Stochastic model of cancer growth with the effect of glycosaminoglycans (GAGs) as anticancer therapeutics - Mazma Syahidatul Ayuni, Mazlan (2019)
Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) have been widely used to describe the biological process of cancer growth. In natural phenomena, the untreated cancer growth is influenced by random effects as the result of uncontrolled factors in the human body. In addition, the dynamical behaviour of cancer cell growth rate depends on not only its structure at the present time, but also on its structure at a previous time. Thus, ODEs and SDEs are not capable to model the uncontrolled fluctuation and delay feedback for the untreated cancer growth process. It is necessary to model the untreated cancer growth process via stochastic delay differential equations (SDDEs). Nowadays, cancers are traditionally treated with surgery, chemotherapy, and radiotherapy. However, the most advanced treatment for cancer is targeted therapies. In this research, the drug that is used is Glycosaminoglycans (GAGs). The content of GAGs indicates the presence of Chondroitin Sulphate (CS). The effects of CS on the processes related to biological systems is crucial to promote apoptosis. For this research, CS is extracted from Blue-spotted stingrays, taken from Wild Life Handler Resource, Selangor. For the treated cancer growth, CS can be employed for targeted cancer therapy. The untreated cervical and breast cancer data for this research is taken from Hospital Sultanah Nur Zahirah (HSNZ), Kuala Terengganu. Laboratory experiments of CS for treated cancer cell is done in International Islamic University Malaysia (IIUM) on HeLa (cervical cancer) and MCF-7 (breast cancer) cell lines. The experimental treated data is used to validate the stochastic model. CS has significantly reduced cell viability of Hela and MCF-7 cell lines. Futhermore, the mRNA gene expression of HeLa and MCF-7 cells are studied using the RT-qPCR technique. The apoptotic gene, activation caspase3 is only presented in HeLa cell line. Understanding the quantitative dynamics of the protective anticancer, CS to cancer cell proliferation is required in designing an effective treatment. Mathematical model can be used as a tool in promoting knowledge about the effects of CS in cancer growth. The cell growth of cancer is influenced by uncontrolled factors, which is referred to as noise. To date, no deterministic or stochastic models have been formulated to represent the growth of cancer affected by CS. Thus, this research is carried out to formulate the deterministic and stochastic models for cancerous growth affected by CS as anticancer therapeutics. A new stochastic system for the treated cancer growth affected by anticancer therapeutics of CS is formulated via SDEs. The kinetic parameters is estimated via non-parametric stimulated maximum likelihood function. Numerical method of 4-stage stochastic Runge-Kutta (SRK4) is employed to simulate the solution. The algorithms of simulating the numerical solution are then developed. Numerical solution of stochastic model is adequately described the effects of CS on HeLa and MCF-7 cell lines compare than its deterministic counterpart. The newly developed of stochastic model is expected to be appropriate for other types of cancer cells as well. The findings of this research may help physicians and biologists planning better strategies for treatment of cancer.