid dynamics (CFD) models suggest that stent geometry may cause local alterations in wall shear stress (WSS) that have been associated with neointimal hyperplasia and subsequent restenosis. However, previous CFD studies have ignored histological evidence of vascular straightening between circumferential stent struts. We tested the hypothesis that consideration of stent-induced vascular deformation may more accurately predict alterations in indexes of WSS that may subsequently account for histological findings after stenting. We further tested the hypothesis that the severity of these alterations in WSS varies with the degree of vascular deformation after implantation. Steady-state and time-dependent simulations of three-dimensional CFD arteries based on canine coronary artery measurements of diameter and blood flow were conducted, and WSS and WSS gradients were calculated. Circumferential straightening introduced areas of high WSS between stent struts that were absent in stented vessels of circular cross section. The area of vessel exposed to low WSS was dependent on the degree of circumferential vascular deformation and axial location within the stent. Stents with four vs. eight struts increased the intrastrut area of low WSS in vessels, regardless of cross-sectional geometry. Elevated WSS gradients were also observed between struts in vessels with polygonal cross sections. The results obtained using three-dimensional CFD models suggest that changes in vascular geometry after stent implantation are important determinants of WSS distributions that may be associated with subsequent neointimal hyperplasia.     

Hydrodynamic effects of compliance mismatch in stented arteries

Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and development of treatment options imperative. The most common modality for treatment of occlusive coronary artery diseases is the use of stents. Stent design profoundly influences the postprocedural hemodynamic and solid mechanical environment of the stented artery. However, despite their wide acceptance, the incidence of stent late restenosis is still high (Zwart et al., 2010, "Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment," Current Treatment Options in Cardiovascular Medicine, 12(1), pp. 46-57), and it is most prevailing at the proximal and distal ends of the stent. In this work, we focus our investigation on the localized hemodynamic effects of compliance mismatch due to the presence of a stent in an artery. The compliance mismatch in a stented artery is maximized at the proximal and distal ends of the stent. Hence, it is our objective to understand and reveal the mechanism by which changes in compliance contribute to the generation of nonphysiological wall shear stress (WSS). Such adverse hemodynamic conditions could have an effect on the onset of restenosis. Three-dimensional, spatiotemporally resolved computational fluid dynamics simulations of pulsatile flow with fluid-structure interaction were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with uniform elastic modulus is used as the baseline control case. In order to study the effect of compliance variation on local hemodynamics, this baseline model is compared with models where the elastic modulus was increased by two-, five-, and tenfold in the middle of the vessel. The simulations provided detailed information regarding the recirculation zone dynamics formed during flow reversals. The results suggest that discontinuities in compliance cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients. The change in pressure gradient at the discontinuity was as high as 90%. The corresponding changes in WSS and oscillatory shear index calculated were 9% and 15%, respectively. We demonstrate that these changes are attributed to the physical mechanism associating the pressure gradient discontinuities to the production of vorticity (vorticity flux) due to the presence of the stent. The pressure gradient discontinuities and augmented vorticity flux are affecting the wall shear stresses. As a result, this work reveals how compliance variations act to modify the near wall hemodynamics of stented arteries.     

Computational simulation of flow-induced arterial remodeling of the pancreaticoduodenal arcade associated with celiac artery stenosis

Arterial remodeling of the pancreaticoduodenal arcade, which enables collateral flow to the liver, spleen, and stomach, is a well-recognized clinical sign of celiac artery (CA) stenosis. However, the hemodynamic changes due to remodeling are poorly understood, despite their importance in surgical procedures such as pancreaticoduodenectomy. In this study, a framework to simulate remodeling of the arterial network following pathological flow alterations was developed and applied to investigate the hemodynamic characteristics of patients with CA stenosis. A one-dimensional–zero-dimensional cardiovascular model was used for blood flow simulation. After introducing CA stenosis into the normal network, arterial remodeling was simulated by iteratively changing the diameter of each artery until time-averaged wall shear stress reached its value under normal conditions. A representative case was simulated to validate the present framework, followed by simulation cases to investigate the impact of stenosis severity on remodeling outcome. A markedly dilated arcade was observed whose diameter agreed well with the corresponding values measured in subjects with CA stenosis, confirming the ability of the framework to predict arterial remodeling. A series of simulations clarified how the geometry and hemodynamics after remodeling change with stenosis severity. In particular, the arterial remodeling and resulting blood flow redistribution were found to maintain adequate organ blood supply regardless of stenosis severity. Furthermore, it was suggested that flow conditions in patients with CA stenosis could be estimated from geometric factors, namely, stenosis severity and arcade diameter, which can be preoperatively and non-invasively measured using diagnostic medical images.     

Computational fluid dynamics simulation to evaluate aortic coarctation gradient with contrast-enhanced CT

Coarctation of aorta (CoA) is a narrowing of the aorta leading to a pressure gradient (ΔP) across the coarctation, increased afterload and reduced peripheral perfusion pressures. Indication to invasive treatment is based on values of maximal (systolic) trans-coarctation ΔP. A computational fluid dynamic (CFD) approach is herein presented for the non-invasive haemodynamic assessment of ΔP across CoA. Patient-specific CFD simulations were created from contrast-enhanced computed tomography (CT) and appropriate flow boundary conditions. Computed ΔP was validated with invasive intravascular trans-CoA pressure measurements. Haemodynamic indices, including pressure loss coefficient (PLc), time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI), were also quantified. CFD-estimated ΔP values were comparable to the invasive ones. Moreover, the aorta proximal to CoA was exposed to altered TAWSS and OSI suggesting hypertension. PLc was found as a further geometric marker of CoA severity. Finally, CFD-estimated ΔP confirmed a significant reduction after percutaneous balloon dilatation and stenting of the CoA in one patient (e.g. from ΔP～52 mmHg to ΔP～3 mmHg). The validation of the ΔP computations with catheterisation measurements suggests that CFD simulation, based on CT-derived anatomical data, is a useful tool to readily quantify CoA severity.     

Hemodynamics in stented vertebral artery ostial stenosis based on computational fluid dynamics simulations

Hemodynamic factors may affect the potential occurrence of in-stent restenosis (ISR) after intervention procedure of vertebral artery ostial stenosis (VAOS). The purpose of the present study is to investigate the influence of stent protrusion length in implantation strategy on the local hemodynamics of the VAOS. CTA images of a 58-year-old female patient with posterior circulation transient ischemic attack were used to perform a 3D reconstruction of the vertebral artery. Five models of the vertebral artery before and after the stent implantation were established. Model 1 was without stent implantation, Model 2–5 was with stent protruding into the subclavian artery for 0, 1, 2, 3 mm, respectively. Computational fluid dynamics simulations based on finite element analysis were employed to mimic the blood flow in arteries and to assess hemodynamic conditions, particularly the blood flow velocity and wall shear stress (WSS). The WSS and the blood flow velocity at the vertebral artery ostium were reduced by 85.33 and 35.36% respectively after stents implantation. The phenomenon of helical flow disappeared. Hemodynamics comparison showed that stent struts that protruded 1 mm into the subclavian artery induced the least decrease in blood speed and WSS. The results suggest that stent implantation can improve the hemodynamics of VAOS, while stent struts that had protruded 1 mm into the subclavian artery would result in less thrombogenesis and neointimal hyperplasia and most likely decrease the risk of ISR.     

Hemodynamics of patient-specific aorta-pulmonary shunt configurations

Optimal hemodynamics in aorta-pulmonary shunt reconstruction is essential for improved post-operative recovery of the newborn congenital heart disease patient. However, prior to in vivo execution, the prediction of post-operative hemodynamics is extremely challenging due to the interplay of multiple confounding physiological factors. It is hypothesized that the post-operative performance of the surgical shunt can be predicted through computational blood flow simulations that consider patient size, shunt configuration, cardiac output and the complex three-dimensional disease anatomy. Utilizing only the routine patient-specific pre-surgery clinical data sets, we demonstrated an intelligent decision-making process for a real patient having pulmonary artery atresia and ventricular septal defect. For this patient, a total of 12 customized candidate shunt configurations are contemplated and reconstructed virtually using a sketch-based computer-aided anatomical editing tool. Candidate shunt configurations are evaluated based on the parameters that are computed from the flow simulations, which include 3D flow complexity, outlet flow splits, shunt patency, coronary perfusion and energy loss. Our results showed that the modified Blalock-Taussig (mBT) shunt has 12% higher right pulmonary artery (RPA) and 40% lower left pulmonary artery (LPA) flow compared to the central shunt configuration. Also, the RPA flow regime is distinct from the LPA, creating an uneven flow split at the pulmonary arteries. For all three shunt sizes, right mBT innominate and central configurations cause higher pulmonary artery (PA) flow and lower coronary artery pressure than right and left mBT subclavian configurations. While there is a trade-off between energy loss, flow split and coronary artery pressure, overall, the mBT shunts provide sufficient PA perfusion with higher coronary artery pressures and could be preferred for similar patients having PA overflow risk. Central shunts would be preferred otherwise particularly for cases with very low PA overflow risk.     

Can time-averaged flow boundary conditions be used to meet the clinical timeline for Fontan surgical planning?

Cardiovascular simulations have great potential as a clinical tool for planning and evaluating patient-specific treatment strategies for those suffering from congenital heart diseases, specifically Fontan patients. However, several bottlenecks have delayed wider deployment of the simulations for clinical use; the main obstacle is simulation cost. Currently, time-averaged clinical flow measurements are utilized as numerical boundary conditions (BCs) in order to reduce the computational power and time needed to offer surgical planning within a clinical time frame. Nevertheless, pulsatile blood flow is observed in vivo, and its significant impact on numerical simulations has been demonstrated. Therefore, it is imperative to carry out a comprehensive study analyzing the sensitivity of using time-averaged BCs. In this study, sensitivity is evaluated based on the discrepancies between hemodynamic metrics calculated using time-averaged and pulsatile BCs; smaller discrepancies indicate less sensitivity.The current study incorporates a comparison between 3D patient-specific CFD simulations using both the time-averaged and pulsatile BCs for 101 Fontan patients. The sensitivity analysis involves two clinically important hemodynamic metrics: hepatic flow distribution (HFD) and indexed power loss (iPL). Paired demographic group comparisons revealed that HFD sensitivity is significantly different between single and bilateral superior vena cava cohorts but no other demographic discrepancies were observed for HFD or iPL. Multivariate regression analyses show that the best predictors for sensitivity involve flow pulsatilities, time-averaged flow rates, and geometric characteristics of the Fontan connection. These predictors provide patient-specific guidelines to determine the effectiveness of analyzing patient-specific surgical options with time-averaged BCs within a clinical time frame.     

Aerodynamic study of different cyclist positions: CFD analysis and full-scale wind-tunnel tests

Three different cyclist positions were evaluated with Computational Fluid Dynamics (CFD) and wind-tunnel experiments were used to provide reliable data to evaluate the accuracy of the CFD simulations. Specific features of this study are: (1) both steady Reynolds-averaged Navier–Stokes (RANS) and unsteady flow modelling, with more advanced turbulence modelling techniques (Large-Eddy Simulation – LES), were evaluated; (2) the boundary layer on the cyclist’s surface was resolved entirely with low-Reynolds number modelling, instead of modelling it with wall functions; (3) apart from drag measurements, also surface pressure measurements on the cyclist’s body were performed in the wind-tunnel experiment, which provided the basis for a more detailed evaluation of the predicted flow field by CFD. The results show that the simulated and measured drag areas differed about 11% (RANS) and 7% (LES), which is considered to be a close agreement in CFD studies. A fair agreement with wind-tunnel data was obtained for the predicted surface pressures, especially with LES. Despite the higher accuracy of LES, its much higher computational cost could make RANS more attractive for practical use in some situations. CFD is found to be a valuable tool to evaluate the drag of different cyclist positions and to investigate the influence of small adjustments in the cyclist’s position. A strong advantage of CFD is that detailed flow field information is obtained, which cannot easily be obtained from wind-tunnel tests. This detailed information allows more insight in the causes of the drag force and provides better guidance for position improvements.     

A Patient-Specific Computational Fluid Dynamic Model of Middle Cerebral Artery Aneurysm Before and One Year After Surgery

Computational fluid dynamics (CFD) has been widely used for studying intracranial aneurysm hemodynamics, while its use for guiding clinical strategy is still in development. In this study, CFD simulations helped inform treatment decision for a middle cerebral artery (MCA) aneurysm case was investigated. A patient with a 10.4 × 9.8 mm aneurysm attached with a small aneurysm at the edge of the trifurcation in the left MCA was included in this study. For removing the MCA aneurysm, two scenarios were considered: Plan-A involved clipping the small aneurysm and Plan-B involved clipping the whole aneurysm. A suitable treatment plan was decided by comparing the clinical measurements and CFD analysis between these two plans. One-year after the surgery, the CFD analysis was conducted again on the post-operative aneurysm model to verify the selected surgical plan in terms of morphometric and hemodynamic properties changes in the aneurysm. Based on the CFD simulation and clinical experience, surgical Plan-A was adopted. One-year after the surgery, both the hemodynamic and morphological properties improved in the post-operative aneurysm model, indicating the recovery of the patient. The patient-specific aneurysm CFD analysis can help to determine a better surgical plan for patients with special cerebral aneurysms. This study showed how CFD analysis can be used to aid clinical diagnosis and treatment.     

Multiscale models of the hybrid palliation for hypoplastic left heart syndrome

A less-invasive procedure that combines interventional stent placement in the ductus arteriosus and surgical banding of the branch pulmonary arteries has been recently introduced in the treatment of the hypoplastic left heart syndrome (HLHS). The hemodynamic behaviour of this hybrid approach has not been examined before in a mathematical model. In this study, a mathematical model of the hybrid procedure for HLHS is described, applying a multiscale approach that couples 3D models of the area of the surgical operation and lumped parameter models of the remaining circulation. The effects of various degrees of pulmonary banding and different stent sizes inserted in the ductus arteriosus on pulmonary-systemic flow ratio, cardiac output and oxygen delivery were assessed. Computational results suggest that balanced systemic and pulmonary blood flow and optimal systemic oxygen delivery are sensitive to the degree of pulmonary arterial banding and not to the size of the ductal stent.     

In vitro validation of finite-element model of AAA hemodynamics incorporating realistic outlet boundary conditions

The purpose of this study is to validate numerical simulations of flow and pressure in an abdominal aortic aneurysm (AAA) using phase-contrast magnetic resonance imaging (PCMRI) and an in vitro phantom under physiological flow and pressure conditions. We constructed a two-outlet physical flow phantom based on patient imaging data of an AAA and developed a physical Windkessel model to use as outlet boundary conditions. We then acquired PCMRI data in the phantom while it operated under conditions mimicking a resting and a light exercise physiological state. Next, we performed in silico numerical simulations and compared experimentally measured velocities, flows, and pressures in the in vitro phantom to those computed in the in silico simulations. There was a high degree of agreement in all of the pressure and flow waveform shapes and magnitudes between the experimental measurements and simulated results. The average pressures and flow split difference between experiment and simulation were all within 2%. Velocity patterns showed good agreement between experimental measurements and simulated results, especially in the case of whole-cycle averaged comparisons. We demonstrated methods to perform in vitro phantom experiments with physiological flows and pressures, showing good agreement between numerically simulated and experimentally measured velocity fields and pressure waveforms in a complex patient-specific AAA geometry.     

Phasic hemodynamics and reverse blood flows in the aortic isthmus and pulmonary arteries of preterm lambs with pulmonary vascular dysfunction

Time-domain representations of the fetal aortopulmonary circulation were carried out in lamb fetuses to study hemodynamic consequences of congenital diaphragmatic hernia (CDH) and the effects of endothelin-receptor antagonist tezosentan (3 mg/45 min). From the isthmic aortic and left pulmonary artery (PA) flows (Q) and isthmic aortic, PA, and left auricle pressures (P) on day 135 in 10 controls and 7 CDH fetuses (28 ewes), discrete-triggered P and Q waveforms were modelized as Pt and Qt functions to obtain basic hemodynamic profiles, pulsatile waves [P, Q, and entry impedance (Ze)], and P and Q hysteresis loops. In the controls, blood propelling energy was accounted for by biventricular ejection flow waves (kinetic energy) with low Ze and by flow-driven pressure waves (potential energy) with low Ze. Weak fetal pulmonary perfusion was ensured by reflux (reverse flows) from PA branches to the ductus anteriosus and aortic isthmus as reverse flows. Endothelin-receptor antagonist blockade using tezosentan slightly increased the forward flow but largely increased diastolic backward flow with a diminished left auricle pre- and postloading. In CHD fetuses, the static component overrode phasic flows that were detrimental to reverse flows and the direction of the diastolic isthmic flow changed to forward during the diastole period. Decreased cardiac output, flattened pressure waves, and increased forward Ze promoted backward flow to the detriment of forward flow (especially during diastole). Additionally, the intrapulmonary arteriovenous shunting was ineffective. The slowing of cardiac output, the dampening of energetic pressure waves and pulsatility, and the heightening of phasic impedances contributed to the lowering of aortopulmonary blood flows. We speculate that reverse pulmonary flow is a physiological requirement to protect the fetal pulmonary circulation from the prominent right ventricular stream and to enhance blood flow to the fetal heart and brain.     

Effects of stent stiffness on local haemodynamics with particular reference to wave reflections

The placement of a rigid stent within an elastic vessel produces wave reflection sites at the entrance to and exit from the stent. The net haemodynamic effects of these reflections depend critically on the degree of stiffness of the stent and on its length and position within the diseased vessel, variables that have been found to affect the clinical performance of a stent. Here these effects are examined analytically, using a segmented tube model. The results indicate that the presence of the stent within the larger diseased vessel has the effect of producing higher pressure at the vessel entrance than that at exit. This pressure difference, when superimposed on the underlying pressure distribution within the vessel, has the net effect of actually aiding rather than impeding the flow, but the extent of this depends on the length and position of the stent. A short stent placed near the entrance of the diseased vessel may be favoured clinically for producing the least perturbation in the underlying haemodynamics and thus reducing the chance of restenosis, while a long stent placed near the exit may be favoured for producing a positive pressure difference and thus aiding the flow.