TY - JOUR
T1 - Nonreflecting Boundary Conditions for a CSF Model of Fourth Ventricle: Spinal SAS Dynamics
AU - Donatelli, Donatella
AU - Romagnoli, Licia
PY - 2020
Y1 - 2020
N2 - In this paper we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order non-linear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flows, for the particular dynamics we are dealing with, the most desirable option is to employ the nonreflecting boundary conditions, that allow the simple wave associated to the outgoing characteristic to exit the computational domain with no reflections. Finally, we carry out some numerical simulations related to different cerebral physiological conditions.
AB - In this paper we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order non-linear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flows, for the particular dynamics we are dealing with, the most desirable option is to employ the nonreflecting boundary conditions, that allow the simple wave associated to the outgoing characteristic to exit the computational domain with no reflections. Finally, we carry out some numerical simulations related to different cerebral physiological conditions.
KW - cerebrospinal fluid
KW - nonreflecting
KW - cerebrospinal fluid
KW - nonreflecting
UR - http://hdl.handle.net/10807/176557
U2 - 10.1007/s11538-020-00749-4
DO - 10.1007/s11538-020-00749-4
M3 - Article
SN - 0092-8240
SP - 77
EP - 116
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
ER -