Noninvasive real-time monitoring of cellular spatiotemporal dynamics via machine learning–enhanced electrical impedance spectroscopy

Abstract

Monitoring cellular spatiotemporal dynamics is essential for understanding complex biological processes such as organ development and cancer progression. Using live-cell fluorescence microscopy to track cellular dynamics is often limited by dye-induced cytotoxicity and cellular photodamage. Here, we demonstrate an alternative methodology combining microelectrode arrays, electrical impedance spectroscopy (EIS), and machine learning (ML) that enables real-time monitoring of cellular spatiotemporal dynamics in a noninvasive and label-free manner. The platform is applied to normal and cancerous breast epithelial cells in either mono- or coculture, correlating EIS measurements with cell growth parameters obtained from automated microscopy image analysis. An ML model is implemented to accurately predict the spatiotemporal evolution of cell density and size and to classify the different cell types based solely on EIS recordings. The technology is also shown to be capable of tracking pertinent biological processes including spatial heterogeneities in cell proliferation patterns and cell competition in coculture.

A machine learning–enhanced sensor array enables noninvasive tracking of interactions between normal and cancer cells.

INTRODUCTION

Understanding how cells organize in both space and time is crucial for explaining a wide range of physiological and pathological processes. For instance, the proper regulation of cellular spatiotemporal dynamics plays a central role in tissue morphogenesis during embryonic development (1, 2), determines tissue repair and regeneration after injury (3–5), and coordinates immune responses during infection and inflammation, contributing to homeostasis (6, 7). Conversely, dysregulation of cellular spatiotemporal dynamics can lead to various disorders including cardiovascular complications such as intimal hyperplasia and atherosclerosis (8, 9), impairment of neuronal function and cognitive decline in neurodegenerative diseases (10, 11), and tumor progression and cancer metastasis (12, 13).

Now, the predominant method for monitoring cellular spatiotemporal dynamics is live-cell fluorescence microscopy (14). However, this technique suffers from several important limitations including cytotoxicity because of cell dye labeling (15, 16) and cell photodamage, particularly in the case of extended periods of light exposure (15, 17–19). Microscopic imaging is also problematic in scenarios where optical access to the sample of interest is limited. Therefore, there is a critical need for noninvasive, label-free methods that enable long-term monitoring of cellular spatiotemporal dynamics with minimal disruption of natural cellular processes.

An alternative to microscopic imaging for monitoring live-cell activity is the use of electrical impedance spectroscopy (EIS), a powerful technique that measures how a system responds to an excitation signal from an applied alternating electric field across multiple frequencies. While EIS has traditionally been used to characterize electrical properties of materials, it has gained popularity in the study of biological systems because of the dielectric properties of the cell membranes (20, 21) and has been used to characterize cell adhesion (22–24), cell migration (22, 25), cytotoxicity (22, 26, 27), cell differentiation (22, 28–30), and cancer cell detection (31–35). EIS is broadly considered to be a noninvasive technique because it uses nonpolarizing alternating currents and electric fields that are generally thought to be too weak to affect cellular behavior (22).

Analysis of EIS signals has typically relied on physical (36–38) or electrical equivalent circuit models that require spectral fitting to extract relevant parameters (39–41). However, these conventional approaches have major limitations including sensitivity to measurement noise, long computational time for parameter minimization, and susceptibility to local minima. Recent advances in machine learning (ML) algorithms have enhanced our ability to analyze and process EIS signals (42). Deep learning (DL) architectures, in particular, hold great promise in extracting meaningful features from complex EIS datasets (43, 44). These ML approaches offer faster parameter prediction, lower sensitivity to noise, and recognition of data patterns; however, they also require quantitative labeled datasets for model training.

In the present study, we propose an integrated methodology, schematically depicted in fig. S1, that combines the use of microelectrode arrays (MEAs) with EIS and ML to monitor and quantify cellular spatiotemporal dynamics. Relative to fluorescence microscopy, this sensing approach offers key advantages including being label-free and noninvasive as well as providing a faster response and lower cost. We show that the MEA platform allows prolonged monitoring of normal and cancerous breast epithelial cells in mono- or coculture, attesting to the robustness and versatility of the device. Using an extensive dataset with more than 30,000 paired EIS measurements and microscopy images, we develop and train a DL model that is subsequently shown to be capable of predicting, based solely on the impedance measurements, the spatiotemporal evolution of a number of important parameters including cell density, cell substrate coverage, mean cell diameter, and cell type. Last, we show that this combined system enables real-time tracking of spatial heterogeneities in cell growth as well as competition between different cell types in coculture.

RESULTS

Simultaneous EIS and microscopy spatiotemporal recordings

A 25–electrode pair MEA platform was designed and microfabricated for the spatiotemporal acquisition of EIS signals in cell cultures as detailed in Materials and Methods. We began by using the platform for the simultaneous acquisition of EIS spectra and optical microscopy images. Given that direct imaging of cells on the electrode surfaces was not possible because of the opacity of the electrodes, the microscopy images were acquired in the immediate vicinity of each electrode pair. We then automated the extraction of cellular monolayer parameters from image segmentation and paired them to EIS measurements in space and time. This process was conducted for three different experimental conditions: monocultures of MCF10A and MCF7 cells in separate devices in their respective cell culture media (MC1 conditions), monocultures of MCF10A-Ac [green fluorescent protein (GFP) actin–transfected MCF10A] cells and MCF7 cells in separate devices in coculture media consisting of a 50:50 mixture of the two culture media (MC2 conditions), and coculture of the two cell types in the same device in coculture media (CC conditions). These three experimental conditions are schematically illustrated in fig. S2.

Validation of cell density on electrode surfaces

Because EIS recordings and optical images were not acquired at exactly the same location, it was important to establish that cell density on the surfaces of the electrodes was representative to that on the regions in the immediate vicinity of the electrodes where the microscopy images were acquired. To this end, cells were fixed at the end of several experiments following regular EIS acquisitions (Fig. 1A). The fixed cell samples were then immunostained and imaged. As shown in Fig. 1A, no significant differences were observed in cell density between the electrode and nonelectrode regions (P = 0.58), which confirmed that cells proliferated on the electrodes at similar rates as they did on the surrounding areas.

Fig. 1. Cellular imaging and segmentation within the MEA platform.

(A) Evaluation of cell adhesion and growth on the electrodes. (a) Immunostaining after an EIS experiment of MCF10A cells on and in the immediate vicinity of the electrodes with DAPI (4′,6-diamidino-2-phenylindole; nuclei) in blue and F-actin (phalloidin) in red. (b and c) Nuclear counting of cells over the electrodes and in an area in the immediate vicinity of the electrodes, respectively. (d) Number of nuclei within the yellow boxes shown in (b) and (c) denoting regions either on or in the immediate vicinity of the electrodes. n = 14 images in each case. A t test revealed no significant difference between the two regions, indicating that cells grow equally well in both regions. (B) Live-cell (a) bright-field image of MCF10A cells and (b) Cellpose segmentation overlays. Each segmented cell is highlighted with a colored overlay. Gray areas indicate the absence of detected cells. (C) Automated (a) segmentation of the electrode tracks and (b) produced threshold mask. (D) Live-cell (a) bright-field and fluorescence merged image of MCF10A-Ac cells and MCF7 cells in coculture, (b) bright-field segmentation of both cell types, and (c) fluorescence segmentation of MCF10A-Ac cells.

Segmentation of live optical microscopy images

Now that we have established that cell density adjacent to each electrode pair was similar to that on the surface of that electrode pair, we set out to investigate live cellular spatiotemporal dynamics. To this end, we trained Cellpose models to automatically segment cells adjacent to the electrodes (Fig. 1B) and used these models to quantify the time evolution of monolayer parameters of interest including cell density, covered area fraction, mean cell diameter, and cell type. During this process, we successfully implemented an automated custom thresholding algorithm that allowed the exclusion of the electrode track areas from the images (Fig. 1C). We also demonstrated the capability to automatically segment cell mixtures across multiple channels (bright-field and fluorescence), rendering the determination of cellular parameters possible for both cell types in coculture (Fig. 1D).

Cell parameter evolution and corresponding EIS recordings in monoculture

Figure 2A provides an example of the time evolution of MCF10A cell density, covered area fraction, and mean cell diameter derived from the segmentation of the microscopy images for the 25 electrode positions over a period of 45 hours under MC1 conditions. The results demonstrate a certain level of spatial heterogeneity in cell proliferation as evidenced by the different dynamics for the different electrode pairs, which translates into spatial differences in the time needed to attain confluence. Broadly speaking, the cell density dynamics exhibit the expected sigmoidal behavior with an initial phase of slow growth during the first ~10 hours, followed by a phase of rapid growth between 10 and 35 hours, before a final phase characterized by slower proliferation during the final 9 hours. Over the course of the 44-hour recording, there is an approximately fourfold increase in cell density. While the entire surface gets covered with cells within ~20 hours for some zones, other zones require ~35 hours to attain full coverage. Last, the mean cell diameter initially increases as the cells spread and proliferate, peaks at around 35 μm ~10 hours after the onset of the recording, and then drops progressively to ~20 μm as the cell density becomes sufficiently high and cellular packing increases substantially.

Fig. 2. Cell parameter evolution and corresponding EIS recordings under MC1 conditions.

(A) Time evolution in hours (h) of cellular parameters determined from image segmentation for an MC1 experiment on normal MCF10A cells. Different colors represent different electrode positions. Red crosses represent one selected electrode pair at selected times. (B) Microscopy images with segmentation overlays of the selected electrode pair position and time. (C) Impedance modulus and phase Bode plots of six acquisitions at the selected times. Different colors represent different electrode pairs. Red represents the selected electrode pair. (D to F) Equivalent figures for an MC1 experiment on cancerous MCF7 cells.

Figure 2B illustrates the result of the segmentation for a particular electrode pair at six selected time points during the recording, providing a visual appreciation of the increase in time of cell density and cell-covered area as well as the decrease in mean cell size at high density. The images also illustrate the ability of the automated segmentation algorithm to effectively segment the cells even at high density. Figure 2C shows the corresponding modulus and phase Bode plots from EIS measurements at the six selected time points, with different colors indicating signals from various electrode pair positions and the selected pair highlighted in red. These results demonstrate the ability to simultaneously acquire impedance recordings with microscopy images.

Figure 2 (D to F) depicts the equivalent information for the cancerous MCF7 cells. The results indicate that the MCF7 cells generally proliferate slower than the MCF10A cells under MC1 conditions with only a 2.5-fold increase in cell density over 44 hours (versus a fourfold increase for MCF10A cells). Many of the recorded zones never become fully covered with cells even at 44 hours.

While the results shown in Fig. 2 were obtained under MC1 conditions, largely similar results were obtained under MC2 conditions as shown in fig. S3. Because MC2 conditions involved GFP actin–transfected MCF10A cells (MCF10-Ac), Fig. 2A additionally includes the correlation between the green fluorescence channel segmentation and that of the bright-field channel (DIA) for MCF10A-Ac cells. The high correlation coefficients demonstrate the ability of our segmentation models to segment cells equally well in the fluorescence and bright-field channels.

Cell parameter extraction and corresponding EIS recordings in coculture

Coculture experiments with MCF10A-Ac and MCF7 cells were conducted under two distinct configurations: bilateral and concentric as detailed in Materials and Methods. Figure 3A depicts stitched maps that merge the bright-field and fluorescence images of the entire sensing area at the initial cell seeding time point. In the bilateral configuration [Fig. 3A(a)], MCF10A-Ac cells were seeded on the left half of the device and MCF7 cells on the right half. The concentric configuration [Fig. 3A(b)] consisted of MCF7 cells in the center surrounded by MCF10A-Ac cells. These maps at the beginning of the experiment demonstrate the effectiveness of our 3D-printed inserts and seeding protocol in delivering each cell type to its target region with minimal cell crossover.

Fig. 3. Cell seeding, EIS recordings, and cell segmentation under CC conditions.

(A) Merged bright-field and green fluorescence map of 25 electrode pair positions at the start of the experiment. (a) In the bilateral configuration, normal MCF10A-Ac cells were seeded on the left (showing green fluorescence signal; edge marked in green) and cancerous MCF7 cells were seeded on the right of the sensing area (edge marked in pink). (b) In the concentric configuration, cancerous MCF7 cells were seeded in the center (edge marked in pink) surrounded by normal MCF10A-Ac cells (edge marked in green). (B) Modulus and phase EIS Bode plots at four different times in the (a) bilateral and (b) concentric coculture configurations. Different colors represent different electrode pairs. (C) Coculture segmentation at t = 33 hours in the bilateral configuration. (a) Merged bright-field and green fluorescence map. (b) Segmentation overlays on the bright-field images. (c) Segmentation overlays on the fluorescence images. (d) Automated reconstruction of cell density and cell type map from segmentation results. (D) Equivalent maps to (C) for the concentric configuration.

Figure 3B depicts the EIS modulus and phase Bode plots at several time points for the different electrode pairs (in different colors) in the bilateral [Fig. 3B(a)] and concentric [Fig. 3B(b)] configurations. The signals show pronounced impedance differences among electrode pairs because of the physical separation between the two cell types, which leaves some electrodes without cells on their surfaces. These results demonstrate the platform’s ability to acquire simultaneous EIS recordings and microscopy images in coculture.

Figure 3C illustrates stitched microscopy maps of the sensing area for the bilateral coculture arrangement after 33 hours toward the end of the experiment. Figure 3C(a) merges bright-field and fluorescence images, Fig. 3C(b) shows the segmentation outlines of bright-field images, and Fig. 3C(c) depicts the segmentation outlines of the fluorescence channel. The segmentation in both channels allowed quantification of the cell parameters as well as the assessment of the percentage of each cell type present in the image. These data were then used to generate cell density and cell type maps as illustrated in Fig. 3C(d), where the color intensity represents cell density and the color denotes cell type. Figure 3D is equivalent to Fig. 3C for the concentric coculture arrangement.

ML prediction of cell parameter evolution from EIS

Now that we have demonstrated that it is possible to acquire simultaneous microscopy images and EIS recordings using the MEA platform, we proceeded to create a large experimental database to train ML models to predict cellular parameters directly from EIS under the different experimental conditions.

Figure 4 illustrates the ML results under MC1 conditions. Figure 4A shows the regression results of the predicted versus true values for the training (blue) and test (pink) sets for the normal (MCF10A) cells, and Fig. 4B shows the equivalent data for the cancerous (MCF7) cells. Different rows in these panels correspond to different regression models for cell density, covered area fraction, and mean cell diameter. The small (inset) plots represent the results for individual folds of the cross-validation (CV), while the larger plots represent the grouped results. In each case, the model performance is evaluated principally through the R² and mean absolute percentage error (MAPE) values of the test set (pink). Regression performance is seen to be different for the three cellular parameters and between the two cell types. More specifically, the cell density and covered area fraction achieve higher R² than the mean cell diameter but do not necessarily yield lower MAPE. In general, the predictions are more accurate for MCF10A cells than for MCF7 cells. Figure 4C illustrates the ML results for classification of cell type. Both the confusion matrix and receiver operating characteristic (ROC) curve demonstrate that the model is highly effective in distinguishing between MCF10A and MCF7 cells.

Fig. 4. ML model results under MC1 conditions.

(A) Regression results (predicted versus true value) for EIS measurements on normal MCF10A cells to predict cell density, covered area fraction, and mean cell diameter. Blue represents training sets, and pink represents test sets. (B) Regression results for EIS measurements on cancerous MCF7 cells. (C) Classification results for normal versus cancerous EIS acquisitions. The top graph presents the confusion matrix. The bottom graph presents the ROC curve. (D) Time evolution of cell density, covered area fraction, and mean cell diameter determined from microscopy image segmentation for all normal MCF10A and cancerous MCF7 experiments. The solid line corresponds to the median of all electrode positions per experiment, while shaded areas represent the 50% quartile. (E) Parameter evolution predicted by ML regression models from EIS acquisitions.

Figure 4D depicts the time evolution of cell density, covered area fraction, and mean cell diameter computed from microscopy imaging results for five experiments conducted on MCF10A cells and five experiments conducted on MCF7 cells under MC1 conditions. Figure 4E shows the ML prediction of the same dynamics from the EIS recordings for the same experiments. The results demonstrate that the ML model is highly effective in capturing cellular growth dynamics as well as cell size evolution. These findings provide evidence that ML-enhanced EIS recordings can be used as a noninvasive methodology for monitoring cellular spatiotemporal dynamics.

Equivalent results to those in Fig. 4 are depicted in figs. S4 and S5 for the MC2 and CC experiments. As evidenced by the confusion matrices and the area under the curve (AUC) values in the ROC curves, the results demonstrate that culturing the two different cell types separately but in the 50:50 mixed culture medium (MC2 conditions) leads to some reduction in the efficacy of cell type classification relative to the case where each cell type is cultured in its own specialized medium (MC1 conditions) (AUC of 0.81 versus 0.96 in the ROC curves). Coculturing the two cell types together in the mixed culture medium results in further degradation in the classification performance (AUC of 0.72), even though the classification remains largely acceptable.

Figure 5 provides a global view of the efficacy of the ML predictions from EIS recordings for cell density, covered area fraction, mean cell diameter, and cell type classification for the MC1, MC2, and CC experimental conditions. These results confirm that the ML model produced different scores for the different experimental conditions, with better results for MCF10A cells than for MCF7 cells and with cell density and covered area fraction more accurately predicted than the mean cell diameter as has already been mentioned. Notably, the model predictions for MCF10A cells generally achieved excellent results, with cell density and covered area fraction having R² > 0.8. Although the model’s performance in coculture is inferior to that in monoculture experiments, the model shows consistent regression and classification capabilities across all conditions.

Fig. 5. Comparison of ML scores for different experimental conditions.

(A) Regression performance for normal MCF10A and cancerous MCF7 cells. Top row: R² scores; bottom row: MAPE values. Blue, red, and yellow columns depict the scores of the ML regression model predictions based on EIS signals for MC1, MC2, and CC conditions, respectively. (B) Comparison of classification scores. The bars represent the AUC calculated for each set of conditions.

Biological insight from EIS spatiotemporal recordings

Quantifying spatial heterogeneities in cellular proliferation dynamics

While analyzing one of the MC1 experiments on MCF10A cells, we observed that the increase in cell density and covered area fraction over time was slower for some electrode pairs than for others (Fig. 6A). Extracting cell density maps at different time points (Fig. 6, B and C) confirmed the presence of spatial heterogeneities in cell proliferation and demonstrated our ability to quantify the evolution in time of these heterogeneities. We note that the spatial cell density maps derived from EIS recordings (Fig. 6C) were largely similar to those obtained from microscopy images (Fig. 6B), providing further evidence for the efficacy of our ML model to accurately predict cell density based solely on EIS data. In addition, we used the EIS cell density predictions to quantify spatial variations in cellular proliferation rates during different time intervals as depicted in Fig. 6D. This analysis revealed that during the time interval Δt = 10 to 20 hours, cell proliferation rates were higher in the upper region of the sensing area, with the rate of change in cell density $\left({\dot{\mathrm{\rho }}}_{\text{cell}}\right)>100$ cells/mm²·hour in the top three electrode rows, compared to ${\dot{\mathrm{\rho }}}_{\text{cell}}<70$ cells/mm²·hour in the lower two rows. As time progressed (Δt = 20 to 30 hours), the proliferation rates became more evenly distributed across the sensing area. In the latter stages (Δt = 30 to 40 hours), the cell proliferation rate in the upper region decreased to ${\dot{\mathrm{\rho }}}_{\text{cell}}<70$ cells/mm²·hour, while it increased in the lower region to ${\dot{\mathrm{\rho }}}_{\text{cell}}>70$ cells/mm²·hour. These results provide an appreciation for the spatial variations in cellular proliferation rates across the device and demonstrate the ability to quantify the temporal evolution of these rates based solely on the EIS signals. Last, we also examined the time required to achieve a 0.7 cell-covered area fraction in the device, as illustrated in Fig. 6E. Consistent with the proliferation rate results, the lower two rows of the device took longer (t > 10 hours) to reach this level of surface coverage compared to the upper three rows (t < 9.3 hours). These results are particularly interesting in light of the fact that the ability to quantitatively assess the extent of surface coverage in a noninvasive manner and in real time is highly desirable in a number of tissue engineering and implantable medical device applications.

Fig. 6. Spatiotemporal monitoring of monoculture proliferation dynamics.

(A) Time evolution of MCF10A cell density, covered area fraction, and mean cell diameter from microscopy image segmentation and EIS predictions. For the EIS predictions, both the raw data and smoothed (filtered) curves are shown. (B) Spatial mapping of cell density at four time points [shown in (A) with dashed vertical red lines]. Each box represents the position of an electrode pair, and the number within the box indicates the cell density value. (C) Spatiotemporal mapping of cell density based on EIS predictions at the same four time points shown in (B). (D) Spatiotemporal mapping of cell density proliferation rates based on EIS predictions for the three time intervals shown. (E) Spatial mapping of the time required to attain a 0.7 covered area fraction.

Monitoring competition between MCF10A and MCF7 cells

Figure 7 illustrates the spatiotemporal monitoring of a coculture experiment in a bilateral configuration, where normal MCF10A-Ac cells were seeded on the left side and cancerous MCF7 cells on the right side of the device. The time evolution of the spatial cell density maps determined from microscopy image segmentation is shown in Fig. 7A. Over time, the increasing cell density led to the closure of the initial gap between the two cell types (dark regions of low cell density). Gap closure was driven principally by the faster proliferation and migration of the MCF10A-Ac cells. Figure 7B presents the equivalent results derived from impedance measurements. Although the model initially distinguished between the two cell types, its classification accuracy declined as the experiment progressed. Nevertheless, the impedance-based predictions effectively captured the overall increase in cell density and the gradual closure of the interface by MCF10A-Ac cells. These findings highlight the promise of this method for monitoring the competition between normal and cancerous cell populations while also acknowledging the need for further refinement in cell type classification.

Fig. 7. Monitoring of cell competition under bilateral CC conditions.

(A) Spatiotemporal evolution of cell density and cell type from microscopy cell segmentation. (B) Spatiotemporal monitoring of cell density and cell type from EIS predictions. In all panels, each box represents the position of an electrode pair. The numbers in the boxes are the cell density values. The color intensity depicts cell density, while the color represents cell type. White rectangles denote electrodes without usable measurements at that time point.

Parameter sensitivity of EIS recordings

Because our ML model was trained on the EIS recordings and in light of the “black box” nature of this model, we wished to explore which parameters in the experiments are the key drivers of the ML-based EIS predictions. To this end, we considered the four parameters that we have studied thus far, namely cell density, substrate covered area fraction, mean cell diameter, and cell type, as well as the particular experiment to account for interexperiment variability. As shown in Fig. 8A, the experiments conducted on the three different cell types (MCF10A, MCF7, and MCF-10A-Ac) and under the three experimental conditions (MC1, MC2, and CC) spanned a wide range of values. Figure 8B provides an estimation of how the various parameters considered influence the impedance changes, with the results displayed in the Bode plots (Fig. 8, C to E). This analysis was conducted for two cases: (i) by considering all the data acquired (labeled “All Data”) and (ii) by constraining the analysis to a selected parameter range delineated by the green bars in Fig. 8A (labeled “Selected Data”). As shown in Fig. 8B, when the entire dataset was taken into account, the covered area fraction had the strongest impact on EIS, followed by interexperiment variability. In contrast, for the case of constrained parameter range, the influence of cell type becomes more pronounced, although the effect of interexperiment variability remains substantial, especially in coculture. This provides an initial indication of how the various parameters considered influence the EIS recordings.

Fig. 8. Analysis of the sources of variability on EIS signals.

(A) Distributions of cell density, covered area fraction, and mean cell diameter determined from microscopy segmentation for all cell types and under all the different experimental conditions (MC1, MC2, and CC). The green-shaded areas denote a selected subset of the parameter ranges. (B) Weighted feature importance to estimate the relative contributions of individual parameters to the EIS predictions. The analysis was performed on the entire dataset (left) and on the selected data subset with the specific parameter ranges shown in the green-shaded areas in (A) (right). (C) Comparison of impedance signals for various cellular parameter intervals. In all cases, the two central panels depict the modulus and phase Bode plots, while the two lateral panels show modulus and phase values at the selected frequencies shown by the vertical dashed red lines. Top row: impedance signals for six covered area fraction intervals ranging from 0.2 to 1. Middle row: impedance signals, after a 0.7 covered area fraction has been attained, for five cell density intervals ranging from 0 to 5000 cells/mm². Bottom row: impedance signals, after a 0.7 covered area fraction has been attained, for six mean cell diameter intervals ranging from 15 to 35 μm. (D) Comparison of impedance signals from different cell types and different experimental conditions for the selected subset of parameter ranges shown in the green-shaded areas in (A). For each curve, the solid line represents the median and the shaded envelope represents the 50% quartiles. (E) Comparison of impedance signals from different experiments for the selected subset of parameter ranges shown in the green-shaded areas in (A). Each curve represents the median of a single experiment.

We subsequently sought to gain a finer appreciation of the subranges of parameters that drive changes in EIS signal shape. To this end, we subdivided the range of each of the parameter values into subintervals and performed our sensitivity analysis on each interval. The top row of Fig. 8C illustrates the EIS changes for six intervals of covered area fraction. The impedance modulus increases progressively with increasing covered area fraction before plateauing at a covered area fraction of 0.7. As the electrodes become covered with cells, the phase plots shift from an S-like shape (purple) to a tilde-like shape (light pink). The middle row shows the EIS signal at different cell density intervals for a covered area fraction above 0.7. The modulus value at low frequencies (10 kHz) decreases as the cell density increases. Conversely, the phase value at high frequencies (1 MHz) increases with cell density. The bottom row depicts the changes in the EIS signal caused by variations in mean cell diameter. The impedance modulus at low frequencies shows a slow consistent increase with cell diameter, whereas the phase at high frequencies decreases. These findings are consistent because cell density is inversely proportional to the square of cell diameter for a constant covered area (see Eq. 1).

Figure 8D illustrates how EIS measurements vary among the three cell types under the different experimental conditions. The largest differences between the two cell types appear under MC1 conditions, with smaller differences under MC2 conditions and even smaller differences under CC conditions. This pattern aligns with the decreasing classification accuracy of the ML model as we go from MC1 to MC2 and lastly to CC conditions.

Figure 8E illustrates the interexperiment variability of the EIS signals. The data reveal progressively increasing variability as one goes from MC1 to MC2 and lastly to CC conditions. Ultimately, the increasing interexperiment variability hampers the model’s ability to reliably detect cell types, which helps explain why cell type classification is less accurate under CC conditions. Ideally, reducing this variability would make the model more sensitive to changes in cell type and in the other cellular parameters, leading to more accurate cell type discrimination.

DISCUSSION

The present study describes a noninvasive approach for reliable real-time monitoring of spatiotemporal dynamics of adherent cells over extended periods. The approach is based on the use of a MEA for the acquisition of wide-frequency EIS signals and combining these electrical recordings with predictive ML algorithms that, once appropriately trained and validated against microscopy images, obviate the need for microscopy imaging in subsequent monitoring. Although other studies have validated the temporal evolution of EIS signals against microscopy images (22, 23, 45, 46), this validation was only qualitative and did not provide information on any possible spatial heterogeneities. To the best of our knowledge, the system presented here is unique in its ability to provide quantitative real-time monitoring of cellular spatiotemporal dynamics using EIS measurements. The principal advantage of the system, and the reason we believe that it would be beneficial in a broad array of settings, is that it circumvents limitations inherent to long-term live-cell fluorescence microscopy imaging including the toxicity of fluorescent dyes, cellular photodamage because of prolonged light exposure, and the inability to image through opaque media such as blood or biological tissues.

As an illustration of its capabilities, the system developed here was shown to be able to track the spatiotemporal evolution of cellular density, substrate area coverage, mean cell diameter, and cell type classification of normal and cancerous breast epithelial cells. This spatiotemporal monitoring was demonstrated in the two cell types not only cultured separately but also cocultured together. The basic premise behind the ability to detect the cellular presence on the electrodes is that cells are less conductive than cell culture medium and their membranes present insulating properties, thus yielding substantially different EIS signals. Cell type discrimination is enabled principally by differences in cell membrane composition, intracellular conductivity, and intercellular junctions (47). The ability of the current platform to monitor the spatiotemporal evolution of other cellular parameters that are expected to influence EIS signals such as cell circularity, cell size heterogeneity, and cell motility certainly merits future investigation.

An important feature of our current approach is its spectral nature. Previous studies have used single-frequency impedance measurements by selecting a frequency relevant to their specific application (45, 48, 49). However, this approach may not capture the full range of information that a complete impedance spectrum provides, which is necessary for its correlation with the various cellular parameters. The present study focused on wide-frequency EIS acquisitions ranging from 3 kHz to 10 MHz. This range was limited at lower frequencies because of the double-layer effect of the gold electrodes and at higher frequencies by parasitic or stray capacitance from the electronic components. In future iterations of the system, the electronics can be improved and the double-layer effects reduced through the use of nonpolarizable materials.

A particularly distinctive aspect of the current work is that after automation of the microscopic image acquisition and cellular segmentation paired with EIS signals, the quantitative database was used for training various ML models. Traditional techniques for analyzing wide-frequency EIS measurements, such as electrical equivalent circuit and physical models, are time-consuming and produce noisy results when applied to large volumes of impedance data as we have here. Therefore, we resorted to the use of ML, developing a long short-term memory (LSTM)–based model. The LSTM model architecture is particularly well suited for sequential data such as time series or, in this case, frequency series (50). Moreover, LSTM models have already been shown to be effective in interpreting EIS in both materials science (51) and other biological applications (52). The ML regression results for determining cellular parameters from EIS signals were not the same for the different cell types studied. Generally speaking, the regression scores for MCF10A cells were better than those for MCF7 cells. This difference likely stems from the inherent spatial heterogeneity observed in MCF7 cultures and their tendency to form clusters rather than a uniform monolayer (53, 54).

The ML classification for cell type identification, i.e., for distinguishing MCF10A cells from MCF7 cells, performed best under conditions where each cell type was cultured in its own specialized medium (MC1 conditions), which may reflect differences in impedance between the two types of cell culture media and their influence on cellular characteristics. When the two cell types were cultured in the same medium (50:50 mixture of the two specialized media; MC2 conditions), the classification accuracy decreased somewhat. The lowest classification scores were obtained when the two cell types were cocultured together, possibly suggesting some level of interaction between the two cell types that tends to mask some characteristics of the EIS signals on which the cell type discrimination is based. This issue needs to be investigated further in future studies. Nonetheless, all the regression and classification ML models demonstrated positive predictive capability when tested versus previously unseen experimental data in cross-validation, indicating that the ML models can capture the complex relationships between EIS signals and cellular parameters.

As a concrete demonstration of the capabilities provided by the system described here, we were able to quantitatively assess spatial heterogeneities in cellular proliferation rates and to track the temporal evolution of these heterogeneities noninvasively based solely on impedance recordings. It is recognized that additional factors such as differences in initial cell seeding density and/or nonuniform fibronectin coating may have contributed to the observed spatial variations in cell density. From a basic science perspective, the capability demonstrated by the system is useful for understanding differential proliferation patterns within a cellular monolayer or a tissue as well as for elucidating the impact of certain genetic mutations or sources of cellular dysfunction on cellular proliferation patterns. From a more applied viewpoint, the ability to detect spatial heterogeneities in cellular coverage is particularly useful for assessing wound healing rates as well as for determining the efficacy of integration of an implantable medical device within a tissue. The coculture studies that investigated how the space initially separating normal and cancerous cells progressively became occupied by one cell type or the other provided a preliminary demonstration of competition between the two cell types. Future extension of these coculture investigations promises to provide valuable insight into the spatiotemporal patterns of cancer cell invasion of normal tissue.

To better understand the key determinants of the ML-based predictions, we investigated which cellular parameters contributed to the greatest variations in EIS. The results showed that cell covered area fraction had the highest contribution, which is consistent with physical principles because of the large difference in conductivity between cell culture media and cells. As cells proliferate and approach confluence, EIS signals become increasingly more dependent on cell density and cell size, which are inversely related, as well as on cell type. Larger cells create fewer intercellular paths for electrical current flow, resulting in higher impedance and more capacitive behavior (lower phase values). This observation is in line with the Bode diagrams in the literature based on the Giaever-Keese physical model (55).

Several challenges remain to be addressed to improve the robustness of the monitoring methodology described in the current study. These include increasing the prediction accuracy through improved labeling methods, reducing interexperiment variability, and determining the minimum number of training experiments needed for the optimal performance of the ML model. Furthermore, future versions of the system would benefit from technical improvements including the use of complementary metal-oxide semiconductor high-density MEAs to increase spatial resolution and the extension of the spatiotemporal EIS recordings to three-dimensional (3D) cellular configurations that better mimic in vivo conditions.

In conclusion, the versatility of the system developed here promises to affect a wide range of applications including monitoring cellular responses to various biophysical and biochemical challenges, elucidating the impact of various molecules on cellular behavior during drug testing and development, tracking spatial heterogeneities in wound healing and in tumor cell invasion of healthy tissues, and monitoring long-term cellular proliferation and differentiation in microphysiological systems and tissue engineering applications. By providing an integrated noninvasive approach for real-time exploration of cellular spatiotemporal dynamics, the technology described here has the potential to considerably advance our understanding of cellular behavior and interactions.

MATERIALS AND METHODS

MEA platform design and fabrication

The MEA platform (34 by 34 mm), developed for performing EIS measurements on cell monolayers at multiple positions over time, is equipped with a central sensing area of 5.4 mm by 3.5 mm containing 25 electrode pairs housed within a 16-mm-diameter well for cell culture (fig. S6A). Fifty contact pads are distributed along the two opposite ends to connect to the impedance spectrometer. Each electrode measures 200 μm by 60 μm, with a 30-μm spacing between electrode pairs.

The platform was produced using standard microfabrication procedures (fig. S7). Briefly, a glass wafer (800-μm thickness and 100-mm diameter) was coated with a hexamethyldisilazane primer and positive-tone photoresist (AZ5214) for a total thickness of 1.4 μm. Standard photolithography techniques were used to pattern the surface. A thin metal bilayer (10-nm Ti/90-nm Au) was deposited via electron beam evaporation and subsequently etched. A 2.4-μm SU-8-2002 passivation layer was then applied and selectively removed over the electrodes and contact pads. After cutting the wafer into four individual devices, a polymethyl methacrylate ring was attached to each device using liquid polydimethylsiloxane, creating a well for cell culture and medium reservoir.

The measurement setup includes an impedance spectrometer (Sciospec ISX-3) connected to a multiplexer (Sciospec MUX) that switches among the different electrode pairs. The multiplexer connects to the device through a custom-designed printed circuit board with a flexible polyimide segment that facilitates sample handling. Spring-loaded contacts were soldered to the printed circuit board to establish the connection with the device, and a 3D-printed alignment piece set was produced to ensure proper positioning between the contacts. The setup is equipped with a custom-designed transparent lid that limits medium evaporation during the extended recordings while ensuring sufficient gas exchange for cellular viability (fig. S6B).

Cell culture

Two cell types were used in the current study: normal breast epithelial (MCF10A) cells and breast cancer epithelial (MCF7). In the case of MCF10A cells, either unlabeled or GFP actin–transfected (MCF10A-Ac) cells were used depending on the experiment. The cells were cultured using standard procedures. Briefly, MCF10A and MCF10A-Ac cells in passages 1 to 20 were cultured to 80 to 90% confluence in Dulbecco’s modified Eagle’s medium (DMEM)/F12 supplemented with 5% horse serum, epidermal growth factor (20 ng/ml), cholera toxin (100 ng/ml), insulin (0.5 to 1 ml/liter), hydrocortisone (0.5 μg/ml), and 1% penicillin/streptomycin. MCF7 cells in passages 1 to 20 were cultured to 60 to 70% confluence in DMEM supplemented with 10% fetal bovine serum and 1% penicillin/streptomycin.

Three types of cellular spatiotemporal dynamics experiments were performed: (i) MCF10A and MCF7 cells in separate devices maintained in their respective culture media, henceforth referred to as the monoculture-1 (MC1) condition; (ii) MCF10A-Ac and MCF7 cells in separate devices maintained in coculture media consisting of a 50:50 mix of the two culture media (MC2); and (iii) coculture of the two cell types in the same device in coculture media (CC). The 50:50 mix was independently verified to provide the optimal growth of the different cell types in the coculture experiments. These experimental conditions are depicted in fig. S2.

For the MC1 and MC2 experiments, the device surface was coated with 25 μl of fibronectin (F1141-1mg, Sigma-Aldrich) after which 120,000 cells (MCF10A or MCF7 cells in the MC1 experiments and MCF10A-Ac or MCF7 cells in the MC2 experiments) were seeded, and the device was filled with 1200 μl of the appropriate culture medium. The cells were then allowed to adhere for 1 hour before positioning the device on the microscope stage for simultaneous bright-field imaging and impedance measurements.

For the coculture experiments, two different cellular spatial arrangements were established using custom 3D-printed inserts (fig. S6C): a concentric configuration with 7500 MCF7 cells in the center encircled by 200,000 MCF10A-Ac cells and a bilateral pattern where 100,000 cells of each type were placed on opposite halves of the device. A cell seeding protocol was developed to optimize the separation between the two cell types. This protocol consisted of initially coating the device with fibronectin before securing a coculture insert in place. Cell suspensions were then introduced into the designated chambers and allowed to adhere. Nonadhered cells were removed via media aspiration and gentle phosphate-buffered saline washing. A fresh culture medium was then added for a second period of adhesion. The medium was aspirated a second time, the insert was removed, and the surface was carefully washed once more before a final addition of fresh medium. These multiple steps were effective in preventing any cell crossover between the two regions.

EIS acquisition and processing

EIS measurements were performed using a two-electrode mode between adjacent electrodes. The measurements used a 250-mV amplitude signal with 30 frequency points ranging from 3 kHz to 10 MHz. Data were collected every 15 min across all 25 electrode pairs during a 40-hour experimental period, yielding ~4000 EIS spectra per experiment. Baseline measurements were taken before fibronectin coating and cell seeding, including an open measurement (empty well) and a load measurement (with a 1× phosphate-buffered saline electrolyte).

The data were processed using a custom Python pipeline. Signal compensation was performed using open/load measurements to eliminate high-frequency hardware artifacts. Signals from nonfunctional electrodes were automatically filtered out, and principal components analysis was used to identify and remove potential outliers from the dataset.

Microscopy and image analysis

An inverted phase contrast microscope (Nikon Eclipse Ti) was used for image acquisition. The microscope was equipped with a charge-coupled device camera (Hamamatsu Orca-flash4.0) and a stage-top incubator to control the temperature and CO₂. Images were captured using a 20× objective with the “Perfect Focus System” option to minimize image drifting out of focus during the extended recordings. Images were acquired hourly at each of the 25 electrode positions throughout the 40-hour experiments, resulting in ~1000 images per experiment. Image focus was maintained using the Perfect Focus System, with regular z-axis adjustments performed to ensure optimal focus.

Image analysis was performed in two steps. First, electrode tracks were identified using automated thresholding, thereby determining the available image area. Second, cells were segmented in both bright-field and fluorescent channels using the open-source software Cellpose 2.0 (56). Specific Cellpose models were trained for accurate segmentation of the different cell types in both monoculture and coculture. Three parameters were extracted for each image: cell density, covered area fraction, and mean cell diameter.

The cell-covered area on the electrode surface plays an important role in the measured EIS signal because cells are less conductive than the cell culture medium and cell membranes present insulating properties. The impact of cellular size on EIS has been analyzed in experimental studies (57) and physical models (38). However, in the context of cellular dynamic studies, cell density can be a more relevant variable and can be derived from the covered area fraction and mean cell diameter as follows

$$\mathrm{\rho }=f_{\text{Covered area}}\frac{4}{\mathrm{\pi }{\overline{D}}^2}$$ (1)

where $\mathrm{\rho }$ denotes the cell density, $f_{\text{Covered area}}$ represents the fraction of the cell-covered area, and $\overline{D}$ indicates the mean cell diameter.

ML analysis

Corresponding microscopy images and EIS measurements were acquired for each electrode pair position and at each time point, providing a comprehensive dataset for ML analysis. The dataset contained 34 experiments: 10 MC1 experiments (5 for MCF10A cells and 5 for MCF7 cells) with a specialized culture medium for each cell type, 12 MC2 experiments (6 for MCF10A cells and 6 for MCF7 cells) with mixed media, and 12 CC experiments (4 concentric and 8 bilateral). Each experiment generated ~1000 paired image and EIS measurements, resulting in a total dataset with more than 30,000 samples.

Traditional ML approaches were initially tested for EIS-based prediction of the image parameters; however, better performance and reduced overfitting were achieved through DL architectures. A hybrid model was implemented, wherein a convolutional neural network–based feature extractor was combined with a bidirectional LSTM network. Two layers and a hidden state dimension of 256 units were used in the LSTM component. The EIS input features were enhanced through the addition of signal derivatives and EIS measurements from four previous time points, thereby providing the temporal evolution of the signal.

Two types of DL models were developed: classifiers to distinguish between normal and cancer cells and regression models to predict cellular parameters. The classifiers were trained separately for each experimental condition, and the performance was evaluated using the ROC-AUC metric. The regression models, designed to predict either cell density, covered area fraction, or mean cell diameter, were developed specifically for each cell type because of their distinct impedance signatures. Regression performance was assessed using R² and MAPE scores to ensure scale-independent evaluation.

A leave-one-experiment-out cross-validation approach was implemented to ensure robust model evaluation and to prevent data leakage. For each iteration, one experiment was held out as the test set, while the model was trained on the remaining experiments. Within the training process, 25% of the training data were reserved for validation, with the split stratified on the basis of experiment identifiers to maintain a balanced representation of each experiment.

Supplementary Materials

The PDF file includes:

Figs. S1 to S7

Legends for movies S1 and S2

Other Supplementary Material for this manuscript includes the following:

Movies S1 and S2