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J Thorac Cardiovasc Surg 2006;131:785-791
© 2006 The American Association for Thoracic Surgery
Surgery for Congenital Heart Disease |
a Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Ga
b Pediatric Cardiology, Emory University, Atlanta, Ga
c Department of Surgery, Emory University, Atlanta, Ga
d Division of Cardiology, The Children's Hospital of Philadelphia, Philadelphia, Pa
Received for publication August 25, 2005; revisions received October 17, 2005; accepted for publication November 8, 2005. * Address for reprints: Ajit P. Yoganathan, PhD, Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology & Emory University, Room 2119, U. A. Whitaker Building, 313 Ferst Dr, Atlanta, GA 30332-0535 (Email: ajit.yoganathan{at}bme.gatech.edu).
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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METHODS: A 3-dimensional model of a total cavopulmonary connection with bilateral superior venae cavae was reconstructed from a patient's magnetic resonance images and investigated experimentally and numerically to assess the power losses and flow structures within the connection. On the basis of these results, a virtual operation was performed in the computer to improve the original connection design. The modified anatomy was studied numerically.
RESULTS: Because of a smooth connection with an extracardiac conduit and no major dimension mismatch between the baffle and the connecting vessels, the original anatomy yielded smooth flow fields, low power losses, and few disturbances. However, a large offset between the inferior vena cava and the left superior vena cava resulted in flow stasis and unbalanced hepatic flow distribution. Shifting the inferior vena cava and positioning it between the 2 superior venae cavae resulted in a 7% decrease in power losses and eliminated the associated flow stasis regions in the main pulmonary artery segment.
CONCLUSIONS: This study demonstrates the potential use of computer-aided design and numeric simulations for surgical planning. It shows that locating the inferior vena cava between the superior venae cavae may lead to better-balanced lung perfusion. This may require suturing the right and left superior venae cavae closer to each other during the hemi-Fontan or Glenn stage.
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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Among the multiple variables that determine the outcome and quality of life of these patients, one that allows for some degree of control is the surgically created design of the bypass connection. From a geometrical point of view, this problem is that of optimizing a double-inlet, double-outlet connection. Parametric in vitro and computational fluid dynamics (CFD) studies have attempted to identify the contribution of different geometric parameters to the overall flow fields. This has led to suggestions for improvement, such as including a caval offset
2
or enlarging the inferior vena cava (IVC) anastomosis.
3
These studies, however, do not account for patients with a persistent left superior vena cava (SVC). Normally, the left precardinal vein drains blood from the upper body into the primitive atrium during the first weeks of embryonic development and then joins its right counterpart, thus forming the SVC, and its distal part persists as the coronary sinus.
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Persistent left SVC (LSVC) arises from a faulty embryogenesis between the fifth and eighth week and affects approximately 0.3% of the population. Its prevalence increases to 2% to 4.5% in patients with other congenital heart defects.
5,6
The addition of that third inflow introduces supplementary parameters and issues into the quest for an optimal total cavopulmonary connection (TCPC) design and has not yet been investigated.
This study features an extracardiac TCPC with bilateral SVCs. The associated hemodynamic efficiency and flow structures were investigated by using a combined experimental and CFD approach. On the basis of these observations, an alternative surgical design is proposed and studied that demonstrates the potential applications of computer-aided design and CFD tools to presurgical planning.
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Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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The patient retained for this study was an 8-year-old white boy who was born with a hypoplastic left heart and persistent LSVC. He had undergone a bilateral cavopulmonary anastomosis at the age of 6 months, followed by an extracardiac TCPC at 24 months. Forty-five T1-weighted axial MRIs were acquired over the entire span of the connection with a 256 x 192-pixel field of view. In addition to the anatomical slices, magnetic resonance phase velocity maps were acquired, which provided 3-dimensional velocity information in the venae cavae: mean flow rates across the IVC, right SVC (RSVC), and LSVC were 1.1, 0.5, and 0.45 L/min, respectively.
Anatomical Model Reconstruction and Virtual Surgery
The raw anatomical MRIs were first interpolated in the out-of-plane direction
7
to enhance the dataset resolution. The TCPC blood volume (Figure 1, A) was reconstructed from the interpolated MRI data and used to generate both the numeric mesh and the experimental model.
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Fluid Dynamic Analysis
The main criteria that were retained to characterize the TCPC hemodynamics were (1) the flow structure; (2) the power losses, which directly relate to the pressure drops across the connection; and (3) the distribution of the total venous return and of the IVC flow between the right (RPA) and left (LPA) pulmonary artery. A concise overview of the patient-specific, fluid dynamic analysis methodology is provided in the following paragraphs, and more detailed descriptions may be found in the studies by de Zélicourt and associates
8
and Pekkan and colleagues.
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All experiments and CFD simulations were run under steady inflow conditions. Resting cardiac and caval flow ratios were taken from the flow data acquired in the scanner. Additional runs using the same caval flow ratios were performed at 3 and 4 L/min to simulate active and exercise conditions.
Flow structure
The flow structures associated with this specific TCPC design were investigated both qualitatively and quantitatively by combining the experimental results from flow visualization and digital particle velocimetry with those of the numeric simulations.
Hydrodynamic power losses
The power losses across the connection were computed by using an integrated control volume energy balance
2
:
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| (1) |
in the experimental case) and the volumetric flow rate, respectively, in each vessel.
Equal pulmonary vascular resistance
To assess the quality of the lung perfusion associated with the original and the modified TCPC design, a simple lumped-parameter model was implemented to incorporate the pulmonary vascular resistance
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:
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| (2) |
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| (3) |
Note that R Left and R Right account for only the pulmonary resistances. The EPVR operating point depends on the resistance encountered by the flow when going from the Venae Cavae (VCs) to either one of the PAs. In a perfectly symmetric TCPC geometry, the pressure head needed to drive the flow into the LPA should equal the one needed to drive the flow into the RPA, thus resulting in an EPVR of 50:50 RPA/LPA.
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Results |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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Flow structure
Qualitative and quantitative assessments of the flow structures are shown in Figure 2. Run under steady flow conditions, the bilateral TCPC connection was characterized by smooth and steady flow fields. The only disturbances were observed at the point where the IVC and RSVC flow collided before going into the PAs. Because of the proximity of the LSVC to the LPA, the LSVC flow went exclusively to the LPA (Figure 2, C and G). The intermediate PA section was perfused only by the blood coming from the IVC and RSVC and going into the LPA (Figure 2, A, B, E, F, I, and J; see also supplementary movies E1 and E2).
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The perfusion of this intermediate MPA segment improved as more flow was directed to the LPA. At 30:70 RPA/LPA, the IVC and RSVC streams collided in the middle of the connection and splitted between the LPA and RPA. Most of the IVC and RSVC streams flowed along the inferior aspect of the MPA.
Pressure drops and power loss
No significant difference among the 3 caval pressures was demonstrated for all flow conditions (P >.05). As expected, the pulmonary pressures decreased as more flow was forced through the corresponding PA. However, except at 70:30 RPA/LPA, the LPA pressure remained lower than that of the RPA for all the pulmonary flow splits, meaning that a higher IVC-to-PA pressure drop was needed to drive the flow through the LPA than through the RPA. Accordingly, the power losses calculated across the connection strongly depended on the RPA/LPA flow split, decreasing with an increasing RPA flow (Figure 3). As a result, this design favored right lung perfusion. The EPVR point corresponded to an RPA/LPA flow split of approximately 60:40 for all the tested cardiac outputs, going from 61:39 RPA/LPA at 2 and 3 L/min to 62:38 RPA/LPA under exercise conditions at 4 L/min.
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The power losses were 7% lower than in the original anatomy, and the EPVR did not significantly differ from that of the original anatomy. In the original configuration, at the EPVR point, most of the IVC flow went to the RPA (Figure 4, A-2). In the modified anatomy for the same flow split (Figure 4, B-2), the right and LSVCs flows went into the closest PA. The IVC stream splitted in 2 to adjust to the desired pulmonary flow split so that both lungs received a similar amount of hepatic flow. When compared with the original anatomy (Figure 4, A-1; see also the supplementary movie E4), this new configuration minimized the regions of flow stasis, and the only region with low flow velocities was the flow separation region at the IVC anastomosis site (Figure 4, B-1; see also the supplementary movie E5).
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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PA Anastomosis Design and LPA Stenosis
To provide some more insights into the effect of the different geometric parameters on the flow structures observed here, we compared our results with those of another study previously conducted in our laboratory on an intra-atrial TCPC with a single SVC.
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This former anatomy featured smaller vessels (hydraulic diameters of 13.1, 4.6, 5.4, and 4.6 mm for the IVC, SVC, RPA, and LPA, respectively) and an important mismatch between the baffle dimensions and the vessel diameters. This configuration generated important flow instabilities within the baffle and flow separation within the SVC. It also accelerated the flow as it went down the shrinking PAs, resulting in high pressure drops and power losses.
The PA diameters of this intra-atrial TCPC 2 cm downstream of the anastomosis site were of the same order as that of the bilateral SVC model, but the resulting pressure drops and power losses at the EPVR were 2 to 3 times lower in the bilateral SVC model than in the intra-atrial TCPC. This was believed to be due to the dimension of the connection area with respect to the connecting vessels and to the design of the PA anastomosis. In the bilateral SVC model, the extracardiac graft resulted in a smooth connection design. The PA diameters were only 30% smaller than the diameter of the corresponding anastomosis site, and the vessels were slowly tapered down to their final dimensions. In the intra-atrial model, conversely, the tunnel resulted in a bulgy pouchlike connection design. The PA diameters were 50% smaller than the corresponding anastomosis sites, and the vessels quickly tapered down to their final diameter. The fast tapering of the LPA accelerated the flow and reinforced the helical pattern.
These considerations are similar to assessing the effect of diffuse LPA hypoplasia on the TCPC energy consumption and lung perfusion. In their parametric study of LPA stenosis in Fontan patients, Pekkan and colleagues
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concluded that diffuse LPA hypoplasia of less than 40% was tolerable, whereas a larger one significantly decreased left lung perfusion and increased the energy consumption. As a general rule, changes in vessel diameters will result in energy losses. However, there is a threshold under which this increase will not be significant. For similar vessel dimensions, the dimensions of the connection area and the rate at which the PAs are tapered down to their final dimensions may result in drastically different flow and energy consumption patterns.
Lung Perfusion
The original connection design favors right lung perfusion, with an EPVR corresponding to a 60:40 RPA/LPA flow split. Lung perfusion is not perfectly balanced even in healthy subjects. However, having a large unbalanced flow perfusion is not desirable because it increases the overall energy dissipation and, thus, the workload imposed on the heart.
To give a simple example, let us consider the energy dissipation through wall friction alone and assume both PAs to have equal diameters. Friction losses will be proportional to the square of the flow rate going through the corresponding vessel. If we have a perfectly balanced lung perfusion with Q L/min going through each PA, the total power losses will scale as 2Q
2. In an unbalanced configuration with (Q + 
Q) L/min going to the RPA and (Q – Q) L/min to the LPA, the power losses will scale as 2Q
2 + 2Q
2. If the lung perfusion is only slightly unbalanced (Q/Q << 1), then this increase will be negligible, but if the flow is truly unbalanced (Q/Q no longer << 1), the increase of 2Q
2 in overall losses will be significant. Large unbalanced lung flow may also affect the growth of the PAs, resulting in even more unbalanced lung perfusion and giving rise to the formation of collateral vessels.
Hepatic Flow Distribution
Another parameter of interest considered in this study was the hepatic flow distribution, which was assessed through the IVC flow distribution. In the original anatomy, the LSVC flow represented 22.5% of the total incoming flow and was entirely directed to the LPA. Subsequently, at the EPVR point only 17.5% of the flow went through the intermediate MPA section, resulting in regions of flow stasis. This implies that, in the original configuration, the IVC accounted for 22% and 81% of the LPA and RPA flows, respectively. This problem was not encountered in the modified anatomy, where the IVC was relocated in between the 2 SVCs and contributed in equal proportion to the LPA and RPA flows. Even if the exact contribution of hepatic flow to the development of the pulmonary vascular structure is still unclear, the exclusion of hepatic blood has been demonstrated to be strongly correlated with pulmonary venous malformations,
12-14
and the contribution of the IVC flow to both lungs may be a criterion of importance.
IVC Location
Setting the IVC in between the 2 SVCs appeared as a good alternative: it decreased the power losses by 7% and had a significant effect on the lung perfusion, the distribution of the IVC flow, and the flow structures within the connection. Pekkan and colleagues
15
developed a lumped parameter model of the Fontan circulation in which the TCPC was represented by the resistance it offered to the flow. When this model was applied to our study, the 7% decrease in power losses translated to a 7% decrease in TCPC resistance, which in turn led to a 10% increase in cardiac output under resting conditions.
In geometries with a single SVC, offsetting the IVC and SVC by 1.0 to 1.5 caval diameter minimizes the flow disturbances caused by the colliding inflows.
2
Similarly, with dual SVCs, setting the IVC in between the 2 SVCs results in an offset between the IVC and each one of the SVCs, which in turn decreases flow instabilities, such as those observed in the original anatomy distal to the RPA (Figure 2, D).
Finally, setting the IVC in between the 2 SVCs drastically decreased the amount of flow stasis in the intermediate MPA segment. This is of major importance because vessels with little flow perfusion may not grow as well as other vessels and may be prone to thrombosis, which in turn will lead to additional complications. For example, considering the anatomy presented in this article, a smaller-diameter intermediate MPA segment would limit the perfusion of the left lung further and increase the vascular resistance.
In this case, our only manipulation was to shift the IVC by 24 mm. However, the spatial constraints encountered by the surgeon may not allow for such a shift. Suturing the LSVC closer to the RSVC in the hemi-Fontan or Glenn stage may be a better way to decrease the distance by which the IVC should be shifted in the final TCPC stage.
VC Anastomosis Type
The connection studied here featured both a right hemi-Fontan and a left bidirectional Glenn. Looking at the shape of both connection types, the hemi-Fontan connection should have preferably directed the blood to one side, whereas the bidirectional Glenn should not have. However, in this bilateral SVC connection, the type of SVC anastomosis did not seem to have any real effect on the repartition of the SVC flows. Rather, it was the distance between the anastomosis sites (LSVC to LPA vs LSVC to RPA) that seemed to have a predominant effect. In the modified anatomy, the RSVC flow (with a hemi-Fontan connection) went exclusively to the RPA, whereas the LSVC flow (with a bidirectional Glenn) goes to the LPA. The IVC, positioned at equal distance from the 2 SVCs, splitted between the 2 PAs. The effect of the connection type may be more predominant in single-SVC cases, where the IVC and SVC should be close to each other.
Toward Surgical Planning
Figure 3 shows CFD and experimental results side by side. As has previously been pointed out by Pekkan and associates,
9
the commercial CFD package used for these simulations captures the macro-scale, time-averaged features with good accuracy. Furthermore, the power losses are within 1 SD from the experimental results for RPA flow splits lower than 67%. When 67% or more of the flow is directed to the RPA, the flow instabilities increase (Reynold's number = 2299 in the RPA at 70:30 RPA/LPA), reaching the limitations of our commercial CFD package.
In this study we used CFD and computer-aided design in combination to perform a virtual operation and assess its effect on the TCPC efficiency. This demonstrates the potential use of computer-aided design and CFD tools in surgical planning. However, as pointed out in the previous paragraph, the results should be considered with a critical mindset and weighed against the surgeon's judgment. Numerical simulations constitute a formidable tool, but their limitations should not be forgotten.
Surgical Constraints
It is important to keep in mind that this study only suggests some possible TCPC design improvements. In extracardiac cases, for example, shifting the IVC toward the LSVC may compress the pulmonary veins and worsen the patient's outcome rather than improving it. All the recommendations made in this article should thus be carefully balanced against the space constraints imposed by other vessels and organs and any other clinical considerations.
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Conclusions |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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Using computer-aided design and CFD tools in combination, this study demonstrates potential developments in pediatric cardiac surgical planning. However, special attention should be paid to the strengths and limitations of the CFD modeling before any final clinical conclusions are drawn.
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Supplementary video |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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Footnotes |
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References |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsSupplementary videoReferences |
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