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).     

The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection (TCPC) with caval centerline offset

BACKGROUND: The total cavopulmonary connection (TCPC), a palliative correction for congenital defects of the right heart, is based on the corrective technique developed by Fontan and Baudet. Research into the TCPC has primarily focused on reducing power loss through the connection as a means to improve patient longevity and quality of life. The goal of our study is to investigate the efficacy of including a caval offset on the hemodynamics and, ultimately, power loss of a connection. As well, we will quantify the effect of vessel wall compliance on these factors and, in addition, the distribution of hepatic blood to the lungs. METHODS: We employed a computational fluid dynamic model of blood flow in the TCPC that includes both the non-Newtonian shear thinning characteristics of blood and the nonlinear compliance of vessel tissue. RESULTS: Power loss in the rigid-walled simulations decayed exponentially as caval offset increased. The compliant-walled results, however, showed that after an initial substantial decrease in power loss for offsets up to half the caval diameter, power loss increased slightly again. We also found only minimal mixing in both simulations of all offset models. CONCLUSIONS: The increase in power loss beyond an offset of half the caval diameter was due to an increase in the kinetic contribution. Reduced caval flow mixing, on the other hand, was due to the formation of a pressure head in the offset region which acts as a barrier to flow.     

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.     

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.     

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.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

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.     

Volume flow estimation in the precapillary mesenteric microvasculature in vivo and the principle of constant pressure gradient

Volume flow was estimated from axial erythrocyte velocity measurements in 30 mesenteric microvessels of 6 rabbits and was compared to Murray's law predictions. The diameters of capillaries and precapillary arterioles ranged between 5.6 and 12 microm. The significant pulsating flow component existing in these microvessels was taken into account by measuring instantaneous axial blood velocity throughout the course of a cardiac cycle and then averaging over the period. In addition, the effect of the velocity profile variation with diameter was taken into account, for the first time, by using a profile factor function. According to Murray's law, the relation between blood volume flow and diameter is governed by a 'cube' law. Curve fitting to volume flow and diameter data pairs for rabbits, showed a dependence of volume flow on diameter raised to the 4th power (with a correlation coefficient equal to 0.97). The above result supports the hypothesis that, in the precapillary part of microvasculature, the principle of constant longitudinal pressure gradient rather than the principle of minimum work may be valid.     

Effect of exercise on blood flow through the aortic valve: a combined clinical and numerical study

The aim of this study was to measure the cardiac output and stroke volume for a healthy subject by coupling an echocardiogram Doppler (echo-Doppler) method with a fluid–structure interaction (FSI) simulation at rest and during exercise. Blood flow through aortic valve was measured by Doppler flow echocardiography. Aortic valve geometry was calculated by echocardiographic imaging. An FSI simulation was performed, using an arbitrary Lagrangian–Eulerian mesh. Boundary conditions were defined by pressure loads on ventricular and aortic sides. Pressure loads applied brachial pressures with (stage 1) and without (stage 2) differences between brachial, central and left ventricular pressures. FSI results for cardiac output were 15.4% lower than Doppler results for stage 1 (r = 0.999). This difference increased to 22.3% for stage 2. FSI results for stroke volume were undervalued by 15.3% when compared to Doppler results at stage 1 and 26.2% at stage 2 (r = 0.94). The predicted mean backflow of blood was 4.6%. Our results show that numerical methods can be combined with clinical measurements to provide good estimates of patient-specific cardiac output and stroke volume at different heart rates.     

An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel

The propulsion mechanics of cilia-induced flow is studied through a mathematical model. The problem of two-dimensional motion of a power law fluid inside a channel with ciliated walls is considered. The characteristics of ciliary systems are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Solutions for the longitudinal, transverse, and resultant velocities are obtained. The pressure gradient and volume flow rate for different values of the power law index are also calculated. The flow properties for the power law fluid are determined as a function of the cilia and metachronal wave velocity. The viscous and power law fluid are compared and discussed graphically.     

RV filling modulates LV function by direct ventricular interaction during mechanical ventilation

During mechanical ventilation, phasic changes in systemic venous return modulate right ventricular output but may also affect left ventricular function by direct ventricular interaction. In 13 anesthetized, closed-chest, normal dogs, we measured inferior vena cava flow and left and right ventricular dimensions and output during mechanical ventilation, during an inspiratory hold, and (during apnea) vena caval constriction and abdominal compression. During a single ventilation cycle preceded by apnea, positive pressure inspiration decreased caval flow and right ventricular dimension; the transseptal pressure gradient increased, the septum shifted rightward, reflecting an increased left ventricular volume (the anteroposterior diameter did not change); and stroke volume increased. The opposite occurred during expiration. Similarly, the maneuvers that decreased venous return shifted the septum rightward, and left ventricular volume and stroke volume increased. Increased venous return had opposite effects. Changes in left ventricular function caused by changes in venous return alone were similar to those during mechanical ventilation except for minor quantitative differences. We conclude that phasic changes in systemic venous return during mechanical ventilation modulate left ventricular function by direct ventricular interaction.     

Noninvasive measurement of time-varying three-dimensional relative pressure fields within the human heart

Understanding cardiac blood flow patterns is important in the assessment of cardiovascular function. Three-dimensional flow and relative pressure fields within the human left ventricle are demonstrated by combining velocity measurements with computational fluid mechanics methods. The velocity field throughout the left atrium and ventricle of a normal human heart is measured using time-resolved three-dimensional phase-contrast MRI. Subsequently, the time-resolved three-dimensional relative pressure is calculated from this velocity field using the pressure Poisson equation. Noninvasive simultaneous assessment of cardiac pressure and flow phenomena is an important new tool for studying cardiac fluid dynamics.     

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.     

Quantitative characterization of postnatal growth trends in proximal pulmonary arteries in rats by phase-contrast magnetic resonance imaging

Malformations of the pulmonary arteries can increase right heart workload and result in morbidity, heart failure, and death. With the increased use of murine models to study these malformations, there is a pressing need for an accurate and noninvasive experimental technique that is capable of characterizing pulmonary arterial hemodynamics in these animals. We describe the growth trends of pulmonary arteries in 13 male Sprague-Dawley rats at 20, 36, 52, 100, and 160 days of age with the introduction of phase-contrast MRI as such a technique. PCMRI results correlated closely with cardiac output measurements by ultrasound echocardiography and with fluorescent microspheres in right-left lung flow split (flow partition). Mean flow, average cross-sectional area, distensibility, and shear rates for the right and left pulmonary arteries (RPA and LPA) were calculated. The RPA was larger and received more flow at all times than the LPA (P < 0.0001). Right-left flow split did not change significantly with age, and arterial distensibility was not significantly different between RPA and LPA, except at 160 days (P < 0.01). Shear rates were much higher for the LPA than the RPA (P < 0.0001) throughout development. The RPA and LPA showed different structure-function relationships but obeyed similar allometric scaling laws, with scaling exponents comparable to those of the main pulmonary artery. This study is the first to quantitatively describe changes in RPA and LPA flows and sizes with development and to apply phase-contrast MRI techniques to pulmonary arteries in rats.     

Experimental cardiac tamponade: correlation of pressure, flow velocity, and echocardiographic changes

Seven episodes of experimental cardiac tamponade were induced in five anesthetized closed-chest dogs. Simultaneous pericardial and intracavitary pressures were synchronized with superior vena caval and transvalvular pulsed-Doppler flow tracings. The earliest indication of tamponade was the development of a negative transmural right atrial pressure that occurred during early ventricular diastole and was associated with echocardiographic evidence of right atrial collapse. This was also associated with reversal of diastolic flow in the superior vena cava and with diminished early diastolic flow velocity across the tricuspid as well as the mitral valve. During more advanced cardiac tamponade, the transmural right atrial pressure became negative during both early and late ventricular diastole as well as during isovolumic ventricular systole. This was associated with a disappearance of early diastolic ventricular filling and right ventricular diastolic collapse as observed on two-dimensional echocardiography. In hypotensive cardiac tamponade (cardiac output diminished by 70%), the decreased transmural right atrial pressure that developed during ventricular systole was accompanied by diminished antegrade flow in the superior vena cava. In advanced and hypotensive tamponade, ventricular filling occurred mainly during atrial contraction.     

Evaluation of magnetic resonance velocimetry for steady flow

Whole body magnetic resonance (MR) imaging has recently become an important diagnostic tool for cardiovascular diseases. The technique of magnetic resonance phase velocity encoding allows the quantitative measurement of velocity for an arbitrary component direction. A study was initiated to determine the ability and accuracy of MR velocimetry to measure a wide range of flow conditions including flow separation, three-dimensional secondary flow, high velocity gradients, and turbulence. A steady flow system pumped water doped with manganese chloride through a variety of test sections. Images were produced using gradient echo sequences on test sections including a straight tube, a curved tube, a smoothly converging-diverging nozzle, and an orifice. Magnetic resonance measurements of laminar and turbulent flows were depicted as cross-sectional velocity profiles. MR velocity measurements revealed such flow behavior as spatially varying velocity, recirculation and secondary flows over a wide range of conditions. Comparisons made with published experimental laser Doppler anemometry measurements and theoretical calculations for similar flow conditions revealed excellent accuracy and precision levels. The successful measurement of velocity profiles for a variety of flow conditions and geometries indicate that magnetic resonance imaging is an accurate, non-contacting velocimeter.     

Computer modeling of the human systemic arterial tree

A model of the human systemic arterial tree has been devised, based on a lumped-parameter-circuit approximate form. This model has been set up and studied on an analog computer. A feature of this simulation is the division of the arterial system into sections whose lengths are inversely proportional (approximately) to their cross-sectional area-or what is termed ‘equal-volume’ modeling.

Great care was exercised in the determination of the model parameters, using expressions for these parameters from a recent paper by Rideout and Dick on fluid flow in distensible tubes, with numerical values based on measurements reported in the medical literature.

The simulated pressure and flow waveforms obtained with the model compare favorably with data recorded from the normal adult human, and exhibit such well-known features as distal delay and peaking of pressure pulses. The aortic input impedance vs. frequency curve checks well against measurements on the human. The model also provides a simple means for determination of cardiac output, cardiac work and cardiac power under various assumed conditions such as variation of heart rate.     

树干自然温度梯度变化对热扩散法测算树干液流速率的影响

为了揭示树干自然温度梯度的变化规律及其对树干液流速率测算结果的影响,于2007年5月至10月利用改进的SF-L型热扩散式树液流测定装置,对北京低山区生长的油松和侧柏的树干自然温度梯度、加热温差和气象、土壤水分因子进行了连日同步监测。结果表明:(1)树干自然温度梯度对加热针温差的影响,侧柏大于油松。(2)树干自然温度梯度对液流速率计算结果的影响具有显著的统计意义(P0.01),平均误差大于30%,误差峰值出现在太阳高度角较小的时候。(3)影响树干自然温度梯度最重要的环境因子是光照强度,其次是空气温度。上述结果说明,树干自然温度梯度对热扩散法测定的液流速率的影响不可忽视,研究树木耗水机制时应予以充分考虑。光照强度和空气温度是影响树干自然温度梯度最重要的两个因子,但其影响机制仍需进一步研究。     

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.