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A comparison of two mathematical models of the cerebrospinal fluid dynamics

1 Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy
2 GSSI - Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L’Aquila, Italy

In this paper we provide the numerical simulations of two cerebrospinal fluid dynamics models by comparing our results with the real data available in literature (see Section 4). The models describe different processes in the cerebrospinal fluid dynamics: the cerebrospinal flow in the ventricles of the brain and the reabsorption of the fluid. In the appendix we show in detail the mathematical analysis of both models and we identify the set of initial conditions for which the solutions of the systems of equations do not exhibit blow up. We investigate step by step the accuracy of these theoretical outcomes with respect to the real cerebrospinal physiology and dynamics. The plan of the paper is provided in Section 1.5.
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Keywords cerebrospinal fluid; fluid dynamics; one-dimensional flow; physiological flows; hyperbolic equations; global well posedness

Citation: Donatella Donatelli, Pierangelo Marcati, Licia Romagnoli. A comparison of two mathematical models of the cerebrospinal fluid dynamics. Mathematical Biosciences and Engineering, 2019, 16(4): 2811-2851. doi: 10.3934/mbe.2019140

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