Currently, size is used as the predetermining factor to judge whether a saccular aneurysm is likely to rupture. Recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that they enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and finite element analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, an even greater need to quantify regional multiaxial wall stresses, which because of the membrane-like behavior of aneurysms implicates the need for better data on regional surface curvatures. By using a convenient function, such as a Legendre polynomial, a quick, accurate approximation can be made for the size and shape of a saccular aneurysm that allows for stress analysis that surgeons can use to determine if the risk of rupture warrants the risk of treatment.

We introduce the notion of special spherical symmetry and classify the complete regular minimal surfaces in the three sphere having this symmetry. We also show that the Clifford torus is the unique embedded minimal torus in three sphere possessing special spherical symmetry.

Currently, size is used as the predetermining factor to judge whether a saccular aneurysm is likely to rupture. Recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that they enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and finite element analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, an even greater need to quantify regional multiaxial wall stresses, which because of the membrane-like behavior of aneurysms implicates the need for better data on regional surface curvatures. By using a convenient function, such as a Legendre polynomial, a quick, accurate approximation can be made for the size and shape of a saccular aneurysm that allows for stress analysis that surgeons can use to determine if the risk of rupture warrants the risk of treatment.

Thesis (doctoral)--Friedrich-Wilhelms-Universität Berlin, 1853. / Vita.

Thesis (doctoral)--Westfälische Wilhelms-Universität zu Münster, 1911. / Vita.

Inaug.-diss.-Münster i. W. / Lebenslauf.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.

Thesis (M.S.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 56).

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