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Ann Thorac Surg 2007;83:2182-2190
© 2007 The Society of Thoracic Surgeons
a Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia
b Carnegie Mellon University, Pittsburgh, Pennsylvania
c Pediatric Cardiology Associates, Department of Surgery, Emory University, Atlanta, Georgia
d Division of Cardiology, The Children’s Hospital of Philadelphia, Philadelphia, Pennsylvania
Accepted for publication December 4, 2006.
* Address correspondence to Dr Yoganathan, Wallace H. Coulter Department 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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Methods: A rapid prototype model of the OptiFlo TCPC was built and in vitro control volume flow analysis was performed to evaluate the fluid mechanical power loss performance of the model. Furthermore, computational fluid dynamics simulations were used to investigate the flow patterns in the model, which were compared with those in the planar one-diameter offset TCPC with flared anastomosis sites, the best known TCPC configuration to date.
Results: Compared with the one-diameter offset reference model, the OptiFlo showed lower power losses: –26%, –31%, and –42% for increasing cardiac outputs of 2, 4, and 6 L/minute, respectively. No statistically significant differences were found in power loss between 40:60 and 50:50 SVC/IVC flow ratios (p > 0.1) for the OptiFlo model. The power loss characteristic curve for different left and right pulmonary artery ratios was flatter for the OptiFlo than the one-diameter offset reference model. Pulmonary artery flow was much more streamlined in the OptiFlo compared with the one-diameter offset model.
Conclusions: The OptiFlo TCPC design exhibits lower power losses with better adaptive distribution of hepatic blood to both lungs and lower blood flow disturbances compared with the planar one-diameter offset TCPC model. Its significantly superior hemodynamic performance at higher cardiac outputs (exercise) rationalizes further design and feasibility studies toward a workable clinical model.
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Introduction |
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Among the multiple variables determining the outcome of the Fontan procedure, it has long been hypothesized that lowering the fluid mechanical power loss caused by the "inefficient" Fontan connection geometry could reduce the workload on the single ventricle and increase exercise capacity. This hypothesis was recently confirmed by the lumped parameter modeling studies of the single-ventricle circulation [3], where the power losses were shown to have a significant impact on the cardiac output (CO) and postoperative venous compliance remodeling. Isolated clinical cases demonstrating an acute recovery with improved designs of TCPC pathways are also reported [4]. To date, a number of suggested Fontan connection configurations have been investigated spanning from the original unidirectional connection [5] to the total cavopulmonary connection (TCPC). Despite good hemodynamics and streamlined flows going to the pulmonary arteries (PAs), the unidirectional connections resulted in poor clinical outcomes mainly due to the fact that the hepatic blood was directed exclusively to one lung causing serious pulmonary arteriovenous malformations and diminished lung growth [6–8]. Furthermore, these unidirectional configurations were not adaptive to the changes in independent pulmonary circuits. The TCPC circumvents these problems by connecting both venae cavae (VCs) to both Pas, allowing the hepatic blood to mix and be distributed to both lungs. However, the head-on collision of the caval flows was shown to have a detrimental effect, increasing the amount of energy dissipation. From a theoretical point of view, the planar one-diameter offset TCPC model with flared anastomosis sites (1D offset model) [9] proved to be the best idealized TCPC design with the lowest predicted power losses. The caval offset prevented the head-on inflow collision, while a vortex located at the center of the connection helped redistribute the hepatic flow. On the other hand this central vortex is also an inherent source of energy dissipation and was observed to yield helical flow patterns in the PAs, increasing the friction losses even further. Further insight in to the pathway hemodynamics has been revealed by many earlier dedicated computational flow studies [10–13]. Based on these observations, this study presents an optimized Fontan connection, code-named "Optiflo," which avoids the dissipative inflow collision while still allowing for hepatic blood distribution and adaptation to flow ratio changes between the inlets and the outlets.
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Material and Methods |
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An experimental physical model was created using the rapid prototyping technique previously described by our group [15]. The computer-aided design model was converted to a stereolithographic (STL) file and imported into, and manufactured by, a rapid prototyping (RP) machine (SLA 250; 3D Systems, Valencia, CA). A clear resin was used (RenShape SL 5510/7510; Huntsman, East Lansing, MI). To enable sanding and polishing of the inside of the model, it was created of four subparts that were later assembled together using regular cyanoacrylate adhesive.
In Vitro Hydrodynamic Power Loss Analysis
The OptiFlo configuration was investigated by a control volume flow analysis to evaluate its fluid mechanical power loss performance compared with existing idealized TCPC models. Furthermore, computational fluid dynamics (CFD) was used to elucidate the flow and velocity patterns of the connection. All experiments and CFD simulations were run under steady flow conditions.
The physical model was investigated with control volume flow analysis using an in vitro flow loop that has been described previously [9, 14]. Static pressure and flow rate measurements at each inlet and outlet were used to calculate the power loss in the model volume. The inflow conditions were steady and maintained by a constant pressure head, where the model was lying flat on a table, mimicking a supine position. Fully developed inflow profiles were achieved and a blood analogue solution of water and glycerin was used to match the viscosity of blood. Differential static pressures were measured at the wall of each vessel 2 cm away from the inlet and outlet ends. Energy losses were then computed by an integrated control volume energy balance:
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Flow Conditions
The total CO was chosen to be 2, 4, and 6 liters per minute (LPM). The SVC/IVC flow ratios were chosen to be 40:60 and 50:50, whereas the LPA/RPA flow ratios ranged from 30:70 to 70:30 in 10% increments. These flow values matched those of the other in vitro studies [9, 14, 16] and enabled one-to-one performance comparison with the previous idealized TCPC geometries.
Numerical Studies
To understand the detailed three-dimensional flow fields, CFD studies are performed for the OptiFlo TCPC configuration. OptiFlo geometry is created in ProEngineer (PTC Inc, TX). The overall size and the uniform vessel diameter of 13.34 mm is chosen to enable performance comparison between the planar 1D offset configuration with flared anastomosis sites representing the standard lowest power loss TCPC configuration. The CFD methodology and the computational results of the idealized 1D offset configuration have been described earlier [17, 18]. The same CFD methodology is used for the new OptiFlo configuration. Particular emphasis is given to achieve the same mesh density (finest mesh density) in both models. Computational mesh is further refined around the confluence and bifurcation regions. An unstructured mesh of approximately 98,000 nodes was generated (Gambit; Fluent Inc, Lebanon, NH) from the same STL file used for manufacturing the physical RP model. To ensure steady laminar flow at the inlet and convergence at the outlets, the inlets and outlets were extended 5 cm and 10 cm, respectively, giving 15-cm and 20-cm long inlets and outlets, respectively, when measured from the center of the model. The flow conditions were the same for the two models: steady flow with CO of 4 LPM, 40:60 SVC/ IVC ratio, and 40:60 LPA/RPA flow ratio. For both models, steady-state flow fields were computed using the parallelized segregated finite-element CFD solver FIDAP (Fluent Inc). The pressure projection algorithm with the second-order streamwise upwinding was utilized. Fourth-order convergence for the Euclidean norm of velocity and pressure was established in the presented results. This solution methodology has demonstrated good agreement with the in vitro experiments in our previous studies with more complex anatomical models [18, 19].
The Tecplot (Tecplot Inc, Bellevue, WA) software package with the CFD analyzer add-on was used for analysis of the OptiFlo models flow and velocity patterns. Power losses were determined for each of the finite elements in the CFD mesh using the viscous dissipation method as described by Healy and colleagues [20]. This method calculates power losses entirely based on the velocity gradients between the finite elements, which enables a good qualitative look at the power loss "hot spots" in the investigated volume. The higher the velocity gradient between neighboring finite element volumes is, the higher the power loss is.
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Results |
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The 1D offset model showed more disturbed flow compared with that of the OptiFlo, which is clear in both Figures 4A and 4C. One of the reasons for this was that the majority of the flow entered from the IVC and exited through the RPA. Therefore, some of the fluid entering from the IVC was forced to exit through the RPA, causing some collision of the SVC and IVC flows marked with the black arrow in Figure 4C.
The cross-sectional area of each split in the OptiFlo was equal to that of the inlets and outlets. Consequently, the velocity magnitude of the flow after the bifurcation was lower than upon entering the VCs. Furthermore, in the IVC, there was a region before the point where the flow collided with the flaring site (marked C in Fig 1), at which the velocity magnitude decreased. After the split was complete and the flow had passed the flaring site, the velocity magnitude increased again. The low velocity magnitude region was caused by the elevated pressure at the flaring site.
Local Contribution to the Power Loss
Depicting the viscous power dissipation on a color scale throughout the model provides a good insight to the flow structures causing elevated power losses which can be termed as "hot spots." From Figures 4E and 4F it was evident that there were distinct regions in both models with elevated power losses. In the OptiFlo this was observed at the inner sides of the splits where the flow collided with the splits, thus increasing the shear stresses. The flow separations between the low and high velocity flow in the splits of the OptiFlo model also increased the power losses.
The regions with elevated power losses for the 1D offset model were not as confined as for the OptiFlo model. For the 1D offset model, increased power losses were observed in four regions: (1) where the IVC flow entered the middle of the 1D offset connection colliding with the flow from the SVC (black arrow in Fig 4C): (2) the flow separation between the high velocity VC flow entering the connection and the low velocity flow in the middle of the connection; (3) the helical flow in the Pas; and (4) the walls due to wall friction and (or) flow collision. The regions with elevated power losses in the OptiFlo model were overall smaller both in size and magnitude compared with those in the 1D offset model.
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Comment |
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Comparing two TCPC designs side-by-side has contributed to our understanding of the Fontan circulation and emphasized that there is still room for further hemodynamic optimization to avoid unnecessary power loss and hopefully increase the longevity of the Fontan circulation. Superior performance of the 1D offset model is usually attributed to the beneficial recirculating vortex at the center[21]. In reality, ranging the caval offset from zero to larger offset diameters reduces the shear zone (and in parallel the power loss) but does not completely eliminate it. Furthermore, "+" shaped junctions introduce complex constraints to the development of the secondary PA flows contributing the global power loss. Optiflo configuration eliminates this shear zone completely and gives more room for the secondary flows (due to VC to PA turning) to develop, which reduces the velocity gradients significantly; improving hemodynamics even further.
Having a flatter power loss curve, the OptiFlo is more tolerant to changes in flow ratios between the inlets and (or) outlets compared with traditional TCPC configurations. This is important considering that the LPA/RPA flow ratio is rarely constant and may change due to stenoses, unbalanced lung resistances, and (or) cardiopulmonary interactions. More importantly, the IVC and SVC flow contribution to the total venous return changes with respect to age[22]. In view of this fact, Fogel and colleagues [23] suggested guiding the IVC blood mainly to the larger lung through the RPA, and the SVC blood mainly to the LPA and the smaller lung when performing the Fontan operation. The design of the OptiFlo ensures proper adaptive distribution of both incoming and outgoing flow to the lungs, at no expense of increased power loss.
Equal left and right lung hepatic flow distribution (essential for normal lung development) is compromised for better power loss in the traditional "+" shaped TCPC configurations. Increasing the offset will lower the power losses; however, it will also disturb the proper distribution of the hepatic blood. It is well-recognized that the "beneficial vortex" of the 1D offset model preferentially diverts the IVC blood to the RPA if the IVC offset is toward the right lung. The new symmetric OptiFlo design naturally assures equal hepatic blood split which can be further customized by varying the split sizes to incorporate unequal left and right lung resistances.
While the OptiFlo model geometry is symmetric, there was a slight asymmetry in the experimental in vitro power loss curves (Fig 2) around the 50:50 LPA/RPA flow ratio. This is attributed to the four-part assembly of the physical OptiFlo model and to the unavoidable little grooves and bulges at the assembly lines, surface roughness, and uneven model polishing.
Results of this study are based on in vitro experimental measurements performed on the bench-top flow loops. Therefore, within the bounds of practical experimentation it could not mimic all details of the complex in vivo univentricular hemodynamics and physiology (like cardiopulmonary interactions, compliant vessels, etc) completely. At the same time, the average steady flow conditions presented in this study are considered an acceptable point for performance comparison, because the impact of the neglected components and influencing factors will be in the same order for both the traditional TCPC configuration and the proposed fluid dynamically efficient OptiFlo configuration.
Exercise Performance
Fontan patients are known to have a decreased exercise capacity as compared with healthy controls and this may have a significant impact on their quality of life, particularly as they get older. At the CFD simulated exercise conditions TCPC power loss increases in a dramatically nonlinear fashion with increasing cardiac output. On average, there is a ninefold (6 to 12) increase from baseline to the 2x-exercise and 33-fold (29 to 45) to the 3x-exercise conditions in traditional anatomic TCPC connections [24]. Because the hydrodynamic benefit of OptiFlo over the traditional TCPCs increases with increasing CO, the OptiFlo configuration would be particularly advantageous at the exercise conditions. Specifically for the intense leg-exercise, only an IVC bifurcation could potentially suffice to realize the hemodynamic advantage of the OptiFlo and further eliminate a likely IVC flow recirculation into the SVC [4, 24].
Surgical Arrangement and Feasibility
The OptiFlo configuration presented here is in its most basic idealized in vitro test configuration. Its clinical utility and implementation require further more detailed considerations in order to improve its clinical feasibility through less cumbersome designs. The superior hemodynamic performance of Optiflo justifies such detailed studies, which can be undertaken in the future. In this section only some preliminary thoughts toward a workable clinical model will be presented.
The OptiFlo connection can be created using reasonably sized native vessels, as sketched in Figure 5. However, creating the connection this way would be difficult for several reasons. First, the total cross-sectional areas of the splits would only be half that of the mother vessel. Our studies showed that a reduced diameter split will act as a stenosis causing increased power losses. Second, the vessels in the TCPC are not the same size. This would cause considerable diameter mismatches between the splits from the inlets and outlets, whereby the flow in the splits would be less streamlined, increasing the power losses. Third, there might not be enough vessel material to construct the OptiFlo connection; even though the lengths of the splits would be less than the length had they been connected in a standard 1D offset configuration, the IVC ends at the right atrium level. Fourth, the shape of the splits would most likely not be curved nicely as seen in Figure 1, leading to a more rhombus-shaped connection with less streamlined PA flow mixing.
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Future Directions
It must be emphasized again that the Optiflo geometry studied here features the most primitive and basic configuration with uniform and constant diameters. Further analysis should reveal whether the OptiFlo configuration can be improved even further. Changing the planarity, flaring of anastomosis sites, and diameters of the vessels in other idealized TCPC models have been found to affect the power losses and can be translated to the Optiflo configuration. In this study, the flaring at the bifurcation sites was found to introduce some recirculation and secondary flow. Removing the flaring at bifurcation and merging sites is likely to reduce power losses even more. Sharper bifurcations (no flaring) would avoid stagnation zones (at B and D in Fig 1) and reduce head-on wall collision (at A and C in Fig 1). For the splits, designing oval vessel cross-sections instead of the perfect circular vessel areas could control the flow separations observed at the caval bifurcations without compromising the actual flow. Changing the idealized vessel and split diameters and making them more physiologically correct will also impact the power losses in the connection. Furthermore, increasing the radius of curvature and decreasing the split length should decrease the power losses, but this speculation needs to be evaluated and quantified.
The OptiFlo configurations should be constructed using the actual surgical materials and native vessels for further in vitro flow loop tests. To evaluate its in vivo performance, the next step is to practice this configuration in an acute single ventricle animal model and, when available, in chronic experiments. These studies are essential and would reveal if the splitting and merging of venous blood return would introduce any unforeseen complications such as thrombosis and (or) stenosis formations, lung perfusion anomalies, potential kinks, or pressure build-ups.
Conclusion
A new idealized total cavopulmonary connection was introduced and evaluated with control volume flow analysis and CFD. The power loss performance of the new connection was compared with the 1D offset idealized model [9, 14, 16], which has been considered to be the best idealized model so far. The newly designed OptiFlo connection was found to exhibit lower power losses, less helical PA flow, equal distribution of hepatic blood to both lungs, and a better tolerance to varying flow splits compared with the 1D offset reference model. The new Optiflo configuration has potential to be optimized further and could be customized for use in patient-specific anatomies.
This study demonstrated that there is still room for hemodynamic improvement, up to approximately 40% in power loss, even over the "best"-known TCPC designs (1D offset configuration). While a drastically different TCPC geometry is introduced to realize this improvement to its full extent, it must be highlighted that at least some part of the presented improvement can be fulfilled in the existing traditional TCPC pathway designs with additional caution and surgical fluid flow considerations but without a drastic change in the "+" shaped TCPC configuration. By this study the traditionally "best" one-diameter offset configuration is replaced with the presented Optiflo configuration as a new target to approach for low power loss in surgical designs.
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) and flared planar one-diameter (1D) offset model (
) at cardiac output of 4 L/minute, and with a 40:60 superior vena cava to inferior vena cava flow ratio. Both are rapid prototyping models with a 13.34-mm diameter. Error bars indicate one standard deviation. (RPA = right pulmonary artery.)
