Accuracy of the Bernoulli equation for estimation of pressure gradient across stenotic Blalock-Taussig shunts: an in vitro and numerical study

Hemodynamics in Doppler ultrasonography

The cardiovascular system operates through complex hemodynamic processes involving pulsatile blood flow, varying viscosity, and the branching architecture of vessels. Interactions between blood flow and the vascular wall, which are characterized by shear and normal stress, along with wall stiffness, are crucial for maintaining vascular health. Doppler ultrasonography is a highly valuable noninvasive tool for assessing these hemodynamic parameters, enabling the measurement of key indices such as blood flow velocity, flow patterns, wall shear stress, and wall stiffness. This paper emphasizes the clinical significance of these indices and methods of measuring them using Doppler ultrasonography while addressing potential challenges. Accurate interpretation of these measurements is vital for reliable cardiovascular diagnostics and effective clinical decision-making.

Echocardiographic measured shunt velocity does not predict pulmonary blood flow in patients with Blalock-Thomas-Taussig shunt

INTRODUCTION

Catheterisation is the gold standard used to evaluate pulmonary blood flow in patients with a Blalock-Thomas-Taussig shunt. It involves risk and cannot be performed frequently. This study aimed to evaluate if echocardiographic measurements obtained in a clinical setting correlate with catheterisation-derived pulmonary blood flow in patients with a Blalock-Thomas-Taussig shunt as the sole source of pulmonary blood flow.

METHODS

Chart review was performed retrospectively on consecutive patients referred to the catheterisation lab with a Blalock-Thomas-Taussig shunt. Echocardiographic parameters included peak, mean, and diastolic gradients across the Blalock-Thomas-Taussig shunt and forward and reverse velocity time integral across the distal transverse aorta. In addition to direct correlations, we tested a previously published formula for pulmonary blood flow calculated as velocity time integral across the shunt × heart rate × Blalock-Thomas-Taussig shunt area. Catheterisation parameters included pulmonary and systemic blood flow as calculated by the Fick principle.

RESULTS

18 patients were included. The echocardiography parameters and oxygen saturation did not correlate with catheterisation-derived pulmonary blood flow, systemic blood flow, or the ratio of pulmonary to systemic blood flow. As the ratio of reverse to forward velocity time integral across the transverse aorta increased, the probability of shunt stenosis decreased.

CONCLUSION

Echocardiographic measurements obtained outside the catheterisation lab do not correlate with catheterisation-derived pulmonary blood flow. The ratio of reverse to forward velocity time integral across the transverse aortic arch may be predictive of Blalock-Thomas-Taussig shunt narrowing; this finding should be investigated further.

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.

Modeling single ventricle physiology: review of engineering tools to study first stage palliation of hypoplastic left heart syndrome

First stage palliation of hypoplastic left heart syndrome, i.e., the Norwood operation, results in a complex physiological arrangement, involving different shunting options (modified Blalock-Taussig, RV-PA conduit, central shunt from the ascending aorta) and enlargement of the hypoplastic ascending aorta. Engineering techniques, both computational and experimental, can aid in the understanding of the Norwood physiology and their correct implementation can potentially lead to refinement of the decision-making process, by means of patient-specific simulations. This paper presents some of the available tools that can corroborate clinical evidence by providing detailed insight into the fluid dynamics of the Norwood circulation as well as alternative surgical scenarios (i.e., virtual surgery). Patient-specific anatomies can be manufactured by means of rapid prototyping and such models can be inserted in experimental set-ups (mock circulatory loops) that can provide a valuable source of validation data as well as hydrodynamic information. Such models can be tuned to respond to differing the patient physiologies. Experimental set-ups can also be compatible with visualization techniques, like particle image velocimetry and cardiovascular magnetic resonance, further adding to the knowledge of the local fluid dynamics. Multi-scale computational models include detailed three-dimensional (3D) anatomical information coupled to a lumped parameter network representing the remainder of the circulation. These models output both overall hemodynamic parameters while also enabling to investigate the local fluid dynamics of the aortic arch or the shunt. As an alternative, pure lumped parameter models can also be employed to model Stage 1 palliation, taking advantage of a much lower computational cost, albeit missing the 3D anatomical component. Finally, analytical techniques, such as wave intensity analysis, can be employed to study the Norwood physiology, providing a mechanistic perspective on the ventriculo-arterial coupling for this specific surgical scenario.

CSF pressure and velocity in obstructions of the subarachnoid spaces

According to some theories, obstruction of CSF flow produces a pressure drop in the subarachnoid space in accordance with the Bernoulli theorem that explains the development of syringomyelia below the obstruction. However, Bernoulli's principle applies to inviscid stationary flow unlike CSF flow. Therefore, we performed a series of computational experiments to investigate the relationship between pressure drop, flow velocities, and obstructions under physiologic conditions. We created geometric models with dimensions approximating the spinal subarachnoid space with varying degrees of obstruction. Pressures and velocities for constant and oscillatory flow of a viscid fluid were calculated with the Navier-Stokes equations. Pressure and velocity along the length of the models were also calculated by the Bernoulli equation and compared with the results from the Navier-Stokes equations. In the models, fluid velocities and pressure gradients were approximately inversely proportional to the percentage of the channel that remained open. Pressure gradients increased minimally with 35% obstruction and with factors 1.4, 2.2 and 5.0 respectively with 60, 75 and 85% obstruction. Bernoulli's law underestimated pressure changes by at least a factor 2 and predicted a pressure increase downstream of the obstruction, which does not occur. For oscillatory flow the phase difference between pressure maxima and velocity maxima changed with the degree of obstruction. Inertia and viscosity which are not factored into the Bernoulli equation affect CSF flow. Obstruction of CSF flow in the cervical spinal canal increases pressure gradients and velocities and decreases the phase lag between pressure and velocity.

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.

Beta3 integrin-mediated ubiquitination activates survival signaling during myocardial hypertrophy

Identifying the molecular mechanisms activated in compensatory hypertrophy and absent during decompensation will provide molecular targets for prevention of heart failure. We have previously shown enhanced ubiquitination (Ub) during the early growth period of pressure overload (PO) hypertrophy near intercalated discs of cardiomyocytes, where integrins are important for mechanotransduction. In this study, we tested the role of integrins upstream of Ub, whether enhanced Ub contributes to survival signaling in early PO, and if loss of this mechanism could lead to decreased ventricular function. The study used a beta(3) integrin (-/-) mouse and a wild-type mouse as a control for in vivo PO by transverse aortic constriction (TAC) and for cultured cardiomyocytes in vitro, stimulated with the integrin-activating peptide RGD. We demonstrate beta(3) integrin mediates transient Ub of targeted proteins during PO hypertrophy, which is necessary for cardiomyocyte survival and to maintain ventricular function. Prosurvival signaling proceeds by initiation of NF-kappaB transcription of the E3 ligase, cIAP1. In PO beta(3)(-/-) mice, absence of this mechanism correlates with increased TUNEL staining and decreased ventricular mass and function by 4 wk. This is the first study to show that a beta(3) integrin/Ub/NF-kappaB pathway contributes to compensatory hypertrophic growth.

A direct test of the hypothesis that increased microtubule network density contributes to contractile dysfunction of the hypertrophied heart

Contractile dysfunction in pressure overload-hypertrophied myocardium has been attributed in part to the increased density of a stabilized cardiocyte microtubule network. The present study, the first to employ wild-type and mutant tubulin transgenes in a living animal, directly addresses this microtubule hypothesis by defining the contractile mechanics of the normal and hypertrophied left ventricle (LV) and its constituent cardiocytes from transgenic mice having cardiac-restricted replacement of native β4-tubulin with β1-tubulin mutants that had been selected for their effects on microtubule stability and thus microtubule network density. In each case, the replacement of cardiac β4-tubulin with mutant hemagglutinin-tagged β1-tubulin was well tolerated in vivo. When LVs in intact mice and cardiocytes from these same LVs were examined in terms of contractile mechanics, baseline function was reduced in mice with genetically hyperstabilized microtubules, and hypertrophy-related contractile dysfunction was exacerbated. However, in mice with genetically hypostabilized cardiac microtubules, hypertrophy-related contractile dysfunction was ameliorated. Thus, in direct support of the microtubule hypothesis, we show here that cardiocyte microtubule network density, as an isolated variable, is inversely related to contractile function in vivo and in vitro, and microtubule instability rescues most of the contractile dysfunction seen in pressure overload-hypertrophied myocardium.

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.

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

The Fontan operation is a palliative surgical procedure performed on children born with congenital defects of the heart that have yielded only a single functioning ventricle. The total cavo-pulmonary connection (TCPC) is the most popular variant of the Fontan procedure. The objective of the study was to quantify and compare the efficiency of numerical models of the TCPC with rigid versus elastic vessel wall models. The pressure drop and power loss through both type TCPC models was measured. Significant differences in efficiencies exist between rigid versus elastic numerical models. We have shown incorporating elasticity into numerical models of the total cavo-pulmonary connection is important when determining circuit efficiencies.

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.

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.

Flow in the early embryonic human heart: a numerical study

Computational fluid dynamic (CFD) experimentation provides a unique medium for detailed examination of flow through complex embryonic heart structures. The purpose of this investigation was to demonstrate that streaming blood flow patterns exist in the early embryonic heart and that fluid surface stresses change significantly with anomalous alterations in fetal heart lumen shape. Stages 10 and 11 early human embryo hearts were digitized as calibrated two-dimensional (2D) cross-sectional sequential images. A 3D surface was constructed from the stacking of these 2D images. CFD flow solutions were obtained (steady and pulsatile flow). Particle traces were placed in the inlet and outlet portions of these two stages. Sections of the embryonic heart were artificially reshaped. CFD flow solutions were obtained and surface stress changes analyzed. Streaming was shown to exist, with particles released on one or the other side of the cardiac lumen tending not to cross over and mix with particles released from the opposite side of the cardiac lumen. Shear stress changes (stage 10) occur in the altered lumens. Streaming exists in steady and pulsatile flow scenarios in the embryonic heart models. There are differences in local shear stress distributions with surface shape anomalies of the fetal heart lumen. These observations may help shed light on the potential role of fluid dynamic factors in determining patterns of abnormal heart development.

Insights into the effect of aortic compliance on Doppler diastolic flow patterns seen in coarctation of the aorta: a numeric study

BACKGROUND

In the echocardiographic evaluation of coarctation of the aorta, the degree of antegrade diastolic flow (diastolic runoff) noted on spectral Doppler tracings traditionally was thought to be solely dependent on lesion severity. However, recent in vitro experiments suggest the presence of this spectral Doppler pattern is as much related to the severity of coarctation as it is with changes in aortic compliance. Using state-of-the-art, multidisciplinary, numeric analysis tools, the purpose of this study was to investigate the specific fluid and wall mechanics present in coarctation of the aorta to further understand these relationships.

METHODS

Three computational numeric models of coarctation were developed with high, low, and no wall compliance. Flow simulations were run representing high- and low-flow states.

RESULTS

In both the low- and high-flow states, the degree of diastolic runoff increased with increasing vessel compliance. The high compliance model had larger changes in aortic dilatation in the precoarctation region compared with the low compliance model.

CONCLUSIONS

Increased aortic compliance brings about greater dilatation of the precoarctation aorta in systole, resulting in a persistence of stored upstream energy. This stored energy, released downstream in diastole as the precoarctation aortic walls contract, leads to increased degrees of diastolic runoff. Numeric methods offer a unique perspective into the mechanisms behind such clinical measures.

Influence of connection geometry and SVC-IVC flow rate ratio on flow structures within the total cavopulmonary connection: a numerical study

The total cavopulmonary connection (TCPC) is a palliative cardiothoracic surgical procedure used in patients with one functioning ventricle that excludes the heart from the systemic venous to pulmonary artery pathway. Blood in the superior and inferior vena cavae (SVC, IVC) is diverted directly to the pulmonary arteries. Since only one ventricle is left in the circulation, minimizing pressure drop by optimizing connection geometry becomes crucial. Although there have been numerical and in-vitro studies documenting the effect of connection geometry on overall pressure drop, there is little published data examining the effect of SVC-IVC flow rate ratio on detailed fluid mechanical structures within the various connection geometries. We present here results from a numerical study of the TCPC connection, configured with various connections and SVC:IVC flow ratios. The role of major flow parameters: shear stress, secondary flow, recirculation regions, flow stagnation regions, and flow separation, was examined. Results show a complex interplay among connection geometry, flow rate ratio and the types and effects of the various flow parameters described above. Significant changes in flow structures affected local distribution of pressure, which in turn changed overall pressure drop. Likewise, changes in local flow structure also produced changes in maximum shear stress values; this may have consequences for platelet activation and thrombus formation in the clinical situation. This study sheds light on the local flow structures created by the various connections andflow configurations and as such, provides an additional step toward understanding the detailed fluid mechanical behavior of the more complex physiological configurations seen clinically.

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.