IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2008i3p521-538.html
   My bibliography  Save this article

Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery

Author

Listed:
  • Schittkowski, Klaus

Abstract

The purpose of this paper is to present some numerical tools which facilitate the interpretation of simulation or data fitting results and which allow computation of optimal experimental designs. They help to validate mathematical models describing the dynamical behavior of a biological, chemical, or pharmaceutical system, without requiring a priori knowledge about the physical or chemical background. Although the ideas are quite general, we will concentrate our attention to systems of one-dimensional partial differential equations and coupled ordinary differential equations. A special application model serves as a case study and is outlined in detail. We consider the diffusion of a substrate through cutaneous tissue, where metabolic reactions are included in form of Michaelis–Menten kinetics. The goal is to simulate transdermal drug delivery, where it is supposed that experimental data are available for substrate and metabolic fluxes. Numerical results are included based on laboratory data to show typical steps of a model validation procedure, i.e., the interpretation of confidence intervals, the compliance with physical laws, the identification and elimination of redundant model parameters, the computation of optimum experimental designs and the identifiability of parameters by determining weight distributions.

Suggested Citation

  • Schittkowski, Klaus, 2008. "Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 521-538.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:521-538
    DOI: 10.1016/j.matcom.2008.02.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475408001201
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2008.02.025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gallant, A. Ronald, 1975. "Seemingly unrelated nonlinear regressions," Journal of Econometrics, Elsevier, vol. 3(1), pages 35-50, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aslanidis, Nektarios, 2007. "Business Cycle Regimes in CEECs Production: A Threshold SURE Approach," Working Papers 2072/5318, Universitat Rovira i Virgili, Department of Economics.
    2. Gary King, 1989. "A Seemingly Unrelated Poisson Regression Model," Sociological Methods & Research, , vol. 17(3), pages 235-255, February.
    3. Perry Warjiyo & Wallace E. Huffman, 1997. "Dynamic input demand functions and resource adjustment for US agriculture: state evidence," Agricultural Economics, International Association of Agricultural Economists, vol. 17(2-3), pages 223-237, December.
    4. David Besanko & Sachin Gupta & Dipak Jain, 1998. "Logit Demand Estimation Under Competitive Pricing Behavior: An Equilibrium Framework," Management Science, INFORMS, vol. 44(11-Part-1), pages 1533-1547, November.
    5. Yuquan Chen & Xiaohua Yu, 2022. "Estimating market power for the Chinese fluid milk market with imported products," Agribusiness, John Wiley & Sons, Ltd., vol. 38(2), pages 386-401, April.
    6. Marcela Munizaga & Sergio Jara-Díaz & Paulina Greeven & Chandra Bhat, 2008. "Econometric Calibration of the Joint Time Assignment--Mode Choice Model," Transportation Science, INFORMS, vol. 42(2), pages 208-219, May.
    7. Winston T. Lin, 2005. "Currency forecasting based on an error components-seemingly unrelated nonlinear regression model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 593-605.
    8. Krebs, Tom & Krishna, Pravin & Maloney, William F., 2012. "Income risk, income mobility and welfare," Policy Research Working Paper Series 6254, The World Bank.
    9. Korolev, Ivan, 2021. "Identification and estimation of the SEIRD epidemic model for COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 63-85.
    10. von Auer, Ludwig & Weinand, Sebastian, 2022. "A nonlinear generalization of the country-product-dummy method," Discussion Papers 45/2022, Deutsche Bundesbank.
    11. Paul Cashin, 1991. "A Model Of The Disaggregated Demand For Meat In Australia," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 35(3), pages 263-283, December.
    12. Naranjo, Andy & Protopapadakis, Aris, 1997. "Financial market integration tests: an investigation using US equity markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(2), pages 93-135, July.
    13. Hanrahan, Kevin F. & Westhoff, Patrick C. & Young, Robert E., II, 2001. "Trade Allocation Modeling: Comparing The Results From Armington And Locally Regular Ai Demand System Specifications Of A Uk Beef Import Demand Allocation Model," 2001 Annual meeting, August 5-8, Chicago, IL 20510, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    14. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    15. Cordeiro, Gauss M. & Vasconcellos, Klaus L. P., 1997. "Bias correction for a class of multivariate nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 155-164, September.
    16. W. Viscusi & William Evans, 2006. "Behavioral Probabilities," Journal of Risk and Uncertainty, Springer, vol. 32(1), pages 5-15, January.
    17. Musthapha Mufeeth & Senal Weerasooriya & Jeevika Weerahewa, 2024. "Assessing the Degree of Market Power in the Rice Milling Industry of Sri Lanka: An Application of the NEIO Approach," Studies in Microeconomics, , vol. 12(2), pages 115-134, August.
    18. Rulon D. Pope & Richard E. Just, 1977. "On The Competitive Firm Under Production Uncertainty," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 21(2), pages 111-118, August.
    19. Xu, Qinfeng & You, Jinhong & Zhou, Bin, 2008. "Seemingly unrelated nonparametric models with positive correlation and constrained error variances," Economics Letters, Elsevier, vol. 99(2), pages 223-227, May.
    20. Julie Bertrand & Emmanuelle Comets & Marylore Chenel & France Mentré, 2012. "Some Alternatives to Asymptotic Tests for the Analysis of Pharmacogenetic Data Using Nonlinear Mixed Effects Models," Biometrics, The International Biometric Society, vol. 68(1), pages 146-155, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:521-538. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.