PK/PD model for Tumor Growth Kinetics under Therapy

This document presents a SimBiology model characterizing the pharmacokinetic /pharmacodynamic (PK/PD) behavior of anticancer agents as described in the article, “Predictive Pharmacokinetic-Pharmacodynamic Modeling of Tumor Growth Kinetics in Xenograft Models after Administration of Anticancer Agents” by Simeoni et al.

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Model Description

In 2004, Simeoni et al [1] proposed a PK/PD model to quantify the effect of anticancer drugs on tumor growth kinetics from in vivo animal studies. The drug pharmacokinetics were described by a 2-compartment model with bolus IV dosing and linear elimination (ke) from the Central compartment. Tumor growth was described as a biphasic process with an initial exponential growth followed by linear growth. The growth rate of the proliferating tumor cells, x1, was described by:

$$ \frac{\lambda_0*x_1}{[1+(\lambda_0/(\lambda_1*w)^\phi]^{1/\phi}} $$


$\lambda_0, \lambda_1$


are tumor growth parameters, x1 is the weight of the proliferating tumor cells, and w is the total tumor weight. In the absence of drug, tumor is comprised only of proliferating cells, i.e. w=x1 . In the presence of an anticancer agent, it was assumed that a fraction of the proliferating cells were transformed into non-proliferating cells. The rate of this transformation was assumed to be a function of the plasma drug concentration and an efficacy factor, k2 . The non-proliferating cells, x2 , go through a series of transit stages ( x3 and x4 ) and are eventually cleared from the system. The transit stages were added to incorporate delay between the addition of the drug and observable reduction of tumor weight. Flow through the transit compartments was modeled as a first order process ( k1 ).
PK/PD model for Tumor Growth Kinetics under Therapy


[1] Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I, and Rocchetti M (2004) Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Research 64: 1094-1101