VIGRE2 Vertical Intergration of Research and Education Department of Mathematics, University of Utah

Casandra Hutchinson








Mentor: Elena Cherkaev
Major: Mathematics, emphasis in Statistics

Fall 2006 project description:

My research will be focused on the detection and characterization of differences between osteoporotic and healthy bone structures. Osteoporosis is currently diagnosed with a bone density test, but is often not noticed until a fracture has occurred. I would like to research a new statistical way to characterize and model bone structure and diagnose osteoporosis. The structure of an osteoporotic bone is different from the structure of a healthy bone, and the void is much larger than that of a healthy bone. I will be looking at the structure of bone to see if there is a way to quantitatively describe it. Given a particular slice of bone material I would like to see if there is a way to look at many statistics of it in order to numerically characterize the bone - void structure and see how this statistics is different for healthy and osteoporotic bones. I will also be researching the reverse of the above process. I would like to see if, given some statistics, I can create some sort of model for the bone with void structure. Using these characteristics, I would like to see if there is a way to homogenize the theoretical bone structure, in order to predict the reaction of the bone. To be able to homogenize all bone structures would help to understand how different structures react to stress and how high is the risk of fracture. Being able to characterize a bone slice with statistics, and create a model of bone given certain statistics, would allow us to inspect the bone - void structure of each individual. Bones that are less dense have more void are osteoporotic, and at higher risk for fracture. These methods would hopefully allow doctors to more easily diagnose and perhaps predict the occurrence of osteoporosis before a fracture.

Fall 2006 REU Symposium presentation slides

Fall 2006 final report