RESUMO
Three nonlinear models of tumour cell growth under continuous delivery of cycle nonspecific anticancer agents are studied. A dynamical optimization problem with the objective of minimizing the final level of tumour cells is posed for these mathematical setups. The simplest setup does not possess toxicity constraints, whereas the other setups contain a dynamical equation describing the therapy burden as a toxicity criterion. In addition, the third setting contains the dynamics of drug resistant cells. A discussion concerning the optimal strategies of the respective models is performed.
Assuntos
Antineoplásicos/uso terapêutico , Resistencia a Medicamentos Antineoplásicos/fisiologia , Modelos Biológicos , Neoplasias/tratamento farmacológico , Antineoplásicos/efeitos adversos , Humanos , Modelos Lineares , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.
Assuntos
Antineoplásicos/uso terapêutico , Matemática , Neoplasias/tratamento farmacológico , Divisão Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Modelos Biológicos , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improvement of the patient's health when treatment is discontinued. Contrary to our early results which also take drug resistance into account, in this context strategies of continuous chemotherapy in which rest periods take part may be better than maximum drug concentration throughout the treatment (which appears to be in accordance with clinical practice). This bears out our previous conjecture that when drug resistance is accounted for, the imperfections in the usual modelling of treatment criteria, which in general do not allow for patient recuperation, ruled out the possibility of rest periods in optimal continuous chemotherapy.
Assuntos
Antineoplásicos/efeitos adversos , Antineoplásicos/uso terapêutico , Neoplasias/tratamento farmacológico , Morte Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Matemática , Modelos Biológicos , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.
Assuntos
Antineoplásicos/farmacologia , Antineoplásicos/farmacocinética , Neoplasias/tratamento farmacológico , Divisão Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Matemática , Modelos Biológicos , Neoplasias/metabolismo , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available.
Assuntos
Antineoplásicos/farmacologia , Neoplasias/tratamento farmacológico , Antineoplásicos/efeitos adversos , Antineoplásicos/farmacocinética , Morte Celular/efeitos dos fármacos , Divisão Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Matemática , Modelos Biológicos , Neoplasias/metabolismo , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumour cell growth in a cycle-nonspecific chemotherapy is presented. A rate-of-kill term of saturation type, drug resistance, and toxicity are taken into account in a class of optimal control problems. Some results are obtained for general tumour cell growth rates. A detailed analysis is presented for the Malthusian cell growth, which shows a variety of optimal treatments according to the values of the model parameters and initial tumour level.
Assuntos
Antineoplásicos/uso terapêutico , Resistência a Medicamentos , Matemática , Neoplasias/tratamento farmacológico , Neoplasias/patologia , Antineoplásicos/administração & dosagem , Antineoplásicos/toxicidade , Ciclo Celular , Divisão Celular , Humanos , Modelos TeóricosRESUMO
A system of differential equations for the control of the growth of certain populations by the use of chemical treatment is presented. Rather general growth rates and kill rates of drugs, as well as drug resistance, are considered. A class of optimal control problems with a performance criterion depending on a parameter is formulated and shown to admit the same basic optimal strategy. Applications to cycle nonspecific chemotherapy and control of the growth of bacterial populations in cellulose media in paper production plants are described.