Parameterization of the shape of intracranial saccular aneurysms using Legendre polynomials

Abstract

Our recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that these lesions enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and biomechanical analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, a pressing need to quantify regional multiaxial wall stresses which, because of the membrane-like behavior of many aneurysms, necessitates better information on the applied loads and regional surface curvatures. Herein, we present and illustrate a method whereby regional curvatures can be estimated easily for sub-classes of human aneurysms based on clinically available data from magnetic resonance angiography (MRA). Whereas Legendre polynomials are used to illustrate this approach, different functions may prove useful for different sub-classes of lesions.

Keywords:

• Intracranial saccular aneurysms
• Legendre polynomials
• Biosolid mechanics
• Rupture-potential

Acknowledgements

This research was supported, in part, by a grant from the NIH (R01 HL-54957).

Notes

§Present address: Advanced MRI Technologies, Sebastopol, CA.

¶Present address: Texas Tech University School of Medicine, Lubbock, TX.

¶Present address: Texas Tech University School of Medicine, Lubbock, TX.

Additional information

Notes on contributors

J. D. Humphrey

§Present address: Advanced MRI Technologies, Sebastopol, CA. ¶Present address: Texas Tech University School of Medicine, Lubbock, TX.