A Mathematical Analysis of Cylindrical Shaped Aneurysms

Kwembe, Tor A.; Jones, Shatondria N.

doi:10.1142/9789812773685_0003

Cited by 2 publications

(3 citation statements)

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“…APPENDIX: THE STANDARD EXPRESSIONS FOR P 0 (z,t) AND P 1 (z,t) P 0 (z,t) = (t)e 4 z + (t)3 4 z + P e P 1 (z,t) = (t)e 4 z + (t)3 4 (g 3 (t)e 8 + g 4 (t)e 8 ) e 4 48 (g 3 (t) + g 4 (t)) g 5 (t)…”

Section: Acknowledgementmentioning

confidence: 99%

“…The genesis of a nontraumatic aneurysm is contingent on any condition that causes the walls of the blood vessel to weaken [3][4][5][6][7][8]. The most commonly investigated forms of aneurysms are the aortic, cerebral artery and intracranial aneurysm [3,[5][6][7][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…There are many hypotheses regarding aneurysm enlargement and rupture [3][4][5][6][7][8][9][10]. However, the roles of the Poisson ratio and the thinning of the membrane wall are not well understood.…”

Section: Introductionmentioning

confidence: 99%

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Modeling Nontraumatic Aneurysm Evolution, Growth and Rupture

Kwembe

Sanders

2014

J. Basic Appl. Sci.

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We have presented a mathematical model to study the evolution, growth and risk rupture of nontraumatic aneurysms contained within a cylindrical region of blood vessels. Analytical and numerical solutions are studied. Results affirmed that the intra-aneurysmal pressure and bloodstream flow account for the evolution and growth of aneurysms, and we find that an aneurysm may rupture when the ratio of the lateral membrane contraction to longitudinal membrane extension approaches one. Numerical properties of intra-aneurysmal pressure, impact fluid velocity, membrane displacement and the deformed radius with respect to the Poisson ratio, membrane thickness and extensional rigidity are studied. The importance of the findings is rested on the fact that they can be used to improve noninvasive means for predicting aneurysm rupture, and treatment and management decisions after rupture.

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Section: Acknowledgementmentioning

confidence: 99%