scholarly journals Computational Study of Three Numerical Methods for Some Linear and Non-Linear Advection-Diffusion-Reaction Problems

2015 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Rao Appadu ◽  
Ndivhuwo Mphephu
Keyword(s):  
Numerical Methods ◽  
Computational Study ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Non Linear

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Estimating the extent of glioblastoma invasion

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Christian Engwer ◽  
Michael Wenske
Keyword(s):  
Analytic Solution ◽  
Glioma Cells ◽  
Diffusion Reaction ◽  
Kpp Equation ◽  
Advection Diffusion ◽  
Clinical Interest ◽  
Inhomogeneous Diffusion ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations ◽  
Tumor Extent

AbstractGlioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection–diffusion–reaction equations. The patient-wise parametrization of these models, and their validation via experimental data has been found to be difficult, as time sequence measurements are mostly missing. Also the clinical interest lies in the actual (invisible) tumor extent for a particular MRI/DTI scan and not in a predictive estimate. Therefore we propose a stationalized approach to estimate the extent of glioblastoma (GBM) invasion at the time of a given MRI/DTI scan. The underlying dynamics can be derived from an instationary GBM model, falling into the wide class of advection-diffusion-reaction equations. The stationalization is introduced via an analytic solution of the Fisher-KPP equation, the simplest model in the considered model class. We investigate the applicability in 1D and 2D, in the presence of inhomogeneous diffusion coefficients and on a real 3D DTI-dataset.

scholarly journals Numerical Simulation of the Coagulation Dynamics of Blood

2008 ◽  
Vol 9 (2) ◽  
pp. 83-104 ◽  
Author(s):  
T. Bodnár ◽  
A. Sequeira
Keyword(s):  
Blood Coagulation ◽  
Computational Study ◽  
Time Integration ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Clot Formation ◽  
Diffusion Reaction ◽  
Numerical Code ◽  
Injured Region ◽  
Reaction Equations

The process of platelet activation and blood coagulation is quite complex and not yet completely understood. Recently, a phenomenological meaningful model of blood coagulation and clot formation in flowing blood that extends existing models to integrate biochemical, physiological and rheological factors, has been developed. The aim of this paper is to present results from a computational study of a simplified version of this coupled fluid-biochemistry model. A generalized Newtonian model with shear-thinning viscosity has been adopted to describe the flow of blood. To simulate the biochemical changes and transport of various enzymes, proteins and platelets involved in the coagulation process, a set of coupled advection–diffusion–reaction equations is used. Three-dimensional numerical simulations are carried out for the whole model in a straight vessel with circular cross-section, using a finite volume semi-discretization in space, on structured grids, and a multistage scheme for time integration. Clot formation and growth are investigated in the vicinity of an injured region of the vessel wall. These are preliminary results aimed at showing the validation of the model and of the numerical code.

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