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Am J Physiol Cell Physiol (May 4, 2005). doi:10.1152/ajpcell.00103.2005
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Submitted on March 7, 2005
Accepted on May 2, 2005

Modeling Error and Stability of Endothelial Cytoskeletal-Membrane Parameters Based on Modeling Transendothelial Impedance as Resistor and Capacitor in Series

James E Bodmer1, Anthony English2, Megan Brady3, Ken Blackwell3, Kari Haxhinasto3, Sunaina Fotedar4, Kurt Borgman3, Er-Wei Bai5, and Alan B Moy4*

1 Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa, USA; Internal Medicine, University of Iowa and Veterans Administration Hospital, Iowa City, Iowa, USA
2 Department of Aeronautical, Mechanical and Biomedical Engineering, University of Tennessee, Knoxville, Tennessee, USA
3 Internal Medicine, University of Iowa and Veterans Administration Hospital, Iowa City, Iowa, USA
4 Biomedical Engineering, University of Iowa, Iowa City, Iowa, USA; Internal Medicine, University of Iowa and Veterans Administration Hospital, Iowa City, Iowa, USA
5 Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa, USA

* To whom correspondence should be addressed. E-mail: alan-moy{at}uiowa.edu.

Transendothelial impedance across an endothelial monolayer grown on a microelectrode has been previously modeled as a repeating pattern of disks in which the electrical circuit consists of a resistor and capacitor in series. Although this numerical model breaks down barrier function into measurements of cell-cell adhesion, cell-matrix adhesion and membrane capacitance, such solution parameters can be inaccurate without understanding model stability and error. In this report we evaluate modeling stability and error by using a Chi square evaluation and Levenburg-Marquardt method for non-linear least squares (LM-NLS) of the real and/or imaginary data in which the experimental measurement is compared with the calculated measurement derived by the model. Modeling stability and error were dependent on current frequency and the type of experimental data that was modeled. Solution parameters of cell-matrix adhesion were most susceptible to modeling instability. Further, the LM-NLS displayed frequency-dependent instability of the solution parameters regardless of whether the real or imaginary data was analyzed. However, the LM-NLS identified stable and reproducible solution parameters between all types of experimental data when a defined frequency spectrum of the entire data set was selected based on a criterion of minimizing error. The frequency bandwidth that produced stable solution parameters varied greatly among different data types. Thus, a numerical model based on characterizing transendothelial impedance as a resistor and capacitor in series and as a repeating pattern of disks is not sufficient in characterizing the entire frequency spectrum of experimental transendothelial impedance.




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