Dr. Roman M. Zaritski's Ph.D.
Research
SUNY at Buffalo, Math. Dept., 1996-1999
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In my PhD research I modeled the complex dynamics of the nephron Glomerular
Filtration Rate (GFR). Each human kidney has about a million nephrons (which
filtrate blood).
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The most important component of the existing GFR models is the so-called
Tubular-Glomerular Feedback (TGF). Thus, TGF is responsible for the famous
oscillatory dynamics of the GFR, but it does not explain more complex filtration
dynamics, which was observed experimentally. Mathematically TGF is usually
modeled by a nonlinear PDE with delay.
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One of my directions included modeling two neighboring nephrons, which
affect each other, thus producing more interesting dynamics (e.g. beats).
Mathematically this model is a system of two coupled nonlinear PDE's with
delay.
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The second approach I used is an attempt to model a nephron together with
its afferent arteriole, which delivers blood to the nephron, and which
is known to have a complex dynamics itself (myogenic mechanism). The mathematics
here involves PDE's, ODE's, algebraic systems, and integral equations.
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I studied the above models in two directions:
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Analytical: mostly bifurcation analysis
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Numerical: difference schemes and computer simulations
Run a Java Applet
for graphical demonstration of the GFR in two coupled nephrons.