Tuesday, October 8, 2013

Cancer treatment with Doxorubicin (a mathematical model)

Cytotoxic antineoplastic drugs are administered to treat many different types of cancer including breast, lung, bladder and liver cancer. Doxorubicin (DOX) is a chemotherapy agent (also called Adriamycin) which is given by injection or drip (infusion) through a fine tube inserted into the vein (e.g. cannula), through a fine plastic tube inserted into a vein near your collarbone (central line) or into a vein in the crook of your arm (PICC line). Mathematical modeling can be used to determine DOX drug concentration in in systemic plasma, aggregate body tissue, tumor plasma, tumor interstitial space, and tumor cells. Such mathematical models allow optimization of drug delivery systems to achieve a better therapeutic index.

In the section below I present a mathematical model according to (http://www.musc.edu/ablation/pubs/Gasselhuber,%20PLos%20One%202012.pdf) to predict systemic and tumor drug concentrations for DOX in mice.

Overview about the mathematical model including compartments for body plasma, body tissue, tumor plasma, extra and intracellular compartment for tumor tissue. The transport mechanism between the compartments are indicated via arrows.

The ordinary differential equation model was built and solved via Python.

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