A blog hosted on github discussing topics related to data science, machine learning, and computer science.
A mini course I put together intended to provide an introduction to a few topics related to data science.
Diffusion of particles is described in terms of their root mean square displacement over some diffusion time. The motion of a freely diffusing particle is hindered only by collisions with other particles, and the net displacement of this particle is a random walk process as it bounces from one particle to the next. However, within a confined space a particle's motion is also impeded by the walls of the confining structure, and the diffusion process can no longer be described by a simple gaussian distribution of displacement. Rather, the distribution of displacements is specific to the geometry of the restricting walls. Because diffusion can be measured via Nuclear Magnetic Resonance, NMR and MRI provide a powerful technique for studying the microstructure of porous media such as lungs.
Magnetic Resonance Imaging is a non-invasive imaging technique that provides high contrast images of many medically important structures and processes in the human body. While pulmonary MR Imaging has traditionally been difficult due to the sparsity of lung tissue, the advent of new techniques in hyperpolarizing gasses such as 3He make it possible to image lung air spaces rather than tissue. In addition to high resolution images of lung ventilation, diffusion MRI provides information about the size and shape of the microscopic airways that account for over 90% of total lung volume making diffusion MRI an important new tool in diagnosing mild to severe emphysema and studying physiological changes of lung microstructure during a normal breathing cycle.
3He has several important advantages over other potential nuclear candidates for lung imaging. For starters, it's stable (non-radioactive) and inert (safe for human consumption). But 3He also has one gigantic disadvantage: it's rare, and, consequentally, very expensive (a big breath of helium-3 could cost over $2000). But this hasn't always been the case. Read the article I wrote for the Washington University Physics Department newsletter to learn more about why the cost went up (and why it was so low in the first place), why we will continue to use 3He, and what the science community is doing to ensure that important research using 3He continues. The article is on the second page of the newsletter and is titled "Reducing, Reusing, and Renewing Interest in Alternatives to 3He".