Geodesic
A simple one-dimensional model of a~false aneurysm in the femoral artery
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 64-86

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Using the dimension reduction procedure, one-dimensional model of the periodic blood flow in the artery, which flows out through a small hole in the thin elastic artery wall connected to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff matching conditions. Despite the simplicity, the constructed model allows us to describe a damping of pulsating blood flow by the hematoma and determine the conditions of its growth. In medicine, considered biological object is called a false aneurysm. 
@article{ZNSL_2014_426_a6,
     author = {V. A. Kozlov and S. A. Nazarov},
     title = {A simple one-dimensional model of a~false aneurysm in the  femoral artery},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--86},
     publisher = {mathdoc},
     volume = {426},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a6/}
}
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V. A. Kozlov; S. A. Nazarov. A simple one-dimensional model of a~false aneurysm in the  femoral artery. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 64-86. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a6/