Branching development occurs in many organs such as the salivary
lung, and kidney. We have developed several alternative mechanical
of the tissue deformations of such branching development. We hope to
including (1) Is it necessary to assume a contribution from morphogens?
(2) Is active deformation of the epithelium or of the mesenchyme
for branching morphogenesis, or are both necessary in tandem? Are
or neither sufficient? (3) What is the mechanical role of the basal
separating the tissues? (4) What is the difference in mechanism which
to the very different morphologies of lung, salivary gland, etc.? (5)
How does the lumen form? This
work is supported by the NSF, and is in collaboration with Prof. Yasuo
Nakanishi of Osaka University, Prof. Zhilin Li of NC State
University, Dr. David Warburton of Children's Hospital Los Angeles, and graduate students Xioahai Wan (now at Capital One),
Qunlei Jiang, Oswaldo Lozoya, Erin Jerkins, and Megan Sawyer.
Lactic acid bacteria (LAB) are used in fermentation of food products, and may have an important future in preventing food poisoning through competitive exclusion of pathogens by inoculated LAB on fresh foods. We are studying several issues related to the growth, death, ecology, and metabolism of LAB: sensitivity to temperature, pH, and other factors, acid production, internal energy stores, life phases (lag, exponential, death), and interaction with other organisms. The mathematical modeling, parameter identification, and statistical analysis are leading to a much better understanding of the population dynamics of these important organisms. This work is in collaboration with Drs. Fred Breidt and Roger McFeeters of NC State, and has involved NCSU graduate students Dan Dougherty (now faculty at Michigan State), Prashant Mudgal, and Althea Smith.
A biomechanical question in cancer is how a capsule forms around a benign tumor, and why it fails to form around a malignant tumor. Capsules make diagnosis and surgical removal of tumors substantially easier, and are believed also to inhibit the growth of tumors. The existing competing theories of the mechanism of capsule formation are (1) expansion of the tumor compresses the passive normal tissue surrrounding it, (2) the tumor secretes copious amounts of fibrin, which stimulate an active wound healing response in the surrounding tissue. My two-phase model of the mechanics of tumor growth and tissue response provides a quantitative evaluation of the contribution which both phenomena provide to the formation of the capsule, applicable to the vast variety of types of cancer and types of host tissue and their associated mechanical parameter ranges.
Spectacular spatial patterns can be formed from the aggregation of
in an initially homogeneous environment, as they interact with each
and with their environment. We developed a chemotactic model of pattern
formation in cultures of E. coli and Salmonella typhimurium,
and a mechanical model of a non-chemotactic aggregating eukaryotic
which appears to generate pattern in vitro using only traction forces.
Our simplest assumptions led to experimentally observed patterns in all
of these systems under a wide range of conditions. The eukaryotic
is dependent on the cells dynamically changing the material properties
of their extracellular matrix. Our full model included large-strain
of an anisotropic viscoelastic material, and anisotropic diffusion.
A persistent problem in cancer chemotherapy is the similar toxicity levels of the agents in tumor and healthy tissue. As a result, many potential cures are missed because sufficient drug levels are not achieved. A patented two-step process involving monoclonal antibody-enzyme conjugates followed by relatively high doses of a nontoxic prodrug appears to succeed at localizing high doses of the toxic drug in the tumor while minimizing toxicity in the blood, and has had dramatic results in animal models. The modeling and analysis of this promising two-step process was joint work with Prof. J.D. Murray of the University of Washington, and graduate student Trachette Jackson (now faculty at U of Michigan), in collaboration with the research group of Dr. Peter Senter at the Bristol-Myers Squibb Pharmaceutical Research Institute in Seattle, who developed the process in nude mouse models.
In 25+ years' psychophysiological study of 4500+ married couples, Prof. John Gottman and his colleagues in the Department of Psychology at the University of Washington have determined astonishingly accurate criteria predicting the success or failure of marriages. We collaborated on his 5-year NIMH study which uses our mathematical framework to help determine appropriate therapeutic interventions to change the phase portrait of a distressed marriage. The specific aim is to determine the Minimal Marital Therapy necessary to cross the bifurcation between the stable and unstable systems.
Feline Leukemia Virus (FeLV) is a slow retroviral autoimmune disease of cats which is transmitted primarily by allogrooming (shared saliva). In collaboration with Joseph Romatowski, DVM, of the Cat Clinic of NE Seattle, we developed an SIRS model of the endemic epidemiology of FeLV. Analysis and parameter estimation allowed us to make estimates of the potential impact of two control measures, vaccination and euthanasia. We concluded that in the low-density free-roaming population, where the incidence is low, very low levels of intervention are needed to control the disease, but in the high-risk subpopulation of cats in high-density living arrangements, no amount of intervention can control the disease once it has taken hold. Thus the high-risk population acts as a reservoir for infection of the low-risk population.
Twining vines climb supports by means of a flagellar motion called
circumnutation. In Darwin's books on the subject it was observed that
most vines twine only to the right and the rest to the left. Inspired
by this chiral symmetry-breaking we studied what structural features
could lead to plausible chiral symmetry-breaking in common biological
models, including reaction-diffusion systems and coupled oscillators.
Our 1992 results are considered by some to be the first published work
leading to the now burgeoning field of Brownian ratchets.