Accuracy of the Maxwell–Wagner and the Bruggeman–Hanai mixture models for single cell dielectric spectroscopy

Abstract

Dielectric spectroscopy (DS) is a non-invasive, label-free, and promising technique for measuring dielectric properties of biological cells. Recent developments in microfabrication techniques made it possible to perform DS measurements with minute volume of cell suspensions. However, when the cell size approaches the size of the measurement chamber, especially, for single cell measurements, the analytical models [Maxwell-Wagner and Bruggeman-Hanai (BH) mixture models] to extract cell parameters lose their accuracy. Moreover, variations in the cell position relative to the measurement electrodes decrease the accuracy of the analytical solutions. Impedance spectrum of a typical eukaryotic mammalian cell is generated for different geometrical configurations using finite element. The generated data are fitted to the analytical models and extracted cell parameters are compared with the original values. The results show that BH model works more effectively when chamber to cell radius ratio is <3.5 and chamber height to cell radius ratio is <3. Moreover, it is observed that analytical models estimate cell parameters with major errors when the cells are in the vicinity of the electrodes. However, for high-volume fraction simulations, the BH model was able to predict cell parameters better even in the vicinity of the electrodes.

Effects of electrode size and surface morphology on electrode polarization in physiological buffers

“…In order to assess the dielectric spectroscopy response, the impedance spectra of Jurkat cells are analytically generated for planar and rough surfaces using previously published cell data . The Jurkat cells are modeled using the double shell model, which depicts the cells as perfectly spherical particles surrounded by cell membrane and contain cytoplasm and a spherical nucleus separated by a nuclear envelope.…”

“…An inverse model based on Maxwell‐Wagner and double shell model was used to extract sub‐cellular properties for both cases. The computational flow chart used for the inverse model was given in our previous study . For both cases, medium, cytoplasm, and nucleoplasm permittivity values were fixed at 80, 60, and 120, respectively and medium conductivity was fixed at 1.5 S/m.…”

“…in food and water matrices . In addition to cell detection, impedance measurements over a wide frequency range can provide information on membrane, cytoplasm, and nucleoplasm dielectric properties . Despite all these advantages, microfluidic impedance spectroscopy undergoes electrode polarization (EP) effect especially in physiological media .…”

Positional dependence of particles and cells in microfluidic electrical impedance flow cytometry: origin, challenges and opportunities

“…The latter is implemented in the software MyDEP 59 with the full methodology explained in the supplementary material of that article and in 10,60 . For higher volume fractions, the Hanai formulation has proven to be more accurate than the Maxwell-Garnett formulation 61 . However, variation of the vertical position of the particle has shown that both models exhibit significant errors when the particle is in close vicinity to the electrodes.…”

“…Confidence in the obtained results depends on the tolerance set for the solving as well as the validation of the mesh used through a mesh convergence study 37 . Error calculation can also be used for adaptive mesh refinement in which the error estimate is used to refine the areas in the volume where the error is the largest 61,78 .…”