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Research Papers

Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

[+] Author and Article Information
Sajjad Seyedsalehi

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824-1226

Liangliang Zhang

Department of Statistics and Probability,
Michigan State University,
East Lansing, MI 48824-1027

Jongeun Choi

Department of Mechanical Engineering,
Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824-1226

Seungik Baek

Department of Mechanical Engineering,
Michigan State University,
2457 Engineering Building,
East Lansing, MI 48824-1226
e-mail: sbaek@egr.msu.edu

1Corresponding author.

Manuscript received January 7, 2015; final manuscript received July 6, 2015; published online August 6, 2015. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 137(10), 101001 (Aug 06, 2015) (13 pages) Paper No: BIO-15-1007; doi: 10.1115/1.4031116 History: Received January 07, 2015

For the accurate prediction of the vascular disease progression, there is a crucial need for developing a systematic tool aimed toward patient-specific modeling. Considering the interpatient variations, a prior distribution of model parameters has a strong influence on computational results for arterial mechanics. One crucial step toward patient-specific computational modeling is to identify parameters of prior distributions that reflect existing knowledge. In this paper, we present a new systematic method to estimate the prior distribution for the parameters of a constrained mixture model using previous biaxial tests of healthy abdominal aortas (AAs). We investigate the correlation between the estimated parameters for each constituent and the patient's age and gender; however, the results indicate that the parameters are correlated with age only. The parameters are classified into two groups: Group-I in which the parameters ce, ck1, ck2, cm2,Ghc,andϕe are correlated with age, and Group-II in which the parameters cm1, Ghm, G1e, G2e,andα are not correlated with age. For the parameters in Group-I, we used regression associated with age via linear or inverse relations, in which their prior distributions provide conditional distributions with confidence intervals. For Group-II, the parameter estimated values were subjected to multiple transformations and chosen if the transformed data had a better fit to the normal distribution than the original. This information improves the prior distribution of a subject-specific model by specifying parameters that are correlated with age and their transformed distributions. Therefore, this study is a necessary first step in our group's approach toward a Bayesian calibration of an aortic model. The results from this study will be used as the prior information necessary for the initialization of Bayesian calibration of a computational model for future applications.

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References

Figures

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Fig. 1

Different configurations of the cut specimen and constituents of the aorta

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Fig. 2

Schematic drawing of Bayesian calibration of a G&R model. P(θ| age, gender), P(X|θ, age, gender), and P(θ|X, age, gender) denote the conditional joint (prior) distribution, likelihood function, and posterior distribution of the model parameters, respectively.

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Fig. 3

Flow chart illustrating the steps involved in the construction of the prior distribution

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Fig. 4

Stress–stretch curves for experimental results (dots) from Vande Geest et al. [40,46], and best-fit constitutive model (lines) for seven biaxial tension controlled protocols with Tzz:Tθθ equal to (i) 0.1:1, (ii) 0.5:1, (iii) 0.75:1, (iv) 1:1, (v) 1:0.75, (vi) 1:0.5, and (vii) 1:0.1. (a) and (b) Nonaneurysmal AA of a 19-year-old male axial and circumferential, respectively. (c) and (d) Nonaneurysmal AA of a 78-year-old female axial and circumferential, respectively.

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Fig. 5

Comparison between simulation results using five different parameter sets, 45, 60, and 75 years, are results of the simulation using parameters reported in Table 6. “Mean” and “Median” are the results of the simulation using the mean and median of estimations for each parameter in Table 2, respectively.

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