Modeling the Fontan circulation: where we are and where we need to go.

The Fontan procedure and its subsequent modifications over the past 30 years can be described as a class of surgical procedures for patients born with complex congenital heart disease exhibiting a single-ventricle physiology. The long-term outcome for children currently undergoing a Fontan procedure remains worrisome because of multiple late morbidities observed. Despite significant modeling efforts spanning three decades, improvements to the Fontan procedure have occurred without comprehensive validation from these modeling studies. Careful examination shows that modeling studies to date offer only a "glimpse through a keyhole" into understanding and modeling a representative range of the variations in anatomy and physiology that exist in Fontan patients. Suggestions for future investigations are provided.

First-order system least-squares (FOSLS) for modeling blood flow.

The modeling of blood flow through a compliant vessel requires solving a system of coupled nonlinear partial differential equations (PDEs). Traditional methods for solving the system of PDEs do not scale optimally, i.e., doubling the discrete problem size results in a computational time increase of more than a factor of 2. However, the development of multigrid algorithms and, more recently, the first-order system least-squares (FOSLS) finite-element formulation has enabled optimal computational scalability for an ever increasing set of problems. Previous work has demonstrated, and in some cases proved, optimal computational scalability in solving Stokes, Navier-Stokes, elasticity, and elliptic grid generation problems separately. Additionally, coupled fluid-elastic systems have been solved in an optimal manner in 2D for some geometries. This paper presents a FOSLS approach for solving a 3D model of blood flow in a compliant vessel. Blood is modeled as a Newtonian fluid, and the vessel wall is modeled as a linear elastic material of finite thickness. The approach is demonstrated on three different geometries, and optimal scalability is shown to occur over a range of problem sizes. The FOSLS formulation has other benefits, including that the functional is a sharp, a posteriori error measure.

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.

Doppler echocardiography.

We describe concepts important in the clinical application of continuous wave, pulsed wave, and color Doppler flow imaging. In the second half of this manuscript, the application of these tools in pediatric echocardiography is addressed.

Effect of vessel size on the flow efficiency of the total cavopulmonary connection: in vitro studies.

The total cavopulmonary connection (TCPC) creates a passive system of blood flow into the pulmonary circulation. We hypothesize that the efficiency differences found in models with superior vena cava-inferior vena cava (SVC-IVC) offsets is dependent on vessel size, with flow efficiency improving with larger size vessels. Two sets of in vitro TCPC models (TCPC-3 and TCPC-15) were constructed corresponding to average vessel diameters of 3- and 15-year-old patients. The model with full SVC-IVC offset was the most efficient in TCPC-3 models. There was no significant difference between geometric arrangements in TCPC-15 models; however, the average efficiencies were significantly higher. Among the models representing vessel sizes of the younger age group, the model with the full-diameter SVC-IVC offset was the most efficient. The models representing vessel sizes of the older age group showed marked improvement in efficiencies throughout without obvious differences between various geometric arrangements. This suggests that geometric considerations in TCPC surgical techniques may be of lower than expected significance over the life span of a patient. More important, after balancing the effects of improved flow efficiency with larger vessels against the effects of chronic volume overload, the trend of performing the Fontan surgery on increasingly younger patients may need to be reconsidered after further studies.

Development of a noninvasive ultrasound color M-mode means of estimating pulmonary vascular resistance in pediatric pulmonary hypertension: mathematical analysis, in vitro validation, and preliminary clinical studies.

BACKGROUND: Accurate determination of pulmonary vascular resistance (PVR) is an important component in the evaluation and treatment of pediatric patients with pulmonary hypertension. We developed a novel technique, based on the concept of flow propagation, to estimate PVR noninvasively. The hypothesis is that changes in PVR cause changes in the velocity propagation (Vel(prop)) within the main pulmonary artery and that Vel(prop) can be quantified using color M-mode imaging. METHODS AND RESULTS: We tested the hypothesis using mathematical modeling, in vitro experiments, and preliminary clinical studies. The mathematical model showed that pressure and velocity tracings are closely correlated in time and that 6 to 18 ms time resolution was needed to resolve propagation times within typical main pulmonary artery lengths (2 to 5 cm). The in vitro experiments demonstrated that it was feasible to use color M-mode to measure Vel(prop) and that Vel(prop) correlated well with downstream resistance [y=(-1.01x)+22.77; R=0.96]. The method was then evaluated on patients undergoing acute pulmonary reactivity testing (n=22 measurements). Good correlation between Vel(prop) and PVR was found [y=(-1.71x)+26.0; R=0.90; SEE=2.41]. CONCLUSION: This newly developed method promises to be useful in the noninvasive evaluation of adults and children with pulmonary hypertension.

Emergency pulmonary autograft mitral valve replacement in a child.

Mitral valve replacement in small children imposes significant clinical difficulties because of the relatively small mechanical prosthetic valves required and the need for lifelong anticoagulation therapy. A child weighing 10.4 kg presented with thrombosis of her 19-mm mechanical mitral prosthesis 4 weeks after implantation despite appropriate oral anticoagulation therapy. An emergency mitral valve replacement with a pulmonary autograft was successfully performed with encouraging short-term results.

Artificial neural network-based method of screening heart murmurs in children.

BACKGROUND: Early recognition of heart disease is an important goal in pediatrics. Efforts in developing an inexpensive screening device that can assist in the differentiation between innocent and pathological heart murmurs have met with limited success. Artificial neural networks (ANNs) are valuable tools used in complex pattern recognition and classification tasks. The aim of the present study was to train an ANN to distinguish between innocent and pathological murmurs effectively. METHODS AND RESULTS: Using an electronic stethoscope, heart sounds were recorded from 69 patients (37 pathological and 32 innocent murmurs). Sound samples were processed using digital signal analysis and fed into a custom ANN. With optimal settings, sensitivities and specificities of 100% were obtained on the data collected with the ANN classification system developed. For future unknowns, our results suggest the generalization would improve with better representation of all classes in the training data. CONCLUSION: We demonstrated that ANNs show significant potential in their use as an accurate diagnostic tool for the classification of heart sound data into innocent and pathological classes. This technology offers great promise for the development of a device for high-volume screening of children for heart disease.

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

Accurate assessment of the pressure gradient (PG) across a modified Blalock-Taussig (mBT) shunt is important in planning for staging to a cavopulmonary anastomosis for many patients with cyanotic congenital heart disease. The mBT shunt Doppler velocity has been used in the simplified echo Bernoulli equation to predict this PG with variable results. The purpose of this investigation is to provide analysis of the flow dynamics through stenotic mBT shunts and to assess the accuracy of Doppler techniques in determining PGs and the presence and location of stenosis. Three-dimensional models of mBT shunts were created, with and without stenosis. In vitro and computational fluid dynamic flow experiments were carried out. In vitro experiments demonstrated that the Doppler-measured PG underestimated catheter-measured PG in the mBT shunt with diffuse stenosis. In nonstenotic mBT and those that had outlet and inlet stenosis, the Doppler-measured PG showed underestimation of catheter PG at low PG and generally improved estimation at higher PG. In the mBT shunt model with inlet stenosis, there was slight overestimation at higher PG. Numerical simulations provide an "observation window" into events occurring in and around mBT shunts showing that the hemodynamics vary significantly. Changing hemodynamic processes are at work through stenotic mBT shunts causing variations in overestimation and underestimation of catheter-measured PG using the simplified echo Bernoulli equation. Our results have relevance to the assessment of patients with mBT shunts, helping to explain some of the discrepancies that investigators have found in the past.

Utility of the proximal jet width in the assessment of regurgitant and stenotic orifices--effect of low velocity filter and comparison to actual vena contracta width: an in vitro and numerical study.

AIM: The colour Doppler proximal jet width (CDPJW) has been shown to be directly related to the severity of regurgitant and stenotic valve lesions. It is generally assumed that the CDPJW is equivalent to the vena contracta width (VCW). The purpose of this numerical and in vitro study was to evaluate how changing low velocity filter (LVF) settings on colour Doppler imaging devices may affect the CDPJW and its estimate of the VCW. METHODS: Computational fluid dynamic software was used to create models of round orifices (0.785, 1.13, 1.76, 3.14 cm2) at set flow rates (0.37-25 1/min). In vitro experiments were performed with round orifices (0.2, 0.95 and 1.76 cm2) with set flow rates (1.8-3.6 1/min). Laser flow visualization was used to obtain gold standard vena contracta widths for comparison to CDPJW for various LVF settings (4-24 cm/s). RESULTS: With the LVF set 'too low', overestimation errors occur. In contrast, with the LVF set 'too high', underestimation errors occur. Optimal LVF settings are required to avoid over- and underestimation errors of up to 280%. SUMMARY: The VCW is related to regurgitant or stenotic lesion severity, and the CDPJW is an approximation of the VCW. The CDPJW closely resembles the actual VCW only at optimally chosen LVF settings. LVF settings can have a significant impact on the accuracy of the CDPJW. Inter mediate filter settings remove unnecessary background noise while maintaining actual flow regions, thereby providing the best agreement between the CDPJW and the VCW. If treatment decisions are to be based on these measurements, understanding such dependencies becomes quite important.

Congenital erythrocytosis with elevated erythropoietin level: an incorrectly set "erythrostat"?

PURPOSE: A child who was extensively evaluated for polycythemia is reported. Polycythemia, or erythrocytosis, is seen rarely in children. The mechanisms for congenital and/or familial erythrocytosis are discussed. PATIENT AND METHODS: A 10 1/2-year-old white girl was referred for evaluation of polycythemia, which was detected incidentally during an emergency room visit for a febrile illness. She underwent extensive evaluation to determine the cause of the polycythemia. The literature was reviewed to determine the occurrence of congenital and/or familial erythrocytosis in children and its various causes. RESULTS: Despite extensive evaluation, no specific cause of the erythrocytosis could be determined in our patient. The erythrocytosis appeared to be secondary to an inappropriately elevated serum erythropoietin concentration. Serum erythropoietin rose further after phlebotomy, suggesting nonautonomous hypersecretion. After a review of the literature, we hypothesize that she had an inappropriate erythropoietin expression related to an abnormality in the renal oxygen-sensing mechanism governing erythropoietin synthesis. DISCUSSION: A discussion of congenital and familial erythrocytosis is presented, and a review of the literature regarding the possible mechanisms causing erythrocytosis is included.

Evaluating isovelocity surface area flow convergence method with finite element modeling.

Through numerical experimentation we investigated the isovelocity surface area flow convergence method used in estimating regurgitant valve flow rates. Recent advances in three-dimensional color Doppler flow imaging have created renewed interest in this method. Experimentation was based on the use of depth-averaged finite element models of the left heart. The heart models studied varied from "synthetic" representations to a model of a left heart traced from an actual echocardiographic image of a patient with a prolapsed mitral valve. The isovelocity surface area flow convergence method overestimated regurgitant flow rates throughout the Nyquist limits considered with a critical Nyquist limit in which this overestimation is minimized. The angle dependence of Doppler color flow imaging partially corrects for this overestimation. The isovelocity surface area flow convergence method is a viable alternative to methods currently in use. Through numerical experimentation, we have begun to shed light on the inaccuracies inherent in this flow convergence method.

Analysis of the effect of flow rate on the Doppler continuity equation for stenotic orifice area calculations: a numerical study.

BACKGROUND: Flow-rate dependencies of the Doppler continuity equation are addressed in this study. METHODS AND RESULTS: By use of computational fluid dynamic (CFD) software with turbulence modeling, three-dimensional axisymmetric models of round stenotic orifices were created. Flow simulations were run for various orifice area sizes (0.785, 1.13, 1.76, and 3.14 cm2) and flow rates (0.37 to 25.0 L/min). Reynolds numbers ranged from 100 to 8000. Once adequate convergence was obtained with each simulation, the location of the vena contracta was determined. For each run, maximum and average velocities across the cross section of the vena contracta were tabulated and vena contracta cross-sectional area (effective orifice area) determined. The difference between the maximum velocity and the average velocity at the vena contracta was smallest at high-flow states, with more of a difference at low-flow states. At lower-flow states, the velocity vector profile at the vena contracta was parabolic, whereas at high-flow states, the profile became more flattened. Also, the effective orifice area (vena contracta cross-sectional area) varied with flow rate. At moderate-flow states, the effective orifice area reached a minimum and expanded at low- and high-flow states, remaining relatively constant at high-flow states. CONCLUSIONS: We have shown that significant differences exist between the maximum velocity and the average velocity at the vena contracta at low flow rates. A likely explanation for this is that viscous effects cause lower velocities at the edges of the vena contracta at low flow rates, resulting in a parabolic profile. At higher-flow states, inertial forces overcome viscous drag, causing a flatter profile. Effective orifice area itself varies with flow rate as well, with the smallest areas seen at moderate-flow states. These flow-dependent factors lead to flow rate-dependent errors in the Doppler continuity equation. Our results have strong relevance to clinical measurements of stenotic valve areas by use of the Doppler continuity equation under varying cardiac output conditions.

Utility of three-dimensional ultrasound Doppler flow reconstruction of the proximal jet to quantify effective orifice area: in vitro steady and pulsatile flow studies.

We examined the utility of three-dimensional (3D) reconstruction of two-dimensional color Doppler images of the proximal jet to quantify the effective area of an orifice in an in vitro model. Steady and pulsatile flows were directed through various orifices; orifice vena contracta areas were quantified with laser flow visualization, thus providing gold standard effective orifice areas. Three-dimensional areas followed vena contracta areas well, although variations in color Doppler gain and 3D gray levels for thresholding produced significant changes in reconstructed images. These variations were minimized by using minimum color gain and 50% gray level threshold. At these settings, 3D areas still overestimated vena contracta areas by approximately 25% because of the poor lateral resolution of the color Doppler system, which caused bleeding of the flow signal past the edges of the proximal jet. Nevertheless, 3D flow images provided a superior format for qualitative and quantitative appreciation of proximal jet shape and dimensions.

Quantification of mitral flow by Doppler color flow mapping.

This study was performed to develop and validate Doppler color flow methods for quantifying forward transmitral flow rates and volumes with isovelocity aliasing contours. We undertook computer modeling of flows and studied an animal model with strictly controlled mitral flows. Finite element analysis was first used to establish the isovelocity surface contours reconstructed from the magnitudes and directions of the velocity vectors proximal to the normal mitral orifice. We modeled finite element-simulated Doppler color flow isovelocity surfaces and computed non-angle-dependent simulated isovelocities to compare them. Then 24 pharmacologically induced hemodynamic states in six sheep in which mitral regurgitation had been previously created surgically were studied. Three methods were used for peak flow (PF) computation: (1) the classic hemispheric methods: PF = 2 pi r2.aliasing velocity; (2) a modified hemispheric method: PF = 2 pi r2.aliasing velocity Vo/Vo-aliasing velocity; and (3) a new segment of sphere method: PF = pi p2.aliasing velocity, where p is the chord from the zenith of the first aliasing contour to the circumference at its base. Mean volume flow was also calculated in combination with phasic flow information from continuous-wave Doppler echocardiography: mean volume flow = PF.VTI/Vmax.heart rate, where VTI and Vmax are the velocity-time integral and maximal velocity of mitral inflow by continuous-wave Doppler echocardiography. Compared with the flow rates obtained by electromagnetic flowmeters, different correlations and agreements were achieved for these methods. Correlation (r = 0.86) and agreement were best for the segment of sphere method for computation of forward mean volume flows in our model. Color flow Doppler quantitation with a segment of sphere or modified hemispheric method appears applicable for quantification of forward transmitral valve flow rates and volumes with reasonable accuracy.