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- Title
Glioma Concentration Growth Simulation Using The Crank Nicolson Method.
- Authors
Noviantri, Viska; Tjandra, Tomy; Nariswari, Rinda
- Abstract
The most common type of central nervous system tumor in adults is glioma, accounting for about 70% of all brain tumors. Prediction of glioma growth became interesting to be analyzed to measure how severe the glioma is, plan the proper treatment, and estimate how long the patient can survive. This paper uses the Reaction-diffusion equation to interpret the glioma concentration in the grey and white matter of the brain based on three different growth functions. These are exponential, logistic, and Gompertzian growth functions. The Crank-Nicolson scheme is applied here to solve this model as an initial step to carry out the simulation. It is used since this scheme is unconditionally stable and has a higher order of accuracy. This scheme produces a linear system equation for exponential growth function while a nonlinear system for logistic and Gompertzian growth function. The simulation results include concentration, maximum concentration, cell number, and average speed of glioma cells for each growth function given here. As a result, the maximum glioma concentration grows infinitely for exponential growth but converges to specific values for logistic and Gompertzian growth functions. Furthermore, this paper gives the sensitivity analysis for the model to see the behavior of glioma concentration based on parameter changes. These are initial glioma position, net proliferation rate, and diffusivity coefficient in grey and white matter. It shows that net proliferation affects glioma concentration growth more than others.
- Subjects
CRANK-nicolson method; CENTRAL nervous system tumors; GLIOMAS; BRAIN tumors; REACTION-diffusion equations
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 4, p1607
- ISSN
1992-9978
- Publication type
Article