A mathematical model of drug resistance applied to treatment for small-cell lung cancer.

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Abstract
A mathematical model has been applied to patients with small-cell lung cancer (SCLC) in order to estimate the proportions of resistant and sensitive tumor at presentation, and the efficacy of the treatment, measured in terms of proportions of tumor killed with each cycle of therapy. The model uses estimates of tumor volume obtained from computed tomographic (CT) scans of the chest before each course of chemotherapy. Application of the model to a trial using single-agent high-dose cyclophosphamide (HDC) showed that HDC killed approximately 94% of the sensitive tumor on each application, but that the proportion of tumor resistant to HDC rose from an average of 1% to an average of 15% after the first cycle, assuming a 30-day tumor doubling time. These estimates proved fairly insensitive to different assumptions about tumor doubling time and inaccuracies in volume measurement and may thus provide a useful additional evaluation technique for some clinical trials.

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