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Bioinformatics of the Brain

a mathematical model of glioma development and diffusion. The patient had

recurrent anaplastic astrocytoma. By using the quantitative measures of pro-

liferation and diffusion, the model described the development of the glioma

cell population.

In mathematical words, rate of change of tumor cell density = diffusion of

tumor cells + growth of tumor cells,

∂τB(x, τ) = D ¹

x^{2 ∂x(x2∂xB(x, τ)) + ρB(x, τ)}

(6.6)

The model above was created to add a lethal term to equation (6.6) as

follows:

In mathematical words, rate of change of tumor cell density = diffusion of

tumor cells + growth of tumor cells-killing rate of tumor cells,

∂τB(x, τ) = D ¹

x^{2 ∂x(x2∂xB(x, τ)) + ρB(x, τ) −kτB(x, τ)}

(6.7)

This model is expressed as follows:

∂τB(x, τ) = D(∂xxB(x, τ) + ²

x^{∂xB(x, τ)) + (ρ −kτ)B(x, τ)}

(6.8)

This problem was solved by Ganji and friends as a fractional Burgess

equation [51]. The most prevalent primary brain tumor in adults, glioblastoma,

usually results in early death. Radiation therapy, chemotherapy, and surgery

are the usual treatments for brain tumors. In recent years, brain tumors that

have been treated and those that have not, have been investigated by applying

mathematical models. The Burgess equation is used to simulate glioblastomas

(brain tumors) and includes the two main variables controlling tumor growth:

the rate of cell proliferation and the diffusion of cancer cells. This model aims

to improve on previous studies. The fractional Burgess equation is taken to

be considered in terms of Caputo in their study. Owing to the model being

studied, a method to solve this model is suggested.

6.7

Conclusions

Expressing real-world problems by mathematical modeling has shown to be

very effective. Following the creation of the modeling, solution approaches

are looked at, contrasted, and the best approach is found. Fractional opera-

tors and equations have improved the effectiveness of events that had been

expressed using ordinary differential equations. It has completed the miss-

ing parts of ordinary differential equations. Fractional derivatives offered by