Orestis Papatryfonos (1), James Yates (2), Michael J. Chappell (1)
(1) School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom (corresponding author e-mail: orestis.papatryfonos@warwick.ac.uk), (2) DMPK, Preclinical Sciences, GSK, Gunnels Wood Road, Stevenage, Hertfordshire, SG1
Objectives: This project aimed to compare the performance of models recently published in the literature that characterise tumour volume over time [1] for control data and data following administration of the anti-cancer agent Docetaxel from the PDXPortal database [2]. Novel mechanisms for coupling the PK (Docetaxel) model and the PD (Tumour volume) models were also considered. The objective was to determine a model that can be universally applied in a robust, generic manner across cancer cell lines. Various tumour growth models used in preclinical modelling were also considered and analysed to identify the model that provides the most accurate representation of the available data.
Methods: The analysis workflow consisted of two stages: control data analysis and drug data analysis. In both stages, experimental data from xenograft experiments on mice were utilised [2]. The cancer cell line analysed was for Invasive Breast Carcinoma. The unknown parameters in the control models were estimated using Monolix [3] and the corresponding population parameters determined in this phase were then integrated in the later stage of the analysis where Docetaxel was administered. Docetaxel PKs were modelled using a linear two-compartmental model consisting of a plasma and tissue compartment [4]. This model was coupled with the relevant differential equation model for rate of change of tumour volume considering a variety of different mathematical formulations for the coupling mechanisms as functions of the plasma concentration of the drug, and the corresponding parameters within these coupling functions were estimated in a population manner, again within Monolix. The two tumour volume models compared and analysed are those presented in [1] and [5]. In both, nutrient availability within the tumour is assumed to determine the rate of growth, with a distinction between proliferative and necrotic compartments.
Results: The control data analysis demonstrated the effectiveness of the various growth models, previously used in preclinical modelling studies, such as the Proliferative Rim, Surface Growth and Gompertz models [1] – all exhibiting satisfactory fits to the control data. This analysis was conducted using the Tumour Volume Model (TVM) from [1]. The Surface Growth model proved to be more suitable, since the RSE (%) for the unknown parameter a (coefficient of tumour volume growth term) in the Proliferative Rim model (= 14.73 (9.8×103)) (=value (RSE)) was 3 orders of magnitude larger compared to the Surface Growth model (= 0.26 (6.31)). Comparing the Diffusion-Limited (DL) growth model [1] with the model presented in [5], both of which incorporate Growth Fraction (GF) as a state variable, it was observed that both models exhibited similar fits to the data. However, a variation of the initial GF value revealed that for GF(0) = 0.25, the rate of cell death in the proliferating compartment μP (= 24×10-13 (600)) had a higher RSE (%) of 600 compared to GF(0) = 0.5 (= 91×10-9 (191)). A similar pattern was noted for the DL model. When drug was also considered, it was shown that the Gompertz model, when linearly coupled with the Docetaxel PK model, accurately fits the provided data, even with variations (outliers) in the population data. Similarly, for the case of the corresponding GF over time, coupling the DL model with a squared power of the plasma concentration formulation, yielded the most accurate results, as opposed to the model from [5] coupled with a Michaelis-Menten type formulation for the plasma concentration, which yielded some individual variations in the fits. The population estimates for the initial tumour volume value (V0) and drug potency (Kkill) specific to the DL model, obtained in Monolix, were 165.16 mm3 and 0.000056 (μMday)-1, respectively. Further validation of the models was achieved by examining the corresponding AIC and BIC model fit measures generated within Monolix.
Conclusions: Overall, this project aimed to develop a TVM that can generically describe real tumour growth data, with and without Docetaxel administration with respect to Invasive Breast Carcinoma population data. The effectiveness and validity of two distinct TVMs has been compared and analysed, providing significant insights. While both TVM from [1] and [5] demonstrate accuracy in the fits obtained, specific coupling mechanisms are identified as more adept at encapsulating the observed dynamics in the data for the different models considered.
References:
[1] Nasim, J. Yates, G. Derks, and C. Dunlop, “A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions,” Cancer Research Communications, vol. 2, no. 8, pp. 754–761, 08 2022. [Online]. Available: https://doi.org/10.1158/2767-9764.CRC-22-0032
[2] S. Bridges, “Pdxnet portal,” 2024, https://portal.pdxnetwork.org/ [Accessed: 13-03-2024].
[3] LIXOFT, “Monolix, the best tool for model based drug development,” 2024, https://lixoft.com/products/monolix/ [Accessed: 13-03-2024].
[4] N. D. Evans, R. J. Dimelow, and J. W. Yates, “Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts,” Computer Methods and Programs in Biomedicine, vol. 114, no. 3, pp. e3-e13, 2014. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0169260713002009
[5] J. Yates and D. Fairman, “How translational modeling in oncology needs to get the mechanism just right,” Clinical and Translational Science, vol. 15, 11 2021.
Reference: PAGE 32 (2024) Abstr 10921 [www.page-meeting.org/?abstract=10921]
Poster: Drug/Disease Modelling - Oncology