Aymara Sancho-Araiz (1,2), Zinnia P Parra-Guillen (1,2), VÃctor Mangas-Sanjuan (3,4), Iñaki F. Trocóniz (1,2 )
(1) Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain. (2) Navarra Institute for Health Research (IdiSNA), Pamplona, Spain. (3) Department of Pharmacy Technology and Parasitology, Faculty of Pharmacy, University of Valencia, Valencia, Spain. (4) Interuniversity Institute of Recognition Research Molecular and Technological Development. Valencia, Spain.
Objectives:
Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks [1,2]. Most of the commonly used models describe natural growth with a basic function: linear, exponential, Gompertz. More complex models aimed to include tumor heterogeneity or biologic processes have also been described [1]. Despite this, tumor growth curves of these models follow a monotonic increase, and although they tend to capture individual TGD and variability in the data reasonable well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics. The overall goal of this work is to develop a mathematical model to describe tumor growththat can be systematically applied during the preclinical evaluation of new drug candidates.
Methods: Tumor volumes (TV) of 12 different cell lines from 6 tumor types (breast, leukemia, lung, lymphoma, melanoma, and pancreas) were available for the analysis. TVs from the different cell lines were analyzed using NONMEM 7.4. Different models ranging from more empirical to more mechanistic were explored. The model building was performed sequentially. First, the unperturbed tumor growth was characterized using previous models [2], and then the new structure was established. Numerical and graphical metrics, including residual-based diagnostics (weighted residuals and autocorrelation plots) and visual predictive checks (VPCs), were explored and compared for model selection and evaluation.
Results:
All the data were analyzed simultaneously through a joint modeling exercise, using the type of cell line as a categorical covariate. Gompertz TGD model, in which the relative tumor growth rate decreases until reaching its maximum carrying capacity, provided a good description of the data and was used as a core structure. The estimate of the first-order growth rate constant (kge), ranges from 0.0192 – 0.0951 days-1, with an inter-animal variability of 14.6%. With regard to the initial tumor size (TV0) and the maximum carrying capacity (Tmax), the estimates ranged from 10.2-56 mm3 and 228 – 10000 mm3, respectively. Despite VPCs and classical basic goodness of fit indicated and adequate model performance, a systematic missespecification was detected when exploring weighted residuals versus time and autocorrelation plots. From the different structures evaluated to describe the growth dynamics observed in tumor growth over time, the final model developed included an increasing tumor growing capacity dependent on the amount of nutrients and vasculature. In this regard, under restrictive conditions, i.e. the tumor size is a 10% lower than the growing capacity value, cancer cells trigger a signal able to initiate angiogenesis in order to further enable tumor regrowth. The new model significantly improved overall model performance, especially showing an improvement in the weighted residuals versus time and the autocorrelation plots.
Conclusions:
Systematical model misspecifications have been identified when using standard models to describe xenograft tumor growth dynamics from different tumor types and cell lines in preclinical arena. This work presents a new semi-mechanistic model capable of describing the non-monotonic growth and the interactions between tumor growth, angiogenesis, and nutrient supply. This framework constitutes a valuable tool to explore different mechanisms of action, thus supporting the rational design and selection of drug scenarios in monotherapy or combination during preclinical drug development.
References:
[1] Yin, A.; Moes, D.J.A.R.; van Hasselt, J.G.C.; Swen, J.J.; Guchelaar, H.J.; A, Y.; DJAR, M.; JGC, van H.; JJ, S.; HJ, G. A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors. CPT pharmacometrics Syst. Pharmacol. 2019, 8, 720–737, doi:10.1002/PSP4.12450.
[2] Benzekry, S.; Lamont, C.; Beheshti, A.; Tracz, A.; Ebos, J.M.L.L.; Hlatky, L.; Hahnfeldt, P. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth. PLoS Comput. Biol. 2014, 10, e1003800, doi:10.1371/journal.pcbi.1003800.
Reference: PAGE 30 (2022) Abstr 10218 [www.page-meeting.org/?abstract=10218]
Poster: Drug/Disease Modelling - Oncology