Two-mechanism peak concentration model for cellular pharmacodynamics of Doxorubicin

Abstract

A mathematical model is presented for the cellular uptake and cytotoxicity of the anticancer drug doxorubicin. The model assumes sigmoidal, Hill-type dependence of cell survival on drug-induced damage. Experimental evidence indicates distinct intracellular and extracellular mechanisms of doxorubicin cytotoxicity. Drug-induced damage is therefore expressed as the sum of two terms, representing the peak values over time of concentrations of intracellular and extracellular drugs. Dependence of cell kill on peak values of concentration rather than on an integral over time is consistent with observations that dose-response curves for doxorubicin converge to a single curve as exposure time is increased. Drug uptake by cells is assumed to include both saturable and unsaturable components, consistent with experimental data. Overall, the model provides better fits to in vitro cytotoxicity data than previous models. It shows how saturation of cellular uptake or binding with concentration can result in plateaus in the dose-response curve at high concentrations and short exposure, as observed experimentally in some cases. The model provides a unified framework for analyzing doxorubicin cellular pharmacokinetic and pharmacodynamic data, and can be applied in mathematical models for tumor response and treatment optimization.

Figure 1

Cellular pharmacokinetic model fit to cellular uptake data of Kerr et al. [10] for doxorubicin in non-small cell lung tumor cells.

Figure 2

Cellular pharmacodynamic model fits to data of Eliaz et al. [13] for B16F10 murine melanoma cells. (A) Two-mechanism peak concentration model. (B) CⁿT model. (C) Single Hill model of Levasseur et al. [7]. For the exposure times 24, 48, 72, and 96 hours, the data overlapped and only one symbol is visible. The model prediction curves also coincide.

Figure 3

Cellular pharmacodynamic model fits to data of Levasseur et al. [7] for doxorubicin effect on wild-type A2780 human ovarian carcinoma cells. (A) Two-mechanism peak concentration model. (B) CⁿT model. (C) Single Hill model of Levasseur et al. [7].

Figure 4

Cellular pharmacodynamic model fits to doxorubicin cytotoxicity data of Nguyen-Ngoc et al. [15] for mouse sarcoma cells. (A) Two-mechanism peak concentration model. (B) CⁿT model. (C) Single Hill model of Levasseur et al. [7].

Figure 5

Cellular pharmacodynamic model fits to data of Vrignaud et al. [17] data for doxorubicin cytotoxic effect on rat glioblastoma cells. (A) Two-mechanism peak concentration model. (B) CⁿT model. (C). Double Hill model of Levasseur et al. [7].

Figure 6

Cellular pharmacodynamic model fits to data of Walker et al. [18] for doxorubicin effect on human bladder cancer cells. (A) Two-mechanism peak concentration model. (B) CⁿT model. (C) Single Hill model of Levasseur et al. [7].