Pak-Wing Fok
Resources and Links
Education
M.Sci. - Imperial College
Ph. D. - Massachusetts Institute of Technology
Postdoctoral - California Institute of Technology
Postdoctoral - UCLA
Research Interests
I am an Applied Mathematician with 3 main research interests.
Mathematical Modeling of Cardiovascular Systems: Atherosclerosis and Diabetes are costly diseases that have a complex effect on the human vasculature. For example, arteries can remodel, changing their mechanical properties and geometry, and affecting the local hemodynamical environment. In advanced atherosclerosis, dangerous plaques can form: their rupture can result in myocardial infarction or stroke. Diabetic arteries are often calcified with impaired flow characteristics. I am interested in using tissue-level models to gain insight into these diseases.
Mechanics of Growth: Biological tissues are unique in that they can undergo volumetric growth or resorption as they experience mechanical deformation. In solid mechanics, this is often represented by decomposing the deformation gradient into a product of a growth tensor and an elastic tensor. I am interested in modeling biological systems where growth is a dominant feature. Examples include diseased blood vessels and bacterial chains.
Parameter Estimation in Magnetic Resonance Imaging (MRI): The fitting of multi-component exponential functions to a noisy signal underpins much of MRI imaging. However, the process is highly ill-posed – many exponential functions with different parameters (coefficients and decay constants) can appear almost identical. I am interested in developing algorithms and computational methods that can stabilize the inference of these parameters.
