We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

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April 11, 2013

Speaker: Rochelle Albert, Ontario Tech University

Title: Investigating the Effects of an Inhomogeneous Cellular Environment, when Modelling the Apparent Diffusion Coefficient in Diffusion Weighted Imaging

Abstract: An overview behind the physics of MR imaging will briefly be introduced, with greater emphasis placed on how this imaging modality can be refined to measure diffusion levels in the brain i.e. Diffusion Weighted Imaging. The challenge behind modelling inhomogeneous cellular media of the brain will be examined, and a coupled system of one-dimensional cellular and extracellular channels will be posed as a model for this complex problem. An analytical approach to measuring the Apparent Diffusion Coefficient of the system will be explored, by utilizing both probability theory (generating a displacement probability distribution), and finding a solution to a mixed boundary eigenvalue problem. A root finding (secant) continuation algorithm will be introduced as a method for obtaining an infinite array of eigenvalues. Finally, preliminary results for the displacement distribution and ADC of the uncoupled system will be presented, alongside highlights for future endeavors for the coupled model.