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.

Copyright © 2013 by ASME
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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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