Analysis of the immunotherapy model for glioblastoma multiforme brain tumour

High grade malignant gliomas are among the most aggressive and deadly tumours. High grade MGs include such tumour types as anaplastic astrocytoma and anaplastic oligodendroglioma and GBM. These MGs vary in life expectancy but even with optimal care survival does not exceed 1.5 years for GBM and 5 years for the less aggressive forms [13]. Because of their refractiveness to conventional treatments including surgery, radiation and chemotherapy and because of their highly sensitive location – the brain – novel experimental therapies are sought, such as immunotherapy, in hopes they offer a survival advantage. Immunotherapy by exogenous administration of immune cells or immunoregulatory factors, offers a powerful tool which can allegedly destroy tumour cells and spare the healthy tissue. In this paper we model of MG treatment with adoptive alloreactive CTLs as performed in a clinical trial [15, 16] and following the ideas presented in Kronik et al. [14]. To obtain a clearer view of how to apply immunotherapy to MG patients a mathematical understanding of the system behaviour is mandatory. The dynamics of the tumour-immune cell interactions are complex, including cytotoxic function, immune cell cytokine modulation, extra cellular matrix migration, negative and positive feedbacks by paracrine and autocrine factors. As the central nervous system (CNS) is isolated by a selective blood brain barrier (BBB), it provides the tumour an immunologic privilege by excluding many components of the peripheral immune system [10]. Only activated T lymphocytes gain entry to the brain and even then they are short-lived [10]. Cells within the CNS may function as antigen presenting cells of the tumour cell by presenting tumour antigens (Ags) on major histocompatibility complex (MHC) class II molecules thus mediating lymphocytic CD4 T-helper recognition. Tumour cells enable recognition by means of Ags presentation on MHC class I molecules on their surface. However, immune cells that reach the MG itself often die out without performing their expected task [2, 11, 19, 22]. This is probably due to the immunosuppressive role of the cytokine TGF-β, whose levels are naturally high in the CNS [10]. The cytokine TGF-β suppresses the production of MHC class II [23], as well as the activation and proliferation of CTLs [24]. This down regulation of the immune reaction can be balanced by cytokines, such as interferonγ (IFN-γ), which increase MHC class I and MHC class II molecules expression by tumour cells [18, 21, 25]. Carpentier et al. [6] have shown that IFN-γ (together with TNFα) increases MHC class II expression on the surface of astrocytes, as well as T cell migration across the BBB vascular mobility [10]. Lately Kruse et al. [16] have shown alloreactive CTL infusions to be efficient treatment in MG. We include their suggested therapy in the model. Over the past thirty years the complex biological dynamics involved in cancer growth and therapeutics have been studied by mathematical modelling, e.g., [1, 3, 7, 20]. In particular, theoretical models of cancer immunology and immunotherapy have been put forward by, e.g., Kuznetzov et al. [17], focusing on the innate CTL response to the growth of an immunogenic