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Supervisor
Dr. Sanjeev Rajan
(Reader)
Dept. of Mathematics,
Hindu (P.G.) College,
Moradabad
Researcher
Deepak Tandon
SUMMARY
The present thesis entitled “Mathematical Modeling in Pharmacokinetics” has
been completed under the guidance of Dr. Sanjeev Rajan Reader Department of mathematics,
Hindu college Moradabad. In this present thesis, we have discussed the characteristics of
blood flow in small arteries in the pulsatile flow. We have also discussed the Pharmacokinetic
Models of Blood Flow through large compliant vessels in hyperbolic system.
The research work carried out by me on “Mathematical modeling in
pharmacokinetics” is embodied in the present thesis, which is divided into five Chapters.
Two Research Papers have been accepted for publication in a reputed scientific
journal “Acta Ciencia Indica” entitled:
1.
The variability in physiologically based pharmacokinetic model.
2.
Pharmacokinetic model and optimal treatment with linear program.
Chapter One entitled “Introduction”, in this chapter the Historical background of
the Mathematical biosciences and its applications are discussed we survey briefly the various
developments in the field of mathematical modeling in biology and medicines which are
relevant to the Present work and finally given a short outline of the work in the thesis.
The second Chapter entitled “The blood flow characteristics through an artery
and locally constricted tube”. Several theoretical and experimental attempts have been made
to study the blood flow characteristics. It is divided into two sections. In the first section we
have discussed the blood flow character through an artery and in second section we have
discussed the study of blood flow through locally constricted tube. Also, we have given the
Numerical results and Graphical representations in this chapter.
The Third Chapter entitled “Partial differential equations modeling of blood flow
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through
large
compliant
vessels,
in hyperbolic
system”,
it
studies
a
comprehensive rigorous mathematical analysis of the quasilinear partial differential equations
with the initial and boundary data that correspond to pulsatile blood flow in large vessels.
The chapter four entitled “The study of effective equation modeling problem,
including the blood flow in small arteries” deals with derivation of the reduced (effective)
equations that hold the fluid structure interaction problem.
The chapter five entitled “A mathematical approach for pharmacokinetic models”
is divided into two sections. In the first sections we have discussed the modeling variability in
pharmacokinetics. In this part we have presented a theoretical framework and improved
adaptive numerical approach for system of ordinary differential equations affected by
parameter variability and uncertainty distributions. In second section we have discussed the
optimal treatments for photodynamic therapy with pharmacokinetic model.
I have included two research papers, which is my own humble original contribution.
Paper I entitled “The variability in physiologically based pharmacokinetic
model”. In this paper an attempt has been made to study a theoretical framework and
improved adaptive numerical approach for system of ODEs. We have proposed an improved
adaptivity control and demonstrate its power in application to typical systems in
Pharmacokinetics, where variability and uncertainty play an important role.
Paper II entitled “Pharmacokinetic model and optimal treatment with linear
program”. In this paper an attempt has been made to study the photosensitizer distribution so
that an optimization model is designed that answers, several questions related on the
photosensitizer’s affinity for cancerous cells and how light should be focused during
treatment.
In the end, as evident from above, the work done in the thesis has many mathematical
and biological applications and it may prove useful to the studies in mathematics,
Haematology and Biosciences.
June 2007
Deepak Tandon