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Model Mathematics

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Component: environment

Exposure = \{\begin{matrix} Dose if time < Cycle_Int N_Cycle \land Dose_Int1 < rem_time \land rem_time < Dose_Length \\ Dose if time < Cycle_Int N_Cycle \land Dose_Int2 < rem_time \land rem_time < Dose_Int2 + Dose_Length \\ 0 otherwise \end{matrix} rem_time = \frac{(time conversion_factor) mod (Cycle_Int conversion_factor)}{conversion_factor}

Component: effect_compartment

k_1 = \frac{\ln 2}{t_half_eq} \frac{d}{d time} (Ce) = \frac{Exposure}{1} - (Ce k_1) Effect = 1 - (\frac{E_max Ce}{Amt_50 + Ce})

Component: response_compartment

RateIn = Size_0 k_2 k_2 = \frac{\ln 2}{T_Turnover} \frac{d}{d time} (Size) = (RateIn Effect - (k_2 Size)) Size

Source: Derived from workspace Tham 2008 at changeset 3b9df6fb9fb5.

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A pharmacodynamic model for the time course of tumor shrinkage by gemcitabine + carboplatin in non-small cell lung cancer patients