Mixed-effect modelling of transient tumour growth dynamics following anti-angiogenic therapy
L G Hutchinson (1), E A Gaffney (1), P K Maini (1), J Wagg (2), A Phipps (3), H J Mueller (4), H M Byrne (1), B Ribba (2)
(1) Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, UK (2) Roche Pharmaceutical Research and Early Development, Clinical Pharmacology, Roche Innovation Centre Basel, Switzerland (3) Roche Pharmaceutical Research and Early Development, Clinical Pharmacology, Roche Innovation Centre Welwyn, UK (4) Roche Pharmaceutical Research and Early Development, Roche Innovation Centre Penzberg, Germany
Objectives: Anti-angiogenic (AA) therapy may give rise to a transient period where tumour blood vessels are less permeable and tortuous, and the tumour is better perfused . Experimental evidence suggests that the efficacy of radiotherapy and chemotherapy may be enhanced during this period . Identification of the timing of the normalization window could enable optimal design of combination therapy regimen.
Our objective is to characterize the vessel normalization window leveraging only tumour volume (TV) data in preclinical models treated with bevacizumab (BEV) and vanucizumab (VAN). To conclude, we simulate tumour response to a hypothetical cytotoxic drug administered inside and outside the inferred window.
Methods: BEV is an anti-VEGF antibody and VAN is a bispecific anti-VEGF/anti-Ang2 antibody. KPL-4 xenografted mice were randomized into control, BEV, and VAN treatment groups with n=10 per group. Each group received 5 weekly doses and tumour size measurements were taken twice per week.
We draw inspiration from seminal and recent models of tumour growth kinetics with and without AA therapies . In our model, we assume that TV undergoes logistic growth with a dynamic carrying capacity proportional to vascular volume.
We assume that the normalized vasculature transiently improves delivery of oxygen and nutrients, enhancing tumour growth via an increased carrying capacity. For model selection and fitting, we used Monolix for a mixed effects approach that leverages TV data. For model selection we compared the Bayesian Information Criterion (BIC) for each model, alongside visual predictive checks (VPC) and residual standard error (RSE) of population parameters and inter-individual variability (IIV).
Results: A model accounting for a transient period during which vessels deliver more oxygen and nutrients to the tumour describes the data well, as evidenced by diagnostic plots such as VPC and RSE<30% for population parameters and RSE<50% for IIV parameters.
Our simulations of the administration of a hypothetical cytotoxic drug show that the drug is more efficacious if administered during the transient window, leading to a greater reduction in TV than when it is administered outside the transient window.
Conclusions: Mixed effects modelling can be used to locate and parameterise the window of enhanced tumour growth, which may be a direct or indirect effect of the vessel normalization window, for KPL-4 xenografts leveraging only TV data. Our model predicts that cytotoxic therapy would be more efficacious if administered within the transient window.
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