Electrical Modeling of the Growth and Differentiation of Skeletal Myoblasts Cell Cultures for Tissue Engineering

In tissue engineering, of utmost importance is the control of tissue formation, in order to form tissue constructs of clinical relevance. In this work, we present the use of an impedance spectroscopy technique for the real-time measurement of the dielectric properties of skeletal myoblast cell cultures. The processes involved in the growth and differentiation of these cell cultures in skeletal muscle are studied. A circuit based on the oscillation-based test technique was used, avoiding the use of high-performance circuitry or external input signals. The effect of electrical pulse stimulation applied to cell cultures was also studied. The technique proved useful for monitoring in real-time the processes of cell growth and estimating the fill factor of muscular stem cells. Impedance spectroscopy was also useful to study the real-time monitoring of cell differentiation, obtaining different oscillation amplitude levels for differentiated and undifferentiated cell cultures. Finally, an electrical model was implemented to better understand the physical properties of the cell culture and control the tissue formation process.


Introduction
In tissue engineering, the control of tissue formation is of the utmost importance in order to form tissue constructs of clinical relevance. One of the techniques that can be used for this purpose is impedance spectroscopy, which is nowadays used for real-time monitoring of different biological processes, such as cellular proliferation, cell toxicity, and cell invasion or inflammation [1][2][3]. Impedance spectroscopy has the advantage of being a non-invasive technique (current intensity can be kept at minimum levels) and a relatively inexpensive method (only one sample or Petri plate is required for a performance curve).

Oscillation-Based Circuit
The employed circuit was based on the technique of the oscillation-based test [18][19][20], incorporating the electrode-cell impedance value (Zcell-electrode) as part of a voltage oscillator. The oscillation parameters (frequency of the oscillation or amplitude of the oscillation) are dependent on different biological parameters of the cell culture, such as the fill-factor (percentage of area covered by cells) or the attachment of cells to the electrode surface. Figure 1 shows the schematics of the circuit used. Cell cultures were incorporated into the circuit analysis through the electrode-cell impedance value Zcell-electrode. This circuit works as a voltage oscillator, being characterized by its oscillation parameters-frequency of oscillation (fosc) and amplitude of oscillation (aosc) at the output voltage signal (Vout). The circuit avoids the use of very high-performance circuitry or equipment, as well as accurate current/voltage generators, instrumentation amplifiers (IA), and exact precise demodulation circuits. The circuit was composed of a bioimpedance block, a comparator, and a band-pass filter, as shown in Figure 1. The operation of the circuit prototype with other well-established cell lines is detailed in [18][19][20].
Sensors 2020, x, x FOR PEER REVIEW 3 of 12 The employed circuit was based on the technique of the oscillation-based test [18][19][20], incorporating the electrode-cell impedance value (Zcell-electrode) as part of a voltage oscillator. The oscillation parameters (frequency of the oscillation or amplitude of the oscillation) are dependent on different biological parameters of the cell culture, such as the fill-factor (percentage of area covered by cells) or the attachment of cells to the electrode surface. Figure 1 shows the schematics of the circuit used. Cell cultures were incorporated into the circuit analysis through the electrode-cell impedance value Zcell-electrode. This circuit works as a voltage oscillator, being characterized by its oscillation parameters-frequency of oscillation (fosc) and amplitude of oscillation (aosc) at the output voltage signal (Vout). The circuit avoids the use of very high-performance circuitry or equipment, as well as accurate current/voltage generators, instrumentation amplifiers (IA), and exact precise demodulation circuits. The circuit was composed of a bioimpedance block, a comparator, and a band-pass filter, as shown in Figure 1. The operation of the circuit prototype with other well-established cell lines is detailed in [18][19][20].
The aim of this application was to analyze whether the circuit can be useful to characterize skeletal myoblast cell cultures' growth and differentiation level through these parameters, with the use of an electrical model to correlate measurements and biological properties. For cell culture assays, commercial electrodes (8W10E PET) from Applied Biophysics (AB, New York, NY, USA) [21] were employed. The multi-well was composed of eight separate wells, each one containing ten circular biocompatible gold microelectrodes of 250 µm diameter in parallel and a surrounding reference electrode, which can be also seen in Figure 1. The intensity applied to the cell cultures was limited to 10 µA, although this could be changed by modifying the resistances in the bioimpedance block (shown in Figure 1).

Figure 1.
Oscillation-based circuit. (a) Block diagram of the circuit proposed, composed by the bioimpedance block (Hz(s)), comparator, and bandpass filter (HBP(s)). The complete circuit prototype is detailed in [18][19][20]. (b) Detail of one of the eight wells of the 8W10E PET cultureware from Applied Biophysics [21] that were used in the experiments, where e1 is one of the 10 circular gold electrodes (the sensing area is the sum of the 10 gold electrodes) and e2 is the reference or ground electrode. Each well has an area of 0.8 cm 2 . (c) General diagram for the implemented prototype system. Sensor devices are located on the cell culture reactor, gathering information from the cell culture assay. This Figure 1. Oscillation-based circuit. (a) Block diagram of the circuit proposed, composed by the bioimpedance block (H z (s)), comparator, and bandpass filter (H BP (s)). The complete circuit prototype is detailed in [18][19][20]. (b) Detail of one of the eight wells of the 8W10E PET cultureware from Applied Biophysics [21] that were used in the experiments, where e1 is one of the 10 circular gold electrodes (the sensing area is the sum of the 10 gold electrodes) and e2 is the reference or ground electrode. Each well has an area of 0.8 cm 2 . (c) General diagram for the implemented prototype system. Sensor devices are located on the cell culture reactor, gathering information from the cell culture assay. This is sent to the gateway device (Intel Edison), which manages and controls the measurement acquisition system. The aim of this application was to analyze whether the circuit can be useful to characterize skeletal myoblast cell cultures' growth and differentiation level through these parameters, with the use of an electrical model to correlate measurements and biological properties. For cell culture assays, commercial electrodes (8W10E PET) from Applied Biophysics (AB, New York, NY, USA) [21] were employed. The multi-well was composed of eight separate wells, each one containing ten circular biocompatible gold microelectrodes of 250 µm diameter in parallel and a surrounding reference electrode, which can be also seen in Figure 1. The intensity applied to the cell cultures was limited to 10 µA, although this could be changed by modifying the resistances in the bioimpedance block (shown in Figure 1).

Experimental Growth and Differentiation of Muscle Stem Cells in the 8W10E PET Cultureware
Three sets of experiments were performed, two of them with the 8W10E PET cultureware, following the distribution of Table 1, and another experiment using traditional Petri plates, with the objective to obtain the cell culture growth control curve. All the experiments were carried out with the same protocol explained in Section 2.2.
All the cell cultures in the 8W10E PET cultureware (wells 2, 3, 4, 6, 7) were held in growth medium for control the first days. The differentiation in myotubes (wells 6, 7) was initialized by treatment with differentiation medium when 70% confluence was reached, as explained in Section 2.2., whereas the rest (wells 2, 3, 4) were held in growth medium for control. For each of these two groups of cells (cells for differentiation and cells without differentiation), one well was left without measuring impedance (wells 4 and 7) as a control in order to detect any possible effect of current intensity on stem cells.
In wells where the impedance measurement was used (1, 2, 3, 5, 6), a limited maximum current intensity of 10 µA was applied to the cell cultures every 60 min (sample period). The cell culture growth medium and differentiation medium were also measured by the oscillating impedance system (wells 1, 5), in order to analyze any possible effect of the medium used. Table 1 summarizes the wells used in the 8W10E PET cultureware. microscope, and a visual inspection and estimation of the percentage of differentiated cells were carried out.
A western blot analysis was carried out at the end of the experiment to establish the level of expression of the anti-alpha smooth muscle actin antibody (ab5694) in the differentiated cell cultures in comparison with undifferentiated ones. Different muscle-specific proteins (Myogenin, Phos-Akt (Ser 473) and Akt) were measured in differentiated cells during different experimental days, to validate the differentiation achieved in a similar way as was carried out in [22].

Study of the Effect of Current on Cell Growth and Differentiation
No significant differences were observed at the levels of current used (maximum 10 µA, applied every 60 min) between the wells where electrical impedance was used to monitor cell cultures and those used as a control without using electrical impedance (W2, W3, in comparison with W4, and W6 compared to W7, as shown in Figure 2). Good cell adhesion to the microelectrodes and to the plastic substrate was confirmed by visual inspection, in all cases.
Sensors 2020, x, x FOR PEER REVIEW 5 of 12 (Ser 473) and Akt) were measured in differentiated cells during different experimental days, to validate the differentiation achieved in a similar way as was carried out in [22].

Study of the Effect of Current on Cell Growth and Differentiation
No significant differences were observed at the levels of current used (maximum 10 µA, applied every 60 min) between the wells where electrical impedance was used to monitor cell cultures and those used as a control without using electrical impedance (W2, W3, in comparison with W4, and W6 compared to W7, as shown in Figure 2). Good cell adhesion to the microelectrodes and to the plastic substrate was confirmed by visual inspection, in all cases. (stem cells without differentiation, using electrical impedance) and Well 4 (stem cells without differentiation, non-monitored), on day 8 of the experiment. No significant difference is observed between them. (b) Well 7 (stem cells for differentiation, without using electrical impedance), used as a control, on the eighth day after the start of the differentiation process and Well 6 (stem cells for differentiation, using electrical impedance) at the same time. No significant difference is observed between Well 6 and Well 7 at any moment of the differentiation process. This lack of difference between impedance-monitored and non-monitored cell cultures was also confirmed by comparison with the traditional cell growth cultures in traditional Petri plates using the protocol explained in Section 2.2. The number of cells, counted by visual inspection, and the cell culture behavior (see Figure 3) are similar to the cell cultures reported on the 8W10E PET cultureware (Figure 4), monitored with the oscillation-based circuit. This enables validation of the performance of cell adhesion to the presented sensing device, similar to traditional Petri plates. This validation, on the other hand, has also been well established in the different works referenced by Applied Biophysics [21] for other cell types. (b) Well 7 (stem cells for differentiation, without using electrical impedance), used as a control, on the eighth day after the start of the differentiation process and Well 6 (stem cells for differentiation, using electrical impedance) at the same time. No significant difference is observed between Well 6 and Well 7 at any moment of the differentiation process.
This lack of difference between impedance-monitored and non-monitored cell cultures was also confirmed by comparison with the traditional cell growth cultures in traditional Petri plates using the protocol explained in Section 2.2. The number of cells, counted by visual inspection, and the cell culture behavior (see Figure 3) are similar to the cell cultures reported on the 8W10E PET cultureware (Figure 4), monitored with the oscillation-based circuit. This enables validation of the performance of cell adhesion to the presented sensing device, similar to traditional Petri plates. This validation, on the Sensors 2020, 20, 3152 6 of 12 other hand, has also been well established in the different works referenced by Applied Biophysics [21] for other cell types.
Sensors 2020, x, x FOR PEER REVIEW 6 of 12

Monitoring of the Growth and Differentiation of Myoblasts in the 8W10E
PET Cultureware. Figure 4 shows the signal registered for the different cell cultures, corresponding to the amplitude of the oscillations of the circuit during the different days of the experiment. It can be seen that the behavior of muscle stem cells without differentiation (wells W2, W3) followed a similar behavior pattern to other cell cultures [5,6], compared with muscle stem cells that followed a differentiation process (W6).
The oscillation-based circuit detected initial cell growth in a similar way to other cell types [2,3]. The stem cells that did not follow a differentiation process (W2, W3) reached the confluent state in 4-5 days (as shown in Figure 4), with a good correlation between the registered amplitudes and the microscopy observations. The amplitude of the oscillations proved to be a useful parameter to determine the confluence level of the cell culture or fill factor (defined as the area occupied by cultured cells divided by the total culture area).
Stem cells cultures that changed to the differentiation medium show an initial decrease in cell proliferation after the change of medium to differentiation medium, as growth is then limited (the amplitude oscillation values stabilize for a mean of 0.8 days, between day 3 and 4, with a standard deviation of 0.1 days). However, afterward (days 4 to 7), Figure 4 shows a linear increase in the monitored amplitude for these cells corresponding to the differentiation process, which contrasts with the microscope images (where elongation and fusion among stem cells were observed), reaching a final amplitude level higher than cell cultures that did not differentiate. A more detailed analysis of the differences in the measured oscillation voltage registered is presented in Figure 5, where we show the measurement of differences of amplitude in voltage to observe the difference between differentiated and undifferentiated cultures. The microscope images can be seen in Figure 6.  Figure 4 shows the signal registered for the different cell cultures, corresponding to the amplitude of the oscillations of the circuit during the different days of the experiment. It can be seen that the behavior of muscle stem cells without differentiation (wells W2, W3) followed a similar behavior pattern to other cell cultures [5,6], compared with muscle stem cells that followed a differentiation process (W6).

Monitoring of the Growth and Differentiation of Myoblasts in the 8W10E PET Cultureware
The oscillation-based circuit detected initial cell growth in a similar way to other cell types [2,3]. The stem cells that did not follow a differentiation process (W2, W3) reached the confluent state in 4-5 days (as shown in Figure 4), with a good correlation between the registered amplitudes and the microscopy observations. The amplitude of the oscillations proved to be a useful parameter to determine the confluence level of the cell culture or fill factor (defined as the area occupied by cultured cells divided by the total culture area).
Stem cells cultures that changed to the differentiation medium show an initial decrease in cell proliferation after the change of medium to differentiation medium, as growth is then limited (the amplitude oscillation values stabilize for a mean of 0.8 days, between day 3 and 4, with a standard deviation of 0.1 days). However, afterward (days 4 to 7), Figure 4 shows a linear increase in the monitored amplitude for these cells corresponding to the differentiation process, which contrasts with the microscope images (where elongation and fusion among stem cells were observed), reaching a final amplitude level higher than cell cultures that did not differentiate. A more detailed analysis of the differences in the measured oscillation voltage registered is presented in Figure 5, where we show the measurement of differences of amplitude in voltage to observe the difference between differentiated and undifferentiated cultures. The microscope images can be seen in Figure 6.   Cellular growth and differentiation were observed with microscope images, as shown in Figure 6. In each medium change, cells were seen under the microscope, and photographs of all wells were taken, estimating the percentage of differentiated stem cells following traditional protocols. A good level of mV * Figure 4. Obtained amplitude signals. Amplitude signals monitored for stem cells without differentiation (W2, W3) and with differentiation (W6). The cell culture medium was also measured (W1). It can be observed that after an initial transient regime, all signals corresponding to cell cultures started to rise, corresponding to cellular growth. After the differentiation medium was used (day 2) and after a transitory stop in the measured amplitude corresponding to a decrease in cell proliferation (with a mean delay of 0.8 days; and standard deviation of 0.1 days), stem cells following the differentiation process (W6) showed a greater increase in the monitored amplitude in comparison with the undifferentiated cell cultures (W2, W3).   Cellular growth and differentiation were observed with microscope images, as shown in Figure 6. In each medium change, cells were seen under the microscope, and photographs of all wells were taken, estimating the percentage of differentiated stem cells following traditional protocols. A good level of differentiation was observed at the end of the process (tubular structures corresponding to Sensors 2020, 20, 3152 8 of 12 myotubes were observed at the end of the differentiation process; shown in Figure 6). A Western blot analysis was also carried out at the end of the experiment to establish the level of expression of the anti-alpha smooth muscle actin antibody in the differentiated cell cultures in comparison with undifferentiated ones. The results of this Western blot analysis are shown in Figure 6, demonstrating the difference between differentiated and undifferentiated cell cultures.
Sensors 2020, x, x FOR PEER REVIEW 8 of 12 differentiation was observed at the end of the process (tubular structures corresponding to myotubes were observed at the end of the differentiation process; shown in Figure 6). A Western blot analysis was also carried out at the end of the experiment to establish the level of expression of the anti-alpha smooth muscle actin antibody in the differentiated cell cultures in comparison with undifferentiated ones. The results of this Western blot analysis are shown in Figure 6, demonstrating the difference between differentiated and undifferentiated cell cultures. (d)

Monitoring of the Growth and Differentiation of Myoblasts
The impedance spectroscopy technique is presented here for the first time for non-invasive and real-time monitoring of the cellular growth and differentiation processes of skeletal muscle. The technique proved to be useful for monitoring the processes of cell growth and estimating the fill factor of muscle stem cells. The oscillation-based circuit proposed successfully detected cell growth. A useful threshold could be set at a fill factor of 70%, as cells should change to the differentiation medium at this moment. The obtained growth curves correlate well with the traditional curves measured by traditional methods, as shown in Figure 3.
Impedance spectroscopy was also useful for the real-time monitoring of cell differentiation. An initial decrease in cell proliferation was detected at the point of change of medium to differentiation medium. This decrease in cell proliferation is in accordance with other works [5]. After a few hours, a linear increase in the monitored amplitude was recorded, corresponding to the differentiation process, which contrasted with microscope images. Similar behavior is found in other works with stem cells [5][6][7]. A higher final amplitude level in differentiated cell cultures was detected. The technique could be useful for determining the degree of differentiation achieved, although more detailed tests would be needed to better characterize the differentiation process and establish the parameters of the electrical model. No significant differences were found between cell cultures where electrical impedance was used and the control. However, higher levels of intensity could be used, which can influence the process of cellular differentiation and facilitate the development of cells, even facilitating the contraction of muscular structures, which could be of importance in the design of new bioreactors for tissue engineering.
The oscillation-based test system proved to be successful in the real-time monitoring of growth and differentiation of muscle stem cells. Our system could be used to improve the system properties with other researched electrodes, such as the 2D ink-jet printed electronics with biocompatible substrates and conductive inks presented in [16]. Although initially implemented for 2D cell cultures, the system could be adapted to 3D scaffolds, as in other works [13].

Electrical Modeling of the Cellular Growth and Differentiation
An initial electrical model of the cell culture can be drafted based on some previous works [18,23] (see Figure 7a). R gap models the resistance between the cell layer and the electrodes; R s models the resistance between the cell layer and the reference electrode; R 1 and C 1 form the impedance of the area of the electrodes that are not covered by cells; and R 2 and C 2 model the impedance of the area of the electrodes that is covered by cells.
Equation (1) is reproduced following the equations of the oscillation-based test model described in [18,23]: For the initial and final experimental assessment of the myoblasts cell cultures, the fill factor can be defined as: where Acell is the average area of cells in each cell line, Ap is the well area and Ncell is the number of cells. The online estimation of the fill factor was obtained and is shown in Figure 7b. A good correlation was found between experimental measurements and the estimations of this model. Sensors 2020, x, x FOR PEER REVIEW 10 of 12 In cultures where differentiation takes place, a different model must be designed. When the differentiation process starts, cell growth is limited by the change of medium and all the parameters of the model remain fixed. Once the cells start to elongate and to fuse, the fill factor (percentage of electrodes covered by cells) increases, modifying some of these parameters-Rs, R1 and C2 increase, while C1 and R2 decrease. Once the tissue is differentiated, we can adopt a similar model as the one described in [24], depicted in Figure 8, where Rgap is substituted by two resistances in series, Rbulk, modeling the resistance between the microelectrode and the tissue, and Rtissue, modeling the resistance of the tissue. Rct and Cdl model the impedance of the area of the electrodes that are covered by the tissue [18]. If we consider Rbulk is equal to the mean Rgap of the cell-electrode model of the undifferentiated wells (theoretical value of Rbulk is near to 1k_ohm), we can obtain the value of Rtissue from the new model when ff 1. The values of Rgap (for non-differentiated wells), Rbulk, and Rtissue (for differentiated wells) obtained from the two experiments are shown in Table 2. Further experiments are needed to define with more precision the electrical model and make use of this model to predict the impedance changes in the cell culture and tissue.   In cultures where differentiation takes place, a different model must be designed. When the differentiation process starts, cell growth is limited by the change of medium and all the parameters of the model remain fixed. Once the cells start to elongate and to fuse, the fill factor (percentage of electrodes covered by cells) increases, modifying some of these parameters-R s , R 1 and C 2 increase, while C 1 and R 2 decrease. Once the tissue is differentiated, we can adopt a similar model as the one described in [24], depicted in Figure 8, where R gap is substituted by two resistances in series, R bulk , modeling the resistance between the microelectrode and the tissue, and R tissue , modeling the resistance of the tissue. R ct and C dl model the impedance of the area of the electrodes that are covered by the tissue [18]. If we consider R bulk is equal to the mean R gap of the cell-electrode model of the undifferentiated wells (theoretical value of R bulk is near to 1k_ohm), we can obtain the value of R tissue from the new model when ff →1. The values of R gap (for non-differentiated wells), R bulk, and R tissue (for differentiated wells) obtained from the two experiments are shown in Table 2. Further experiments are needed to define with more precision the electrical model and make use of this model to predict the impedance changes in the cell culture and tissue. In cultures where differentiation takes place, a different model must be designed. When the differentiation process starts, cell growth is limited by the change of medium and all the parameters of the model remain fixed. Once the cells start to elongate and to fuse, the fill factor (percentage of electrodes covered by cells) increases, modifying some of these parameters-Rs, R1 and C2 increase, while C1 and R2 decrease. Once the tissue is differentiated, we can adopt a similar model as the one described in [24], depicted in Figure 8, where Rgap is substituted by two resistances in series, Rbulk, modeling the resistance between the microelectrode and the tissue, and Rtissue, modeling the resistance of the tissue. Rct and Cdl model the impedance of the area of the electrodes that are covered by the tissue [18]. If we consider Rbulk is equal to the mean Rgap of the cell-electrode model of the undifferentiated wells (theoretical value of Rbulk is near to 1k_ohm), we can obtain the value of Rtissue from the new model when ff 1. The values of Rgap (for non-differentiated wells), Rbulk, and Rtissue (for differentiated wells) obtained from the two experiments are shown in Table 2. Further experiments are needed to define with more precision the electrical model and make use of this model to predict the impedance changes in the cell culture and tissue.

Conclusions
In this work, we explored the use of impedance spectroscopy for the study of the processes of growth and differentiation of skeletal myoblasts' cell cultures. A circuit based on the oscillation-based test technique was used, converting different biological parameters of the cell culture, such as the fill-factor (percentage of area covered by cells) or the attachment of cells to the electrode surface, into the electrical oscillation parameters (frequency of the oscillation or amplitude of the oscillation), avoiding the need of an external input signal. This is translated into low-cost equipment that can be integrated with other biomedical systems for real-time analysis.
The technique used proved to be useful for monitoring the processes of cell growth and estimating the fill factor of muscle stem cells in real-time. Furthermore, impedance spectroscopy was useful for real-time monitoring of cell differentiation, obtaining different oscillation amplitude levels for differentiated and undifferentiated cell cultures. No significant differences were found between cell cultures where electrical impedance was used and the controls, validating the obtained results.
The proposed system is compatible with other biocompatible and conductive substrates researched to implement electrodes and monitor cell and tissue evolution in 2D and 3D scaffolds for practical tissue engineering equipment. Further work on each particular cell type is necessary in order to elucidate the optimal system to be used in each tissue engineering application.

Patents
The work presented in this paper has been protected by a patent included on the invention registered as "Bioimpedance measurement system for wirelessly monitoring cell cultures in real-time, based on an oscillation test using integrated circuits"; register number WO2016020561A1.