On a synthesis of controls for a mathematical model of cancer chemotherapy

2002 ◽  
Author(s):  
U. Ledzewicz ◽  
H. Schattler
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy

Mathematical model of cancer chemotherapy. periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivty of therapy

1985 ◽  
Vol 73 (1) ◽  
pp. 1-31 ◽  
Author(s):  
B.F. Dibrov ◽  
A.M. Zhabotinsky ◽  
Yu.A. Neyfakh ◽  
M.P. Orlova ◽  
L.I. Churikova
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Cytotoxic Agent

A mathematical model of cancer chemotherapy with an optimal selection of parameters

1990 ◽  
Vol 99 (2) ◽  
pp. 205-230 ◽  
Author(s):  
R.B. Martin ◽  
M.E. Fisher ◽  
R.F. Minchin ◽  
K.L. Teo
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Optimal Selection ◽  
Selection Of

Application of the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

2019 ◽  
Vol 42 (4) ◽  
pp. 1167-1193 ◽  
Author(s):  
Victor Fabian Morales-Delgado ◽  
José Francisco Gómez-Aguilar ◽  
Khaled Saad ◽  
Ricardo Fabricio Escobar Jiménez
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Fractional Derivatives

scholarly journals Optimal control for a mathematical model for chemotherapy with pharmacometrics

2020 ◽  
Vol 15 ◽  
pp. 69
Author(s):  
Maciej Leszczyński ◽  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Drug Effects ◽  
Optimal Controls ◽  
Angiogenic Therapy ◽  
Single Drug ◽  
Qualitative Changes

An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.

scholarly journals Development and Validation of a Mathematical Model to Describe Anti-Cancer Prodrug Activation by Antibody-Enzyme Conjugates

2000 ◽  
Vol 2 (2) ◽  
pp. 93-111 ◽  
Author(s):  
Trachette L. Jackson ◽  
Peter D. Senter ◽  
James D. Murray
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Critical Parameters ◽  
Treatment Protocols ◽  
Drug Permeability ◽  
Drug Levels ◽  
Anti Cancer ◽  
Model Predictions ◽  
Development And Validation ◽  
Systemic Drug

A mathematical model has been developed for a two-step approach to cancer chemotherapy involving the use of targeted monoclonal antibody-enzyme conjugates for the selective activation of anti-cancer prodrugs. Theoretical analysis and numerical simulation are used to characterize critical parameters for intratumoral and systemic drug generation. The model suggests that the most important pharmacokinetic and clinical parameters for increased drug production in the tumor are the rate of prodrug clearance from the blood and the initial injected dose of prodrug. The physiological parameters with the most influence are the prodrug and drug permeability. The ratio of tumor to blood drug generation can best be improved by increasing the conjugate clearance from the blood and decreasing the rate at which prodrug is converted to active drug. Predictions from this model concerning intratumoral prodrug and drug levels are validated by comparison with experimental data. Finally, the effects of certain barriers to chemotherapeutic treatments including vascular heterogeneity and radially outward convection are studied. If vascular heterogeneity alone is considered, the model predicts that the highest drug levels will occur in the most poorly vascularized sections of the tumor. However, when the effects of convection directed radially outward is considered, the highest drug levels are seen in the semi-well vascularized regions. This implies that the rapidly growing periphery of the tumor and the semi-necrotic tumor interior will receive the least amount of drug. These mathematical model predictions can lead to improved treatment protocols for this two step approach to cancer chemotherapy.

A mathematical model of the development of drug resistant to cancer chemotherapy

1987 ◽  
Vol 23 (9) ◽  
pp. 1421-1427 ◽  
Author(s):  
Brian G. Birkhead ◽  
Elaine M. Rankin ◽  
Stephen Gallivan ◽  
Leanne Dones ◽  
Robert D. Rubens
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Drug Resistant
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