2. Impedance measurements in 3D cell culture
The implementation of EIS in 2D cultures relies on cells attaching to the electrodes, this does not occur in 3D cultures as they contain matrices such as biopolymers (collagen, fibrin), polymer scaffolds or discrete suspended cell clusters. As a result, there are a number of areas that the EIS system needs to be adapted for 3D applications:
1) Ensuring sensitivity of the electrode array to cells suspended in or attached to the matrix/scaffold by ensuring there is an even electric field through the whole system.
2) Adaptable to a range of different 3D cell culture formats – systems are often designed to address a specific biological research question or tissue function and so their architecture varies.
3) Ensuring that electrodes do not influence cell responses or change the mechanical environment in 3D cell culture systems.
The design and integration of electrodes within culture systems appears to be central to the effective monitoring of cells within scaffolds and hydrogels. It has been demonstrated that the electrical properties of cells can be monitored when they are immersed within a hydrogel rather than directly attached to a planar electrode.(S.-M. Lee et al., 2016) Lee et al. incorporated a matrix of vertical electrodes (Figure 1a) that were able to monitor the migration, proliferation and apoptosis of cells through a gel matrix in 3D. In this system, cells were grown in an alginate hydrogel scaffold and vertical parallel electrodes were used to measure the capacitance of the system. An increase in capacitance was shown to be proportional to an increase in seeded cell density within the hydrogel (Figure 1b and Figure 1c) , showing that by measuring capacitance of the system it is possible to monitor cell number. To monitor cell proliferation and migration, one frequency (1 kHz) was used to obtain the capacitance of the system rather than the whole impedance spectrum. The chosen frequency coincides with the frequency typically used to monitor cells in 2D,(Benson et al., 2013; Srinivasan et al., 2015) but the study did not explore how cell death or migration affects the whole spectrum or whether other changes in the spectrum could be correlated to these cellular processes.
In many instances, cells are grown in a 3D spheroidal structure in which the cells clump together and proliferate. These models are used extensively in cancer research to understand drug treatments for tumors. Lei et al. used in-plane electrodes to monitor the viability of spheroids developed in an agarose hydrogel using the hanging drop technique (Figure 2a) .(Lei et al., 2018) Changes in the impedance magnitude was successfully correlated with different cell numbers seeded in the hydrogel (Figure 2b) . It is interesting to note here that while the authors chose the standard 1 kHz as the optimal sensing frequency, as was seen in the earlier study, there were larger variations in the impedance magnitude at lower frequencies. These variations were accounted for by the authors as being related to the increases in the noise as the frequency is reduced, due to noise being proportional to 1/f.
The position of the electrodes within 3D culture systems (parallel vs in-plane) has also been shown to affect detection outcomes.(Y. Xu et al., 2015) Pan et al. found that in-plane electrodes were not able to significantly detect the proliferation of spheroids in a matrigel, whereas parallel electrodes successfully monitored their proliferation over time (Figure 3a and Figure 3c) . This data corresponds with the theory that parallel electrodes can achieve more sensitive detection due to a more uniform electric field.(Y. Xu et al., 2015) Nevertheless, this challenges the results from the earlier studies from Lei et al. using in-plane electrodes. Factors influencing these differences may be gel thickness and electrode design. When in-plane electrodes are used in a 3D system, the applied current can only penetrate a small volume and distance, whereas parallel electrodes force the applied current to go across the entire sample. In this instance it is to be expected that more signal can be detected and signal to noise increases as the current penetrates a larger volume of the 3D culture.
While the integration of standard metal electrodes into 3D culture is challenging due to the stiffness of the electrode materials and the need to connect them back to the outside world, one group has been exploring the application of conductive polymers as both the cell scaffold and the electrodes.(Khan et al., 2019) As the cells adhere to this conductive scaffold, its impedance changes enabling cell adhesion to be detected(Figure 4a and Figure 4c) .(Del Agua et al., 2018) Interestingly, the optimal sensing frequency found using a poly(3,4-ethyenedioythiophene): xanthan scaffold was between 0.1 and 100 Hz (Figure 4b) . As mentioned in the previous example, noise varies with 1/f, so at lower frequencies we would expect that noise would increase significantly. The potentiostat used for the impedance measurements may be able to compensate, however, little information is given by the authors of this study to determine if this approach has been implemented. Acquisition rate may also be problematic at low frequencies, though in the case of cell monitoring this may not be an issue since these are long-term cultures of days and weeks rather than minutes and hours.
In 2D, it is well established that low frequency signals are dominated by the double layer capacitance of the electrodes.(Benson et al., 2013) Nevertheless, in this study the electrode properties change as the cells are growing within the conductive hydrogel and is consistent with other studies using conductive scaffolds.(Inal et al., 2017) Further, modifying the properties of the 3D scaffolds (physical and chemical properties) should be done with caution as scaffold properties can have a big influence on cell behavior and function (Bahcecioglu, Hasirci, & Hasirci, 2019; Caliari & Burdick, 2016; Sridharan, Ryan, Kearney, Kelly, & O’Brien, 2019) and these influences need to be understood and cross-validated with other characterization tools prior to implementation. This suggests that the nature of the scaffold, its potential use as a working electrode and the nature of the 3D model (spheroids or tissue) plays a significant role in the final outcome of the measurements and as such models are needed to compare results with theoretical systems.
Several equivalent circuits have been designed to model and quantify the electrical properties of cells grown in 2D systems. Figure 5shows the equivalent circuit generally used to describe live cells in a monolayer.(Benson et al., 2013) This circuit takes into account the resistance of the solution or electrolyte (phosphate buffered saline (PBS) or cell media) Rmedium, the resistance and capacitance of the cell monolayer that contributes to the total spectrum RTEER and Ccl, respectively, and the capacitance of the electrodes and electrode-medium interphase CEl.(Benson et al., 2013) The electrical circuit and electrode setup for 2D adherent cells are well developed in EIS and comprehensive reviews of impedance measurements of cells are available and demonstrated.(Benson et al., 2013; Canali et al., 2016; Elbrecht et al., 2018; Srinivasan et al., 2015) In undertaking this review we could find only one study that has directly compared equivalent circuits for 2D and 3D systems.(Pan et al., 2019) They demonstrated that a matrigel matrix resistance component was in parallel with the electrical components representing cell impedance (Figure 3b). This in contrast to a typical 2D equivalent circuit which shows that the media component is in series with the components representing cell impedance (Figure 5). This is explained by looking at the fundamental differences in cell interactions occurring in the two different models. In 2D, the cells reside below the media (series circuit) while in 3D, the cells reside within the scaffold, which resembles more of a parallel circuit. Furthermore, Pan and colleagues paired simulations derived from their 3D equivalent circuit with their experimental data using epithelial cells and found that the presence of cells in 3D decreased the overall impedance of the system. This was due to an increase in gel conductivity after the addition of cells, which was attributed to the presence of gap junctions between cells that allowed electrical connection between neighboring cell membranes.(Pan et al., 2019) However, other studies with similar cell types have shown the opposite effect, with the introduction of cells increasing the overall impedance of 3D systems.(Inal et al., 2017; S.-M. Lee et al., 2016; Lei et al., 2018)
Groeber et al. are amongst the only published groups using the whole EIS spectrum and information provided by an equivalent circuit to monitor tissue growth in a co-culture system. They used parallel electrodes to measure the impedance of an artificially grown epidermis at different levels of maturity as shown in Figure 6b .(Groeber et al., 2015) They developed an equivalent circuit in which there are a series of connections of n parallel resistor-capacitor circuits which correlated with a different maturity phase of the artificially grown epidermis (seeFigure 6a ). The data obtained was validated against an isolated human epidermis showing that the artificially grown epidermis at days 9-12 had the same electrical characteristics as the human epidermis. In the study, 1kHz was found to be an optimal sensing frequency, suggesting that it may well be the nature of the conductive scaffold that reduced the frequency in the study by Agua et al. To measure the impedance of the tissue, Groeber et al. grew the tissue in a transwell and transferred the transwell to an impedance platform every time a measurement was required. It is possible to use ideas from the literature to envisage how electrodes could be inserted into the transwell to monitor the system in situ or within a microfluidic device as undertaken by Sriram et al.(Sriram et al., 2018) A natural extension of this approach would be to design electrodes, so they are small enough to contact only one layer of tissue construct. This could enable the extraction of information of cells within a select region and monitoring of the individual features as the tissue grows. While Groeber and colleagues monitored growth and differentiation of epidermal cells, electrodes placed at different layers of a full thickness skin equivalent may allow for multicellular monitoring as well as the potential monitoring of skin processes such as wound healing and barrier function. Currently, skin tissue maturity is assessed by histology and immunostaining at different time points, so a layer-by-layer electrode setup which monitors tissue impedance as it grows could allow researchers to track growth and cellular processes quickly and without destroying the model.