TY - JOUR

T1 - Modeling of a false aneurysm in an artery: equilibrium and development of a hematoma

AU - Kozlov, V.A.

AU - Nazarov, S. A.

N1 - Kozlov, V.A., Nazarov, S.A. Modeling of a False Aneurysm in an Artery: Equilibrium and Development of a Hematoma. J Math Sci 239, 309–328 (2019). https://doi.org/10.1007/s10958-019-04307-9

PY - 2019

Y1 - 2019

N2 - We present a new one-dimensional model of a false aneurysm in an artery describing several stages of development of aneurysm by expanding a hematoma that exchanges blood with a vessel channel through a small hole in the thin elastic vessel wall. The model involves one hyperbolic and two parabolic partial differential equations joined by common unknowns (the artery and hematoma pressures and the radial displacement of the wall) and by the classical Kirchhoff transmission conditions on the pressure and blood flows which simulate the blood exchange through the hole. We obtain the equilibrium state condition for an aneurysm and propose criteria for aneurysm developing by hematoma thickening or lengthening. We propose a simplified “0-dimensional” model applicable only for detecting an aneurysm by using peripheral examination and solving inverse problems.

AB - We present a new one-dimensional model of a false aneurysm in an artery describing several stages of development of aneurysm by expanding a hematoma that exchanges blood with a vessel channel through a small hole in the thin elastic vessel wall. The model involves one hyperbolic and two parabolic partial differential equations joined by common unknowns (the artery and hematoma pressures and the radial displacement of the wall) and by the classical Kirchhoff transmission conditions on the pressure and blood flows which simulate the blood exchange through the hole. We obtain the equilibrium state condition for an aneurysm and propose criteria for aneurysm developing by hematoma thickening or lengthening. We propose a simplified “0-dimensional” model applicable only for detecting an aneurysm by using peripheral examination and solving inverse problems.

UR - http://www.scopus.com/inward/record.url?scp=85065433156&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04307-9

DO - 10.1007/s10958-019-04307-9

M3 - Article

VL - 239

SP - 309

EP - 328

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -