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 are correlated with age, and Group-II in which the parameters 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.
Issue Section:
Research Papers
Keywords:
Biomechanics
References
1.
Chien
, S.
, Li
, S.
, and Shyy
, Y. J.
, 1998
, “Effects of Mechanical Forces on Signal Transduction and Gene Expression in Endothelial Cells
,” Hypertension
, 31
(1 Pt 2
), pp. 162
–169
.2.
Guo
, D.-C.
, Papke
, C. L.
, He
, R.
, and Milewicz
, D. M.
, 2006
, “Pathogenesis of Thoracic and Abdominal Aortic Aneurysms
,” Ann. N.Y. Acad. Sci.
, 1085
, pp. 339
–352
.3.
Humphrey
, J. D.
, and Holzapfel
, G. A.
, 2012
, “Mechanics, Mechanobiology, and Modeling of Human Abdominal Aorta and Aneurysms
,” J. Biomech.
, 45
(5
), pp. 805
–814
.4.
Thorne
, B. C.
, Hayenga
, H. N.
, Humphrey
, J. D.
, and Peirce
, S. M.
, 2011
, “Toward a Multi-Scale Computational Model of Arterial Adaptation in Hypertension: Verification of a Multi-Cell Agent Based Model
,” Front. Physiol.
, 2
, p. 20
.5.
Murtada
, S.-I.
, Kroon
, M.
, and Holzapfel
, G. A.
, 2010
, “A Calcium-Driven Mechanochemical Model for Prediction of Force Generation in Smooth Muscle
,” Biomech. Modell. Mechanobiol.
, 9
(6
), pp. 749
–762
.6.
Wilson
, J. S.
, Baek
, S.
, and Humphrey
, J. D.
, 2012
, “Importance of Initial Aortic Properties on the Evolving Regional Anisotropy, Stiffness and Wall Thickness of Human Abdominal Aortic Aneurysms
,” J. R. Soc. Interface R. Soc.
, 9
(74
), pp. 2047
–2058
.7.
Upchurch
, G. R.
, and Schaub
, T. A.
, 2006
, “Abdominal Aortic Aneurysm
,” Am. Fam. Physician
, 73
(7
), pp. 1198
–1204
.8.
Wilmink
, T. B.
, Quick
, C. R.
, Hubbard
, C. S.
, and Day
, N. E.
, 1999
, “The Influence of Screening on the Incidence of Ruptured Abdominal Aortic Aneurysms
,” J. Vasc. Surg.
, 30
(2
), pp. 203
–208
.9.
Assar
, A. N.
, and Zarins
, C. K.
, 2009
, “Ruptured Abdominal Aortic Aneurysm: A Surgical Emergency With Many Clinical Presentations
,” Postgrad. Med. J.
, 85
(1003
), pp. 268
–273
.10.
Pearce
, W. H.
, Zarins
, C. K.
, and Bacharach
, J. M.
, 2008
, “Atherosclerotic Peripheral Vascular Disease Symposium II Controversies in Abdominal Aortic Aneurysm Repair
,” Circulation
, 118
(25
), pp. 2860
–2863
.11.
Zeinali-Davarani
, S.
, Raguin
, L. G.
, Vorp
, D. A.
, and Baek
, S.
, 2011
, “Identification of In Vivo Material and Geometric Parameters of a Human Aorta: Toward Patient-Specific Modeling of Abdominal Aortic Aneurysm
,” Biomech. Modell. Mechanobiol.
, 10
(5
), pp. 689
–699
.12.
Rodríguez
, J. F.
, Ruiz
, C.
, Doblaré
, M.
, and Holzapfel
, G. A.
, 2008
, “Mechanical Stresses in Abdominal Aortic Aneurysms: Influence of Diameter, Asymmetry, and Material Anisotropy
,” ASME J. Biomech. Eng.
, 130
(2
), p. 021023
.13.
Fillinger
, M. F.
, Marra
, S. P.
, Raghavan
, M. L.
, and Kennedy
, F. E.
, 2003
, “Prediction of Rupture Risk in Abdominal Aortic Aneurysm During Observation: Wall Stress Versus Diameter
,” J. Vasc. Surg.
, 37
(4
), pp. 724
–732
.14.
Vande Geest
, J. P.
, Di Martino
, E. S.
, Bohra
, A.
, Makaroun
, M. S.
, and Vorp
, D. A.
, 2006
, “A Biomechanics-Based Rupture Potential Index for Abdominal Aortic Aneurysm Risk Assessment
,” Ann. N.Y. Acad. Sci.
, 1085
(1
), pp. 11
–21
.15.
Fillinger
, M. F.
, Raghavan
, M. L.
, Marra
, S. P.
, Cronenwett
, J. L.
, and Kennedy
, F. E.
, 2002
, “In Vivo Analysis of Mechanical Wall Stress and Abdominal Aortic Aneurysm Rupture Risk
,” J. Vasc. Surg.
, 36
(3
), pp. 589
–597
.16.
Dorfmann
, A.
, Wilson
, C.
, Edgar
, E. S.
, and Peattie
, R. A.
, 2009
, “Evaluating Patient-Specific Abdominal Aortic Aneurysm Wall Stress Based on Flow-Induced Loading
,” Biomech. Modell. Mechanobiol.
, 9
(2
), pp. 127
–139
.17.
Raghavan
, M. L.
, and Vorp
, D. A.
, 2000
, “Toward a Biomechanical Tool to Evaluate Rupture Potential of Abdominal Aortic Aneurysm: Identification of a Finite Strain Constitutive Model and Evaluation of Its Applicability
,” J. Biomech.
, 33
(4
), pp. 475
–482
.18.
Maier
, A.
, Gee
, M. W.
, Reeps
, C.
, Pongratz
, J.
, Eckstein
, H.-H.
, and Wall
, W. A.
, 2010
, “A Comparison of Diameter, Wall Stress, and Rupture Potential Index for Abdominal Aortic Aneurysm Rupture Risk Prediction
,” Ann. Biomed. Eng.
, 38
(10
), pp. 3124
–3134
.19.
Baek
, S.
, Rajagopal
, K. R.
, and Humphrey
, J. D.
, 2006
, “A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms
,” ASME J. Biomech. Eng.
, 128
(1
), pp. 142
–149
.20.
Watton
, P. N.
, Hill
, N. A.
, and Heil
, M.
, 2004
, “A Mathematical Model for the Growth of the Abdominal Aortic Aneurysm
,” Biomech. Modell. Mechanobiol.
, 3
(2
), pp. 98
–113
.21.
Watton
, P. N.
, and Hill
, N. A.
, 2007
, “Evolving Mechanical Properties of a Model of Abdominal Aortic Aneurysm
,” Biomech. Modell. Mechanobiol.
, 8
(1
), pp. 25
–42
.22.
Kroon
, M.
, and Holzapfel
, G. A.
, 2007
, “A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling
,” J. Theor. Biol.
, 247
(4
), pp. 775
–787
.23.
Kroon
, M.
, and Holzapfel
, G. A.
, 2009
, “A Theoretical Model for Fibroblast-Controlled Growth of Saccular Cerebral Aneurysms
,” J. Theor. Biol.
, 257
(1
), pp. 73
–83
.24.
Hariton
, I.
, deBotton
, G.
, Gasser
, T. C.
, and Holzapfel
, G. A.
, 2006
, “Stress-Driven Collagen Fiber Remodeling in Arterial Walls
,” Biomech. Modell. Mechanobiol.
, 6
(3
), pp. 163
–175
.25.
Fung
, Y. C.
, Fronek
, K.
, and Patitucci
, P.
, 1979
, “Pseudoelasticity of Arteries and the Choice of Its Mathematical Expression
,” Am. J. Physiol.
, 237
(5
), pp. H620
–H631
.26.
Takamizawa
, K.
, and Hayashi
, K.
, 1987
, “Strain Energy Density Function and Uniform Strain Hypothesis for Arterial Mechanics
,” J. Biomech.
, 20
(1
), pp. 7
–17
.27.
Holzapfel
, G. A.
, Gasser
, T. C.
, and Ogden
, R. W.
, 2000
, “A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,” J. Elast. Phys. Sci. Solids
, 61
(1–3
), pp. 1
–48
.28.
Holzapfel
, G. A.
, Gasser
, T. C.
, and Ogden
, R. W.
, 2004
, “Comparison of a Multi-Layer Structural Model for Arterial Walls With a Fung-Type Model, and Issues of Material Stability
,” ASME J. Biomech. Eng.
, 126
(2
), pp. 264
–275
.29.
Hu
, J.-J.
, Baek
, S.
, and Humphrey
, J. D.
, 2007
, “Stress–Strain Behavior of the Passive Basilar Artery in Normotension and Hypertension
,” J. Biomech.
, 40
(11
), pp. 2559
–2563
.30.
Wan
, W.
, Dixon
, J. B.
, and Gleason
, R. L.
, Jr., 2012
, “Constitutive Modeling of Mouse Carotid Arteries Using Experimentally Measured Microstructural Parameters
,” Biophys. J.
, 102
(12
), pp. 2916
–2925
.31.
Gasser
, T. C.
, Ogden
, R. W.
, and Holzapfel
, G. A.
, 2006
, “Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations
,” J. R. Soc. Interface
, 3
(6
), pp. 15
–35
.32.
Zeinali-Davarani
, S.
, Choi
, J.
, and Baek
, S.
, 2009
, “On Parameter Estimation for Biaxial Mechanical Behavior of Arteries
,” J. Biomech.
, 42
(4
), pp. 524
–530
.33.
Ferruzzi
, J.
, Vorp
, D. A.
, and Humphrey
, J. D.
, 2011
, “On Constitutive Descriptors of the Biaxial Mechanical Behaviour of Human Abdominal Aorta and Aneurysms
,” J. R. Soc. Interface R. Soc.
, 8
(56
), pp. 435
–450
.34.
Humphrey
, J. D.
, and Rajagopal
, K. R.
, 2002
, “A Constrained Mixture Model for Growth and Remodeling of Soft Tissues
,” Math. Models Methods Appl. Sci.
, 12
(3
), pp. 407
–430
.35.
Valentín
, A.
, and Holzapfel
, G. A.
, 2012
, “Constrained Mixture Models as Tools for Testing Competing Hypotheses in Arterial Biomechanics: A Brief Survey
,” Mech. Res. Commun.
, 42
, pp. 126
–133
.36.
Zeinali-Davarani
, S.
, Sheidaei
, A.
, and Baek
, S.
, 2011
, “A Finite Element Model of Stress-Mediated Vascular Adaptation: Application to Abdominal Aortic Aneurysms
,” Comput. Methods Biomech. Biomed. Eng.
, 14
(9
), pp. 803
–817
.37.
Sheidaei
, A.
, Hunley
, S. C.
, Zeinali-Davarani
, S.
, Raguin
, L. G.
, and Baek
, S.
, 2011
, “Simulation of Abdominal Aortic Aneurysm Growth With Updating Hemodynamic Loads Using a Realistic Geometry
,” Med. Eng. Phys.
, 33
(1
), pp. 80
–88
.38.
Martufi
, G.
, and Gasser
, T. C.
, 2012
, “Turnover of Fibrillar Collagen in Soft Biological Tissue With Application to the Expansion of Abdominal Aortic Aneurysms
,” J. R. Soc. Interface R. Soc.
, 9
(77
), pp. 3366
–3377
.39.
Geest
, J. P. V.
, Sacks
, M. S.
, and Vorp
, D. A.
, 2005
, “Age Dependency of the Biaxial Biomechanical Behavior of Human Abdominal Aorta
,” ASME J. Biomech. Eng.
, 126
(6
), pp. 815
–822
.40.
Roccabianca
, S.
, Figueroa
, C. A.
, Tellides
, G.
, and Humphrey
, J. D.
, 2014
, “Quantification of Regional Differences in Aortic Stiffness in the Aging Human
,” J. Mech. Behav. Biomed. Mater.
, 29
, pp. 618
–634
.41.
Baek
, S.
, Valentín
, A.
, and Humphrey
, J. D.
, 2007
, “Biochemomechanics of Cerebral Vasospasm and Its Resolution: II. Constitutive Relations and Model Simulations
,” Ann. Biomed. Eng.
, 35
(9
), pp. 1498
–1509
.42.
Burton
, A. C.
, 1954
, “Relation of Structure to Function of the Tissues of the Wall of Blood Vessels
,” Physiol. Rev.
, 34
(4
), pp. 619
–642
.43.
Vande Geest
, J. P.
, Sacks
, M. S.
, and Vorp
, D. A.
, 2006
, “The Effects of Aneurysm on the Biaxial Mechanical Behavior of Human Abdominal Aorta
,” J. Biomech.
, 39
(7
), pp. 1324
–1334
.44.
Zeinali-Davarani
, S.
, Raguin
, L. G.
, and Baek
, S.
, 2011
, “An Inverse Optimization Approach Toward Testing Different Hypotheses of Vascular Homeostasis Using Image-Based Models
,” Int. J. Struct. Change Solids
, 3
(2
), pp. 33
–45
.45.
Kennedy
, M. C.
, and O'Hagan
, A.
, 2001
, “Bayesian Calibration of Computer Models
,” J. R. Stat. Soc. Ser. B Stat. Methodol.
, 63
(3
), pp. 425
–464
.46.
Osborne
, C.
, “Statistical Calibration: A Review
,” Int. Stat. Rev.
, 59
(3
), pp. 309
–336
.47.
Reeps
, C.
, Maier
, A.
, Pelisek
, J.
, Härtl
, F.
, Grabher-Meier
, V.
, Wall
, W. A.
, Essler
, M.
, Eckstein
, H.-H.
, and Gee
, M. W.
, 2012
, “Measuring and Modeling Patient-Specific Distributions of Material Properties in Abdominal Aortic Aneurysm Wall
,” Biomech. Modell. Mechanobiol.
, 12
(4
), pp. 717
–733
.48.
Enevoldsen
, M. S.
, Henneberg
, K.-A.
, Jensen
, J. A.
, Lönn
, L.
, and Humphrey
, J. D.
, 2011
, “New Interpretation of Arterial Stiffening Due to Cigarette Smoking Using a Structurally Motivated Constitutive Model
,” J. Biomech.
, 44
(6
), pp. 1209
–1211
.49.
Forsell
, C.
, Swedenborg
, J.
, Roy
, J.
, and Gasser
, T. C.
, 2013
, “The Quasi-Static Failure Properties of the Abdominal Aortic Aneurysm Wall Estimated by a Mixed Experimental–Numerical Approach
,” Ann. Biomed. Eng.
, 41
(7
), pp. 1554
–1566
.50.
Sakia
, R. M.
, 1992
, “The Box–Cox Transformation Technique: A Review
,” J. R. Stat. Soc. Ser. Stat.
, 41
(2
), pp. 169
–178
.51.
Johnson
, R. A.
, and Wichern
, D. W.
, 2007
, Applied Multivariate Statistical Analysis, 6/E
, Pearson Education, New York. 52.
Sawabe
, M.
, 2010
, “Vascular Aging: From Molecular Mechanism to Clinical Significance
,” Geriatr. Gerontol. Int.
, 10
(Suppl 1
), pp. S213
–S220
.53.
Greenwald
, S. E.
, 2007
, “Ageing of the Conduit Arteries
,” J. Pathol.
, 211
(2
), pp. 157
–172
.54.
Spina
, M.
, Garbisa
, S.
, Hinnie
, J.
, Hunter
, J. C.
, and Serafini-Fracassini
, A.
, 1983
, “Age-Related Changes in Composition and Mechanical Properties of the Tunica Media of the Upper Thoracic Human Aorta
,” Arteriosclerosis
, 3
(1
), pp. 64
–76
.55.
Rizzo
, R. J.
, McCarthy
, W. J.
, Dixit
, S. N.
, Lilly
, M. P.
, Shively
, V. P.
, Flinn
, W. R.
, and Yao
, J. S.
, 1989
, “Collagen Types and Matrix Protein Content in Human Abdominal Aortic Aneurysms
,” J. Vasc. Surg.
, 10
(4
), pp. 365
–373
.56.
He
, C. M.
, and Roach
, M. R.
, 1994
, “The Composition and Mechanical Properties of Abdominal Aortic Aneurysms
,” J. Vasc. Surg.
, 20
(1
), pp. 6
–13
.57.
O'Leary
, S. A.
, Healey
, D. A.
, Kavanagh
, E. G.
, Walsh
, M. T.
, McGloughlin
, T. M.
, and Doyle
, B. J.
, 2014
, “The Biaxial Biomechanical Behavior of Abdominal Aortic Aneurysm Tissue
,” Ann. Biomed. Eng.
, 42
(12
), pp. 2440
–2450
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