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Research Papers

Using In Vivo Cine and 3D Multi-Contrast MRI to Determine Human Atherosclerotic Carotid Artery Material Properties and Circumferential Shrinkage Rate and Their Impact on Stress/Strain Predictions

[+] Author and Article Information
Haofei Liu

Mathematical Sciences Department,  Worcester Polytechnic Institute, Worcester, MA 01609

Gador Canton, Chun Yuan

Department of Radiology,  University of Washington, Seattle, WA 98195

Chun Yang

Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609;School of Mathematics,  Beijing Normal University, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, China

Kristen Billiar

Department of Biomedical Engineering,  Worcester Polytechnic Institute, Worcester, MA 01609

Zhongzhao Teng

Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609;University Department of Radiology,  University of Cambridge, Cambridge, UK

Allen H. Hoffman

Department of Mechanical Engineering,  Worcester Polytechnic Institute, Worcester, MA 01609

Dalin Tang1

Mathematical Sciences Department,  Worcester Polytechnic Institute, Worcester, MA 01609dtang@wpi.edu

1

Corresponding author.

J Biomech Eng 134(1), 011008 (Feb 09, 2012) (9 pages) doi:10.1115/1.4005685 History: Received July 14, 2011; Revised January 03, 2012; Posted January 24, 2012; Published February 08, 2012; Online February 09, 2012

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young’s modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young’s modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) 3D geometry of a human carotid plaque sample reconstructed from MRI, (b) stacked contours, (c) selected slice from 3D MRI, Cine with maximum and minimum lumen, and Adina model output corresponding to maximum and minimum pressure

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Figure 2

Stress-stretch plot of uniaxial test of a circumferential strip sample from a human carotid artery. The red curve is from the Mooney-Rivlin model fitting experimental data. The green straight line is from the linear model fitting the experimental data. Parameter values of the Mooney-Rivlin model and linear model fitting the experimental data are: c1  = 94.6 kPa, D1  = 6.81 kPa, c2  = 0, D2  = 2.0, YM = 570 kPa.

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Figure 3

The iterative procedure to determine material parameters and vessel shrinkage rate

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Figure 4

Stress-stretch curves from Mooney-Rivlin models using parameter values determined from Cine MRI for the 12 patients studied

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Figure 5

Plots of plaque stress distributions showing the effect of material stiffness on stress predictions

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Figure 6

Plots of plaque strain distributions showing that the material stiffness has much greater impact on strain predictions. Predicted maximum strain values for softer materials were 200–700% higher than those from the stiff material. Uniform color scales were applied for (b)–(d) and (f)–(h), respectively.

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Figure 7

Plots of plaque stress (Stress-P1 ) from models without preshrinkage gave inflated plaque stress predictions. Uniform color scales were applied for (b)–(d) and (f)–(h), respectively.

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Figure 8

Plots of plaque strain (Strain-P1 ) from models without preshrinkage gave inflated plaque strain predictions. Uniform color scales were applied for (b)–(d) and (f)–(h), respectively.

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