Special Issues
Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response
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1.
Universidade de São Paulo, Depto de Matemática Aplicada e Estatística, ICMC, USP, 13560-970, São Carlos
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2.
Universidade Estadual Paulista, Depto de Bioestatística, IBB, UNESP, 18618-970, Botucatu
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Received:
01 April 2012
Accepted:
29 June 2018
Published:
01 December 2012
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MSC :
Primary: 92B05; Secondary: 37N25.
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Special Issue: Mathematical Oncology: New Challenges for Systems Biomedicine
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Dosage and frequency of treatment schedulesare important for successful chemotherapy.However, in this work we argue that cell-kill response and tumoralgrowth 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 andsurgery. Our purpose is to investigate treatments for large human tumoursconsidering a suitable cell-kill dynamics. Weuse some biological and pharmacological data in a numerical approach,where drug administration occurs in cycles (periodic infusion)and surgery is performed instantaneously. Moreover, we alsopresent an analysis of stabilityfor a chemotherapeutic model with continuous drug administration.According to Norton & Simon [22], our results indicate that chemotherapy is lessefficient in treating tumours that have reached a plateau level of growingand that a combination with surgical treatment can provide better outcomes.
Citation: Diego Samuel Rodrigues, Paulo Fernando de Arruda Mancera. Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 221-234. doi: 10.3934/mbe.2013.10.221
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Abstract
Dosage and frequency of treatment schedulesare important for successful chemotherapy.However, in this work we argue that cell-kill response and tumoralgrowth 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 andsurgery. Our purpose is to investigate treatments for large human tumoursconsidering a suitable cell-kill dynamics. Weuse some biological and pharmacological data in a numerical approach,where drug administration occurs in cycles (periodic infusion)and surgery is performed instantaneously. Moreover, we alsopresent an analysis of stabilityfor a chemotherapeutic model with continuous drug administration.According to Norton & Simon [22], our results indicate that chemotherapy is lessefficient in treating tumours that have reached a plateau level of growingand that a combination with surgical treatment can provide better outcomes.
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