Noninvasive fluid dynamic power loss assessments for total cavopulmonary connections using the viscous dissipation function: a feasibility study

The total cavopulmonary connection (TCPC) has shown great promise as an effective palliation for single-ventricle congenital heart defects. However, because the procedure results in complete bypass of the right-heart, fluid dynamic power losses may play a vital role in postoperative patient success. Past research has focused on determining power losses using control volume methods. Such methods are not directly applicable clinically without highly invasive pressure measurements. This work proposes the use of the viscous dissipation function as a tool for velocity gradient based estimation of fluid dynamic power loss. To validate this technique, numerical simulations were conducted in a model of the TCPC incorporating a 13.34 mm (one caval diameter) caval offset and a steady cardiac output of 2 L x min(-1). Inlet flow through the superior vena cava was 40 percent of the cardiac output, while outflow through the right pulmonary artery (RPA) was varied between 30 and 70 percent, simulating different blood flow distributions to the lungs. Power losses were determined using control volume and dissipation function techniques applied to the numerical data. Differences between losses computed using these techniques ranged between 3.2 and 9.9 percent over the range of RPA outflows studied. These losses were also compared with experimental measurements front a previous study. Computed power losses slightly exceeded experimental results due to different inlet flow conditions. Although additional experimental study is necessary to establish the clinical applicability of the dissipation function, it is believed that this method, in conjunction with velocity gradient information derived from imaging modalities such as magnetic resonance imaging, can provide a noninvasive means of assessing power losses within the TCPC in vivo.     

Distribution of hepatic venous blood in the total cavo pulmonary connection: an in vitro study into the effects of connection geometry.

The total cavo pulmonary connection, or TCPC, is a surgical correction to congenital heart defects. The geometry of this connection has been shown to determine the fluid power loss as well as the distribution of hepatic fluid that enters through the inferior vena cava. In vitro studies were performed to measure the power loss and hepatic fluid distribution in models of the TCPC with four different geometries. It was found that a zero offset straight geometry provided good hepatic fluid distribution but large power loss. A zero offset flared geometry provided low power loss but poor hepatic fluid distribution. The optimal geometry from those tested was found to be the zero offset cowl geometry whereby an enlargement was made on one side of the inferior and superior vena cava. So long as the cowl was directed toward the pulmonary artery of lowest flow rate, low power loss and relatively good distribution of hepatic flow could be obtained.     

Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis

Fluid dynamics of Total Cavo-Pulmonary Connection (TCPC) were studied in 3-D models based on real dimensions obtained by Magnetic Resonance (MR) images. Models differ in terms of shape (intra- or extra-cardiac conduit) and cross section (with or without patch enlargement) of the inferior caval (IVC) anastomosis connection. Realistic pulsatile flows were submitted to both the venae cavae, while porous portions were added at the end of the pulmonary arteries to reproduce the pulmonary afterload. The dissipated power and the flow distribution into the lungs were calculated at different values of pulmonary arteriolar resistances (PAR). The most important results are: i) power dissipation in different TCPC designs is influenced by the actual cross sectional area of the IVC anastomosis and ii) the inclusion of a patch minimizes the dissipated power (range 4-13 mW vs. 14-56 mW). Results also show that the perfusion of the right lung is between 15% and 30% of the whole IVC blood flow when the PAR are evenly distributed between the right and the left lung.     

The effect of respiration-driven flow waveforms on hemodynamic metrics used in Fontan surgical planning

ObjectivePoor total cavopulmonary connection (TCPC) hemodynamics have been hypothesized to be associated with long-term complications in Fontan patients. Image-based Fontan surgical planning has shown great potential as a clinical tool because it can pre-operatively evaluate patient-specific hemodynamics. Current surgical planning paradigms commonly utilize cardiac-gated phase contrast magnetic resonance (MR) imaging to acquire vessel flows. These acquisitions are often taken under breath-held (BH) conditions and ignore the effect of respiration on blood flow waveforms. This study investigates the effect of respiration-driven flow waveforms on patient-specific hemodynamics using real-time MR acquisitions.MethodsPatient-specific TCPCs were reconstructed from cardiovascular MR images. Real-time phase contrast MR images were acquired under both free-breathing (FB) and breath-held conditions for 9 patients. Numerical simulations were employed to assess flow structures and hemodynamics used in Fontan surgical planning including hepatic flow distribution (HFD) and indexed power loss (iPL), which were then compared between FB and BH conditions.ResultsDifferences in TCPC flow structures between FB and BH conditions were observed throughout the respiratory cycle. However, the average differences (BH – FB values for each patient, which are then averaged) in iPL and HFD between these conditions were 0.002 ± 0.011 (p = 0.40) and 1 ± 3% (p = 0.28), respectively, indicating no significant difference in clinically important hemodynamic metrics.ConclusionsRespiration affects blood flow waveforms and flow structures, but might not significantly influence the values of iPL or HFD. Therefore, breath-held MR acquisition can be adequate for Fontan surgical planning when focusing on iPL and HFD.     

Functional analysis of Fontan energy dissipation

We formalize the hydrodynamic energy dissipation in the total cavopulmonary connection (TCPC) using dimensional analysis and examine the effect of governing flow variables; namely, cardiac output, flow split, body surface area, Reynolds number, and certain geometric characteristics. A simplistic and clinically useful mathematical model of the dependence of energy dissipation on the governing variables is developed. In vitro energy loss data corresponding to six patients' anatomies validated the predicted dependency of each variable and was used to develop a predictive, semi-empirical energy dissipation model of the TCPC. It is shown that energy dissipation is a cubic function of pulmonary flow split in the physiological range. Furthermore, non-dimensional energy dissipation, which is a measure of resistance of the connection, is dependent on Reynolds number and geometrical factors alone. Non-dimensional energy dissipation decreases with Reynolds number as Re(-0.25) (R(2)>0.95). In addition, for high Reynolds numbers, within physiological exercise limits, dissipation strongly correlates to minimum PA area as a power law decay with an exponent of -5/4 (R(2)>0.88). This study presents a simple analytical form of energy dissipation rate in complex patient-specific TCPCs that accurately captures the effect of cardiac output, flow split, body surface area, Reynolds number, and pulmonary artery size within physiological limits. Further studies with larger sample sizes are necessary for incorporating finer geometrical parameters such as vessel curvatures and offsets.     

The effects of different mesh generation methods on computational fluid dynamic analysis and power loss assessment in total cavopulmonary connection

The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.     

Power dissipation associated with surgical operations' hemodynamics: critical issues and application to the total cavopulmonary connection

The issue of the correct determination of the mechanical power dissipated by the blood flow in the circulatory system is very important. This parameter is particularly critical when the patient's circulation has to overcome structural impairments, such as, e.g., in the case of only one functional ventricle. The surgical palliation of such a condition, which is a relatively common form of congenital heart disease, calls for an optimization of the new connection's hydrodynamics. Starting from the general formulation of the energy dissipation rate in a given control volume, this paper discusses the critical assumptions of the formula usually employed to assess the power dissipation in complex connections, such as the total cavopulmonary connection (TCPC). A new formula is derived, in which the mean elevation of the outlet and inlet sections is shown to be relevant, through the use of the piezometric pressure. Moreover, the flow profile at the boundary of the control volume is also important, since the usual approach implicitly assumes that the flow is perfectly flat: this assumption is doubtful, especially in the venous return (as in the TCPC). In the experimental part of the study, the power dissipation was measured in a physical model of the TCPC, and a large difference was found between the usual method and the proposed one, especially at low regime (85% relative difference, at 1.5 l/min total cardiac output). The proposed approach should be adopted in order to improve the accuracy of the hydrodynamical performance's assessment of surgical connections (e.g., TCPC) or implantable devices (e.g., valved conduit).     

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.     

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.     

Performance of a shaking vessel with current pole

To improve solid particle suspensions in liquids in a shaking vessel, a pole was installed at the axis of the shaking vessel, which was referred to as the "current pole". The performance of a shaking vessel with current pole at its central axis was examined experimentally with respect to particle dispersion, power consumption, mixing time and solid-liquid mass transfer coefficient. The current pole improved the particle suspension without an increase in power consumption and reduced the critical circulating frequency for complete suspension. The current pole was very effective in eliminating the stagnation point on the vessel bottom and to decrease the mixing time. The mass transfer coefficient with a current pole had the same value as that without a current pole above the critical circulating frequency for complete suspension. As the diameter of the current pole increased, the mixing time decreased. A pole diameter of 5% of the vessel diameter was effective for suspension.     

Temporal and spatial variations of cell-free layer width in arterioles

Separation of red blood cells and plasma in microcirculatory vessels produces a cell-free layer at the wall. This layer may be an important determinant of blood viscosity and wall shear stress in arterioles, where most of the hydraulic pressure loss in the circulatory system occurs and flow regulatory mechanisms are prominent. With the use of a newly developed method, the width of the cell-free layer was rapidly and repeatedly determined in arterioles (10- to 50-microm inner diameter) in the rat cremaster muscle at normal arterial pressure. The temporal variation of the cell-free layer width was non-Gaussian, but calculated mean and median values differed by <0.2 microm. The correlation length of the temporal variations downstream (an indication of mixing) was approximately 30 microm and was independent of pseudoshear rate (ratio of mean velocity to vessel diameter) and of vessel diameter. The cell-free layer width was significantly different on opposite sides of the vessel and inversely related. Increasing red blood cell aggregability reduced this inverse relation but had no effect on correlation length. In the diameter range studied, the mean width of the cell-free layer increased from 0.8 to 3.1 microm and temporal variations increased from 30% to 70% of the mean width. Increased aggregability did not alter either relationship. In summary, the cell-free layer width in arterioles is diameter dependent and shows substantial non-Gaussian temporal variations. The temporal variations increase as diameter increases and are inversely related on opposite sides of the vessel.     

The total cavopulmonary connection resistance: a significant impact on single ventricle hemodynamics at rest and exercise

Little is known about the impact of the total cavopulmonary connection (TCPC) on resting and exercise hemodynamics in a single ventricle (SV) circulation. The aim of this study was to elucidate this mechanism using a lumped parameter model of the SV circulation. Pulmonary vascular resistance (1.96+/-0.80 WU) and systemic vascular resistances (18.4+/-7.2 WU) were obtained from catheterization data on 40 patients with a TCPC. TCPC resistances (0.39+/-0.26 WU) were established using computational fluid dynamic simulations conducted on anatomically accurate three-dimensional models reconstructed from MRI (n=16). These parameters were used in a lumped parameter model of the SV circulation to investigate the impact of TCPC resistance on SV hemodynamics under resting and exercise conditions. A biventricular model was used for comparison. For a biventricular circulation, the cardiac output (CO) dependence on TCPC resistance was negligible (sensitivity=-0.064 l.min(-1).WU(-1)) but not for the SV circulation (sensitivity=-0.88 l.min(-1).WU(-1)). The capacity to increase CO with heart rate was also severely reduced for the SV. At a simulated heart rate of 150 beats/min, the SV patient with the highest resistance (1.08 WU) had a significantly lower increase in CO (20.5%) compared with the SV patient with the lowest resistance (50%) and normal circulation (119%). This was due to the increased afterload (+35%) and decreased preload (-12%) associated with the SV circulation. In conclusion, TCPC resistance has a significant impact on resting hemodynamics and the exercise capacity of patients with a SV physiology.     

Blood flow patterns and pressure loss in the ascending aorta: A comparative study on physiological and aneurysmal conditions

An aortic aneurysm is defined as a balloon-shaped bulging of all three histologic components of the aortic vessel walls (intima, media and adventitia). This dilation results from vessel weakening owing to remodeling, i.e. due to cystic degeneration of the Tunica media (Marfan), progression of atherosclerosis or presence of a bicuspid aortic valve. The growth rate of the aortic diameter varies from patient to patient and may progress until the aneurysm ultimately ruptures. The role of hemodynamics, i.e. blood flow patterns, and shear stresses that are supposed to intensify during aneurysm growth are not yet fully understood, but thought to play a key role in the enlargement process. The aim of this study is to characterize the aortic blood flow in a silicone model of a pathological aorta with ascending aneurysm, to analyze the differences in the blood flow pattern compared to a healthy aortic model, and to single out possible blood flow characteristics measurable using phase contrast magnetic resonance imaging (MRI) that could serve as indicators for aneurysm severity. MRI simulations were performed under physiological, pulsatile flow conditions using data obtained from optical three dimensional particle tracking measurements. In comparison to the healthy geometry, elevated turbulence intensity and pressure loss are measured in the diseased aorta, which we propose as a complimentary indicator for assessing the aneurysmal severity. Our results shed a light on the interplay between the blood flow dynamics and their contribution to the pathophysiology and possible role for future risk assessment of ascending aortic aneurysms.     

Blood flow in the capillary bed

From arteries to veins, the blood has to go through the ‘capillary’ blood vessels. These blood vessels are so small that often their diameter is smaller than that of the red blood cells. Intimate interactions occur, therefore, between the blood cells and the blood vessels.

A general survey of recent works on capillary blood flow is given in this article. Some details are presented for two problems: the problem of deformation of the flexible red blood cells, their motion in the capillary blood vessels, and the pressure drop due to the red cell blood vessel interaction; and the problem of the flow of plasma ‘bolus’ between neighboring red cells.

The solution supplies many details about the microcirculation phenomenon. Taken together, a method is offered for the calculation of pressure drop in the capillary as a function of various physical parameters: the red cell volume per unit blood volume, (hematocrit), the ratio of the cell diameter to the blood vessel diameter, the ratio of the length of the blood vessel to its length, the volume of individual red cells, and a parameter relating the cell membrane elasticity, plasma viscosity and the cell velocity.     

Time course of changes in collateral blood flow and isolated vessel size and gene expression after femoral artery occlusion in rats

The objectives of this study were to assess the time course of enlargement and gene expression of a collateral vessel that enlarges following occlusion of the femoral artery and to relate these responses to the increases in collateral-dependent blood flow to the calf muscles in vivo. We employed exercise training to stimulate collateral vessel development. Rats were exercise trained or kept sedentary for various times of up to 25 days postbilateral occlusion (n=approximately 9/time point). Collateral blood flow to the calf muscles, determined with microspheres, increased modestly over the first few days to approximately 40 ml.min(-1).100 g(-1) in sedentary animals; the increase continued over time to approximately 80 ml.min(-1).100 g(-1) in the trained animals. Diameters of the isolated collateral vessels increased progressively over time, whereas an increased vessel compliance observed at low pressures was similar across time. These responses were greater in the trained animals. The time course of upregulation of vascular endothelial growth factor and placental growth factor, and particularly endothelial nitric oxide synthase and fms-like tyrosine kinase 1, mRNAs in the isolated collateral vessel implicates these factors as integral to the arteriogenic process. Collateral vessel enlargement and increased compliance at low pressures contribute to the enlarged circuit available for collateral blood flow. However, modulation of the functioning collateral vessel diameter, by smooth muscle tone, must occur to account for the observed increases in collateral blood flow measured in vivo.     

Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels

The study of the effect of leukocyte adhesion on blood flow in small vessels is of primary interest to understand the resistance changes in venular microcirculation. Available computational fluid dynamic studies provide information on the effect of leukocyte adhesion when blood is considered as a homogeneous Newtonian fluid. In the present work we aim to understand the effect of leukocyte adhesion on the non-Newtonian Casson fluid flow of blood in small venules; the Casson model represents the effect of red blood cell aggregation. In our model the blood vessel is considered as a circular cylinder and the leukocyte is considered as a truncated spherical protrusion in the inner side of the blood vessel. The cases of single leukocyte adhesion and leukocyte pairs in positions aligned along the same side, and opposite sides of the vessel wall are considered. The Casson fluid parameters are chosen for cat blood and human blood and comparisons are made for the effects of leukocyte adhesion in both species. Numerical simulations demonstrated that for a Casson fluid with hematocrit of 0.4 and flow rate Q = 0.072 nl/s, a single leukocyte increases flow resistance by 5% in a 32 microns diameter and 100 microns long vessel. For a smaller vessel of 18 microns, the flow resistance increases by 15%.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

An innovative numerical approach to resolve the pulse wave velocity in a healthy thoracic aorta model

Aortic dissection and atherosclerosis are highly fatal diseases. The development of both diseases is closely associated with highly complex haemodynamics. Thus, in predicting the onset of cardiac disease, it is desirable to obtain a detailed understanding of the flowfield characteristics in the human cardiovascular circulatory system. Accordingly, in this study, a numerical model of a normal human thoracic aorta is constructed using the geometry information obtained from a phase-contrast magnetic resonance imaging (PC-MRI) technique. The interaction between the blood flow and the vessel wall dynamics is then investigated using a coupled fluid–structure interaction (FSI) analysis. The simulations focus specifically on the flowfield characteristics and pulse wave velocity (PWV) of the blood flow. Instead of using a conventional PC-MRI method to measure PWV, we present an innovative application of using the FSI approach to numerically resolve PWV for the assessment of wall compliance in a thoracic aorta model. The estimated PWV for a normal thoracic aorta agrees well with the results obtained via PC-MRI measurement. In addition, simulations which consider the FSI effect yield a lower predicted value of the wall shear stress at certain locations in the cardiac cycle than models which assume a rigid vessel wall. Consequently, the model provides a suitable basis for the future development of more sophisticated methods capable of performing the computer-aided analysis of aortic blood flows.     

Effect of vessel compliance on the in-vitro performance of a pulsating respiratory support catheter

Intravena caval respiratory support (or membrane oxygenation) is a potential therapy for patients with acute respiratory insufficiency. A respiratory support catheter is being developed that consists of a bundle of hollow fiber membranes with a centrally positioned pulsating balloon to enhance gas exchange. This study examined the influence of vessel compliance on the gas exchange performance of the pulsating respirator, support catheter. Polyurethane elastic tubes were fabricated with compliance comparable to that measured in bovine vena cava specimens. The gas exchange performance of the respiratory catheter was studied in an in-vitro flow loop using either the model compliant tube or a rigid tube as a "mock" vena cava. Balloon pulsation enhanced gas exchange comparably in both rigid and model compliant vessels up to 120 bpm pulsation frequency. Above 120 bpm gas exchange increased with further pulsation in the rigid tube, but no additional increase in gas exchange was seen in the compliant tube. The differences above 120 bpm may reflect differences in the compliance of the elastic tube versus the natural vena cava.     

On the effect of preload and pre-stretch on hemodynamic simulations: an integrative approach

In this work, we address the simulation of three-dimensional arterial blood flow and its effect on the stress state of arterial walls. The novel contribution is the unprecedented combination of several modeling techniques to account for (1) the fact that known configurations for the arterial wall are in a preloaded state, (2) the compliance of the vessel segments, (3) proper boundary data over the non-physical interfaces resulting from the isolation of an arterial district from the rest of the arterial tree, (4) the presence of surrounding tissues in which the vessel is embedded and (5) residual stress state due to pre-stretch. Firstly, we formulate both the forward mechanical problem when the reference (zero-load) configuration is assumed to be known and, the preload problem arising when the known domain is a configuration at equilibrium with a certain load state (typically due to internal pressure and tethering forces). Then, two additional complexities are faced: the fluid–structure interaction problem that follows when the compliant vessels are coupled with the blood flow, and the introduction of non-physical boundaries coming from the artificial isolation of the arterial district from the original vessel. This, in turn, posses the problem of coupling dimensionally heterogeneous models to incorporate the effect of upstream and downstream systemic impedances. Additionally, a viscoelastic support on the external surface of the vessel is also incorporated. Two examples are presented to quantify in a physiologically consistent scenario the differences in simulation results when either considering or not the preload state of arterial walls. These computational simulations shed light on the validity of simplifying hypotheses in most hemodynamic models.