Daniel Keenan


My research has been in three main areas: statistical inference for stochastic processes and complex systems; statistical modeling in image processing, pattern theory and machine learning; and, quantitative modeling in medicine and physiology. My Ph.D. thesis (1980), and subsequent research from 1980-84, was in the area of statistical inference for stochastic processes, in particular, time series analysis. Two of the topics were: determining whether the dynamics of a system are linear or nonlinear and the recovery of phase information from higher-order spectra. In 1984, I went to the Division of Applied Mathematics, Brown University, as an NSF Postdoctoral Fellow in the Mathematical Sciences, with Professor Ulf Grenander as mentor. The fellowship lasted 2 years. I stayed on as an assistant professor (research) until Sept. 1989, working with Prof. Grenander in applied mathematics.

During the early 1980’s, Ulf Grenander introduced the method of stochastic relaxation (later called Markov Chain Monte Carlo, including Gibbs Sampling), by which a variety of previously intractable problems were reduced to the question of being able to simulate, repeatedly, from a very-high dimensional probability distribution. The ideas were part of a broader approach to the statistical inference for large-scale systems, which he termed Pattern Theory (today’s machine learning and regularization can be viewed as special cases). Many of the intractable problems arose from historically difficult issues in computer vision and image processing. Jointly, with Prof. Grenander, I worked on various aspects of this theory, and we applied the methodology to a host of practical problems. We also introduced what has become a widely applied method for object recognition in computer vision, the method of deformable templates, in which an object (of a particular ``shape'') is viewed as a deformation (broader than that of traditional geometries) of a given prototype; we wrote a book on this topic (Springer-Verlag, 1991). I continued working in these areas until 1994. Several specific topics of PhD student theses were: the reconstruction of a fetal head from ultrasound images in order to assess abnormalities (e.g., spina bifida); the detection of minefields using infrared imaging; the recovery of a submarine’s motion from an array of passive non-directional sonar sensors; and, the automated map generation of on-ground material (roads, buildings, water, vegetation) from satellite hyperspectral imagery.

Starting in 1994, I became interested in the application of statistics and mathematics to medicine. I began working with medical scientists, in particular Dr. Johannes Veldhuis, MD, an endocrinologist at the Mayo Clinic. After several years of research, I realized that the greatest potential for discovery would come if I also had a reasonably good understanding of medicine. From 2001-2005, funded by a NIH career award (K-01) and a NSF Interdisciplinary Grant in the Mathematical Sciences, I was able to devote 4 ½ years full-time to training and the merging of math and medicine. I did the MD Years I and II coursework (for credit), as well as other biomedical training (the PhD coursework for pharmacology, etc). I spent one year doing animal surgeries in preparation for writing a Pharmacology PhD thesis, but decided that it was not the best use of limited time.

The research from 1994 to the present has been a statistical and computational biological approach to questions in biology and medicine with the objective being their translation into clinical procedures. The focus was on the development of methods by which one could define and quantify the complex feedback and feed-forward regulatory control mechanisms of hormonal systems. Utilizing the methods, one was able to identify regulatory changes, potentially the pathogenesis, that underlie aging and various disease states. The research began with the construction of a model for the pulsatile secretion of a hormone and its (justified) recovery by the deconvolution of a hormone concentration time profile into secretion and elimination rates. The models allowed one to calculate the various entities of importance: total daily basal and pulsatile secretion and the fast and slow half-lives of elimination. We then began to model the dynamics of entire systems, starting with the simpler male reproductive (GnRH-LH-testosterone) system. It was then extended to the modeling of the so-called stress axis (CRH-ACTH-cortisol), the growth hormone axis (GHRH-GH-IGF-1) and several others. In all of these, a host of issues had to be resolved and modeled, e.g., the advection and diffusion of the hormones throughout the blood and tissue, on- and off-binding to carrier proteins by the steroids, their clearance kinetics, the binding of steroidal hormones to their intracellular receptors and peptide hormones to their plasma membrane receptors, and finally the secretion driven by one or more ligands. The methods have become widely applied in medicine to answer questions of how and why hormonal changes occur with age, gender and various pathologies.

In 2011, I began working with Dr. Donald Pfaff, a neurobiologist at Rockefeller University. For the past several years, he has been laying the groundwork for a theory of brain arousal and this is the topic on which we are jointly working. The experimental framework involves electrophysiological and genetic mouse studies, in addition to Deep Brain Stimulation (DBS) and other experimental settings. The resulting behavior studied in the small animal is that of locomotion, the most primitive form of behavior. This work is my major focus currently. We have recently developed novel methods for reconstructing the brain arousal stimulus-response curves, even though the stimuli are not observed. Based upon this, the concept of Generalized Arousal is made precise. Finally, with some of my PhD students, I have also begun interacting with Dr. Mark Hallett, MD, of NINDS (NIH), where we are developing models for brain-muscle control, utilizing transcranial magnetic stimulation (TMS). The use of TMS for understanding movement disorders has shown great promise.