PK/PD Model Development

A sequential PK/PD approach was utilized to model exposure-response relationships. A two-compartment model, with first-order elimination and inter-compartmental distribution rate constants, was used to fit PK data of TOPO, LURTO, and DB-67. For 9-NC, PK parameters were fixed according to a previously published model. ¹² A two-compartment model was also specified for SN-38; however, the central volume of distribution was defined by a dose-dependent function: V_c = V_max × Dose/(D₅₀ + Dose), with V_max as the maximum volume and D₅₀ is the dose producing 50% V_max. This empirical submodel provided a minimal continuous function to account for nonlinear behavior associated with conversion of irinotecan to SN-38. ¹⁵

For modeling the delayed anti-cancer effects of camptothecin analogs, a time-dependent signal transduction model was modified and fitted. ¹⁶ The model structure is shown in Figure 2a, and the differential equations with initial conditions are as follows:

with R representing population of cycling cells, g(R) the tumor growth function, S an efficacy constant, τ is the mean transit time for each signaling compartment, K, with i = 2–4. The last transit compartment (K₄) acts as a first-order cell kill rate constant operating on proliferating cells (Eq. 1). Two tumor growth models were tested for each analog to allow flexibility and best fitting for each data set:

with k_g as a first-order net growth rate constant (exponential growth model), and Rss is a maximum tumor volume (logistic growth model).

Camptothecin analog pharmacodynamics. (a) Schematic of the final PK/PD model for the anti-tumor effects of five camptothecin analogs. Model-fitted profiles of effects on tumor progression in xenografts are shown for (b) topotecan, (c) lurtotecan, (d) DB-67, (e) 9-nitrocamptothecin, and (f) SN-38. Symbols represent digitized data from original publications (Table 1). Lines represent model-fitted profiles, and drug doses are as indicated.

PK/PD modeling was conducted using the digitized mean data. Parameter estimation was achieved using maximum likelihood method in ADAPT5. ¹⁷ PK/PD model qualification included graphical evaluation, goodness-of-fit plots (observed vs. predicted values), distribution of residuals, and plausibility of the parameter estimates and their precision.