
1032SDigoxinElimination
17 Aug 2018   Contributor(s):: Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1984HaysCompartmentModelsForHumanIodineMetabolism
07 Mar 2018   Contributor(s):: Marguerite Hays
Hays, Marguerite. 1984. Compartmental Models for Human Iodine Metabolism. Mathematical Biosciences. 73: 317335.ABSTRACT: Compartmental models for the various aspects of human iodine metabolism are reviewed, emphasizing the role of Mones Berman in the development of this field. The review...

1986ByoriConnectionsBetweenCompartmentSystemsIntegroDifferentiaoEquations
26 Nov 2017   Contributor(s):: Brian Winkel
1986. Gyori, Istvan. Connections between compartment systems with pipes and integrodifferential equations. Mathematical Modeling. 7: 12151238.Abstract: Compartmental models are a frequently used tool for the mathematical description of physiologic processes. In the classical...

Math 216 Demonstrations
12 Sep 2017   Contributor(s):: Brian Winkel
Math 216 Demonstrations. https://instruct.math.lsa.umich.edu/lecturedemos/ma216/docs/ . Accessed 11 September 2017.This site contains many, many applications with good presentation and analysis as well as Matlab files to illustrate the concepts. For example modeling a swinging door with spring...

2004RescignoUse of Pharmacokinetics Models
11 Sep 2017   Contributor(s):: Brian Winkel
Rescigno, Aldo. 2004. On the use of pharmacokinetic models. Phys. Med. Biol. 49: 46574676.Abstract: Extensive use of models in pharmacology, in physiology and in radiotherapy raises some questions on the nature and utility of models in general and of compartmental models in particular. In...

2012MisraMathematics Model for the Spread of Two Political Parties
11 Sep 2017   Contributor(s):: Brian Winkel
Misra, Arvind Kumar. 2012. A simple mathematical model for the spread of two political parties. Nonlinear Analysis: Modelling and Control. 17(3): 343–354.Abstract. In this paper, a nonlinear mathematical model for the spread of two political parties has been proposed and...

2005HowardModeling with Differential Equations
10 Sep 2017   Contributor(s):: Brian Winkel
Howard P. 2005. Modeling with ODE. Notes. 48 pp.Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are...

ASHP  Intro to Pharmacokinetics and Pharmacodynamics
10 Sep 2017   Contributor(s):: Brian Winkel
ASHP. Intro to Pharmacokinetics and Pharmacodynamics . 18 pp. https://www.ashp.org//media/store%20files/p2418samplechapter1.pdf . Accessed 10 September 2017. American Society of HealthSystem Pharmacists.This is the introductory Lesson 1 in an online set of materials to introduce...

KatulENV264  Applied DE in Env Sci Models
10 Sep 2017   Contributor(s):: Brian Winkel
Katul, Gabriel G. ENV264 Applied Differential Equations in Environmental Sciences. Notes.Many environmental problems require the construction and solution to equations (or systems of equations) that involve relations between rates and states of environmental variables. The objective of this...

AccessPharmacyPharmacokinetics Of Drug Absorption
09 Sep 2017   Contributor(s):: Brian Winkel
AccessPharmacy (McGraw Ill). Applied Biopharmaceutics & Pharmacokinetics. Chapter 7. Pharmacokinetics of Oral. Part of Book series at https://accesspharmacy.mhmedical.com/book.aspx?bookID=1592 . Accessed 7 September 2017.From the web page.“The pharmacokinetics of drugs...

2017PeletierDifferential Equations First Order Applications
09 Sep 2017   Contributor(s):: Brian Winkel
Peletier, L. A. Ordinary Differential Equations in Pharmacodynamics. Notes. 23 pp. http://www.math.leidenuniv.nl/~peletier/azcourse04.pdf . Accessed 8 September 2017.Good mix of theory, application, solution technique in a number of areas of applications of differential...

1999AllenLoveAndDifferentialEquations
09 Sep 2017   Contributor(s):: Brian Winkel
Allen, David M. 1999. Love and differential equations: An Introduction to Modeling. PowerPoint Presentation. 44 slides.This is a set of slides with lots of topics touched upon briefly, but in the end there is an analysis of the Romeo and Juliet relationship.Keywords: differential equation,...

2011KochPharmacokinetic Intro Biomathematical Modeling
09 Sep 2017   Contributor(s):: Brian Winkel
Koch, Gretchen A. 2011. Mathematical Modelling of Natural Phenomena Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling . Preprint of artile to appear in Mathematical Modelling of Natural Phenomena. 6(6): 227244....

Gustafson2250 Systems Differential Equations Applications
08 Sep 2017   Contributor(s):: Brian Winkel
Gustafson, G. B. Systems of Differential Equations, Chapter 11. 69 pp.This material is from a wealth of other material authored by Grant B. Gustafson in the Mathematics Department at the University of Utah. See http://www.math.utah.edu/~gustafso/ for up to date information on his...

1971MetzlerUsefulness Of Two Compartment Open Model In Pharmacokinetics
07 Sep 2017   Contributor(s):: Brian Winkel
Metzler, Carl M. , 1971. Usefulness of the TwoCompartment Open Model in Pharmacokinetics. Journal of the American Statistical Association, 66( 333): 4953Abstract: Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism...

2014BlomhojEtAlCompartmentModels
07 Sep 2017   Contributor(s):: Brian Winkel
Blomhøj, M. , T. H. Kjeldsen, and J. Ottesen. 2014. Compartment models. http://www4.ncsu.edu/~msolufse/Compartmentmodels.pdf . Accessed 7 September 2017.From the first paragraph, “Background: It is important to master the ability to develop models. Modeling of dynamical...

ShareTechNotesDEModelsTanks
05 Sep 2017   Contributor(s):: Brian Winkel
TechShareNotes. Differential Equations Modeling: Example Mixing. http://www.sharetechnote.com/. Accessed 4 September 2017.TechShareNotes is a web site with rich differential equation modeling html pages and this one is about mixing in one, two, and three tanks, with interesting...

1996ErdmanMorelockStudyOfKinetics
03 Sep 2017   Contributor(s):: Brian Winkel
Erdman, Donald (SAS Institute Inc., Cary, NC) and Maurice M. Morelock, (Boehringer Ingelheim Pharmaceuticals). 1996. A Study of Kinetics: The Estimation and Simulation of Systems of FirstOrder Differential...

1086SMedicinalPill
31 Aug 2017   Contributor(s):: Brian Winkel
Administration of a medicinal pill in single and multiple doses is modeled.

Compartment Models
19 Sep 2016   Contributor(s):: Brian Winkel
Blomhøj, M, T.H. Kjeldsen, and J. Ottesen. 2014. Compartment Models.From the Introduction of this 47 page chapter the authors say,"Background: It is important to master the ability to develop models. Modeling of dynamical systems plays a very important role in applied science, and...