Dr. Sanjeev Rajan Deepak Tandon
1
Supervisor Researcher
Dr. Sanjeev Rajan Deepak Tandon
(Reader)
Dept. of Mathematics,
Hindu (P.G.) College,
Moradabad
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:
- The variability in physiologically based pharmacokinetic model.
- 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 characteristicsthrough 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 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