Modeling of tumor growth and anticancer effects of combination therapy

Abstract

Combination therapies are widely used in the treatment of patients with cancer. Selecting synergistic combination strategies is a great challenge during early drug development. Here, we present a pharmacokinetic/pharmacodynamic (PK/PD) model with a smooth nonlinear growth function to characterize and quantify anticancer effect of combination therapies using time-dependent data. To describe the pharmacological effect of combination therapy, an interaction term was introduced into a semi-mechanistic anticancer PK/PD model. This approach enables testing of a pharmacological hypothesis with respect to an anticipated pharmacological synergy of drug combinations, such as an assumed pharmacological synergy of complementary inhibition of a particular signaling pathway. The model was applied to three real data sets derived from preclinical screening experiments using xenograft mice. The suggested model fitted well the observed data from mono- to combination-therapy and allowed physiologically meaningful interpretation of the experiments. The tested drug combinations were assessed for their ability to act as synergistic modulators of tumor growth inhibition by the interaction parameter psi. The presented approach has practical implications because it can be applied to standard xenograft experiments and may assist in the selection of both optimal drug combinations and administration schedules. The unique feature of the presented approach is the ability to characterize the nature of combined drug interaction as well as to quantify the intensity of such interactions by assessing the time course of combined drug effect.

Pharmacokinetic-pharmacodynamic modeling of the anticancer effect of erlotinib in a human non-small cell lung cancer xenograft mouse model

“…A percentage of the proliferating cells become non-proliferative due to drug action and pass through several stages of damage (X 2 , X 3 , …, X n+1 ) before they die (Figure 1), such that the total tumor volume contains the volume of proliferating cells and non-proliferating cells, ie, VOL=X 1 +X 2 +X 3 +…+X n+1 , whereas only X 1 , the volume of proliferating cells can be described by Eq 4. Therefore, it has been proposed that the growth of the tumor was slowed at the rate of X 1 /VOL [26] , and a constant parameter K bio proportional to E·X 1 was applied to describe the antitumor effect of pEGFR. Here, a pEGFR "inhibition index" E [E=1/(pEGFR/pEGFR 0 )-1] was used as the variable describing the pEGFR inhibition as reported [27] .…”

Preclinical PK/PD model for combined administration of erlotinib and sunitinib in the treatment of A549 human NSCLC xenograft mice

“…Although Gilbert Koch's model [20] described tumor growth as a smooth curve between the two growth phases, the linear growth parameter λ 1 could not be obtained in our model development. A semimechanistic model suggested by Simeoni [19] was eventually adopted in this study, with φ fixed at 20, with the assumption of a threshold tumor mass (w th ) existing between the exponential growth and linear growth phases.…”

“…In the combination groups, the combination index (φ) was introduced into the PK/PD model to explain the effect of the interaction of the two drugs on the drug potency [20] , and the model structure is shown in Figure 2. If there was no interaction between the two drugs, φ would equal 1, which indicates that the combinatorial effect of the two drugs is additive.…”

Modeling Tumor Growth for Kidney Cancer Based on Nuclei Clusters of Pathology Slides

“…To compute the growth parameters, the elements of feature data vector are then weighted with a dimensional coefficient matrix . The relation between the features and the parameters can be stated for a patient as: (3) where the vector for number of tumor growth parameters. Weight coefficients matrix, represented as in Eq.…”

“…Exponential-linear tumor growth model [1] built based on experimental observations is a well-accepted empirical model. Tumor mass grows exponentially until it reaches a certain weight and volume, at which increase in tumor size becomes linear due to nutritional and oxygen limitations [3]. In exponential-linear model, tumor growth is expressed as a function of rate constants and tumor weight or volume when no drug is administered [1].…”