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The prediction of the outcome of individual patients with glioblastoma would be of great significance for monitoring responses to therapy. We hypothesise that, although a large number of genetic-metabolic abnormalities occur upstream, there are two 'final common pathways' dominating glioblastoma growth - net rates of proliferation (rho) and dispersal (D).(More)
Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review(More)
Gliomas are brain tumours that differ from most other cancers by their diffuse invasion of the surrounding normal tissue and their notorious recurrence following all forms of therapy. We have developed a mathematical model to quantify the spatio-temporal growth and invasion of gliomas in three dimensions throughout a virtual human brain. The model(More)
Glioblastomas are the most aggressive primary brain tumors, characterized by their rapid proliferation and diffuse infiltration of the brain tissue. Survival patterns in patients with glioblastoma have been associated with a number of clinicopathologic factors including age and neurologic status, yet a significant quantitative link to in vivo growth(More)
Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the(More)
Gliomas are uniformly fatal forms of primary brain neoplasms that vary from low- to high-grade (glioblastoma). Whereas low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic tumors. Thus, interactions between glioma cells and their tissue microenvironment may play an important role in aggressive tumor formation and progression.(More)
AIMS The initial aims were to use recently available observations of glioblastomas (as part of a previous study) that had been imaged twice without intervening treatment before receiving radiotherapy in order to obtain quantitative measures of glioma growth and invasion according to a new bio-mathematical model. The results were so interesting as to raise(More)
Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in(More)
To delineate the causes of death (COD) in adults with supratentorial glioblastoma multiforme (GM) we reviewed 117 consecutive cases examined at autopsy over a nineteen year period at the University of Washington. Twenty cases (17%) had expired unexpectedly without ante mortem diagnosis, 5 patients (4%) had been diagnosed as having lower grade astrocytomas(More)
This paper is a natural three-dimensional extension of a simple two-dimensional mathematical model of glioma growth and diffusion. The model was originally constructed to simulate a case of recurrent anaplastic astrocytoma treated with chemotherapy, and then modified to allow estimation of the effects of the extent of surgical resection and of variations in(More)