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Diffusion with attrition.

N B Grover1

  • 1Hubert H. Humphrey Center for Experimental Medicine and Cancer Research, The Hebrew University Faculty of Medicine, PO Box 12272, 91120, Jerusalem, Israel. norman@md.huji.ac.il

Journal of Mathematical Biology
|August 29, 2006
PubMed
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This study presents methods to estimate parameters like diffusion coefficient (D) and binding-site concentration (mu) from experimental data of diffusing substances interacting with binding sites. New graphical techniques allow direct calculation of these parameters, improving model accuracy.

Area of Science:

  • Physical Chemistry
  • Chemical Engineering
  • Mathematical Modeling

Background:

  • Irreversible reactions between diffusing substances and binding sites create sharp concentration fronts.
  • Nonlinear partial differential equations model this phenomenon but lack closed-form solutions.

Purpose of the Study:

  • Develop methods for estimating model parameters (D, k, mu, c(0)) from experimental data.
  • Provide practical graphical procedures for parameter calculation.

Main Methods:

  • Analytical solution for the limiting case of infinite interaction constant (k --> infinity).
  • Numerical solutions using a finite element analysis package for the general case.
  • Development of graphical procedures for parameter estimation.

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Main Results:

  • Established graphical methods to compute binding-site concentration (mu) and boundary concentration (c(0)).
  • Utilized the advancing front position (xi) to estimate the diffusion coefficient (D).
  • Defined a new measurable quantity S(t) to directly compute the interaction constant (k).

Conclusions:

  • The developed methods enable accurate estimation of key parameters governing diffusion with irreversible binding.
  • Simulations demonstrate the validity and robustness of the methods, even with noise in experimental data.