Research Papers

A Thick-Walled Fluid–Solid-Growth Model of Abdominal Aortic Aneurysm Evolution: Application to a Patient-Specific Geometry

[+] Author and Article Information
Andrii Grytsan

Department of Solid Mechanics,
Royal Institute of Technology (KTH),
Teknikringen 8d,
Stockholm 10044, Sweden

Paul N. Watton

Department of Computer Science,
University of Sheffield,
Sheffield, UK
INSIGNEO Institute of In Silico Medicine,
University of Sheffield,
Sheffield, UK

Gerhard A. Holzapfel

Institute of Biomechanics,
Graz University of Technology,
Kronesgasse 5-I,
Graz 8010, Austria
e-mail: holzapfel@tugraz.at

1Corresponding author.

Manuscript received March 20, 2014; final manuscript received December 1, 2014; published online January 29, 2015. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 137(3), 031008 (Mar 01, 2015) (10 pages) Paper No: BIO-14-1124; doi: 10.1115/1.4029279 History: Received March 20, 2014; Revised December 01, 2014; Online January 29, 2015

We propose a novel thick-walled fluid–solid-growth (FSG) computational framework for modeling vascular disease evolution. The arterial wall is modeled as a thick-walled nonlinearly elastic cylindrical tube consisting of two layers corresponding to the media-intima and adventitia, where each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component. Blood is modeled as a Newtonian fluid with constant density and viscosity; no slip and no-flux conditions are applied at the arterial wall. Disease progression is simulated by growth and remodeling (G&R) of the load bearing constituents of the wall. Adaptions of the natural reference configurations and mass densities of constituents are driven by deviations of mechanical stimuli from homeostatic levels. We apply the novel framework to model abdominal aortic aneurysm (AAA) evolution. Elastin degradation is initially prescribed to create a perturbation to the geometry which results in a local decrease in wall shear stress (WSS). Subsequent degradation of elastin is driven by low WSS and an aneurysm evolves as the elastin degrades and the collagen adapts. The influence of transmural G&R of constituents on the aneurysm development is analyzed. We observe that elastin and collagen strains evolve to be transmurally heterogeneous and this may facilitate the development of tortuosity. This multiphysics framework provides the basis for exploring the influence of transmural metabolic activity on the progression of vascular disease.

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Chen, C.-K., Chang, H.-T., Chen, Y.-C., Chen, T.-J., Chen, I.-M., and Shih, C.-C., 2013, “Surgeon Elective Abdominal Aortic Aneurysm Repair Volume and Outcomes of Ruptured Abdominal Aortic Aneurysm Repair: A 12-Year Nationwide Study,” World J. Surg., 37(10), pp. 2360–2371. [CrossRef] [PubMed]
Greenhalgh, R. M., Brown, L. C., Powell, J. T., Thompson, S. G., Epstein, D., Sculpher, M. J., and United Kingdom EVAR Trial Investigators, 2010, “Endovascular Versus Open Repair of Abdominal Aortic Aneurysm,” N. Engl. J. Med., 362(20), pp. 1863–1871. [CrossRef] [PubMed]
Holzapfel, G. A., and Ogden, R. W., 2010, “Constitutive Modelling of Arteries,” Proc. R. Soc. London Ser. A, 466(2118), pp. 1551–1597. [CrossRef]
Watton, P. N., Hill, N. A., and Heil, M., 2004, “A Mathematical Model for the Growth of the Abdominal Aortic Aneurysm,” Biomech. Model. Mechanobiol., 3(2), pp. 98–113. [CrossRef] [PubMed]
Holzapfel, G. A., 2000, Nonlinear Solid Mechanics. A Continuum Approach for Engineering, Wiley, Chichester, UK.
Schmid, H., Watton, P. N., Maurer, M. M., Wimmer, J., Winkler, P., Wang, Y. K., Röhrle, O., and Itskov, M., 2010, “Impact of Transmural Heterogeneities on Arterial Adaptation: Application to Aneurysm Formation,” Biomech. Model. Mechanobiol., 9(3), pp. 295–315. [CrossRef] [PubMed]
Schmid, H., Grytsan, A., Poshtan, E., Watton, P. N., and Itskov, M., 2013, “Influence of Differing Material Properties in Media and Adventitia on Arterial Adaptation—Application to Aneurysm Formation and Rupture,” Comput. Methods Biomech. Biomed. Eng., 16(1), pp. 33–53. [CrossRef]
Eriksson, T., Watton, P. N., Luo, X. Y., and Ventikos, Y., 2014, “Modelling Volumetric Growth in a Thick-Walled Fibre Composite,” J. Mech. Phys. Solids, 73, pp. 134–150. [CrossRef]
Valentín, A., Humphrey, J. D., and Holzapfel, G. A., 2013, “A Finite Element Based Constrained Mixture Implementation for Arterial Growth, Remodeling, and Adaptation: Theory and Numerical Verification,” Int. J. Numer. Method Biomed. Eng., 29(8), pp. 822–849. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Dua, M. M., and Dalman, R. L., 2010, “Hemodynamic Influences on Abdominal Aortic Aneurysm Disease: Application of Biomechanics to Aneurysm Pathophysiology,” Vasc. Pharmacol., 53(1–2), pp. 11–21. [CrossRef]
Humphrey, J. D., and Taylor, C. A., 2008, “Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models,” Annu. Rev. Biomed. Eng., 10(1), pp. 221–246. [CrossRef] [PubMed]
Figueroa, C. A., Baek, S., Taylor, C. A., and Humphrey, J. D., 2009, “A Computational Framework for Fluid–Solid-Growth Modeling in Cardiovascular Simulations,” Comput. Methods Appl. Mech. Eng., 198(45–46), pp. 3583–3602. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Watton, P. N., Raberger, N. B., Holzapfel, G. A., and Ventikos, Y., 2009, “Coupling the Haemodynamic Environment to the Growth of Cerebral Aneurysms: Computational Framework and Numerical Examples,” ASME J. Biomech. Eng., 131(10), p. 101003. [CrossRef]
Watton, P. N., Selimovic, A., Raberger, N. B., Huang, P., Holzapfel, G. A., and Ventikos, Y., 2011, “Modelling Evolution and the Evolving Mechanical Environment of Saccular Cerebral Aneurysms,” Biomech. Model. Mechanobiol., 10(1), pp. 109–132. [CrossRef] [PubMed]
Aparicio, P., Mandaltsi, A., Boamah, J., Chen, H., Selimovic, A., Bratby, M., Uberoi, R., Ventikos, Y., and Watton, P. N., 2014, “Modelling the Influence of Endothelial Heterogeneity on the Progression of Arterial Disease: Application to Abdominal Aortic Aneurysm Evolution,” Int. J. Numer. Method Biomed. Eng., 30(5), pp. 563–586. [CrossRef] [PubMed]
Watton, P. N., Ventikos, Y., and Holzapfel, G. A., 2009, “Modelling the Mechanical Response of Elastin for Arterial Tissue,” J. Biomech., 42(9), pp. 1320–1325. [CrossRef] [PubMed]
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. Elasticity, 61(1–3), pp. 1–48. [CrossRef]
Watton, P. N., Ventikos, Y., and Holzapfel, G. A., 2009, “Modelling the Growth and Stabilisation of Cerebral Aneurysms,” Math. Med. Biol., 26(2), pp. 133–164. [CrossRef] [PubMed]
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
Ferziger, J. H., and Perić, M., 2002, Computational Methods for Fluid Dynamics, 3rd ed., Springer, New York. [CrossRef]
Tong, J., Cohnert, T., Regitnig, P., Kohlbacher, J., Birner-Gruenberger, R., Schriefl, A. J., Sommer, G., and Holzapfel, G. A., 2014, “Variations of Dissection Properties and Mass Fractions With Thrombus Age in Human Abdominal Aortic Aneurysms,” J. Biomech., 47(1), pp. 14–23. [CrossRef] [PubMed]
“Official Website of CMISS Solver,” www.cmiss.org
Holzapfel, G. A., Sommer, G., Auer, M., Regitnig, P., and Ogden, R. W., 2007, “Layer-Specific 3D Residual Deformations of Human Aortas With Non-Atherosclerotic Intimal Thickening,” Ann. Biomed. Eng., 35(4), pp. 530–545. [CrossRef] [PubMed]
Martin Rodriguez, Z., Kenny, P., and Gaynor, L., 2011, “Improved Characterisation of Aortic Tortuosity,” Med. Eng. Phys., 33(6), pp. 712–719. [CrossRef] [PubMed]
Pappu, S., Dardik, A., Tagare, H., and Gusberg, R. J., 2007, “Beyond Fusiform and Saccular: A Novel Quantitative Tortuosity Index May Help Classify Aneurysm Shape and Predict Aneurysm Rupture Potential,” Ann. Vasc. Surg., 22(1), pp. 88–97. [CrossRef] [PubMed]


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Fig. 1

Patient-specific attachments to the artery model and prescribed boundary conditions: (a) upstream section, inlet with flow rate boundary condition shown aside, outlets with corresponding pressure boundary conditions; (b) downstream section, outlets with corresponding pressure boundary conditions.

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Fig. 2

Cross section of the initial configuration of an artery: complete cross section (left), half (right)

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Fig. 3

Evolution of the WSS distribution τ during FSG

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Fig. 5

Solid model mesh before (left) and after FSG (right) in a cylindrical coordinate system. Locations A1, A2, A3, A4 are shown, at which the transmural distribution of the quantities are analyzed.

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Fig. 4

Evolution of the normalized elastin degradation FD (a), and the normalized elastin density fe (b) in the aneurysm region

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Fig. 10

Distribution of the modified GL strain E¯c of collagen after 11.5 years of FSG using β = 1.4

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Fig. 8

Evolution of the transmural profiles of the modified Green–Lagange strain E¯c of collagen over time t at (a) the posterior (b) the anterior aneurysm wall at z = L/2; (c) the distal and (d) the proximal aneurysm neck at the proximal aneurysm wall. Plots are shown for a time lag ϑ = 0 and 2.

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Fig. 6

Evolution of the transmural profiles of the normalized elastin density fe over time t at (a) the posterior and (b) the anterior aneurysm wall at z = L/2; (c) the posterior distal and (d) the proximal aneurysm neck. Plots are shown for a time lag ϑ = 0 and 2.

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Fig. 7

Evolution of the transmural profiles of the circumferential modified Green–Lagrange strain E¯e of elastin over time t at (a) the posterior (b) the anterior aneurysm wall at z = L/2; (c) the posterior distal and (d) the proximal aneurysm neck. Plots are shown for a time lag ϑ = 0 and 2.

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Fig. 9

Evolution of the transmural profiles of the normalized collagen density fc over time t at (a) the posterior and (b) the anterior aneurysm wall at z = L/2; (c) the posterior distal and (d) the proximal aneurysm neck. Plots are shown for a time lag ϑ = 0 and 2.



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