On April 17, 2017, members of CAMM met with the Center for Biomedical and Brain Imaging (CBBI) for an informal workshop to discuss mutual interests. The faculty were joined for the duration of the meeting by Associate Dean for the Natural Sciences, John Pelesko, and the chairperson of Department of Mathematical Sciences (DMS), Lou Rossi. The workshop also included representatives from DMS, Delaware State University (DSU) and the Christiana Care Health System. The workshop was organized by Richard Braun, associate director for outreach of the Center for Application of Mathematics in Medicine (CAMM), and Keith Schneider, director of CBBI and member of the Dept of Psychological and Brain Sciences (DPBS).

Both CAMM and CBBI are centers located in the College of Arts and Sciences. CAMM is based primarily in DMS, but includes members from the Colleges of Engineering and of Agriculture and Natural Resources. CBBI is based in DPBS but also includes members from these colleges, as well as the College of Health Sciences.

The workshop began with an informative tour of the CBBI facility by Keith Schneider, in which he fielded many questions. The tour featured the state-of-the-art 3 T (tesla) magnet for functional magnetic resonance imaging (fMRI) that can image human and animal subjects. This incredibly strong magnet with extensive supporting infrastructure enables mapping of brain activity via imaging of blood flow to active areas in the subject while an activity is carried out on command. The system can also produce static images at millimeter resolution. The tour could have continued for much longer, but in order to stay close to a schedule, we retired to the CBBI conference room for introductions and then talks.

The talks were very short, aimed to stay within 7 minutes including questions. These short talks are essentially advertisements about the issues and opportunities associated with the projects presented. We alternated between CBBI and CAMM speakers to stimulate cross-fertilization of ideas. The topics from CBBI varied from MRI and fMRI (Schneider, DPBS; Ashutosh Khanda, Physical Therapy; Meg Sions, Physical Therapy) to graph theoretic approaches (Jeff Spielberg, DPBS) to magnetic resonance elastography (Curtis Johnson, Biomedical Engineering). Approaches from DMS included finite element method computation (Constantin Bacuta), modeling of atherosclerosis (Pak-Wing Fok), analysis of large networks (Dominique Guillot) and models for colon cancer and tissue structure (Bruce Boman, DMS and Christiana Care). Shanshan Ding of applied economics and statistics discussed work on model and dimension reduction for large data sets as well.

Chad Giusti, currently a postdoctoral fellow at U Penn, discussed applied topology and topological data analysis for the brain. The approach seems very promising for the features of the complex structures observed. He will join the DMS faculty for the Fall 2017 semester.

Attendees beyond the speakers included Hacene Boukari of DSU's Dept of Engineering and Physics, as well as the following faculty from DMS: Nayantara Bhatnager, Sebastian Cioaba, Toby Driscoll, Mahya Ghandehari, Rakesh, and Gilberto Schleiniger. Toby Driscoll is CAMM's director.

The workshop helped identify some common themes. These included network and topological methods to describe the brain, where the tremendously complex structures seem to demand new mathematical descriptions. They also included segmentation of images from MRI and fMRI images, that is, more automatic ways to find the features to be measured and studied. Mathematical modelers also sought support for imaging the processes that their equations described.

We hope that the workshop spurs collaboration among the varied researchers that participated. Sebastian Cioaba currently works with Jeff Spielberg on network models for the brain, and Gilberto Schleiniger collaborates with Bruce Boman on colon cancer models. More collaborations like these would help advance the missions of both centers.

CAMM and CBBI are grateful for support from the Dean's Office in the College of Arts and Science, and for the organizational assistance of Mrs. Linda Popowich of DMS.