Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

Abstract

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

Optimal regulation of tumour-associated neutrophils in cancer progression

“…-It has been reported that a more realistic clinical situation employs linear cost functions. These types of problems have been used in several works devoted to the administration of single and combination therapies to treat different types of tumours [129][130][131][132][133]. On the contrary, a study by Glick & Mastroberardino [74] concluded that quadratic control yields continuous, low doses of the therapeutic drug producing a better outcome in the eradication of the solid tumour.…”

Computational simulation of gliomas using stochastic methods

“…Stochastic processes are ubiquitous in biological systems. In particular, the interface of cancer cells with surrounding healthy tissue provides a relevant scenario for stochastic processes (Rodríguez et al 2017). In the present work, the stochastic methods of the Causal Cone and Monte Carlo were used.…”

Optimal Combinations of Chemotherapy and Radiotherapy in Low-Grade Gliomas: A Mathematical Approach

“…A number of mathematical studies have constructed in-silico models to determine the optimal delivery scheme for either radiation therapy [ 16 , 17 , 18 , 19 , 20 , 21 ] or chemotherapy [ 22 , 23 , 24 , 25 , 26 , 27 ] alone. However, although mathematical models have potential for the study of optimal combination treatments [ 28 ], no studies have addressed computationally the question of what might be the best combination scheme of TMZ and RT for LGGs.…”