Numerical simulation of vascular tumour growth under antiangiogenic treatment: addressing the paradigm of single-agent bevacizumab therapy with the use of experimental data

Abstract

BackgroundAntiangiogenic agents have been recently added to the oncological armamentarium with bevacizumab probably being the most popular representative in current clinical practice. The elucidation of the mode of action of these agents is a prerequisite for personalized prediction of antiangiogenic treatment response and selection of patients who may benefit from this kind of therapy. To this end, having used as a basis a preexisting continuous vascular tumour growth model which addresses the targeted nature of antiangiogenic treatment, we present a paper characterized by the following three features. First, the integration of a two-compartmental bevacizumab specific pharmacokinetic module into the core of the aforementioned preexisting model. Second, its mathematical modification in order to reproduce the asymptotic behaviour of tumour volume in the theoretical case of a total destruction of tumour neovasculature. Third, the exploitation of a range of published animal datasets pertaining to antitumour efficacy of bevacizumab on various tumour types (breast, lung, head and neck, colon).ResultsResults for both the unperturbed growth and the treatment module reveal qualitative similarities with experimental observations establishing the biologically acceptable behaviour of the model. The dynamics of the untreated tumour has been studied via a parameter analysis, revealing the role of each relevant input parameter to tumour evolution. The combined effect of endogenous proangiogenic and antiangiogenic factors on the angiogenic potential of a tumour is also studied, in order to capture the dynamics of molecular competition between the two key-players of tumoural angiogenesis. The adopted methodology also allows accounting for the newly recognized direct antitumour effect of the specific agent.ConclusionsInteresting observations have been made, suggesting a potential size-dependent tumour response to different treatment modalities and determining the relative timing of cytotoxic versus antiangiogenic agents administration. Insight into the comparative effectiveness of different antiangiogenic treatment strategies is revealed. The results of a series of in vivo experiments in mice bearing diverse types of tumours (breast, lung, head and neck, colon) and treated with bevacizumab are successfully reproduced, supporting thus the validity of the underlying model.ReviewersThis article was reviewed by L. Hanin, T. Radivoyevitch and L. Edler.

Model driven optimization of antiangiogenics + cytotoxics combination: application to breast cancer mice treated with bevacizumab + paclitaxel doublet leads to reduced tumor growth and fewer metastasis

“…Both cytotoxic and anti-angiogenic properties of paclitaxel were integrated in our model (27). However, for the sake of practical usability and identifiability of the model, we skipped the thorough mechanistic description of the process as proposed by other models [ 15 – 18 ], or more detailed modeling of the anti-VEGF effect of bevacizumab [ 28 , 29 ] or paclitaxel tumor penetration [ 30 ]. Despite this, considerable standard errors remained in the estimation of the parameters, in part due to the large uncertainty in the measurement themselves, which is intrinsic to the measurement technique (kinetics of luciferin distribution in heterogeneous tumor mass).…”

Anti-angiogenic drug scheduling optimisation with application to colorectal cancer

“…In this study we extended an ODE model describing vascular tumour growth under angiogenic signalling presented in 18 to account for FOLFOX treatment. To this end, the pharmacokinetic properties of FOLFOX have been incorporated into the model and the combination therapy effect has been simulated for FOLFOX and bvz.…”

“…We adopted this approach because the data we have is primarily in the form of tumour volume time series and hence by saving the output from our ODE model at times corresponding to the experimentally measured tumour volumes, we could make a fair comparison between the model and data. The ODE model we used to simulate vascular tumour growth is defined in great detail in 18 but we summarise here the key assumptions.…”

“…Notwithstanding these studies, widespread application of cellular automaton models is difficult due to their computational cost, which further renders a comprehensive Bayesian parameter estimation study unfeasible. Significant progress has been made by incorporating a refined two-compartmental model to capture bvz pharmacokinetic properties 18 into a previously developed vascular tumour growth model 19 . This approach was based on the ordinary differential equation model of 20 .…”

“…To address this question experimentally, we employed the gold-standard HCT116 CRC xenograft model which underwent treatment with a paradigmatic folinic acid, fluorouracil and oxaliplatin (FOLFOX) chemotherapy + anti-VEGF (bvz) regimen commonly employed in the clinical management of metastatic colorectal cancer (mCRC). With respect to the computational aspect of this work, we expanded the mathematical model of 18 and conducted an extensive Bayesian parameter fitting of this extended model. We fitted the model to time series CRC xenograft tumour volume data obtained from vehicle treated subjects, bvz monotherapy treated subjects, and FOLFOX monotherapy treatment subjects respectively.…”