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Research Papers

Constitutive Modeling of Coronary Arterial Media—Comparison of Three Model Classes

[+] Author and Article Information
Yaniv Hollander, David Durban

Faculty of Aerospace Engineering,  Technion–Israel Institute of Technology, Haifa 3200, Israel

Xiao Lu, Ghassan S. Kassab

Department of Biomedical Engineering Surgery, Cellular and Integrative Physiology,  IN University Purdue University at Indianapolis, Indianapolis, IN 46202

Yoram Lanir1

Faculty of Biomedical Engineering,  Technion–Israel Institute of Technology, Haifa 3200, Israelyoramlanir@yahoo.com

1

Corresponding author.

J Biomech Eng 133(6), 061008 (Jul 05, 2011) (12 pages) doi:10.1115/1.4004249 History: Received December 14, 2010; Revised May 13, 2011; Posted May 17, 2011; Published July 05, 2011; Online July 05, 2011

Accurate modeling of arterial elasticity is imperative for predicting pulsatile blood flow and transport to the periphery, and for evaluating the mechanical microenvironment of the vessel wall. The goal of the present study is to compare a recently developed structural model of porcine left anterior descending artery media to two commonly used typical representatives of phenomenological and structure-motivated invariant-based models, in terms of the number of model parameters, model descriptive and predictive powers, and requisite different test protocols for reliable parameter estimation. The three models were compared against 3D data of radial inflation, axial extension, and twist tests. Also checked are the models predictive capabilities to response data not used for estimation, including both tests outside the range of estimation database, as well as protocols of a different nature. The results show that the descriptive estimation error (model fit to estimation database), measured by the sum of squared residuals (SSE) between full 3D data and model predictions, was about twice as low for the structural (4.58%) model compared to the other two (9.71 and 8.99% for the phenomenological and structure-motivated models, respectively). Similar SSE ratios were obtained for the predictive capabilities. Prediction SSE at high stretch based on estimation of two low stretches yielded an SSE value of 2.81% for the structural model, and 10.54% and 7.87% for the phenomenological and structure-motivated models, respectively. For the prediction of twist from inflation-extension data, SSE values for the torsional stiffness was 1.76% for the structural model and 39.62 and 2.77% for the phenomenological and structure-motivated models. The required number of model parameters for the structural model is four, whereas the phenomenological model requires six to nine and the structure-motivated has four parameters. These results suggest that modeling based on the tissue structural features improves model reliability in describing given data and in predicting the tissue general response.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 7

Structural model (4) stretch predictive power (sample No. 1). Predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under 3 axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

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Figure 8

2D-to-3D predictive power (sample No. 1). Comparison between predicted twist apparent stiffness (lines) and measured data (symbols) at three axial stretch ratios (λ) 1.2 (○), 1.3 (□), and 1.4 (+) for (a) the invariant-based and (b) the structural models.

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Figure 1

Planar schematics of vessel mappings. Left: In the true reference state the vessel is open, unswollen, and stress-free (SF) with inner and outer radii, Ri and Ro, length L, and an opening angle Θ0. In the swollen state (SW) it is open but not stress free, with corresponding dimensions R̂i, R̂o, Λ0L, with Λ0 as the SF-SW transformation stretch ratio, and an opening angle Θ1. The closed unloaded (UL) configuration is not subjected to further swelling, and with dimensions ρi, ρo, and Λ0Λ1L, with Λ1 as the SW-UL stretch ratio. The closed loaded (L) configuration has dimensions: inner and outer radii ri and ro, length λΛ0Λ1L, with λ as the UL-L stretch ratio, and twist per unit length γ (not shown in figure). Right: Force and bending moment resultants of circumferential stress acting on the swollen open sector free edges; both vanish, yielding a boundary constraint on the circumferential stress distribution.

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Figure 2

Fung-type phenomenological model (1) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

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Figure 3

Structure-motivated Invariant-based model (2) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

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Figure 4

Fully structural model (4) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

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Figure 5

Fung-type model (1) stretch predictive power (sample No. 1): predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

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Figure 6

Invariant-based model (2) stretch predictive power (sample No. 1). Predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

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