A minimal model of tumor growth with angiogenic inhibition using bevacizumab

Abstract

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.

Modeling of Tumor Growth Incorporating the Effects of Necrosis and the Effect of Bevacizumab

“…A minimal tumor growth model under bevacizumab treatment was proposed in [13] and is further modified to create a more realistic tumor growth model in the following sections. The minimal tumor growth model can be explained with an analogy to chemical reactions.…”

“…This parameter was not tuned for the measurements in [13,17]; however the other parameters were identified from mice experiments in [13], and their values are = 0.27 1/day and = 0.0074 kg/(mg⋅day).…”

“…In [13], it was shown that tumor dynamics can be described by using a simple, first-order model (without pharmacokinetics) containing a linear and a bilinear term, where the bilinear term defines the effect of the drug on the tumor dynamics and ensures positivity of the system. This model has the ability to explain the experiments in which mice received one injection and almost every fundamental physiological process behind tumor dynamics.…”

“…In [17] it was shown that the therapy is much more effective if we give small doses of the drug each day as opposed to giving a much larger amount at the beginning of the therapy, regardless of the fact that the drug depletes slowly. Using the mixed-order pharmacokinetics and the pharmacodynamics in our model, we are able to describe this phenomenon that could not be described by the minimal model in [13].…”

Bi-compartmental modelling of tumor and supporting vasculature growth dynamics for cancer treatment optimization purpose

“…The vasculature density of the tumor environment is described as a function of the radius (ν(r)), while γ AI denotes the efficiency of the angiogenic inhibitor. The clearance rate of the angiogenic inhibitor is c AI , its value is defined following [11].…”