title: Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment.
abstract: In recent years, it became clear that a better understanding of the interactions among the main elements involved in the cancer network is necessary for the treatment of cancer and the suppression of cancer growth. In this work we propose a system of coupled differential equations that model brain tumour under treatment by chemotherapy, which considers interactions among the glial cells, the glioma, the neurons, and the chemotherapeutic agents. We study the conditions for the glioma growth to be eliminated, and identify values of the parameters for which the inhibition of the glioma growth is obtained with a minimal loss of healthy cells.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE Aberdeen, UK. Electronic address: kiarosz@gmail.com.
authors.forename: Kelly C
authors.initials: KC
authors.lastname: Iarosz
authors.affiliation: Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
authors.forename: Fernando S
authors.initials: FS
authors.lastname: Borges
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE Aberdeen, UK; Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil; Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
authors.forename: Antonio M
authors.initials: AM
authors.lastname: Batista
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE Aberdeen, UK.
authors.forename: Murilo S
authors.initials: MS
authors.lastname: Baptista
authors.affiliation: Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
authors.forename: Regiane A N
authors.initials: RA
authors.lastname: Siqueira
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
authors.forename: Ricardo L
authors.initials: RL
authors.lastname: Viana
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
authors.forename: Sergio R
authors.initials: SR
authors.lastname: Lopes
mesh_terms: D000970:Antineoplastic Agents / Q000494:pharmacology / Q000627:therapeutic use*; D001932:Brain Neoplasms / Q000188:drug therapy / Q000473:pathology*; D002450:Cell Communication / Q000187:drug effects; D005910:Glioma / Q000188:drug therapy / Q000473:pathology*; D006801:Humans; D008954:Models, Biological; D009457:Neuroglia / Q000187:drug effects / Q000502:physiology*; D009474:Neurons / Q000187:drug effects / Q000502:physiology*
chemical_list: D000970:Antineoplastic Agents
keywords: Brain; Chemotherapy; Glioma