Ellsworth C. Alvord

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We have extended a mathematical model of gliomas based on proliferation and diffusion rates to incorporate the effects of augmented cell motility in white matter as compared to grey matter. Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, we have been able to simulate model tumours on an anatomically accurate(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)
During the past two decades computerized tomography (CT) and magnetic resonance imaging (MRI) have permitted the detection of tumours at much earlier stages in their development than was previously possible. In spite of this earlier diagnosis the effects of earlier and more extensive treatments have been difficult to document. This failure has led to an(More)
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)
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)
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)
Microcephaly and mental retardation have been principal features of the fetal alcohol syndrome. This article describes the neuropathologic findings in four human neonates who were exposed to large quantities of ethanol at frequent intervals during gestation. The findings suggest that intrauterine exposure to ethanol can result in structural abnormalities of(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)