Tags: compartment

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  1. 6-029-S-TumorGrowth

    04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis

    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

  2. 2014-Monagan, Michael - The House Warming Model. Department of Mathematics

    05 Apr 2020 | | Contributor(s):: Brian Winkel

    Monagan, Michael. 2014.  The House Warming Model. Department of Mathematics, Simon Fraser UniversitySee http://www.cecm.sfu.ca/~mmonagan/papers/HouseReporter.pdf .Maple commands: s o l v e , c o l l e c t , d s o l v e , o d e p l o t , D E p l o tIntroduction:...

  3. 2019-Selenne Bañuelos, Ty Danet, Cynthia Flores, and Angel Ramos -An Epidemiological Math Model Approach to a Political System with Three Parties. 

    05 Apr 2020 | | Contributor(s):: Brian Winkel

    Selenne Bañuelos, Ty Danet, Cynthia Flores, and Angel Ramos. 2019. An Epidemiological Math Model Approach to a Political System with Three Parties. CODEE Journal. Volume 12 Linking Differential Equations to Social Justice and Environmental Concerns Article...

  4. 2003-Carson, Richard - Tracer kinetic modeling in PET

    02 Apr 2020 | | Contributor(s):: Brian Winkel

    Carson, Richard. 2003. Tracer kinetic modeling in PET. Chapter reproduced from Valk PE, Bailey DL, Townsend DW, Maisey MN. Positron Emission Tomography: Basic Science and Clinical Practice. Springer-Verlag London Ltd 2003,...

  5. 2018-Blomhøj, M. , T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes.

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    M. Blomhøj, T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes 47 pp.    Chapter 1 - Compartment ModelsBackground: It is important to master the ability to develop models. Modeling of dynamical systems plays a very important role in...

  6. 1999-Crooke, P. S. S. Hota, J. J. Martini, and J. R. Hochkiss - A Mathematical Model for Carbon Dioxide Exchange during Mechanical Ventilation with Tracheal Gas Insufflation (TGI).

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    Crooke, P. S. S. Hota, J. J. Martini, and J. R. Hochkiss. 1999. A Mathematical Model for Carbon Dioxide Exchange during Mechanical Ventilation with Tracheal Gas Insufflation (TGI).Abstract: A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the...

  7. 2011-Koch-Noble, G. A. - Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    Koch-Noble, G. A. 2011. Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling. Math. Model. Nat. Phenom. 6(6): 227-244.See https://www.mmnp-journal.org/articles/mmnp/pdf/2011/06/mmnp201166p227.pdf . Abstract: Pharmacokinetics is an excellent way to...

  8. 2009-Noakes, Catherine J. and P. Andrew Sleigh - Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    Noakes, Catherine J. and P. Andrew Sleigh. 2009. Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards. J. R. Soc. Interface. 6: S791-S-800.See https://pubmed.ncbi.nlm.nih.gov/19812072/ .Abstract: Understanding the risk of...

  9. 2014-Hrydziuszko, Olga; Artur Wronaa; Joanna Balbusb; and Krystian Kubicaa - Mathematical Two-compartment Model of Human Cholesterol Transport in Application to High Blood Cholesterol Diagnosis and Treatment.

    27 Mar 2020 | | Contributor(s):: Brian Winkel

    Hrydziuszko, Olga; Artur Wronaa; Joanna Balbusb; and Krystian Kubicaa. 2014. Mathematical Two-compartment Model of Human Cholesterol Transport in Application to High Blood Cholesterol Diagnosis and Treatment. Electronic Notes in Theoretical Computer Science. 306: ...

  10. 2017-Sim, Sy Yi, Sie Long Kek, and Kim Gaik Tay - Optimal control of a coupled tanks system with model-reality differences. 

    25 Mar 2020 | | Contributor(s):: Brian Winkel

    2017-SimEtAl-OptControl-CoupledTanksSystemSim, Sy Yi, Sie Long Kek, and Kim Gaik Tay. 2017.  Optimal control of a coupled tanks system with model-reality differences. AIP Conference Proceedings. 1872, 020012.See https://aip.scitation.org/doi/10.1063/1.4996669 ...

  11. 2000-Erdman, Donald  and Maurice M. Morelock - A Study of Kinetics: The Estimation and Simulation of Systems of First-Order Differential Equations. Notes.

    25 Mar 2020 | | Contributor(s):: Brian Winkel

    Erdman, Donald  and Maurice M. Morelock. 2000. A Study of Kinetics: The Estimation and Simulation of Systems of First-Order Differential Equations. Notes. 8...

  12. 2011-Chitnis, Nakul - Introduction to Mathematical Epidemiology: Deterministic Compartmental Model

    16 Mar 2020 | | Contributor(s):: Brian Winkel

    Chitnis, Nakul. 2011. Introduction to Mathematical Epidemiology: Deterministic Compartmental Model. Notes. 12 pp.See http://www.luchsinger-mathematics.ch/ME-DeterministicCompartmentalModels.pdf .Introduction: Deterministic compartmental models form the simplest models in the...

  13. 1-032-S-DigoxinElimination

    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 ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

  14. 1984-Hays, Marguerite - Compartmental Models for Human Iodine Metabolism.

    07 Mar 2018 | | Contributor(s):: Marguerite Hays

    Hays, Marguerite. 1984. Compartmental Models for Human Iodine Metabolism. Mathematical  Biosciences. 73: 317-335.See https://pubmed.ncbi.nlm.nih.gov/3371254/. ABSTRACT: Compartmental models for the various aspects of human iodine metabolism are reviewed, emphasizing the...

  15. 1986-Gyori, Istvan Connections between compartment systems with pipes and integro-differential equations

    26 Nov 2017 | | Contributor(s):: Brian Winkel

    Gyori, Istvan. 1986. Connections between compartment systems with pipes and integro-differential equations.  Mathematical Modeling. 7:  1215-1238.See https://www.sciencedirect.com/science/article/pii/0270025586900771 .Abstract:  Compartmental models are a...

  16. 2018-Bourne, David W. A. - Pharmacokinetics – Source Material

    12 Sep 2017 | | Contributor(s):: Brian Winkel

    Phamacokinetics –PHAR 7834. https://www.boomer.org/c/p4/?Loc=OUHSC33 . Accessed 11 September 2017.This is a rich source of pharmacokinetics modeling activities and data. These are syllabus notes with homework assignments listed.Online ResourcesBackground Mathematical...

  17. 2017-University of Michigan - 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...

  18. 2004-Rescigno, Aldo - On the use of pharmacokinetic models.

    11 Sep 2017 | | Contributor(s):: Brian Winkel

    Rescigno, Aldo. 2004. On the use of pharmacokinetic models. Phys. Med. Biol. 49: 4657-4676.See https://tauruspet.med.yale.edu/staff/edm42/courses/ENAS_915_2014/papers/Rescigno-use%20of%20models%20PMB%202004%20%200031-9155_49_19_014.pdf .Abstract:  Extensive use of models in...

  19. 2012-Misra, Arvind Kumar - A simple mathematical 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.See https://core.ac.uk/download/pdf/322857553.pdf. Abstract. In this paper, a non-linear mathematical model...

  20. 2005-Howard P. - Modeling with ODE. Notes.

    10 Sep 2017 | | Contributor(s):: Brian Winkel

    Howard P. 2005. Modeling with ODE. Notes. 48 pp.See https://www.math.tamu.edu/~phoward/m412/modode.pdf .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,...