speciosus

Erigeron speciosus (Lindley) de Candolleshowy fleabane;showy daisy;aspen fleabanebelle vergeretteErigeron speciosusE- Front Mountains. Common at the banks of the South Fork Teton River near Trails End Campsire5700'Common at the bank

Numerical simulations of different models describing cerebrospinal fluid dynamics

The aim of this paper is to present an extensive overview of numerical simulations aimed at confirming and completing the theoretical results obtained in the analysis of some cerebrospinal fluid dynamics models which are treated from a purely mathematical view point. The present study is designed to support the first attempts in the approach to these physiological models from a more theoretical standpoint since their investigation in literature only concerns the modelization and the clinical feedback

Nonreflecting Boundary Conditions for a CSF Model of Fourth Ventricle: Spinal SAS Dynamics

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

Analysis of solutions for a cerebrospinal fluid model

The aim of this manuscript is to analyze an intracranial fluid model from a mathematical point of view. The novel aspect of this work with respect to the existing literature is represented by the rigorous mathematical results regarding the analysis of the solutions to the systems of equations which model the different mechanisms in the cerebrospinal fluid compartments. We are able to prove the existence and uniqueness of a local solution and the existence and uniqueness of a global solution under some restriction conditions on the initial data. Moreover the last part of the paper is devoted to numerical simulations for the analyzed cerebrospinal fluid model. In particular, in order to assess the reliability of the stated theoretical results, we carry out the numerical simulations in two different cases: first, we fix initial data which ,satisfy the conditions for the global existence of solutions, then, we choose initial data that violate them

Bidens squarrosa var. tereticaulis (DC.) Roseman

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