NDLI: Cancer Drug Delivery in Three Dimensions For a Distributed Parameter Control Model Using Finite Elements

Content Provider	IEEE Xplore Digital Library
Author	Chakrabarty, S.P. Hanson, F.B.
Copyright Year	2006
Description	Author affiliation: Dept. of Math., Stat., & Comput. Sci., Illinois Univ., Chicago, IL (Chakrabarty, S.P.; Hanson, F.B.)
Abstract	Optimal distributed parameter control and a Galerkin finite element method are used to develop procedures for an ideal model of optimal drug delivery to brain tumors. The mathematical model comprises of a system of three coupled reaction diffusion models, involving the density of tumor cells, normal tissue and also the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing the side effects of the drug. A distributed parameter method based on a simple application of variational calculus is used on a pseudo-Hamiltonian, which is then used to obtain a coupled system of forward state equations and backward co-state equations. The Galerkin finite element method is used to realistically represent the brain structure. Finally, an ideal three dimensional test case is considered and partitioned into a set of brick finite elements in spherical coordinates, with tri-linear basis functions. Non-uniqueness of nodes in spherical coordinates is removed by combining like nodes, such as at the origin, at the poles and at the polar angle discontinuity. The Galerkin ODEs are solved by a combination of Crank-Nicolson and predictor-corrector methods
Starting Page	2088
Ending Page	2093
File Size	251321
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377600
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Cancer drugs Distributed control Finite element methods Moment methods Optimal control Mathematical model Tumors Equations Brain modeling Drug delivery
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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