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MATHEMATICAL APPROACHES TO MODELING,UNDERSTANDING, AND CONTROLLING THEACUTE INFLAMMATORY RESPONSE TOPATHOGEN AND ENDOTOXIN

Day, Judy D. (2007) MATHEMATICAL APPROACHES TO MODELING,UNDERSTANDING, AND CONTROLLING THEACUTE INFLAMMATORY RESPONSE TOPATHOGEN AND ENDOTOXIN. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This thesis includes work dealing with topics related to the modeling, understanding, andcontrolling the acute inflammatory response. After the introductory chapter, the secondchapter discusses a small (four equation) ordinary differential equation (ODE) model of theacute inflammatory response to endotoxin stimuli. Many scenarios of endotoxin toleranceare reproduced and explained in the context of inflammation. The third chapter explores thenumerical aspects of coding an algorithm produced by Bernd Krauskopf and Hinke Osinga[63] for generating 2D (un)stable manifolds for 3D ordinary differential equation systems.The fourth chapter returns to the topic of endotoxin tolerance, but now in an abstractmathematical setting. The fifth chapter presents an exposition regarding the applicationof nonlinear model predictive control to the four equation ODE model (now with pathogeninstead of endotoxin) to explore strategies to modulate the inflammatory response duringsevere infection.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Day, Judy D.judyday@gmail.com
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRubin, Jonathanrubin@math.pitt.eduJONRUBIN
Committee MemberRiviere, Beatriceriviere@math.pitt.edu
Committee MemberChow, Carsoncarsonc@niddk.nih.gov
Committee MemberClermont, Gillesclermontg@ccm.upmc.edu
Committee MemberVodovotz, Yoramvodovotzy@upmc.eduVODOVOTZ
Date: 20 September 2007
Date Type: Completion
Defense Date: 15 June 2007
Approval Date: 20 September 2007
Submission Date: 26 July 2007
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: mathematical biology; ordinary differential equations; acute inflammation; nonlinear model predictive control
Other ID: http://etd.library.pitt.edu/ETD/available/etd-07262007-214641/, etd-07262007-214641
Date Deposited: 10 Nov 2011 19:53
Last Modified: 19 Dec 2016 14:36
URI: http://d-scholarship.pitt.edu/id/eprint/8616

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