Kristyn N. Shaffer
Whites Creek Comprehensive High School
Advanced Placement Calculus AB, Pre-Calculus with Trigonometry, Algebra I 

Ed Donnelly, MD, Ph.D,  - Medical Imaging Lab 

This summer, I had the privilege of working with Ed Donnelly, MD, Ph.D, and Ron Price, Ph.D in the Radiology Department.  Another participant in the RET program, Debbie Brown, also worked in the same lab.  We were able to work on two different research projects this summer.  Our focus for the first portion of our research was on testing to see if a FAXITRON cabinet X-ray system already being manufactured would be able to produce bone mineral density (BMD) images for use with small animals.  We tested this by imaging a phantom and eventually a real mouse at various levels of intensities for various lengths of time.  We also varied the filtering and anti-scattering devices in our attempt to produce an acceptable BMD image.  We processed the images using Image J to produce bone-only images, and we were in fact able to produce a BMD image using the FAXITRON cabinet X-ray system.  We also had the opportunity to present our information to representatives of the FAXITRON system, who were very pleased with our findings and will continue to investigate the scenarios that will produce the best BMD images.   

The second part of our research focused on investigating and evaluating X-rays that are scattered when an image is taken (rather than absorbed).  As part of our research, we examined various materials to see how the materials were scattered, how thickness of the material affected the scattering, and how different combinations of materials affected the scatter.  Eventually, the hope is that this method will allow better characterization of tissues than absorption and provide a way to reduce the radiation dose to the subject.   

The algorithms and processes used to produce the BMD images were based on Beer's Law, which involves logarithms and exponents.  The research I have completed this summer will allow me to write a teaching module concerning X-rays, BMD, and the mathematics involved in acquiring a BMD image.  The focus will be on logarithms and exponents, but there will be an emphasis on how the mathematics studied in class is applicable in the real world.