Oncology Commons^™

Mathematical Models Of Chemotherapy, John Carl Panetta

Mathematics & Statistics Theses & Dissertations

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling …

A Logistic Model Of Periodic Chemotherapy, J. C. Panetta

Mathematics & Statistics Faculty Publications

A logistic differential equation with a time-varying periodic parameter is used to model the growth of cells, in particular cancer cells, in the presences of chemotherapeutic drugs. The chemotherapeutic effects are modeled by a periodic parameter that modifies the growth rate of the cell tissue. A negative growth rate represents the detrimental effects of the drugs. A simple criterion is obtained for the behavior of the chemotherapy.

The Role Of Small Peptides In Cancer Physiology And Chemotherapy, Bao-Ling Tsay

Theses and Dissertations in Biomedical Sciences

The targeting of proven anticancer drugs specifically to cancer cells would provide a unique opportunity to restrict neoplasms without damaging the cancer patient. The present research utilizes the phenomenon of illicit transport, i.e. the coupling of normally impermeant metabolites to permeant metabolites, in targeting the drug melphalan to mouse Ehrlich ascites tumor cells. The dipeptide beta-alanyl-melphalan was synthesized and tested in vitro for toxicity towards mouse Ehrlich ascites tumor cells, mouse liver cells, and mouse 3T3 embryonic cells. The parent compound, melphalan, was used as a control treatment. In addition, both melphalan and beta-alanyl-melphalan were utilized in in vivo chemotherapeutic …