# 211 — Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment

#cancer  #glia  #glioma  #chemotherapy  #tumor  #neuroscience  #simulation  #model  #differential-equations  #system-of-equations

It is very difficult to predict the glial (or even macroscopic) response to chemotherapy in cases of brain cancer and other tumorous diseases. In order to improve our understanding of chemotherapy treatment efficacy, this research proposes a mathematical model of tumor growth or loss as dependent upon measurable parameters.

This technique outputs a system of coupled differential equations which can be solved or approximated to predict the outcome of modeled glioma.

This model ignores spatial considerations, assuming only that the concentration of glial tumor cells changes over time. (This is obviously not a valid assumption, but it approximates glioma behavior to a less accurate but more confident degree.)

The formula uses seven parameters — proliferation rate, loss influences, interaction coefficients, chemotherapy agent rate, Holling type 2 killing function, competition coefficients, and the carrying capacity of tootal cells (glial, gliomal, and neural) — and from these parameters, outputs a glial, gliomal, and neural cell population ratio.

This model embeds its results in one of three categories: Region I is the result of total cell death; Region II is the locally stable equilibrium between healthy and damaged cells; Region III is the case in which the chemotherapy is “successful,” representing a similar equilibrium but with low or zero glioma cell population counts. (The cases on the boundary between II and III are the cases in which glioma will metastasize if treatment stops.)

This sort of work leverages biological studies in order to best understand the relationship between chemotherapy and tumor suppression. After all, large chemo doses are the best at killing tumors, but are also the best at killing healthy cells.

Finding the ideal equilibrium is still very patient-dependent; but this model can inform the diagnostic and prescriptive decisions by fleshing out the landscape of treatment options.