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Well-posedness of Two Mathematical Models for Alzheimer's Disease
, M.Sc. Thesis Sharif University of Technology ; Hesaaraki, Mahmoud (Supervisor)
Abstract
In season 1, we introduce a mathematical model of the in vivo progression of Alzheimer’s disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of Aβ -amyloid plaques based on the concentrations of Aβ oligomers, PrPC proteins, and the Aβ-×-PrPC complex, which are hypothesized to be responsible for synaptic tox- icity. We prove the well posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of β-amyloid is constant and also when it is described by a power law. In seson 2, We consider the existence and uniqueness of solutions of an initial-boundary...
Cellular model of electroporated tissue for ultrasound RF data analysis
, Article 2009 International Conference on Advances in Computational Tools for Engineering Applications, ACTEA 2009, Beirut, 15 July 2009 through 17 July 2009 ; 2009 , Pages 652-655 ; 9781424438341 (ISBN) ; Zahedi, E ; National Instruments; MSC Software; Pro Mech ; Sharif University of Technology
2009
Abstract
Electroporation is permeabilization of the cell membrane, caused by an external electric field. Because of minimal thermal effects and minimal disturbance caused to tissue vasculature electroporation is becoming one of the methods of choice in tumor therapy. There has been no report indicating that reversible electroporation can be detected by ultrasound. In this work a cellular model for monitoring the electroporation process b; ultrasound RF signals is proposed. The density of aqueous pores with different sizes was found by applying the asymptotic model of electroporation and Smoluchowski equation. The cellular model was send to an ultrasound simulation program where pores were modeled by...