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Office: JE 379
Phone: (614) 688-3443
Email: pgrajdeanu@mbi.osu.edu
Personal Homepage: http://people.mbi.ohio-state.edu/pgrajdeanu
Mentors:
Research Area
I am interested in many aspects of mathematical biology including renal
physiology; cell metabolism; immunology; and formulating mathematical
models for various clinical problems. I believe that Math-Bio is a
fascinating subject and I would like to be one who will lead other
students in understanding the beauty, relevance, and importance of
mathematics applied in real life problems.
I completed my doctoral dissertation on stability results for various
problems of convection under the direction of Brian Straughan (University
of Durham/UK, Mathematics). Among the numerous real phenomena which
involves convection, there are two on which I focused: convection in a
layer of a non-Newtonian fluids (3rd and 2nd grade) heated from below
(Paula Budu, 2003; Paula Budu, in review) and convection in a porous media
(Paula Budu, 2001). The mathematical results are strong (unconditional
nonlinear results) and of high accuracy, due to the improved numerical
techniques that I have developed for each specific problem.
Most of my time at Duke University was dedicated to mathematical modeling
of renal physiology with Harold Layton (Duke, Mathematics) and Leon Moore
(SUNY at Stony Brook, Physiology). The projects model renal function at
the level of the nephron, the functional unit of the kidney. In
particular, I am studying the properties of the thick ascending limb (TAL)
and the tubuloglomerular feedback (TGF). The dynamic models for both
involve small systems of semilinear hyperbolic partial differential
equations with time-delays, which are solved numerically for cases of
physiological interest, or which are linearized for qualitative analytical
investigation. Numerical solutions of these PDEs help to integrate and
interpret quantities determined by physiologists in many separate
experiments (Paula Budu-Grajdeanu, Leon Moore, Harold Layton, 2005/2006 -
in review).
I have also worked with Mike Reed (Duke, Mathematics) and Frederick
Nijhout (Duke, Biology) in a research area which involves the applications
of mathematics to the study of various aspects of cell metabolism, in
particular, folate and methionine metabolism. The purpose of the project
is to use mathematics to understand normal folate and methionine
metabolism, DNA methylation, and purine and pyrimidine synthesis and then
to understand how they are affected by alterations in diet and gene
abnormalities (Frederick Nijhout, Michael Reed, Paula Budu, Cornelia
Ulrich, 2004).
I am now collaborating with Avner Friedman (Ohio State, MBI), and Richard
Schugart (Ohio State, MBI), and Brad Rovin (Ohio State Medical Center,
Nephrology), and Chris Valentine (Ohio State Medical Center, Nephrology)
on a project related to vascular access failure in hemodialysis patients.
We are developing a mathematical model that accounts for the influence of
oxidative stress and turbulent flow on growth factors; the interaction
among growth factors, smooth muscle cells, and fibroblasts; the effect of
these interactions on the stenosis at the venous anastomosis; the effect
of the anastomosis on the level of oxidative stress and degree of
turbulent flow. The mathematical model that we are developing can then be
used to make clinical predictions (eg. what happens if the level of a
particular growth factor is suppressed).
I am collaborating with David Terman (Ohio State, Mathematics/MBI), and
Janet Best (Ohio State, Mathematics), and Michael Paulaitis (Ohio State,
Chemical and Biomolecular Engineering) on an immunology project,
developing quantitative models of the adaptive immune system. In this
project, we have molecularly engineered surfaces using novel surface
patterning techniques to present on microarray chips ligands that
selectively bind to specific receptors on T-cell surfaces. Our focus is on
extending current technology to create microarrays for the localization of
cells through interactions of their surface receptors with immobilized
cognate ligands as a means of characterizing heterogeneous cell
populations. Chip development is complemented by the development of
computational methods: molecular computations/simulations of the binding
interactions, and evolution models of clonal expression/proliferation of
specific T-cell sub-populations.
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