Abstract
Gliomas, the most malignant and common primary brain tumor, can be treated aggressively with surgery, radiotherapy and chemotherapy. In spite of the treatment, recurrence seems inevitable and the improvement in survival has been minimal in the past 50 years. According to the recent studies, recruitment plays a significant and unclear role in human gliomas, and a new mathematical model (proliferative invasive recruitment (PIR) model) has been developed to explore the outcomes of cell recruitment, and it focus on the interaction between PDGF (Platelet-derived growth factor) paracrine signals and glial progenitor cells. Based on this, we used the tool of ODE that takes into account free PDGF in extracellular spaces (ECS), recruited glial progenitor cells, no retrovirus infection, and glial progenitor cell populations infected with retrovirus expressing PDGF, to construct a dynamic system of PDGF driving tumor growth. Finally we use some parameter data to calculate all dynamic characteristics, and use Matlab to carry out some numerical simulations to verify our theoretical results. In this study, statistical methods and mathematical theories were used to construct an auxiliary model to construct a dynamic system of PDGF driven tumor growth. All the dynamic characteristics are numerically calculated by using some parameter values, hoping to bring reference significance to clinical medical research.
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