Accession Number : AD0608399

Title :   CHEMOTHERAPY, CONVOLUTION EQUATIONS, AND DIFFERENTIAL APPROXIMATION,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Bellman,Richard ; Kotkin,Bella

Report Date : NOV 1964

Pagination or Media Count : 14

Abstract : A review is given of attempts at developing mathematical techniques for use in digital computer programs applicable to a problem of cancer chemotherapy, that of injecting a chemical agent into the blood stream and determining the time course of the concentrations of the drug and the compounds formed in the organs. In an early model two organs were linked in parallel to the circulation, with the heart acting as a mixing pot. Since only the drug concentrations entering and leaving the capillary bed were measurable, they were replaced by ordinary differential equations, and the capillary bed was regarded as a series of mixing chambers with instantaneous uniform mixing. An iterative scheme was evolved whereby a differentialdifference equation is replaced by a series of ordinary differential equations defined over the initial interval lag in time for injection of a drug by the blood, and where the number of equations depends on the range of integration. Techniques were also worked out for a twoorgan model with the assumption of laminar flow and mixing in the large blood vessels.

Descriptors :   (*CANCER, CHEMOTHERAPY), (*CHEMOTHERAPY, MATHEMATICAL MODELS), (*MATHEMATICAL MODELS, CHEMOTHERAPY), CHEMOTHERAPEUTIC AGENTS, BLOOD CIRCULATION, BIOCHEMISTRY, MEDICAL RESEARCH, NUMERICAL ANALYSIS, DIFFERENTIAL EQUATIONS, DIFFERENCE EQUATIONS, TIME LAG THEORY, ITERATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE