title: Numerical modeling of compensation mechanisms for peripheral arterial stenoses.
abstract: The goal of this paper is to develop a numerical model for physiological mechanisms that help to compensate reduced blood flow caused by a peripheral arterial stenosis. Thereby we restrict ourselves to the following compensation mechanisms: Metabolic regulation and arteriogenesis, i.e., growth of pre-existing collateral arteries. Our model is based on dimensionally reduced differential equations to simulate large time periods with low computational cost. As a test scenario, we consider a stenosis located in the right posterior tibial artery of a human. We study its impact on blood supply for different narrowing degrees by the help of numerical simulations. Moreover, the efficiency of the above compensation mechanisms is examined. Our results reveal that even a complete occlusion of this artery exhibiting a cross-section area of 0.442cm(2) can be compensated at rest, if metabolic regulation is combined with collateral arteries whose total cross-section area accounts for 8.14% of the occluded artery.
authors: Institute for Numerical Mathematics, Technische Universität München, Boltzmannstr. 3, D-85748 Garching b. München, Germany. Electronic address: drzisga@ma.tum.de.
authors: D
authors: D
authors: Drzisga
authors: Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, D-70569 Stuttgart, Germany. Electronic address: tobias.koeppl@iws.uni-stuttgart.de.
authors: T
authors: T
authors: Köppl
authors: Walter-Brendel-Centre of Exp. Medicine, Ludwig-Maximilians-Universität, Marchionistr. 27, D-81377 München, Germany. Electronic address: upohl@lmu.de.
authors: U
authors: U
authors: Pohl
authors: Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, D-70569 Stuttgart, Germany. Electronic address: rainer.helmig@iws.uni-stuttgart.de.
authors: R
authors: R
authors: Helmig
authors: Institute for Numerical Mathematics, Technische Universität München, Boltzmannstr. 3, D-85748 Garching b. München, Germany. Electronic address: wohlmuth@ma.tum.de.
authors: B
authors: B
authors: Wohlmuth
mesh_terms: D003251:Constriction, Pathologic; D005260:Female; D006801:Humans; D008297:Male; D008955:Models, Cardiovascular; D058729:Peripheral Arterial Disease / Q000473:pathology / Q000503:physiopathology*; D016909:Tibial Arteries / Q000473:pathology / Q000503:physiopathology*
keywords: Arteriogenesis; Metabolic regulation; Numerical method of characteristics; Peripheral stenosis; Reduced model