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Research Papers

Optimization of a Y-Graft Design for Improved Hepatic Flow Distribution in the Fontan Circulation

[+] Author and Article Information
Weiguang Yang

Mechanical and Aerospace Engineering,
University of California San Diego,
La Jolla, CA 92093
e-mail: w1yang@ucsd.edu

Jeffrey A. Feinstein

Pediatrics and Bioengineering,
Stanford University,
Stanford, CA 94305
e-mail: jaf@stanford.edu

Shawn C. Shadden

Mechanical, Materials, and
Aerospace Engineering,
Illinois Institute of Technology,
Chicago, IL 60616
e-mail: sshadde1@iit.edu

Irene E. Vignon-Clementel

INRIA Paris-Rocquencourt,
78153 Le Chesnay Cedex, France
e-mail: irene.vignon-clementel@inria.fr

Alison L. Marsden

Mechanical and Aerospace Engineering,
University of California
San Diego, La Jolla, CA 92093
e-mail: amarsden@eng.ucsd.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received December 16, 2011; final manuscript received September 11, 2012; accepted manuscript posted November 28, 2012; published online December 27, 2012. Assoc. Editor: Ender A. Finol.

J Biomech Eng 135(1), 011002 (Dec 27, 2012) (12 pages) Paper No: BIO-11-1531; doi: 10.1115/1.4023089 History: Received December 16, 2011; Revised September 11, 2012; Accepted November 28, 2012

Single ventricle heart defects are among the most serious congenital heart diseases, and are uniformly fatal if left untreated. Typically, a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed, after which the superior vena cava (SVC) and inferior vena cava (IVC) are directly connected to the pulmonary arteries (PA). In an attempt to improve hemodynamic performance and hepatic flow distribution (HFD) of Fontan patients, a novel Y-shaped graft has recently been proposed to replace the traditional tube-shaped extracardiac grafts. Previous studies have demonstrated that the Y-graft is a promising design with the potential to reduce energy loss and improve HFD. However these studies also found suboptimal Y-graft performance in some patient models. The goal of this work is to determine whether performance can be improved in these models through further design optimization. Geometric and hemodynamic factors that influence the HFD have not been sufficiently investigated in previous work, particularly for the Y-graft. In this work, we couple Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Specifically, we investigate the potential of using a Y-graft design with unequal branch diameters to improve hepatic distribution under a highly uneven RPA/LPA flow split. As expected, the resulting optimal Y-graft geometry largely depends on the pulmonary flow split for a particular patient. The unequal branch design is demonstrated to be unnecessary under most conditions, as it is possible to achieve the same or better performance with equal-sized branches. Two patient-specific examples show that optimization-derived Y-grafts effectively improve the HFD, compared to initial nonoptimized designs using equal branch diameters. An instance of constrained optimization shows that energy efficiency slightly increases with increasing branch size for the Y-graft, but that a smaller branch size is preferred when a proximal anastomosis is needed to achieve optimal HFD.

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References

de Leval, M. R., 2005, “The Fontan Circulation: A Challenge to William Harvey?” Nat. Clin. Pract. Cardiovasc. Med., 2, pp. 202–208. [CrossRef] [PubMed]
Marino, B. S., 2002. “Outcomes After the Fontan Procedure,” Curr. Opin. Pediatr., 14, pp. 620–626. [CrossRef] [PubMed]
Rudolph, A. M., 2009, Congenital Diseases of the Heart: Clinical-Physiological Considerations, Wiley-Blackwell, Hoboken.
Duncan, B. W. and Desai, S., 2003. “Pulmonary Arteriovenous Malformations After Cavopulmonary Anastomosis,” Ann. Thorac. Surg., 76, pp. 1759–1766. [CrossRef] [PubMed]
Grossage, J. R., and Kanj, G., 1998, “Pulmonary Arteriovenous Malformations,” Am. J. Respir. Crit. Care Med., 158, pp. 643–661. [PubMed]
Uemura, H., Yagihara, T., Hattori, R., Kawahira, Y., Tsukano, S., and Watanabe, K., 1999, “Redirection of Hepatic Venous Drainage After Total Cavopulmonary Shunt in Left Isomerism,” Ann. Thorac. Surg., 68, pp. 1731–1735. [CrossRef] [PubMed]
Pike, N. A., Vricella, L. A., Feinstein, J. A., Black, M. D., and Reitz, B. A., 2004, “Regression of Severe Pulmonary Arteriovenous Malformations After Fontan Revision and Hepatic Factor Rerouting,” Ann. Thorac. Surg., 78, pp. 697–699. [CrossRef] [PubMed]
McElhinney, D. B., Marx, G. R., Marshall, A. C., Mayer, J. E., and del Nido, P. J., 2011, “Cavopulmonary Pathway Modification in Patients With Heterotaxy and Newly Diagnosed or Persistent Pulmonary Arteriovenous Malformations After a Modified Fontan Operation,” J. Thorac. Cardiovasc. Surg., 141(6), pp. 1362–1370. [CrossRef] [PubMed]
Imoto, Y., Sese, A., and Joh, K., 2006, “Redirection of the Hepatic Venous Flow for the Treatment of Pulmonary Arteriovenous Malformations After Fontan Operation,” Pediatr. Cardiol., 27, pp. 490–492. [CrossRef] [PubMed]
Dubini, G., de Leval, M. R., Pietrabissa, R., Montevecchi, F. M., and Fumero, R., 1996. “A Numerical Fluid Mechanical Study of Repaired Congenital Heart Defects: Application to the Total Cavopulmonary Connection,” J. Biomech., 29(1), pp. 111–121. [CrossRef] [PubMed]
Migliavacca, F., Dubini, G., Bove, E. L., and de Leval, M. R., 2003, “Computational Fluid Dynamics Simulations in Realistic 3-D Geometries of the Total Cavopulmonary Anastomosis: The Influence of the Inferior Caval Anastomosis,” J. Biomech. Eng., 125, pp. 805–813. [CrossRef] [PubMed]
Whitehead, K. K., Pekkan, K., Kitahima, H. D., Paridon, S. M., Yoganathan, A. P., and Fogel, M. A., 2007, “Nonlinear Power Loss During Exercise in Single-Ventricle Patients After the Fontan: Insights From Computational Fluid Dynamics,” Circulation, 116, pp. I-165–I-171. [CrossRef]
Marsden, A. L., Vignon-Clementel, I. E., Chan, F., Feinstein, J. A., and Taylor, C. A., 2007, “Effects of Exercise and Respiration on Hemodynamic Efficiency in CFD Simulations of the Total Cavopulmonary Connection,” Ann. Biomed. Eng., 35(2), pp. 250–263. [CrossRef] [PubMed]
Walker, P. G., Oweis, G. F., and Watterson, K. G., 2001, “Distribution of Hepatic Venous Blood in the Total Cavo Pulmonary Connection: An In Vitro Study into the Effects of Connection Geometry,” J. Biomech. Eng., 123(6), pp. 558–564. [CrossRef] [PubMed]
Bove, E. L., de Leval, M. R., Migliavacca, F., Guadagni, G., and Dubini, G., 2003, “Computational Fluid Dynamics in the Evaluation of Hemodynamic Performance of Cavopulmonary Connections After the Norwood Procedure for Hypoplastic Left Heart Syndrome,” J. Thorac. Cardiovasc. Surg., 126, pp. 1040–1047. [CrossRef] [PubMed]
Shadden, S. C., and Taylor, C. A., 2008, “Characterization of Coherent Structures in the Cardiovascular System,” Ann. Biomed. Eng., 36(7), pp. 1152–1162. [CrossRef] [PubMed]
Marsden, A. L., Bernstein, A. J., Reddy, V. M., Shadden, S., Spilker, R. L., Chan, F. P., Taylor, C. A., and Feinstein, J. A., 2009, “Evaluation of a Novel Y-Shaped Extracardiac Fontan Baffle Using Computational Fluid Dynamics,” J. Thorac. Cardiovasc. Surg., 137(2), pp. 394–403. [CrossRef] [PubMed]
Dasi, L. P., Whitehead, K., Pekkan, K., de Zelicourt, D., Katajima, H., Sundareswaran, K., Kanter, K., Fogel, M. A., and Yoganathan, A. P., 2011, “Pulmonary Hepatic Flow Distribution in Total Cavopulmonary Connections: Extracardiac Versus Intracardiac,” J. Thorac. Cardiovasc. Surg., 141, pp. 207–214. [CrossRef] [PubMed]
Yang, W., Vignon-Clementel, I. E., Troianowski, G., Reddy, V. M., Feinstein, J. A., and Marsden, A. L., 2012, “Hepatic Blood Flow Distribution and Performance in Traditional and Y-Graft Fontan Geometries: A Case Series Computational Fluid Dynamics Study,” J. Thorac. Cardiovasc. Surg., 143, pp. 1086–1097. [CrossRef] [PubMed]
Soerensen, D. D., Pekkan, K., de Zelicourt, D., Sharma, S., Kanter, K., Fogel, M., and Yoganathan, A., 2007, “Introduction of a New Optimized Total Cavopulmonary Connection,” Ann. Thorac. Surg., 83(6), pp. 2182–2190. [CrossRef] [PubMed]
Yang, W., Feinstein, J. A., and Marsden, A. L., 2010, “Constrained Optimization of an Idealized Y-Shaped Baffle for the Fontan Surgery at Rest and Exercise,” Comput. Methods Appl. Mech. Eng., 199(33–36), pp. 2135–2149. [CrossRef]
Marsden, A. L., Feinstein, J. A., and Taylor, C. A., 2008, “A Computational Framework for Derivative-Free Optimization of Cardiovascular Geometries,” Comput. Methods Appl. Mech. Eng., 197(21–24), pp. 1890–1905. [CrossRef]
Cheng, C. P., Herfkins, R. J., Lightner, A. L., Taylor, C. A., and Feinstein, J. A., 2004, “Blood Flow Conditions in the Proximal Pulmonary Arteries and Vena Cavae: Healthy Children During Upright Cycling Exercise,” Am. J. Physiol. Heart Circ. Physiol., 287(2), pp. H921–H926. [CrossRef] [PubMed]
Seliem, M. A., Murphy, J., Vetter, J., Heyman, S., and Norwood, W., 1997, “Lung Perfusion Patterns After Bidirectional Cavopulmonary Anastomosis (Hemi-Fontan Procedure),” Pediatr. Cardiol., 18, pp. 191–196. [CrossRef] [PubMed]
Troianowski, G., Taylor, C. A., Feinstein, J. A., and Vignon-Clementel, I., 2011, “Three-Dimensional Simulations in Glenn Patients: Clinically Based Boundary Conditions, Hemodynamic Results and Sensitivity to Input Data,” J. Biomech. Eng., 133(11). [CrossRef]
Wilson, N., Wang, K., Dutton, R., and Taylor, C. A., 2001, “A Software Framework for Creating Patient Specific Geometric Models From Medical Imaging Data for Simulation Based Medical Planning of Vascular Surgery,” Lect. Notes Comput. Sci., 2208, pp. 449–456. [CrossRef]
Schmidt, J. P., Delp, S. L., Sherman, M. A., Taylor, C. A., Pande, V. S., and Altman, R. B., 2008, “The Simbios National Center: Systems Biology in Motion,” Proc. IEEE, special issue on Computational System Biology, 96(8), pp. 1266–1280. [CrossRef]
Sharma, S., Ensley, A. E., Hopkins, K., Chatzimavrodis, G. P., Healy, T. M., Tam, V. K. H., Kanter, K. R., and Yoganathan, A. P., 2001, “In Vivo Flow Dynamics of the Total Cavopulmonary Connection From Three-Dimensional Multislice Magnetic Resonance Imaging,” Ann. Thorac. Surg., 71(3), pp. 889–898. [CrossRef] [PubMed]
Marsden, A. L., Reddy, V. M., Shadden, S. C., Chan, F. P., Taylor, C. A., and Feinstein, J. A., 2010, “A New Multiparameter Approach to Computational Simulation for Fontan Assessment and Redesign,” Congenital Heart Disease, 5(2), pp. 104–117. [CrossRef] [PubMed]
Taylor, C. A., Hughes, T. J. R., and Zarins, C. K., 1998, “Finite Element Modeling of Blood Flow in Arteries,” Comput. Method. Appl. Mech. Eng., 158(1–2), pp. 155–196. [CrossRef]
Muller, J., Sahni, O., Li, X., Jansen, K. E., Shephard, M. S., and Taylor, C. A., 2005, “Anisotropic Adaptive Finite Element Method for Modeling Blood Flow,” Comput. Methods Biomech. Biomed. Eng., 8(5), pp. 295–305. [CrossRef]
Hjortdal, V. E., Emmertsen, K., Stenbog, E., Frund, T., Rahbek Schmidt, M., Kromann, O., Sorensen, K., and Pedersen, E. M., 2003, “Effects of Exercise and Respiration on Blood Flow in Total Cavopulmonary Connection: A Real-Time Magnetic Resonance Flow Study,” Circulation, 108(10), pp. 1227–1231. [CrossRef] [PubMed]
Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A., 2010, “Outflow Boundary Conditions for 3D Simulations of Non-Periodic Blood Flow and Pressure Fields in Deformable Arteries,” Comput. Methods Biomech. Biomed. Eng., 13(5), pp. 625–640. [CrossRef]
Booker, A. J., Dennis, Jr., J. E., Frank, P. D., Serafini, D. B., Torczon, V., and Trosset, M. W., 1999, “A Rigorous Framework for Optimization of Expensive Functions by Surrogates,” Struct. Optim., 17(1), pp. 1–13. [CrossRef]
Audet, C., and Dennis, Jr., J. E., 2006, “Mesh Adaptive Direct Search Algorithms for Constrained Optimization,” SIAM J. Optim., 17(1), pp. 2–11. [CrossRef]
Audet, C., and Dennis, Jr., J. E., 2003, “Analysis of Generalized Pattern Searches,” SIAM J. Optim., 13(3), pp. 889–903. [CrossRef]
Torczon, V., 1997, “On the Convergence of Pattern Search Algorithms,” SIAM J. Optim., 7, pp. 1–25. [CrossRef]
Marsden, A. L., Wang, M., Dennis, Jr., J. E., and Moin, P., 2004, “Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework,” Optim. Eng., 5(2), pp. 235–262. Special Issue: Surrogate Optimization. [CrossRef]
Audet, C., and Dennis, Jr., J. E., 2004, “A Pattern Search Filter Method for Nonlinear Programming Without Derivatives,” SIAM J. Optim., 14(4), pp. 980–1010. [CrossRef]
Forrester, A. I. J., Sobester, A., and Keane, A. J., 2007, “Multi-Fidelity Optimization via Surrogate Modelling,” Proc. R. Soc. London, Ser. A, 463, pp. 3251–3269. [CrossRef]
Haggerty, C. M., Kanter, K. R., Restrepo, M., de Zelicourt, D. A., Parks, W. J., Rossignac, J., Fogel, M. A., and Yoganathan, A. P., 2012, “Simulating Hemodynamics of the Fontan Y-Graft Based on Patient-Specific In Vivo Connections,” J. Thorac. Cardiovasc. Surg., (in press). [CrossRef]
Kanter, K. R., Haggerty, C. M., Restrepo, M., de Zelicourt, D. A., Parks, W. J., Rossignac, J., Parks, W. J., and Yoganathan, A. P., 2012, “Preliminary Clinical Experience With a Bifurcated Y-Graft Fontan Procedure- A Feasibility Study,” J. Thorac. Cardiovasc. Surg., 144(2), pp. 383–389. [CrossRef] [PubMed]
Sundareswaran, K. S., Pekkan, K., Dasi, L. P., Whitehead, K., Sharma, S., Kanter, K., Fogel, M. A., and Yoganathan, A. P., 2008, “The Total Cavopulmonary Connection Resistance: A Significant Impact on Single Ventricle Hemodynamics at Rest and Exercise,” Am. J. Physiol. Heart Circ. Physiol., 295, pp. H2427–H2435. [CrossRef] [PubMed]
Baretta, A., Corsini, C., Yang, W., Vignon-Clementel, I. E., Marsden, A. L., Hsia, T. Y., Dubini, G., Migliavacca, F., and Pennati, G., 2011, “Virtual Surgeries in Patients With Congenital Heart Disease: A Multiscale Modelling Test Case,” Philos. Trans. R. Soc., 369(1954), pp. 4316–4330. [CrossRef]
Audet, S. S. C., and Marsden, A. L., 2010, “A Method for Stochastic Constrained Optimization Using Derivative-Free Surrogate Pattern Search and Collocation,” J. Comput. Phys., 229(12), pp. 4664–4682. [CrossRef]
Dobrin, P. B., Mirande, P., Kang, S., Dong, Q. S., and Mrkvicka, R., 1998, “Mechanics of End-to-End Artery-to-PTFE Graft Anastomoses,” Ann. Vasc. Surg., 12(4), pp. 317–323. [CrossRef] [PubMed]
Bazilevs, Y., Hsu, M.-C., Besnon, D., Sankaran, S., and Marsden, A. L., 2008, “Computational Fluid-Structure Interaction: Methods and Application to a Total Cavopulmonary Connection,” Comput. Mech., 45(1), pp. 77–89. [CrossRef]

Figures

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Fig. 1

Model parameterization and flared SVC anastomosis. Upper left: Design parameters and centerlines of an idealized Y-graft Fontan model. Upper right: A representative Y-graft model. Parameters DL and DR allow two branches to vary independently. Bottom left: An LPA-flared SVC anastomosis with a straight junction for the RPA side. Bottom right: A curved-to-LPA SVC anastomosis.

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Fig. 2

(1) A patient-specific Glenn model. (2) In the semi-idealized Glenn model, the PA is approximated by uniform circular segmentations and the pulmonary artery branches are neglected. The PA diameter is equal to the averaged diameter of the patient-specific PA. (3) A Y-graft is implanted forming a semi-idealized Fontan model for the same patient. The design parameters for the Y-graft are XL, XR, LIVC, and Dbranch. When large branches are anastomosed, the segmentation at the anastomosis is enlarged to the graft size. Then the rest of the PA segmentations are enlarged linearly according to the distance to the closest anastomosis.

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Fig. 3

Optimal values for the HFD. Based on Eq. (2), the theoretical optimum for the HFD, defined as the value closest to 50/50, is determined given an inflow ratio QIVC/QSVC and a pulmonary flow split FRPA (% inflow to RPA).

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Fig. 4

A comparison of HFD and energy loss for optimal unequal and equal-sized branches. HFDs for the unequal and equal-sized branches are 63/37 and 65/35 (IVC-RPA/IVC-LPA), respectively, but equal-sized branches perform better in reducing energy loss. The pulmonary flow split is 79/21 (RPA/LPA).

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Fig. 5

Optimal Y-grafts with equal-sized branches for a large range of pulmonary flow splits. Theoretical optima given by Eq. (2) are achieved by using optimization. The difference from the theoretical value is shown at each point.

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Fig. 6

Time-averaged flow fields of optimal Y-grafts for a straight SVC-PA junction and two types of flared SVC anastomoses. The pulmonary flow split is 55/45 (RPA/LPA). Compared to the model with a straight SVC-PA junction, the optimal Y-grafts for two flared SVC anastomoses have a more distal anastomosis for the LPA.

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Fig. 7

HFD versus QIVC/Qinflow for an idealized model and a patient-specific model (patient B). Patient B's original inflow ratio QIVC/Qinflow is marked by an arrow. Total inflow is kept constant in this comparison. The idealized Y-graft is optimized for an IVC inflow-to-total inflow ratio of 45%. There is only 1% change in the Y-graft model when the ratio is altered. However, the patient specific model is more sensitive to the change of IVC inflow-to-total inflow ratio.

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Fig. 8

(a) Time-averaged velocity vector fields in the semi-idealized and patient-specific models for patient A. (b) Particle snapshots taken at T = 3 s for the nonoptimized and optimal models. The bar chart shows the semi-idealized model (upper left) has a similar hepatic flow split to the patient-specific model (upper right) for the same optimal Y-graft, and that the optimized Y-graft improves the HFD by 79%, compared to the original nonoptimized design (lower left). The optimal and nonoptimized branch sizes are 12.9 and 15 mm, respectively.

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Fig. 9

Time-averaged velocity vector fields in the semi-idealized and patient-specific models with and without the RUL for patient B. The Y-graft is optimized for an HFD of 50/50. Due to the effect of the RUL, the optimized Y-graft skewed the hepatic flow by around 15% after it was implanted into the patient-specific model. When the RUL is excluded from the patient-specific model, the HFD is consistent with the idealized model prediction.

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Fig. 10

(a) Time-averaged velocity vector fields and HFD for patient B. The Y-graft in the semi-idealized model (upper left) is optimized for a hepatic flow split of 65/35 (RPA/LPA) to account for the overestimation of the RPA hepatic flow in the semi-idealized model. (b) Particle snapshots taken at T = 3 s for the nonoptimized and optimal models. The bar chart shows the optimal Y-graft improves the performance by 94% achieving an even HFD in the patient-specific model (upper right), compared to the nonoptimized design (lower left). The optimal and nonoptimized branch sizes are 16 and 15 mm, respectively.

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Fig. 11

Final results for optimizing energy efficiency with an HFD constraint using a semi-idealized model for patient A. The cost function J and constraint C are defined in Eq. (4). Among undominated points, the least infeasible point achieved the best HFD with the smallest branch diameter, and the point with the largest branch diameter resulted in the highest energy efficiency.

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