Understanding the antiangiogenic effect of metronomic chemotherapy through a simple mathematical model

Abstract

h i g h l i g h t s • A mean field model for antiangiogenic chemotherapy is proposed. • Metronomic and maximum-tolerated schedules are compared by numerical simulations. • Metronomic schedules are found to be more effective in eliminating tumour cells.

Evaluating the efficacies of Maximum Tolerated Dose and metronomic chemotherapies: A mathematical approach

“…[27] (see also Ref. [24]). We assume that normal cells, cancer cells, endothelial cells, and the chemotherapeutic agent move randomly (normal diffusion).…”

“…We simulated two programs of chemotherapy. The first was an MTD protocol consisting of four drug administrations, each 21 days in duration [24]. For this treatment, the parameters used in Eq.…”

“…[23] to compare MTD and metronomic protocols. Rodrigues et al [24] compared a standard protocol of chemotherapy with metronomic chemotherapy, focusing on the antiangiogenic efficiency of metronomic chemotherapy in preventing tumor neovascularization.…”

“…In the present paper, we use a mathematical model to study antiangiogenic chemotherapeutic treatments and understand how they work. Specifically, we create a mathematical model of tumor growth in which (i) normal and cancer cells compete for resources; (ii) the malignant cells induce the proliferation of endothelial cells in order to enlarge the tissue carrying capacity for the growing solid tumor; and (iii) the chemotherapeutic drug, administered according to either the metronomic [5,14,20,[24][25][26] or the usual MTD schedules, has, in addition to cytotoxic, antiangiogenic effects. The use of this model was motivated by Ref.…”

“…The use of this model was motivated by Ref. [24], where the authors propose a system of ODEs to analyze the administration of a cycle-nonspecific chemotherapeutic drug on a tumor, which also acts on vascular endothelial cells, impairing angiogenesis and decreasing the carrying capacity for tumor cells. The present paper is structured as follows: in Section 2, we present the model and chemotherapy protocols; some theoretical results and numerical simulations are presented in Section 3 and discussed in Section 4; finally, we make some concluding remarks in Section 4.…”