BackgroundBevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol.Materials and MethodsWe have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis.ResultsIn the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model.ConclusionOur results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration.

Tumor growth models are important to create an engineering background for cancer treatment either by using the models for simulations and evaluation of treatment protocols or, if combined with control engineering, by designing treatment protocols. A well-defined tumor growth model must describe the physiological processes and the measurements as well. Growing tumors are composed of dead tumor cells (forming the necrotic part) and living, proliferating tumor cells (forming the proliferating part); when tumor volume is measured, these parts are measured together. Most of the known tumor growth models do not consider the modeling of the necrotic part. Starting from a minimal model of the tumor growth under bevacizumab treatment, the aim of the current research is to extend it incorporating the volume and dynamics of the necrotic part and the pharmacodynamics and mixed-order pharmacokinetics of the applied drug. The extended model is validated using measurements with mice as hosts, colon adenocarcinoma as tumor, and bevacizumab as the drug used for treatment. The results show that the extended model can describe the important physiological phenomena and shows a good fit to the average of the measurements.

Abstract-Modeling the tumor growth under angiogenic inhibition is an important step towards designing tumor treatment therapies based on mathematical tools. Our goal is to create a model for tumor growth that describes the underlying physiological processes adequately while being as simple as possible. We propose a second-order model containing linear terms and one bilinear term modeling the dynamics of tumor volume and inhibitor level, and work out the parametric identification process for the model. The parametric identification of the model is done using measurements from experiments on C57Bl/6 mice with C38 colon adenocarcinoma treated with bevacizumab. The control group of the mice received one injection at the beginning of the experiment, these measurement data are used for parametric identification, while the case group of mice received injection at each day of the treatment, these measurements are used to validate the model. The validation showed that the proposed model is capable of describing the tumor growth dynamics.

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