Mathematical Optimization of the Combination of Radiation and Differentiation Therapies for Cancer

Abstract

Cancer stem cells (CSC) are considered to be a major driver of cancer progression and successful therapies must control CSCs. However, CSC are often less sensitive to treatment and they might survive radiation and/or chemotherapies. In this paper we combine radiation treatment with differentiation therapy. During differentiation therapy, a differentiation promoting agent is supplied (e.g., TGF-beta) such that CSCs differentiate and become more radiosensitive. Then radiation can be used to control them. We consider three types of cancer: head and neck cancer, brain cancers (primary tumors and metastatic brain cancers), and breast cancer; and we use mathematical modeling to show that combination therapy of the above type can have a large beneficial effect for the patient; increasing treatment success and reducing side effects.

Incorporating Cancer Stem Cells in Radiation Therapy Treatment Response Modeling and the Implication in Glioblastoma Multiforme Treatment Resistance

“…Therefore, many believe that CSCs are the driving force of cancer progression and that successful therapy must eradicate CSCs. Mathematical models have suggested that perhaps the dynamic equilibrium between the DCC and CSC compartments within a tumor is essential to the treatment outcome (12)(13)(14)(15). A "tumor growth paradox"dCSCs driven out of dormancy owing to spontaneous DCC cell death from therapy interventions resulting in accelerated tumor progressiondhas been previously demonstrated with mathematical models and biological experiments (16)(17)(18).…”

Mathematical Ecology of Cancer

“…Quite often a combination of these modalities is used (see e.g. [2]). The modelling of the expected treatment success by radiation treatment is an excemplary showcase of cross fertilization between ecology and cancer modelling.…”

“…Mathematical optimization of combination therapies has not been carried out in detail but it will be a focus for future studies [2].…”

A non-local model for cancer stem cells and the tumour growth paradox

“…Several candidate drugs are known and currently tested. In Bachman & Hillen (2012), the above ODE stem cell model (1.1) was used to test Lowengrub's hypothesis for specific cancers (secondary brain tumours, breast cancer and head and neck cancer). It was confirmed that for brain and head and neck cancers a combination therapy can reduce the necessary radiation dose, while the benefit for breast cancer treatment was limited (according to the mathematical model).…”