There are numerous mathematical challenges surrounding the theory and practice of medical imaging. Images obtained with the various imaging modalities typically suffer from imperfections such as low resolution, low contrast, high noise level, modality-specific artifacts and geometric deformations. Furthermore, given the vast amount of data collected in these images, automated tools are needed that aid in analyzing the data.
These challenges are ripe for mathematical exploration. The PIs will spend the academic year 2010/11 at the Dartmouth Medical School and the Dartmouth Hitchcock Medical Center immersed in the study and application of medical imaging under the guidance of Dr.John B. Weaver. In addition to Professor Weaver, there is an active and accomplished cohort of faculty with imaging expertise both at the Thayer School of Engineering at Dartmouth and in the Radiology Department at the Medical School with whom the PIs will interact. The PIs will focus mostly on the segmentation problem and the registration problem as applied to digital tomosynthesis, although they intend to gain knowledge in all areas of medical image analysis during their immersion year. The PIs plan to use this experience to open and sustain a new avenue of research in their research profiles.
The PIs will use this experience to broaden the curricular offerings available to Wesleyan students in future years. They will offer a suite of classes at the advanced undergraduate/graduate level in areas such as the mathematics of imaging, data analysis, and medical imaging. They expect that this activity will lead to a significant evolution of course offerings in their department. With ongoing research in medical imaging we would also hope to be able to attract some graduate students into this important field.
Diffuse optical tomography is an emerging medical imaging technology that has considerable clinical promise. In its most common form, this imaging modality seeks to provide high contrast images of tissue via introducing near infrared light into the body and measuring it as it leaves the body. One then uses these measurements to detect certain optical parameters that allow discrimination between healthy and diseased tissue. The benefits of bringing this imaging technology to wide spread clinical prevalence are large, a most basic benefit being that near infrared light is non-ionizing and so in particular this is a very safe way to image a patient without having to be concerned about harmful radiation exposure. Our work during the duration of our Interdisciplinary Grants in the Mathematical Sciences was on using mathematics to understand how to make diffuse optical tomography generated images more sensitive to very small structures (e.g. tumors) in tissue. As near infrared light is highly scattered by tissue and body fluids, the images that one receives from diffuse optical tomography suffer from poor resolution and thus this inhibits its widespread clinical use. We were able to show that certain information is unrecoverable as one uses standard mathematical techniques to formulate an image from the data. Ongoing work hypothesizes that the reason for this information loss is that the standard model that describes light traveling through tissue finds solutions that are too smooth. We are currently investigating other less standard mathematical techniques that are likely to formulate solutions that don't suffer from this information loss problem. It remains our goal to aid the development of this technology as a viable and common patient safe method for the detection and treatment of diseases such as cancer.
