The main strategy in choosing a bacterial strain on which to test the proposed sensor was to select a strain that can form biofilm structures. It is also important that the species can grow in a subsurface environment and within rhizospheric areas. Additionally, the IM sensing platform proposed is to be tested in the laboratory in this work, and thus, ease of growth of the bacteria is an important consideration. A few different strains were investigated as candidates such as Streptomyces Viridosporus (ATCC 39115) that is isolated from soil and is capable of biofilm formation. Other common biofilm formers are Pseudomonas Putida, Pseudomonas Fluorescens, Rhizobium Leguminosarum, Sinorhizobium Melitoti, Bacillus Subtilis, Sinorhizobium Meliloti (Ensifer Meliloti), and Pseudomonas Aeruginosa. Of these species, laboratory growth can be as easy as inoculation in Luria-Bertani (LB) broth (used for Pseudomonas Putida, for example,) or by using a composition of a few different growth nutrients such as yeast extract, mannitol, agar, or soil extract such as that for Rhizobium Leguminosarum. Considering the reasons mentioned above and the risk level of working with these strains, Pseudomonas Putida was chosen as the bacterial strain of interest for the experiments in this work. This risk level I strain can be grown in Luria-Bertani broth medium at 30 °C.

Isolated Pseudomonas Putida bacteria were grown on Petri dishes containing tryptic soy agar at 30 °C overnight. Once the colonies are formed on the agar medium, they are ready to be transferred to the liquid growth medium. A smear of the bacterial colonies formed on the agar plates were extracted using a sterilized inoculation loop and placed in sterilized LB broth. LB broth (Lennox), powder from Sigma Aldrich (ref: L32022-250G) was used for the preparation of bacterial solutions for testing. After 1 day, bacterial cells in the LB broth were grown resulting in a cloudy solution that was ready for serial dilution. As per the usual method of a stepwise dilution, 2 mL of the grown batch was diluted in 18 mL of fresh LB broth medium, and subsequently 2 mL of the newly diluted sample was extracted for dilution in another 18 mL of fresh LB broth. Six sample types offering a wide range of bacteria concentrations created by diluting 10¹, 10², 10³, 10⁴, 10⁵, and 10⁶ fold, were developed for impedance testing. Part of each sample was set aside for optical spectrophotometry measurements while 275 µL of each sample was decanted onto the wells of the E-plate (part of the transducer) for impedance measurements. Thus, as Figure 1C shows, the measurand observed by the sensing platform is bacterial concentration.

Bacterial detection and analysis using impedance-based techniques may be classified into two different approaches: faradaic and non-faradaic. In the faradaic approach, an interface is required for the transfer of charges from the species under the test to the electrodes, which in turn requires the employment of redox-active species (Daniels and Pourmand, 2007). Since there exists no redox species in the proposed setup, this study used a non-faradaic approach for impedance measurements. For non-faradaic impedance measurements there are several models that could be used to describe the impedance data. The models are comprised of hypothetical resistances and capacitances (an RC equivalent circuit) that are formed based on the conductivity of the medium and the electrodes (Brosel-Oliu, et al., 2015). The resistance and capacitance of the growth medium (electrolyte) as well as the resistance and capacitance of the bacterial biofilm are the main elements in most of the suggested models. With the occurrence of biochemical reactions at the surface of the transducer (electrode), a double-layer capacitance could be formed that is induced by the formation of ionic species due to microbial metabolism. As an existing element in an RC equivalent circuit, many researchers suggested using the double-layer capacitance (Kim et al., 2012; Paredes, et al., 2014a) approach. Resistance and capacitance of bacteria can be either in parallel or in series with the solution resistance.

Interdigitated arrays (IDA) are popular tools for monitoring bacteria in impedance sensing platforms. Whether or not there are immobilized antibodies on the electrodes, the key aspect is the size of the electrodes as this quality provides for the level of sensitivity to micro-scale changes in electron transport. IDAs, also known as IDEs (interdigitated electrodes), are structured as comb-like conductive lines of transducers, such as gold and platinum, that are typically comprised of a working electrode and a reference electrode and are coated on the surface of a glass, silicone, or hard plastic substrate. The two electrodes are fabricated in a way such that the parallel fingers of the combs of the two electrodes are interleaved from one finger to another but are not in contact. The IDAs have the advantage of providing low Ohmic drop making it easier to achieve a steady-state current response (Maruyama et al., 2006). When it comes to the optimization of the signal-to-noise ratio (S/N) based on the application of interest, the spacing between the fingers, the length and the width of the fingers, the height of the traces, and the overall active area of the electrodes, are among the most important parameters for IDEs (Min and Baeumner, 2004; Varshney and Li, 2009). As documented by van Gerwen et al. (1998), the smaller the spacing and the width, the higher the sensitivity to the electrochemical changes between the microbands of the electrodes. Using impedance sensing with an IDA microelectrode, Yang et al. (2004) provided successful evidence of the detection of Escherichia coli O157:H7 bacteria. In that study, an indium-tin oxide IDA was used, which had 25 pairs of fingers that were coated on glass substrate that were 15 µm wide (digit width) and 15 µm apart from each other (interdigit width). Kim et al. (2012) manufactured an IDA by depositing gold patterns of microbands on silicon wafers to achieve the rapid detection of bacterial attachment. The configuration of the microelectrodes used for that study was similar to the well-known comb-like structure with 50 pairs of microbands of 10 µm digit width and 10 µm interdigit width. In another study, MacKay et al. (2017), nanofabricated a set of microarrays of gold nanoparticles that had an interdigit width of only 2 µm while the microband width was 4 µm. Turolla et al. (2019) evaluated the possibility of using 10 µm-spaced coplanar microelectrodes in the impedance sensing of slime formation in pipes and tanks. What these studies show is that impedance spectroscopy with biological samples requires electrodes that have comparable dimensions to the cells in the samples. In the case of bacterial cells that are generally smaller than human cells, the width and spacing of the microelectrodes used in the literature are in the range of 1–20 µm (Varshney and Li, 2009).

As far as the sensing electrodes are concerned, after thorough evaluation of the possibility of manufacturing or using interdigitated electrodes on the market, 16-well E-Plates (E-Plate 16) made by ACEA Biosciences Inc., San Diego, CA (now with Agilent Technologies, Inc.) was chosen as the sensing microelectrode. This product is composed of well plates (16 wells in total) that have gold traces deposited in the bottom of each well. The dimensions of the electrodes are within the constraints of this study. Additionally, the fact that the well plates enable one to hold up to 16 different samples simultaneously is advantageous, although not all of the wells were used for testing in this study.

Previous research investigating impedance microbiology can provide useful information for the approximate properties of impedance when studying microbial activity. Grossi et al. (2010) were able to test and verify a portable sensor that detects bacteria at a frequency of 200 Hz and 10 mv peak-to-peak voltage in liquid and semi-liquid samples. This sensor detected the total bacterial concentration at a threshold of 10⁷ CFU/mL within 3–12 h of inoculation and was successful in detecting the occasional and specific bacteria in ice-cream samples. Radke and Alocilja (2004) developed a biosensor using immobilized antibodies on a MEMS electrode using a frequency range of 100 Hz to 100 kHz and at 100 mV. Paredes et al. (2014a) performed impedance-based tests within a range of frequencies between 10 Hz and up to 100 kHz. Higher frequencies have short wavelengths that do not allow the microbial metabolism to cause alterations in the impedance phase and magnitude. Other researchers have suggested a similar frequency range (Davis et al., 2006). In a study on detecting bacterial cells in suspensions using electro-impedance spectroscopy (Yang, 2008), the authors used a frequency range of 1 Hz–100 kHz. Generally, impedance spectroscopy of bacterial cells does not require very high frequencies and can be achieved by using low frequency excitations. As well, operating the system at low excitation frequencies and voltages would minimize the power consumption of the testing unit, which is advantageous.

In addition, one of the most important criteria for a field-based sensor to be used in a rain garden is to be able to conduct automated measurements of several biological samples without the need of human intervention or supervision over the course of the measurements. Automated measurements, in this study, would briefly mean that the setup conducts impedance measurements of up to 8 different biological samples (by making use of 8 wells of the E-Plate), and sweep from low to high excitation frequencies when a certain channel is isolated for measurement. In other words, the experiments would require continuous measurement of the impedance of an array of channels under sequentially varying frequencies. Thus, it is necessary to build a platform that is capable of multiplexing and switching channels on a continuous and orderly basis. The working mechanism of the setup would be based on assigning specific tasks to each component and providing the means for proper communication between components to facilitate the integration of the system. Thus, the controls for switching channels and transducing AC signals as well as the controls of the measurement functions and data storage are a major element in the signal modification system.

ADG708 and the Evaluation Board (EVAL-16TSSOPEBZ) made by Analog Devices Inc (2019). were used in the circuit as the switching component. ADG708 is an 8:1 switching system-on-chip (SoC) that determines when to switch to one of the 8 outputs (S1 to S8) controlled by the 3-bit binary address codes (A0, A1, A2) that it receives [49]. This chip was chosen because of its low current leakage, low power consumption and its portability. GW Instek GPD-4303S power supply was used to provide power to the multiplexer. A microcontroller chip and its development kit (nRF52832 and nRF52-DK) both made by Nordic Semiconductors, Trondheim, Norway, were used as a controlling unit for the transmission of the digital signals required for the multiplexer to switch between channels. Using SEGGER Embedded Studio for ARM V4.10 as editor and compiler/linker/debugger, a code was developed in C programming language for the microcontroller to control the multiplexer.

Other than the frequency range and voltages that determine the choice of a proper impedance measurement device, the affordability of the device is important because it is always desirable to create a device that can be used widely by engineers and technicians working in municipal services. Devices such as potentiostats, dynamic signal analyzers and impedance analyzers have been used by many researchers for the purpose of impedance spectroscopy. However, in this study, the authors selected the much more affordable LCR meter and programmed it in such a way as to provide similar benefits to high-end potentiostats and impedance analyzers. After comparing many LCR meters in terms of the frequency range, the voltage range, the programmability, the basic accuracy, the measurement capabilities, and the price, Keysight E4980AL/032/201 made by Keysight Technologies, Santa Rosa, CA was selected.

The microcontroller is controlled by a series of codes that sequentially commands the change in the digital signals sent to the multiplexing switch. The multiplexer forwards several digital outputs into a single line. The command center for the testing setup is a laptop that is connected to the microcontroller and the LCR meter, and sends commands to both components through universal serial bus USB ports. A “master” software was therefore needed to help with the integration of the components into one coherent system and decrease the complexities in controlling the devices. This master code was implemented in Python using SCPI (Standard Commands for Programmable Instruments) commands to send measurement settings and inquiries to the LCR meter, to collect and save the test data, and to tell the microcontroller to switch to the next channel. The microcontroller receives a serial input from the laptop. Based on that, it creates a route between one of the inputs (S1 to S8) to a single output. This enables the Python program to exercise control between one of the wells and the LCR meter. A delay was incorporated in the code to yield enough time for the LCR meter to finish the measurements on the well before the microcontroller closes the next channel for measurement.

The function of the system starts with a command sent by the command center to the microcontroller, asking the multiplexer to switch to the first channel. When the channel is closed, the command center commands the LCR meter to start sweeping AC signals from low to high frequencies using values defined in the program and measure the R-X values of the sample under the test. The R-X values are the real and imaginary components of the impedance that are later used to calculate the resistance and capacitance properties of the sample as well as the phase shift between the applied and the measured signal. Figure 1C shows the final sensor components for the platform. Figure 2A is a schematic of the sensor system in terms of the main electrical components, while Figure 2B shows photographs of the complete system used in the laboratory.

The measurement by the LCR meter has two parameters, the voltage and the frequency. In order to have a better understanding of the impedance changes in the biological samples, the measurements were done at various frequencies as low as 20 Hz and up to as high as 300 kHz. The AC signal voltage is set to 100 mV peak to peak. One of the system’s channels was used to capture any glitches or disturbances in the system by maintaining a connection to the RC circuit element of known resistance and capacitance of 30 Ω and 474 nF, respectively. The magnitude of the RC element was chosen based on typical magnitudes of the resistance and capacitance observed in preliminary impedance analyses on the bacterial samples.

In-tandem verification of impedance sensing leading to the estimation of bacterial concentration is a necessary part of the proposed device’s proof of concept. Microscopical methods are commonly used as confirmation methods for impedance measurements in the literature, but these require expensive facilities. Pal et al. (2016) used optical density at 600 nm and surface plating techniques to substantiate their impedance sensing results. Optical density spectrophotometry at 600 nm is often used in applications involved with the growth of bacteria in culture (Matlock, 2019). Surface plating, however, is a time-consuming method and should be performed by trained personnel (Wang et al., 2015). Hemocytometry on the other hand, allows the direct count of the number of cells per known volume of sample. Spectrophotometry is an indirect measurement of bacterial concentration of a volume of sample and a much more rapid method than hemocytometry. Therefore, hemocytometry was used to calibrate optical absorbance measurements from spectrophotometry, on samples from similar batches as those under impedance testing. This would eliminate the need for conducting hemocytometry in every test, which is a labor-intensive and time-consuming task in the long-term. This affordable approach would help to estimate bacterial cell concentrations at a given time that may be correlated with impedance spectroscopy results.

Prior to the quantification of the optical absorbance, a set of bacterial samples were diluted step-wise by 50% to find a more accurate relationship between the proportional concentration (unknown count) and the optical absorbance. By assigning a concentration factor of 1 to the saturated (most concentrated) solution and factors of 2^–1, 2^–2, 2^–3, 2^–4, 2^–5, and 2^–6 to the diluted samples, the corresponding absorbances were measured. In order to quantify the absorbance measurements and correlate them to the concentrations by assigning values of cell counts, a set of hemocytometry tests was conducted on the samples with known optical absorbance. SMART^® Spectro 2 spectrophotometer made by Lamotte, Chestertown, MD was utilized for all the optical density measurements. Petroff Hausser Counting Chamber (ref: 3,900) made by Hausser Scientific, Horsham, PA with a cell depth of only 10 microns was used for all hemocytometry measurements. In this way, the spectrophotometer measurements were calibrated and used to estimate the bacterial population in similar samples that were tested simultaneously under impedance sensing. Hence, the samples that were selected for spectrophotometry were based on their potential to represent varying amounts of growth and bacterial populations. This could also be a suitable testing strategy for validating the repetitiveness of the technique.

In addition, replicate experiments were conducted to further verify the results obtained from the 90% dilution samples (also known as 10-fold dilution). In these tests, the saturated bacterial solution, that was prepared by overnight culturing of bacteria in LB broth was serially diluted by a 1:10 ratio, ranging from 10 times more dilute to 10⁷ more dilute bacterial samples. The samples were inoculated inside seven wells of the electrode plate, with the eighth channel intentionally left without a sample. This eighth channel served as a control and kept at a constant RC value to deal with external noise in the system. The test results shown in the Supplementary Material are effectively trials for duplicating the same experiment described above. Note that those results do not show any discrepancy with results or the conclusions arising from the main experiments described below.

The results of a test that was conducted on the six bacterial samples that were diluted serially are presented here in three different ways. First, the impedance results of different samples at a fixed frequency over time are compared. Secondly, the impedance results of different samples under the frequency sweep are explained. Lastly, the relative variations of impedance parameters will be interpreted as the biomass change to provide a clearer explanation of the capabilities of the proposed sensing system.

Measuring the impedance responses of bacterial samples demonstrated a sudden change in terms of real and imaginary impedances after a few hours of inoculation. The sudden changes occurred in all the samples one after another. The sample with the highest initial number of bacteria, approximately 2.444×10⁷ cells/mL, showed changes in impedance properties before every other sample. This sample was diluted 10-fold from the saturated batch and had an optical density absorbance value of 0.14 at the beginning of the experiment. Subsequently, other samples started to show impedance changes one after another in the sequence from the initial concentration that began the experiment. Therefore, the sample that started with the least number of bacteria (approximately 2.44×10² cells/mL) was the last one that showed any sudden changes in impedance as shown in Figure 3. This figure contains the changes in impedimetric parameters of samples over time. All the parameters are normalized over their initial values at time zero of the process of introducing bacterial cells to their growth medium. This eliminates the constant bias available in the measurement system.

As the impedance sensing was being conducted, both the measured resistance and reactance showed changes in their values during the logarithmic growth phase of bacterial samples, which is confirmed by simultaneous hemocytometry and optical density measurements. Changes in phase angle, capacitance and impedance magnitude are expected and thus, the overall impedance magnitude that encompasses both the resistance and capacitance changes may provide a more comprehensive understanding. These sudden changes were noticed at all frequencies, but the results are presented at a frequency of 1,000 Hz, that is low enough to reflect variations in impedances.

As bacteria start to proliferate, the impedance changes occur in a way that the resistance decreases slightly together with some irregularly trended variations, and the capacitance increases sharply at the same time as shown in Figures 3A,B. The overall impedance magnitude, that reflects and includes the changes in the magnitude of both real and imaginary impedance, also showed a sudden decrease in Figure 3D. As suggested by Wang et al. (2015), the decrease in resistance that occurred at the same time as the reproduction of bacteria is probably due to the formation of a bridge of bacterial clusters between the electrodes facilitating the electron transfer among them. Even though there exists a decrease in resistance during the growth phase, the existence of random spikes makes this parameter unreliable in representing and evaluating growth.

The measurements indicate that the normalized phase angle hovers in the range of 0.96–1 (Figure 3C), which also suggests the combinatory existence of both capacitive and resistive properties of the biological samples. Among all forms, the capacitance and impedance magnitude seem to provide the most definitive indicators of biomass change. To prove this theory, the variation from baseline was calculated for each parameter using Equation 2. Variations in impedimetric parameters for all samples before and after growth showed average values of 37.1%, 33.5%, 14.4%, and 1.6% for capacitance, impedance magnitude, resistance, and phase angle, respectively. This demonstrates that the capacitance is the most sensitive to the metabolic changes, even though impedance magnitude could provide a more inclusive value comprising of both resistance and capacitance. Capacitance, therefore, is considered the more potent parameter for monitoring of growth. In all cases, it can be observed that the impedimetric parameters for all samples start to plateau after the occurrence of changes in each sample, and no significant changes occur for any of the samples after that.

The results of the frequency sweeps from 20 Hz to 300 kHz for the sample that was diluted 1,000 times from the saturated batch are presented here. The results from the rest of the samples are added as error bars. The 1,000 times diluted sample was chosen because of its moderate representation of samples of lower and higher initial concentrations. The green, red, and the blue markers in Figure 4 a) to d) represent the values of impedimetric parameters at different times in the experiment normalized by their values at time zero. Therefore, green indicates when the proliferation has not started, red for when the proliferation has started, and blue indicates when the proliferation is finished. By comparing the results of frequency sweeps for a given sample, it is clear that the variations could be differentiated much more easily at lower frequencies than at higher frequencies. This is also in agreement with the results that were obtained by other researchers (Paredes et al., 2012; 2013; 2014a). Over time, the resistance of the sample decreases compared to when the exponential growth has not started, indicating that the growth of bacteria further facilitates the electron transport in the system. At the same time, however, the ability of the system to store the electrical charge applied by the excitation signal is increased. In Figure 4 a), it can be observed that the capacitance values over the progression of time and therefore bacterial growth, are much more distinguishable compared to other impedimetric parameters. In fact, for a given sample, capacitance is the only impedimetric property that shows distinction between the measurements at various states of time and across the whole frequency range as seen in Figure 4 a).

Observations obtained from this portion of the research show that the concentration factor (CF) has a linear relationship with optical density absorbance (OD ₆₀₀ ) as shown in Eq. 4: C F = M ∙ O D 600 (4) where M = 0.8702 calculated from the data in this study and the R2 for this model is 0.986. The linearity of the relationship between the dilution factor and optical density is because bacterial cells at different dilutions were not given the chance to grow in size. In essence, the turbidity induced by each cell is technically the same in all samples resulting in a linear relationship between the concentration factor and optical density. However, when bacterial cells are given the time to grow and proliferate, the relationship between the optical absorbance and cell population is not linear anymore. After thorough analysis and comparison of direct counting results, it was found that the bacterial population P) in cells/mL could be described by an exponential relationship with optical absorbance as shown in Equation 5: P = α ∙ e β ∙ O D 600 (5) where in these experiments, α = 9,202,824 and β = 5.6024 with an R ² value of 0.996. The relationships are shown in Figure 5.

The exponential increase in the number of viable cells growing over time rather than diluting is practically due to the smaller mass (volume)/cell ratio that occurs in the samples at higher optical densities. This behavior over the course of bacterial proliferation was also noticed by Sezonov et al. (2007) where they found that the mass per cell ratio declines at higher optical absorbances. Therefore, as bacterial cells start to reproduce and the number of cells increases, the mass/cell ratio decreases. Hence, the turbidity induced by a certain number of bacterial cells would be lower than expected. This further affirms why the proliferation of bacterial cells in the growth medium does not have a linear relationship with optical density, as opposed to when the samples are prepared by dilution.

Six models were evaluated to determine how well they fit the impedimetric experimental data. Python Zfit software was used to conduct data fitting of impedance measurements and to find the RC elements suggested by each model. The Nelder-Mead downhill simplex method was used to find the best fit by converging RC values to experimental data by keeping the squared-error minimized. Dellis and Carpentier (1993) also reported the high accuracy and capability of the Nelder Mead method in fitting their impedance spectroscopy data. The goodness of fit ξ) that was used to compare the models is the average percent difference of the impedance magnitude calculated by the suggested RC values from each model |Z _model | and from the experimental model |Z _exp | such that: ξ = Z exp − Z m o d e l Z exp ∙ 100 % (6)

The intention here is to evaluate which model could best describe the data obtained from the samples. A model suggested by Liu et al. (2018) suggests that the adherence of bacterial cells to the surface of the microelectrodes and their existence in the growth medium induces an RC circuit consisting of double-layer capacitances (C _dl ), solution resistance (R _s ), bacterial resistance (R _S ) and capacitance (C _b ). As proven by Kim et al. (2011), double-layer capacitance is a key existing element in explaining the impedance spectroscopy data of adhesion and maturation of bacterial biofilm. This theoretical model fits the data of the experiments conducted here with minimal error.

Theoretically, if we imagine a certain value for the double-layer capacitance at the beginning of the test and before the growth, the increase could be explained by a parallel capacitance model. In circuitry, the addition of a new capacitor to a circuit (in this case, capacitance of bacteria C _b ) would only cause an increase to the overall capacitance if it were added in parallel to the existing capacitor(s) (in this case the capacitance of the solution C _dl ). Other than the parallel arrangements of the bacteria and double-layer capacitors, the increase in capacitance could be justified by assuming the capacitance of the growth medium and capacitance of bacteria as a whole (C _T ), and that the bacterial growth enhances the total capacitance property of the sample. Table 1 contains a summary of equivalent circuit models and their potential for fitting the observations obtained in this work as well as the percent error obtained with Eq. 6.

As summarized in Table 1, there is more than one model that provides a reasonable fit to the experimental data that estimates the impedance magnitude with an error of 5% or less. One could however, argue that the presence of microbial biofilm, which has a convoluted structure, could be of such high complexity in terms of equivalent electrical circuits at the micro-level that it could not be explained with any 1D, 2D, or even 3D equivalent models. The microbial metabolism contains such high randomness that a realistic equivalent RC circuit could be impacted by each and every bacterial colony that on its own interacts with other colonies and electrode areas. Thus, finding an absolute value for the resistance and capacitance of bacteria that is defined in a segregated way from the resistance and capacitance of the growth media and the overall system, may not be ideal. That is why the authors suggest that in non-faradaic studies, exploring different equivalent RC circuits would be more realistic if the resistance and capacitance of bacteria and growth media, whether serial or in parallel, are looked at as a whole (C _T , R _T ), and the deviations are calculated accordingly. The impedance sensing data could not be fit to a parallel model, and therefore, a serried combination is presented.

In Table 2, the absolute values found by convergence of the Nelder Mead method on Model 1, are presented for all the samples. The resistance does not show a reliable variation. However, the capacitance of the system shows continuous sudden improvement as time progresses. Even though mathematically describing the growth of bacteria is valuable, what is considered more important in the context of this research is to be able to estimate the biomass in near real-time of the changes occurring with the capacitance magnitudes.

To explore the frequencies where the models deviate from the observed data, a Nyquist plot was produced using Model 1 for the 1,000 times diluted sample and shown in the Supplementary Figure S1. Given the results in Table 2, a resistance R _T of 98.3 Ω was selected and a C _T of 200 nF with Model 1. This model was used because it was one of the three models that generated some of the lowest errors (Models 1, 4 and 6, which provided average errors of 4.3%, 4.2% and 5.1%, respectively), and it was the simplest circuit of the three models shown in Table 1. The values of R _T and C _T were selected because for Model 1 and the 1,000 times diluted sample, these values of resistance and capacitance led to the largest error at 25 h. Supplementary Figure S1 shows that the deviations from model predictions and observations are greatest at the larger and smaller frequencies (right and left side of the curves). According to Mei, et al. (2018), the central portion of the curve is related to the electrode and bulk sample resistance, while the outer region on the right is related to the capacitance in the system. The figure indicates that greater deviation between model and observed data occurs at the larger and smaller sweeping frequencies as shown in Table 2. Furthermore, the authors only considered models with resistors and capacitors. Future work should consider double-layer capacitance models as studied in Mei, et al. (2018) as they may yield better results that are more easily interpreted and greater information on the possible range of the sensor.

The results above indicate that the sensor design could provide real-time growth monitoring. Logarithmic growth of bacteria occurred in all samples and the optical density measurements that were carried out simultaneously to the impedance tracking, facilitated discovery of the absorbance of every sample at a point in time when the impedance sensing device started to see a logarithmic spike in capacitance. By populating the data of all the samples, it was possible to find a relationship between the change in capacitance (C′) and population of bacteria (P′) for all the samples. A lower limit of detection exists due to the limitation of the optical density in finding an absorbance value for samples with lower than 9.2×10⁶ cells/mL (Equation 6). The population estimate was achieved by using the optical density measurements and the pre-derived exponential equation of population against optical density as well as the measured capacitance values at 1,000 Hz over time. Through curve fitting, the model that could provide the smallest standard deviation from the experimental data was obtained. This model is an exponential relationship as shown in Equation 7: P ′ = A ∙ e B ∙ C ′ (7)

The values of the fitting coefficients A and B, are summarized in Figure 6. Since the absolute capacitance values differ from channel to channel due for physical reasons, the change in capacitance C′ over the change in population of bacteria P′ was selected to find correlations between impedance measurements and bacterial concentrations, as shown in Figure 6. The change in capacitance and the change in population at any point in time, C _t and P _t , respectively, from their initial values C ₀ and P ₀ , respectively, were used in Eqs 8, 9 to remove the bias in capacitance measurements arising from the inherent capacitance magnitude in different channels. C ´ = C t − C 0 (8) P ´ = P t − P 0 (9)

By plotting C′ against P′ for all samples, exponential curves could be fit to the data to create population change models as a function of change in capacitance. Figure 6 shows the change in population over the change in capacitance for all the samples. The best fit exponential models are given in the plot along with the fitted coefficients (values A and B in Eq. 7), and their the resulting coefficients of determination.

In order to have a single relationship between the bacterial concentration and capacitance, the data from all samples were fit to an exponential model. This model is developed by calculating the mean of the population estimation curves of all samples. It is capable of estimating bacterial populations of up to 5×10⁸ cells/mL with an R ² value of 0.40. However, the estimation could be found with a better fit if lower concentrations of bacteria are of interest. This model is also governed by an exponential relationship between population change and capacity change, similar to Equation 7, and with A and B values of 10⁶ and 1.79×10⁸, respectively. This model, plotted in Figure 7A, is a depiction of the proposed sensor’s potential range. Figure 7B is developed to show that a pre-derived relationship of population against optical density sets a lower detection limit of 9.2×10⁶ cells/mL, and the stoppage of the capacitance change sets an upper limit of 5×10⁸ cells/mL. The logarithmic growth phase occurs at the same time as the capacitance increase occurs. Figure 7A is intended to show the range of the proposed design with Figure 7B showing a general picture of the proposed sensor’s sensitivity. The figure illustrates that if using capacitance to measure changes, the sensor is only sensitive in the log phase and that this design could be used to monitor the change between lag and stationary phases for a particular system. The values provided by the expression are not absolute and should only be used to describe relative changes in biomass.

It is concluded that the fact that bacterial growth observed via optical density measurements are simultaneous to the spikes in capacitance values allows one to develop an estimation curve between the change of capacitance from an initial value and the change of bacterial population from a starting amount. However, as schematically shown in Figure 7B, the spike in capacitance occurs sometime prior to the exponential increase in the optical density measurements. One may surmise that due to the long-term monitoring of bacterial impedance, some evaporation may occur in the wells that might affect the results. To minimize this effect, during the experiments, lids and caps were used for the samples both in the wells for impedance monitoring, and on the samples in the cuvettes for optical absorbance monitoring, respectively. That being said, further evaluation of how evaporation can affect the impedimetric changes could be conducted.