|
|
|
Dr.
Jiaxu Li is interested in studying real life problems possessing great
practical impacts, and enjoy the process of exploring relevances and offering
solutions to a wide spectrum of real world applications. By utilizing well
calibrated theories of ordinary differential equations (ODE), delay
differential equations (DDE) and dynamical systems, and his industry-tested
computational skills, Dr. Li's current primary research interest is Mathematical Biology and Medicine. In
today's integrative and cross-disciplinary research climate, mathematical
modeling is quickly evolving from a mainstream area of study into a core and
hot domain of scientific activities. Inversely, problems aroused from real
life stimulate the evolution and development of mathematics in novel
approaches and theories. This has been evidenced by the mutual stimulations
between physics and mathematics in past centuries. Life sciences have joined
the arena since last several decades. Most of
his current research work has involved the study of the regulations of
glucose and insulin regarding to the progression of diabetes mellitus.
Diabetes mellitus continues to claim a devastating role in society due to its
life-threatening complications. Diabetes mellitus is a leading cause of heart
disease, kidney failure, blindness and amputations, and other pathologies.
Diabetes affects 25.8 million, or 8.3% of the total population of the United
States, and up to 30% may be at risk according to the Fact Sheet of American
Diabetes Association (ADA), 2011 (http://www.diabetes.org).
This causes huge health care expenses to be 174 billion per year estimated by
ADA in 2007. The worldwide population of affected individuals is now over 200
million and growing rapidly. Despite decades of study, the factors
controlling the initiation and progression of diabetes remain to be fully
elucidated. Without a thorough understanding of the glucose homeostasis
system and its dysfunction in diabetes, researchers will continue to struggle
to develop new approaches to detect, prevent and/or delay the onset of
diabetes. Thus, a lack of basic knowledge and the inability to integrate
important but reductionist experimental findings into comprehensive models
stands in the way of providing more efficient, effective, and economic
therapies. Therefore, there is a pressing need for accurate mathematical
models employing the latest experimental findings. His major interests in
this area is to investigate how the system works, the pathways to diabetes
mellitus, and ultimately to provide more efficient and effective algorithms
for the treatments of diabetes mellitus in clinical applications. Dr.
Jiaxu Li's research interest also includes bioinformatics and gene
differentiations in small to medium sized gene network by mathematical
modeling approach (with Dr. Darling and Dr. Rempala). Pathways of
sequentially expressed transcription factors regulate terminal
differentiation of cells, including muscle cells, neurons, pancreatic acinar
cells, and so on. Cascades of transcription factors regulate, and are
regulated by, other transcription factors as well as extracellular signaling
factors. In such way, networks are formed with the capacity to control the
timing and progression of cell differentiation. Understanding the dynamic
behaviors as they change over the time during differentiation is essential.
Modeling by differential equation system is an appealing approach since it is
more accurate in modeling the functional aspects, provides an understanding
of the insights in the nonlinear behaviors, and can reconstruct the network
pathways by reverse engineering fashion. Information revealed from such
studies provides rational basis for tissue engineering or gene therapies for
diseases. Dr. Li
has great interests in other areas of mathematical biology as well, including
ecological models, and molecule models in chemical reaction. In addition, he
is interested and is ready to utilize his modeling skills in bioengineering,
control engineering and semiconductor industry, whenever opportunity arrives. In earlier days, Dr. Li focused on the qualitative analysis of Lienard's equation. Grants
|
|
|