We present here a coupled mathematical model of growth and failure of the abdominal aortic aneurysm (AAA). The failure portion of the model is based on the constitutive theory of softening hyperelasticity where the classical hyperelastic law is enhanced with a new constant indicating the maximum energy that an infinitesimal material volume can accumulate without failure. The new constant controls material failure and it can be interpreted as the average energy of molecular bonds from the microstructural standpoint. The constitutive model is compared to the data from uniaxial tension tests providing an excellent fit to the experiment. The AAA failure model is coupled with a phenomenological theory of soft tissue growth. The unified theory includes both momentum and mass balance laws coupled with the help of the constitutive equations. The microstructural alterations in the production of elastin and remodeling of collagen are reflected in the changing macroscopic parameters characterizing tissue stiffness, strength and density. The coupled theory is used to simulate growth and rupture of an idealized spherical AAA. The results of the simulation showing possible AAA ruptures in growth are reasonable qualitatively while the quantitative calibration of the model will require further clinical observations and in-vitro tests. The presented model is the first where growth and rupture are coupled.
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ASME 2009 Summer Bioengineering Conference
June 17–21, 2009
Lake Tahoe, California, USA
Conference Sponsors:
- Bioengineering Division
ISBN:
978-0-7918-4891-3
PROCEEDINGS PAPER
Theory of Growth and Rupture of Abdominal Aortic Aneurysm
Konstantin Y. Volokh,
Konstantin Y. Volokh
Technion - Israel Institute of Technology, Haifa, Israel
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David A. Vorp
David A. Vorp
University of Pittsburgh, Pittsburgh, PA
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Konstantin Y. Volokh
Technion - Israel Institute of Technology, Haifa, Israel
David A. Vorp
University of Pittsburgh, Pittsburgh, PA
Paper No:
SBC2009-203540, pp. 1295-1296; 2 pages
Published Online:
July 19, 2013
Citation
Volokh, KY, & Vorp, DA. "Theory of Growth and Rupture of Abdominal Aortic Aneurysm." Proceedings of the ASME 2009 Summer Bioengineering Conference. ASME 2009 Summer Bioengineering Conference, Parts A and B. Lake Tahoe, California, USA. June 17–21, 2009. pp. 1295-1296. ASME. https://doi.org/10.1115/SBC2009-203540
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