Estimating the kinetic parameters of vascular tumor growth models to optimize anti-angiogenesis drugs delivery
B. Ribba, E. Watkin, M. Tod, P. Girard, B. You, B. Tranchand, E. Grenier, G. Freyer
INRIA Rhône-Alpes, Project team NUMED, Ecole Normale Supérieure de Lyon, Lyon, F-69364, France; Université Lyon 1, EA3738, CTO, Faculté de Médecine Lyon Sud, F-69600 Oullins, France
Objectives: Optimizing the delivery of anti-angiogenesis drugs requires the development of relevant drug-disease models of vascular tumor growth. We aim to characterize the dynamic of tumor growth and angiogenesis - the process of intra-tumoral blood vessel formation - in xenografted mice by means of mixed-effect modeling techniques.
Methods: Subcutaneous xenografts of human colorectal HT-29 and HCT-116 cells were implanted in athymic mice. Two diameters were recorded for each animal every 2−3 days and tumor volume was calculated. Mice were sacrificed at different times and tumors were analyzed by means of histochemistry techniques. Blood vessel surfaces and diameters, as well as percentage of necrotic tissue and proliferation index were assessed. Monolix 2.4 [1] was used to estimate the parameters of the mixed-effect models.
Results: Tumor dimension data coming from 29 mice (15 bearing HT-29 cancer cells and 14 bearing HCT-116) representing 314 observations were analyzed separately. A 5-parameters model combining an early exponential growth phase followed by a power-law better fitted the tumor volume data than the usual 3-parameters modified-Gompertz model [2]. The gain Akaike information criteria was -53.8. Tumor diameter data were also analyzed by means of a new model combining a logistic growth coupled to an exponential growth. Population and individual predictions depicted, for some mice, a transient deceleration in tumor growth.
The analysis of the relationship between the tumor growth behavior and histochemical data showed that only the percentage of necrotic tissue could be associated to the switch in tumor growth velocity.
Based on these results, we developed a mechanistic model composed by a system of three ordinary differential equations to describe vascular tumor growth in xenografted mice.
Conclusions: Using mixed-effect modeling techniques, we showed that a structural model combining an exponential growth followed by a power-law may be more relevant than the classical modified-Gompertz model to fit tumor growth volume data. Analyzing tumor diameters led us to propose a mechanistic model of tumor growth and the process of angiogenesis. Monolix software and SAEM were necessary to correctly identify the different parameters of this complex mechanistic model. We are presently using this model to optimize the delivery of anti-angiogenesis drugs Sunitinib in combination with chemotherapy FOLFIRI in xenografted mice.
References:
[1] Kuhn E, Lavielle M. Maximum likelihood estimation in nonlinear mixed effects models. Comp Stat Data Anal. 2005. 49(4):1020-38.
[2] Simeoni M, Magni P, Cammia C, et al. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 2004;64:1094-101.