As we have already commented, the prognosis for a patient with a glioma is not encouraging and depends on many factors, among them the type of neoplasm and the grade of malignancy. The relatively simple mathematical model we propose takes into account the growth and diffusion rates of the glioma and tissue heterogeneity. As we have seen, the results in the previous sections are reasonably consistent with clinical data (Cruywa-gen et al. 1995, Tracqui et al. 1995, Cook et al. 1995, Woodward et al. 1996, Burgess et al. 1997, Swanson et al. 2000), so we believe that the model could be used to make predictions regarding the survival time of the patient following various types of treatment including surgical resection, radiation and chemotherapy.
A major problem with present treatment strategies is the local focus of therapy when the action of the tumour growth and invasion is elsewhere (see, for example, Gaspar et al. 1992 and Liang and Weil 1998). The failure of glioma treatment regimes represents a large portion of glioma clinical and experimental literature (for example, Yount et al. 1998 and other references there). Local therapies are desirable, of course, to reduce the bulk tumour which is mostly responsible for pressure-induced symptoms. However, they can not control the motile invading cells responsible for recurrence (Silbergeld and Chicoine 1997).
The most appropriate treatment for a given glioma tumour is often not at all clear, irrespective of whether or not the subsequent quality of remaining life is taken into account. Because of their invasive characteristics, malignant gliomas can rarely be cured by surgical or radiological resection alone. There is much new research on quite different treatments, such as tumour-attacking viruses. Varying degrees of resection have been shown to increase survival time only marginally for glioblastoma multiforme although the increase is generally more significant for the lower grade (anaplastic) astrocytomas. With the general failure of surgical resection alone, to increase the survival time of patients, multi-modality treatments have been developed combining resection, radiation and chemotherapies and other therapies. Giese and Westphal (1996) in their review article discuss the perspectives for antiinvasive therapy. Numerous clinical studies have attempted to demonstrate the effectiveness of various treatments and combinations (see, for example, Ramina et al. 1999 and numerous other references there). Counterintu-
itively, some combinations of therapies have been shown, for various reasons, to be less effective than each of the therapies separately. Fairly recently, it was found that ionizing radiation can inhibit chemotherapy-induced cell death (apoptosis) in certain glioblas-toma cells (Yount et al. 1998). (There have also been suggestions that antioxidants may in fact be exploited by the cancer cells to help prevent their destruction.) This type of multimodality treatment failure can be attributed to the induced mutation of cells exposed to harsh chemicals or radiation. Cancer cells are, by definition, mutated 'normal' cells, so with the accumulation of mutations, the cancerous cells progressively become more malignant and treatment-resistant. We discuss polyclonal models later when we discuss a modification of the basic model to consider chemotherapy treatment.
Clearly, there is a threshold of treatment sustainable by a given patient and determining the optimal minimal strategies is of major importance. Not only that, even with similar tumour sizes, histologic malignancy and anatomic location, certain treatments work better on some patients than on others. There is no one universal treatment, but in deciding the best course of treatment for patients it is necessary to take into account all of the available information regarding the cancer before proceeding. We believe that realistic modelling can help to address this complicated issue by quantifying certain virtual glioma behaviours with and without treatment.
As we shall see, with relatively slight alterations, our model can take into account the effects of chemotherapy, radiation and resection on the spatiotemporal behaviour of the tumour. This capability lets us compare projected growths and invasion of the tumour under various treatment scenarios, thereby giving some insight into the optimal therapeutic course. Given a sense of the location, size, shape, diffusion coefficient and growth rate of a specific tumour, our model can help to suggest the best type of therapy to maximize survival time, that is, the difference between the time of diagnosis and death.
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