Research Papers

Optimization of Shunt Placement for the Norwood Surgery Using Multi-Domain Modeling

[+] Author and Article Information
Mahdi Esmaily Moghadam

Mechanical and Aerospace Engineering,  University of California San Diego, San Diego, CA 92093mesmaily@ucsd.edu

Francesco Migliavacca

Laboratory of Biological Structure Mechanics, Politecnico di Milano, 20133, Italyfrancesco.migliavacca@polimi.it

Irene E. Vignon-Clementel

INRIA Paris-Rocquencourt, 78153, FranceIrene.Vignon-Clementel@inria.fr

Tain-Yen Hsia

Cardiothoracic SurgeonCardiac Unit, Great Ormond Street Hospital for Children, WC1N 3JH, UKtyhsia@virginmedia.com

Alison L. Marsden

Mechanical and Aerospace Engineering,  University of California San Diego, San Diego, CA 92093amarsden@ucsd.edu


MOCHA Investigators: Edward Bove, M.D. and Adam Dorfman, M.D. (University of Michigan, USA); Andrew Taylor, M.D., Alessandro Giardini, M.D., Sachin Khambadkone, M.D., Marc de Leval, M.D., Silvia Schievano, Ph.D., and T.-Y. Hsia, M.D. (Institute of Child Health, UK); G. Hamilton Baker, M.D. and Anthony Hlavacek (Medical University of South Carolina, USA); Francesco Migliavacca, Ph.D., Giancarlo Pennati, Ph.D., and Gabriele Dubini, Ph.D. (Politecnico di Milano, Italy); Richard Figliola, Ph.D. and John McGregor, Ph.D. (Clemson University, USA); Alison Marsden, Ph.D. (University of California, San Diego, USA); Irene Vignon-Clementel (INRIA, France).

J Biomech Eng 134(5), 051002 (May 25, 2012) (13 pages) doi:10.1115/1.4006814 History: Received August 26, 2011; Revised February 23, 2012; Posted May 14, 2012; Published May 25, 2012; Online May 25, 2012

An idealized systemic-to-pulmonary shunt anatomy is parameterized and coupled to a closed loop, lumped parameter network (LPN) in a multidomain model of the Norwood surgical anatomy. The LPN approach is essential for obtaining information on global changes in cardiac output and oxygen delivery resulting from changes in local geometry and physiology. The LPN is fully coupled to a custom 3D finite element solver using a semi-implicit approach to model the heart and downstream circulation. This closed loop multidomain model is then integrated with a fully automated derivative-free optimization algorithm to obtain optimal shunt geometries with variable parameters of shunt diameter, anastomosis location, and angles. Three objective functions: (1) systemic; (2) coronary; and (3) combined systemic and coronary oxygen deliveries are maximized. Results show that a smaller shunt diameter with a distal shunt-brachiocephalic anastomosis is optimal for systemic oxygen delivery, whereas a more proximal anastomosis is optimal for coronary oxygen delivery and a shunt between these two anatomies is optimal for both systemic and coronary oxygen deliveries. Results are used to quantify the origin of blood flow going through the shunt and its relationship with shunt geometry. Results show that coronary artery flow is directly related to shunt position.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Schematic of modified Blalock-Taussig shunt anatomy [11]

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Figure 2

Overall framework for optimization

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Figure 3

Lumped parameter network coupled to the BT shunt anatomy. This LPN contains blocks for the upper body arteries (UBA), upper body bed (UBB), upper body veins (UBV), pulmonary artery bed (PAB), pulmonary vein bed (PVB), lower body arteries (LBA), lower body bed (LBB), lower body veins (LBV), two coronary arteries (CA1, CA2), coronary bed (CB), coronary veins (CV), left atrium (LA), right atrium (RA), and single ventricle (SV). The ascending aorta (AoA), descending aorta (AoD), brachiocephalic artery (BA), right common carotid artery (RCCA), left common carotid artery (LCCA), left subclavian artery (LSA), left pulmonary artery (LPA), right pulmonary artery (RPA), and right coronary artery (RCA) are shown in the figure.

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Figure 4

Shunt parameterization. Shunt diameter, two anastomoses locations, and anastomosis angle are used as the design parameters. Anastomosis angles at each point are decomposed into two in-plane θi and out-of-plane θo angles. The extent of anastomosis points’ sliding paths are shown (rPA(sA), sA ∈ [0,1] for point A and rBA(sB), sB ∈ [0,1] for point B). In this figure, points A and B are at the middle, i.e., sA=0.5 and sB=0.5.

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Figure 5

Reduction in objective functions versus the optimization history. The set of parameters shown next to each optimal point are design parameters, d={cot(θAo),sA,sB}. (a) J1 optimization history. The shunt diameter is fixed to 3.20 mm in this optimization. (b) J2 optimization history (0.045 J2 is plotted here). The shunt diameter is fixed to 3.41 mm in this optimization. (c) J3 optimization history. The shunt diameter is fixed to 3.36 mm in this optimization.

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Figure 6

Variation of objective function versus the shunt diameter while fixing the other design parameters, i.e., {cot(θAo),sA,sB} = 0.25, 0.1, 0.11

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Figure 7

The time-averaged wall shear stress over a cardiac cycle for: (a) The optimal geometry for systemic oxygen delivery, J1. (b) The optimal geometry for coronary oxygen delivery, J2. (c) The optimal geometry for combined systemic and coronary oxygen delivery, J3. (d) The standard geometry with a shunt diameter of 3.5 mm (the typical post-BT shunt surgery geometry). The two optimal geometries are optimized for the Dshunt, cot(θAo), rPA(sA), and rBA(sB).

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Figure 8

The pressure-volume loop of the single ventricle for the standard geometries with 3.0-, 3.5-, and 4.0-mm shunt

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Figure 9

Total pressure (1 mmHg = 133.3 Pa) in the shunt for: (a) the optimum geometry for systemic oxygen delivery and (b) optimum geometry for coronary oxygen delivery

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Figure 10

The effect of the shunt-PA anastomosis angle on the flow streamlines. For J1 and J3, due to the slight out-of-plane angle, there are helical streamlines, while for the U4 anatomy, the shunt is perpendicular to the PA and there is a rapid change in the flow direction.

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Figure 11

Time-averaged pressure contours of the J2 and J1 geometries. Pressure time variation of outlets are plotted in mmHg (1 mmHg = 133.3 Pa). The solid line in these plots corresponds to the systemic oxygen delivery optimum geometry (right), and the dashed line corresponds to the coronary oxygen delivery optimum geometry (left).

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Figure 12

Volume-rendered time-averaged velocity magnitude of the two optimum geometries. Flow rate variations of each output are plotted in cm3/s. The solid line in these plots corresponds to the systemic oxygen delivery optimum geometry (right), and the dashed line corresponds to the coronary oxygen delivery optimum geometry (left).



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