### Monday, 11 October 2004 - 10:55 AM

### This presentation is part of : Rajagopal Symposium

### Orthotropic modeling of arbitrarily shaped arterial structures: choosing material fiber directions

**Madhavan L. Raghavan**, Baoshun Ma, M.S, and Jia Lu, Ph.D. University of Iowa, 1422 Seamans Center, Iowa City, IA 52242
Orthotropic strain energy density functions have been proposed and evaluated for normal cylindrical arteries by many researchers under the premise that load-bearing fibers are mainly oriented along longitudinal and circumferential directions. However, no such preferential direction exists for regions of arterial bifurcations or for arbitrarily shaped lesions such as aneurysms. We propose that the principal curvature directions are likely the judicious choice for material fiber directions for arbitrarily shaped thin-walled surfaces. Using cerebral aneurysms – outpouching of an artery in the brain usually at a bifurcation – as an example, we have used differential geometry techniques to compute the distribution of principal curvature directions. The patient-specific aneurysm surface contained convex (mean curvature, M > 0; Gaussian curvature, G > 0), saddle-shaped (G<0), and on rare occasions, concave (M<0; G>0) regions. Of the two principal curvature directions, we assumed that the stiffer material fiber will align with the one that is more likely maximum tensile principal stress direction. Thus, for each material point on the surface, the stiffer material fiber direction was assigned to the principal direction where the principal curvature was closer to zero when G>0 or larger (more positive) when G<=0. The methodology was utilized in stress analysis on hypothetical and patient-specific aneurysm models where anisotropic material properties were prescribed.

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