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The Numerical and Mathematical Modeling of Gliadel Transport and Degradation in the Brain


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DOI: https://doi.org/10.15866/iremos.v16i4.22854

Abstract


Glioblastoma is a rapidly progressing form of brain tumor that is extremely fatal and has a poor prognosis. Gliadel wafer is a novel approach for the treatment of glioblastoma. It involves the controlled release of Carmustine from biodegradable polymer wafers. The transport of this mass involved in controlled drug delivery (Gliadel) to living brain tissue is complex and not yet fully understood. Researchers in different fields (medicine, modeling, mathematical simulation...) have found it difficult to obtain high-quality experimental data on Gliadel concentrations in brain tissue. To this end, the aim of this work is to develop a new strategy to simulate this type of problem, to produce more efficient results, and to study the evolution of the concentration of Gliadel within the brain. The mathematical model used here is a coupled system of equations: the transport equation (advection and diffusion) with a first-order equation (small concentrations). The numerical simulation used here is based on the Lie-Trotter (LTM), a first-order division method that solves two sub problems sequentially on sub-intervals. It is a powerful method for the numerical study of complex models. A comparative study of this method (LT) and the Finite Difference Method (FDM) with the exact solution will be conducted. Results that are more efficient have been obtained by using the LT method compared to those obtained by using the Finite Difference Method (FDM), where the error of the LTM (Er-LTM) is less than the FDM error (Er-FDN). The numerical results show that the LT method remains more efficient than the FDM method for this type of problem. Moreover, the results obtained with LTM are stable and they converge more to the exact solution, from which the concentration of Gliadel can be studied.
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Keywords


Modelling; Numerical Simulation; Lie-Trotter Method; Gliadel; Glioblastoma

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References


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