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Mechanics of growth and rupture of abdominal aortic aneurysm

Konstantin Volokh's picture

We present 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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Teng Li's picture

Kosta,

Very neat model! I quickly went through your paper and found it interesting.

Zhigang talked about the inflation of a balloon (or bursting of an aneurysm) in his Solid Mechanics course. I also gave the students a similiar example when I taught Continuum Mechanics.  It's nice to see the latest progress on this topic.  Thank you for sharing your publication.

Konstantin Volokh's picture

Dear Teng,

Thanks for your kind remarks!

The topic itself is of great practical importance because surgeons do not have reliable and rational criteria for predicting the aneurysm development and possible rupture. There exist only empirical criteria based on the previous experience...

Hopefully, the visitors of iMechanica will be able to contribute to the subject!

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