Tumor-growth inhibition in preclinical animal studies: steady-state analysis of biomarker-driven models

Objectives: Three different models describing tumour growth inhibition (TGI) dynamics in xenografted mice are considered, two of which are biomarker-driven. The main objective is finding whether and under which conditions the tumour is eradicated or its volume tends to an asymptote. A further objective is to assess the explanatory capability of the models through their application to experimental preclinical data as well as their identifiability through simulated population data. Methods: A comparison is carried out between the drug-driven Simeoni's TGI model [1,2] and two recent biomarker-driven TGI models, called B1-Simeoni and B2-Simeoni [3]. These two models assume that the biomarker modulation, described by a type I indirect PK-PD model, is causal for tumour growth inhibition. To investigate the steady-state behaviours of the models, possible equilibrium values of the tumour volume have been analytically derived assuming that mice are exposed to constant plasma concentrations of a drug. For the B1- and B2-Simeoni models, the type I indirect model is used to obtain the corresponding steady-state biomarker inhibition, to be plugged into the biomarker-driven TGI model. A visual comparison between steady-state behaviours is obtained by plotting the output (equilibrium tumour volumes) against the input (constant drug concentrations). Models are fitted to literature data [4]. Estimated parameters are used to simulate different steady-state conditions. The models are also assessed in a population context by analysing simulated TGI data. In particular, the issue of model mismatch is considered by fitting data using a model different from the one used for generating them. Results: The stability analysis of the three models highlights two distinct behaviours. Both the standard Simeoni and B2-Simeoni models present a threshold concentration above which tumour eradication is asymptotically achieved. Conversely, in the B1-Simeoni model, the existence of a threshold drug concentration ensuring tumour eradication depends on the values of some parameters. All models explain well the experimental data. Conclusions: The aim of this work is to further investigate two biomarker-driven TGI models, comparing their steady-state behaviours with those of the standard Simeoni model. This analysis highlights the equivalence between standard Simeoni and B2-Simeoni models, whereas achievement of tumour eradication in the B1-Simeoni model depends on the parameters values. This work was supported by the DDMoRe project (www.ddmore.eu). References: [1] M. Simeoni et al. Cancer Research, 64: 1094-1101 (2004). [2] P. Magni et al. Mathematical Biosciences, 200: 127-151 (2006). [3] M. L. Sardu et al. PAGE 21 (2012) Abstr 2498 [www.page-meeting.org/?abstract=2498] [4] L. Salphati et al. DMD, 38: 1436-1442 (2010).