Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response

Diego Samuel Rodrigues; Paulo Fernando de Arruda Mancera

doi:10.3934/mbe.2013.10.221

Article Contents

2013, Volume 10, Issue 1: 221-234. Doi: 10.3934/mbe.2013.10.221

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Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response

Diego Samuel Rodrigues^1, and
Paulo Fernando de Arruda Mancera^2,

1.
Universidade de São Paulo, Depto de Matemática Aplicada e Estatística, ICMC, USP, 13560-970, São Carlos
2.
Universidade Estadual Paulista, Depto de Bioestatística, IBB, UNESP, 18618-970, Botucatu

Received: April 2012

Revised: September 2012

Published online: December 2012

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Abstract

Dosage and frequency of treatment schedules are important for successful chemotherapy. However, in this work we argue that cell-kill response and tumoral growth should not be seen as separate and therefore are essential in a mathematical cancer model. This paper presents a mathematical model for sequencing of cancer chemotherapy and surgery. Our purpose is to investigate treatments for large human tumours considering a suitable cell-kill dynamics. We use some biological and pharmacological data in a numerical approach, where drug administration occurs in cycles (periodic infusion) and surgery is performed instantaneously. Moreover, we also present an analysis of stability for a chemotherapeutic model with continuous drug administration. According to Norton & Simon [22], our results indicate that chemotherapy is less efficient in treating tumours that have reached a plateau level of growing and that a combination with surgical treatment can provide better outcomes.

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Mathematics Subject Classification: Primary: 92B05; Secondary: 37N25.

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