Instrumental noise estimates stabilize and quantify endothelial cell micro-impedance barrier function parameter estimates

Abstract

A novel transcellular micro-impedance biosensor, referred to as the electric cell-substrate impedance sensor or ECIS, has become increasingly applied to the study and quantification of endothelial cell physiology. In principle, frequency dependent impedance measurements obtained from this sensor can be used to estimate the cell–cell and cell–matrix impedance components of endothelial cell barrier function based on simple geometric models. Few studies, however, have examined the numerical optimization of these barrier function parameters and established their error bounds. This study, therefore, illustrates the implementation of a multi-response Levenberg–Marquardt algorithm that includes instrumental noise estimates and applies it to frequency dependent porcine pulmonary artery endothelial cell impedance measurements. The stability of cell–cell, cell–matrix and membrane impedance parameter estimates based on this approach is carefully examined, and several forms of parameter instability and refinement illustrated. Including frequency dependent noise variance estimates in the numerical optimization reduced the parameter value dependence on the frequency range of measured impedances. The increased stability provided by a multi-response non-linear fit over one-dimensional algorithms indicated that both real and imaginary data should be used in the parameter optimization. Error estimates based on single fits and Monte Carlo simulations showed that the model barrier parameters were often highly correlated with each other. Independently resolving the different parameters can, therefore, present a challenge to the experimentalist and demand the use of non-linear multivariate statistical methods when comparing different sets of parameters.