Dr Qianqian Yang - On the study of fractional diffusion equations: a journey from numerical solutions to applications in MRI

Abstract: The concept of fractional calculus had been kept for 300 years among pure mathematicians. But in the last two decades, the applications of models with fractional derivatives in many fields of engineering and science made the concept of fractional calculus become more and more widely spread and accepted. This talk will consist of two parts. In the first part, I will discuss the computational challenges faced by the researchers in solving fractional diffusion equations and introduce some efficient numerical solution techniques, such as the preconditioned Lanczos method. In the second part, I will discuss how we use fractional diffusion models to differentiate tumour layers in a mouse brain tumour study. I will also discuss how the anomalous diffusion model parameters change with age in the human corpus callosum subregions.

Bio: Qianqian is a senior research fellow in the School of Mathematical Sciences at Queensland University of Technology. She has extensive experience in developing computationally efficient methods for solving fractional order partial differential equations. With this background, her recent research interest lies in the application of these fractional-order models to real-world problems, especially in the area of using anomalous diffusion MRI models to probe brain tissue microstructure.