Mathematical model of brain tumour growth with drug resistance

José Trobia; Kun Tian; Antonio Marcos Batista; Celso Grebogi; Hai-Peng Ren; Moises Souza Santos; Paulo Ricardo Protachevicz; Fernando da Silva Borges; José Danilo Szezech Jr; Ricardo Luiz Viana; Iberê Luiz Caldas; Kelly Cristiane Iarosz

doi:10.1016/j.cnsns.2021.106013

Mathematical model of brain tumour growth with drug resistance

José Trobia, Kun Tian, Antonio Marcos Batista^* (Corresponding Author), Celso Grebogi, Hai-Peng Ren, Moises Souza Santos, Paulo Ricardo Protachevicz, Fernando da Silva Borges, José Danilo Szezech Jr, Ricardo Luiz Viana, Iberê Luiz Caldas, Kelly Cristiane Iarosz^* (Corresponding Author)

^*Corresponding author for this work

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Abstract

In this research article, we propose a model with glioma drug resistance for gliomas with glia-neuron interactions and chemotherapy treatment.
We consider continuous and pulsed chemotherapy to destroy glioma cells without harming a large number of neurons and we computed the values of the infusion of chemotherapy agents in which the glioma is suppressed and a minimum number of neurons is lost, without neurogenesis.
The main contribution of this work is the insertion of a new differential equation to the model formulated in 2015 by Iarosz and collaborators. The new equation extend the mathematical model of brain tumour growth and and enables the study of sensitive and resistant glioma cells.

Original language	English
Article number	106013
Number of pages	10
Journal	Communications in Nonlinear Science & Numerical Simulation
Volume	103
Early online date	31 Aug 2021
DOIs	https://doi.org/10.1016/j.cnsns.2021.106013
Publication status	Published - 1 Dec 2021

Keywords

brain
tumor
chemotherapy
drug resistance
glia-neuron interaction

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Submitted manuscript, 1.07 MBLicence: CC BY
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http://arxiv.org/abs/2012.08252v1

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@article{15f36939d18d4efaba4d39fb4134864a,

title = "Mathematical model of brain tumour growth with drug resistance",

abstract = "In this research article, we propose a model with glioma drug resistance for gliomas with glia-neuron interactions and chemotherapy treatment.We consider continuous and pulsed chemotherapy to destroy glioma cells without harming a large number of neurons and we computed the values of the infusion of chemotherapy agents in which the glioma is suppressed and a minimum number of neurons is lost, without neurogenesis.The main contribution of this work is the insertion of a new differential equation to the model formulated in 2015 by Iarosz and collaborators. The new equation extend the mathematical model of brain tumour growth and and enables the study of sensitive and resistant glioma cells.",

keywords = "brain, tumor, chemotherapy, drug resistance, glia-neuron interaction",

author = "Jos{\'e} Trobia and Kun Tian and Batista, {Antonio Marcos} and Celso Grebogi and Hai-Peng Ren and Santos, {Moises Souza} and Protachevicz, {Paulo Ricardo} and Borges, {Fernando da Silva} and Jr, {Jos{\'e} Danilo Szezech} and Viana, {Ricardo Luiz} and Caldas, {Iber{\^e} Luiz} and Iarosz, {Kelly Cristiane}",

note = "Acknowledgments We wish to acknowledge the support: Arauc{\'a}ria Fundation, National Council for Scientific and Technological Development (CNPq, 302665/2017-0 and 407299/2018-1), Coordination for the Improvement of Higher Education Personnel (CAPES), and S{\~a}o Paulo Research Foundation (Processes 2015/07311-7, 2017/18977-1, 2018/03211-6, 2020/04624-2). The authors would like to thank the 105 Group Science (www.105groupscience.com) for the fruitful discussions.",

year = "2021",

month = dec,

day = "1",

doi = "10.1016/j.cnsns.2021.106013",

language = "English",

volume = "103",

journal = "Communications in Nonlinear Science & Numerical Simulation",

issn = "1007-5704",

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TY - JOUR

T1 - Mathematical model of brain tumour growth with drug resistance

AU - Trobia, José

AU - Tian, Kun

AU - Batista, Antonio Marcos

AU - Grebogi, Celso

AU - Ren, Hai-Peng

AU - Santos, Moises Souza

AU - Protachevicz, Paulo Ricardo

AU - Borges, Fernando da Silva

AU - Jr, José Danilo Szezech

AU - Viana, Ricardo Luiz

AU - Caldas, Iberê Luiz

AU - Iarosz, Kelly Cristiane

N1 - Acknowledgments We wish to acknowledge the support: Araucária Fundation, National Council for Scientific and Technological Development (CNPq, 302665/2017-0 and 407299/2018-1), Coordination for the Improvement of Higher Education Personnel (CAPES), and São Paulo Research Foundation (Processes 2015/07311-7, 2017/18977-1, 2018/03211-6, 2020/04624-2). The authors would like to thank the 105 Group Science (www.105groupscience.com) for the fruitful discussions.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - In this research article, we propose a model with glioma drug resistance for gliomas with glia-neuron interactions and chemotherapy treatment.We consider continuous and pulsed chemotherapy to destroy glioma cells without harming a large number of neurons and we computed the values of the infusion of chemotherapy agents in which the glioma is suppressed and a minimum number of neurons is lost, without neurogenesis.The main contribution of this work is the insertion of a new differential equation to the model formulated in 2015 by Iarosz and collaborators. The new equation extend the mathematical model of brain tumour growth and and enables the study of sensitive and resistant glioma cells.

AB - In this research article, we propose a model with glioma drug resistance for gliomas with glia-neuron interactions and chemotherapy treatment.We consider continuous and pulsed chemotherapy to destroy glioma cells without harming a large number of neurons and we computed the values of the infusion of chemotherapy agents in which the glioma is suppressed and a minimum number of neurons is lost, without neurogenesis.The main contribution of this work is the insertion of a new differential equation to the model formulated in 2015 by Iarosz and collaborators. The new equation extend the mathematical model of brain tumour growth and and enables the study of sensitive and resistant glioma cells.

KW - brain

KW - tumor

KW - chemotherapy

KW - drug resistance

KW - glia-neuron interaction

U2 - 10.1016/j.cnsns.2021.106013

DO - 10.1016/j.cnsns.2021.106013

M3 - Article

VL - 103

JO - Communications in Nonlinear Science & Numerical Simulation

JF - Communications in Nonlinear Science & Numerical Simulation

SN - 1007-5704

M1 - 106013

ER -

Mathematical model of brain tumour growth with drug resistance

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