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Research Papers

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

[+] Author and Article Information
Abhay B. Ramachandra

Department of Mechanical and
Aerospace Engineering,
University of California San Diego,
9500 Gilman Drive,
La Jolla, CA 92093

Sethuraman Sankaran

Senior Computational Scientist HeartFlow, Inc.,
1400 Seaport Blvd., Building B,
Redwood City, CA 94063

Jay D. Humphrey

Department of Biomedical Engineering,
Yale University,
55 Prospect Street,
New Haven, CT 06520

Alison L. Marsden

Department of Mechanical
and Aerospace Engineering,
University of California San Diego,
9500 Gilman Drive,
La Jolla, CA 92093
e-mail: amarsden@ucsd.edu

1Corresponding author.

Manuscript received March 21, 2014; final manuscript received October 17, 2014; published online January 29, 2015. Assoc. Editor: Kristen Billiar.

J Biomech Eng 137(3), 031009 (Mar 01, 2015) (10 pages) Paper No: BIO-14-1128; doi: 10.1115/1.4029021 History: Received March 21, 2014; Revised October 17, 2014; Online January 29, 2015

Vein maladaptation, leading to poor long-term patency, is a serious clinical problem in patients receiving coronary artery bypass grafts (CABGs) or undergoing related clinical procedures that subject veins to elevated blood flow and pressure. We propose a computational model of venous adaptation to altered pressure based on a constrained mixture theory of growth and remodeling (G&R). We identify constitutive parameters that optimally match biaxial data from a mouse vena cava, then numerically subject the vein to altered pressure conditions and quantify the extent of adaptation for a biologically reasonable set of bounds for G&R parameters. We identify conditions under which a vein graft can adapt optimally and explore physiological constraints that lead to maladaptation. Finally, we test the hypothesis that a gradual, rather than a step, change in pressure will reduce maladaptation. Optimization is used to accelerate parameter identification and numerically evaluate hypotheses of vein remodeling.

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Figures

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Fig. 1

Schema of a G&R framework illustrating the configurations of a vessel (i.e., constrained mixture) and its constituents at instant s = 0, without hemodynamic perturbations, and at G&R time s, with hemodynamic perturbation. The G&R framework enforces mechanical equilibrium at each instant while accounting for the evolving constituent mass fractions, natural configurations, and strain energy densities as the constituents turn over.

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Fig. 3

Flowchart of the SMF used for identifying the optimal parameter set for vein G&R

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Fig. 4

Biaxial stress–stretch data (dashed lines) for a mouse vena cava and the associated best-fits achieved in the parameter estimation: (a) σθ − λθ, (b) σz − λθ

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Fig. 5

Summary of (a) radius and (b) thickness evolution with time for numerical experiment 3 for case 2: K1k & K2k≤20 and Ghm≤1.8. The radius curves are within a 10% deviation. The arrows indicate the thickness for an ideal adaptation. Thickness curves exhibit a larger deviation from an ideal adaptation for a larger pressure.

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Fig. 6

Comparison of cost functions (Jadapt) for a step change in load with pγmod, a gradual change in load pγmod, and the optimized values from numerical experiment 3. All values reported are for case 2: K1k and K2k≤20 and Ghm≤1.8. Adaptation for a gradual change in load with pγmod is comparable to the best possible adaptation a vein can achieve.

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