Under an alternating electrical signal, biological tissues produce a complex electrical bioimpedance that is a function of tissue composition and applied signal frequencies. By studying the bioimpedance spectra of biological tissues over a wide range of frequencies, we can noninvasively probe the physiological properties of these tissues to detect possible pathological conditions. Electrical impedance spectroscopy (EIS) can provide the spectra that are needed to calculate impedance parameters within a wide range of frequencies. Before impedance parameters can be calculated and tissue information extracted, impedance spectra should be processed and analyzed by a dedicated software program. National Instruments (NI) Inc. offers LabVIEW, a fast, portable, robust, user-friendly platform for designing data-analyzing software. We developed a LabVIEW-based electrical bioimpedance spectroscopic data interpreter (LEBISDI) to analyze the electrical impedance spectra for tissue characterization in medical, biomedical and biological applications. Here, we test, calibrate and evaluate the performance of LEBISDI on the impedance data obtained from simulation studies as well as the practical EIS experimentations conducted on electronic circuit element combinations and the biological tissue samples. We analyze the Nyquist plots obtained from the EIS measurements and compare the equivalent circuit parameters calculated by LEBISDI with the corresponding original circuit parameters to assess the accuracy of the program developed. Calibration studies show that LEBISDI not only interpreted the simulated and circuit-element data accurately, but also successfully interpreted tissues impedance data and estimated the capacitive and resistive components produced by the compositions biological cells. Finally, LEBISDI efficiently calculated and analyzed variation in bioimpedance parameters of different tissue compositions, health and temperatures. LEBISDI can also be used for human tissue impedance analysis for electrical impedance-based tissue characterization, health analysis and disease diagnosis.

#### Keywords

- Electrical Bioimpedance
- Electrical Impedance Spectroscopy (EIS)
- LabVIEW-Based Electrical Bioimpedance Spectroscopic Data Interpreter (LEBISDI)
- Curve Fitting
- Nyquist Plots
- Equivalent Circuit Modelling

Biological tissues are made of complex three-dimensional arrangements of cells embedded in an extracellular matrix called extracellular fluid (ECF). Cells contain intracellular fluid (ICF), called protoplasm, which in an animal cell is enclosed by the cell membrane (CM) and in a plant cell is surrounded by both a CM and a cell wall (CW). When subjected to an alternating current signal, animal and plant cells differ in their electrical responses, indicating that both tissue composition and the frequency of an applied AC signal affect their electrical responses [1, 2, 3, 4]. The electrical behavior of the tissues is usually quantified by its complex bioelectrical impedance [1, 2, 3, 4], which is the physical quantity that we reconstruct from the experimental measurements. Because bioelectrical impedance depends on the physiological and physiochemical status of the probed tissue and because it also varies from subject to subject and with changes in the health status of the tissue [5, 6], such as inflammation, infection and disease, studying how a tissue responds to frequency can provide valuable information about its anatomy and physiology. Many researchers [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23] have investigated electrical bioimpe-dance as an effective, noninvasive method to probe the pathological status of biological tissues.

For example, bioelectrical impedance analysis (BIA) [7, 8, 9, 10], electrical impedance spectroscopy (EIS) [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], impedance plethysmography (IPG) [22, 23] and impedance cardiography (ICG) [24, 25, 26] reveal the impedance response of biological tissues at one, two or more specified frequencies (f). EIS has been proven as an effective technique for noninvasive tissue characterization in medical, biomedical and biological applications [27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. Because EIS is a more generalized method that provides impedance variations over a wide range of frequencies, it can be used on its own to provide information that explains other bioelectrical phenomena like dielectric polarization [37, 38, 39, 40, 41], dielectric relaxation [37, 38, 39, 40, 41] and dielectric dispersion [37, 38, 39, 40, 41].

Impedance spectra obtained from EIS can be used to study the overall anatomy and physiology of organic tissues. Impedance parameter plots, such as Nyquist plots (Imaginary part of Z versus Real part of Z), impedance (Z) versus frequency (f) plots (Bode plots), conductivity (σ) versus frequency (f) plots and permittivity (ε) versus frequency (f) plots, are popular tools for visualizing different aspects of bioelectrical impedance. In particular, Nyquist plots distinguish real from imaginary parts of bioimpedance and serve as a guide to define equivalent electrical circuit parameters. Because equivalent electrical circuit models or equivalent circuit models (ECM) [6, 13] are very useful for understanding the anatomical, physiological and compositional aspects of biological tissues, an accurate analysis of data plots is required for effective assessment of a tissue’s properties.

Impedance analyzers are used either to measure the electrical impedance of materials at a single frequency or to study impedance variation over a wide range of frequencies. Impedance analyzers are typically developed with selected current frequency limits and other fixed specifications. Occasionally, changes to measurement parameters are required for a specific application, making the individual development of impedance measurement systems [42, 43, 44, 45, 46, 47, 48, 49, 50] advantageous and essential. Impedance analyzers or the impedance measurement hardware developed as low-cost [42, 46] and application-specific instrumentation measure the impedance data, but it requires some complementary dedicated software to process and analyze the impedance response of materials. More specifically, this software is required to calculate impedance parameters and extract tissue information by identifying the equivalent electrical circuit of the material being tested. Modern electronics technology offers a number of fast, portable, robust, user-friendly platforms for analog or digital data acquisition and signal processing that can be suitably utilized for developing a standalone impedance measurement workbench. When a standalone impedance measurement workbench is developed to collect the impedance data, it is found essentially required to be complemented by any software program or virtual instrumentation such as LabVIEW (Laboratory Virtual Instrument Engineering Workbench) [51] for impedance data analyzing.

Here, we developed a LabVIEW-based electrical bioimpedance spectroscopic data interpreter (LEBISDI) for tissue impedance analysis in medical, biomedical and biological applications by extracting the equivalent circuit parameters of biological tissues using their Nyquist plots. We tested and calibrated the LEBISDI software with both the computer-simulated impedance data and experimental impedance data collected from a number of electronic circuit combinations developed by high-precision resistors, capacitors and inductors using a standard impedance analyzer using low amplitude, sinusoidal current signal. We then used LEBISDI to interpret impedance data collected from fruits and vegetables under different physiological conditions. We conducted EIS studies on these tissues using a standard impedance analyzer. We used LEBISDI to analyze their Nyquist plots to calculate and correlate the electrical impedance parameters of the compositions, structures and conditions of the tissues.

Biological tissues comprise cells and an extracellular matrix. Both have their own electrical behavior and collectively produce a complex, frequency-dependent bioelectrical impedance, Z_{b}(f) [39]. The impedance Z_{b}(f) and its frequency-dependent phase angle, θ_{b}(f) are given by:

where R_{b}(f) and X_{b}(f) are the real and imaginary parts of Z_{b} respectively and j is the complex number √(-1). Both R_{b}(f) and X_{b}(f) depend on the signal frequency and tissue composition such that

EIS measures Z_{b} and its phase angle (θ_{b}) of a test subject by injecting a constant amplitude, alternating current (AC) signal (I(f)) at different frequency points, f_{i} (f_{i}: f_{1}, f_{2}, f_{3}, … f_{n}), and by measuring the boundary potentials (V(f_{i})) through using a linear array of the surface electrodes attached to the subject (Figure 1) though other configurations could also be used such as placing the electrodes like the corners of a rectangle [52].

The impedance of a material is generally measured either by the two-electrode method [8, 20] or four-electrode method [8, 20, 50]. In the two-electrode method, as the name indicates, two surface electrodes are used for current injection and voltage measurement. As shown in Figure 1a, in the two-electrode method the current injection and voltage measurement are conducted through the same electrode pair [8, 20]. Thus, the measurement data contains the effect of contact impedance (Zc). To avoid the contact impedance problem, the impedance measurement is conducted with the four-electrode method as shown in Figure 1b and Figure 1c. Thus, the four-probe method (Figure 1b) of the impedance measurement process is usually preferred to make the measurement insensitive to the impedance of the electrodes and wiring systems. In the four-probe method, a frequency-dependent constant amplitude sinusoidal current (I(f)) is injected through the outermost two electrodes, called the current or driving electrodes (red electrodes in Figure 1b and 1c), and the frequency-dependent AC voltage (V(f)) is measured [13] across the two inner electrodes, called the voltage or sensing electrodes (blue electrodes in Figure 1b and 1c). From Ohm’s law of AC theory, Z_{b}(f) is the transfer function of the test subject, which is calculated from the voltage-current data by dividing V(f) by I(f):

In bioimpedance spectroscopy, variations in bioelectrical impedance over frequencies are represented as impedance curves and are analyzed to characterize the tissue. As an example, the real part (R_{b}) and imaginary part (X_{b}) of Z_{b} at each frequency point (f_{i}: i = 1, 2, 3, …, n) are calculated and plotted (along the x-axis and y-axis, respectively) to obtain the Nyquist Plot [6, 13] or the R_{b}-X_{b} spectrum.

The lumped electrical impedance value of any material (non-biological and biological) measured at a particular frequency can be represented by the impedance obtained from its equivalent electrical circuit model, which can be a combination of circuit elements such as resistance (R), capacitance (C) and inductance (L). If we define the complex electrical impedance (Z) for any particular material (either non-biological or biological), then

where Re(Z(f)) = R_{z}(f) represents the magnitude of the real part of complex Z and Im(Z(f)) = X_{z}(f) represents the magnitude of the imaginary part of the Z(f).

If the material contains both capacitive and inductive elements, then the reactive component (X_{z}) will have two components called the frequency-dependent inductive reactance component, X_{L}(f), and the frequency-dependent capacitive reactance component, X_{C}(f). Thus, we have:

Similarly, in EIS studies on biological material, the measured Z_{b} of the test subject can also be represented by an equivalent impedance (Z_{eq}). This Z_{eq} can be obtained from a combination of some electrical circuit elements (e.g., R and/or C) because the magnetic effect of the biological tissues at low frequency is negligible [53]. Moreover, the equivalent circuit model of biological tissues may also contain some special circuit elements, such as a constant phase element (CPE) [13] or Warburg impedance (W) [13] and/or some complex bioelectrical phenomena occurring inside the biological tissues due to the physiological changes that take place when they are subjected to AC excitation. Warburg impedance represents the electrode’s interfaces and the CPE is often interpreted as a parameter describing the distribution of relaxation times [54] in the system, e.g. due to a distribution of cell sizes.

The Nyquist plot is the plot of imaginary part of impedance (X_{z}) versus the real part of impedance (R_{z}). The approximate equivalent circuit model of the material can be found from the X_{z}-R_{z} curve (Nyquist plots) which is generally obtained from the EIS data. Electrical impedance spectroscopic analysis followed by the equivalent circuit modeling establishes the relationship between the tissue property and its impedance response. As for example, the Nyquist plots of some basic circuit models have been discussed in the Figure 2.

Figure 2a shows a r-C series circuit and its impedance spectra (Nyquist plot). Figure 2b shows an electrical circuit model containing R_{p} and C_{p} connected in parallel and its Nyquist plot. As shown in Figure 2b, the Nyquist plot contains a semi-circular arc that represent the two parallel circuit blocks, (R_{p}||C_{p}).

If a model contains a series resistance (r) along with the parallel branch (R_{p}||C_{p}) as shown in Figure 2c, the impedance spectra will be shifted toward positive real axis and the amount of the shift will indicate the magnitude of the resistance r. Figure 2d shows an equivalent electrical circuit model of an object containing several R and C components and its impedance spectra. This model contains three sub-circuit blocks or sub-circuit parts connected in series: R_{s}, (R_{p}1||C_{p}1) and (R_{p}2||C_{p}2). As shown in Figure 2d, the Nyquist plot contains two semi-circular arcs that represent the two parallel circuit blocks, (R_{p}1||C_{p}1) and (R_{p}2||C_{p}2). The high-frequency part of the spectra (left side of the graph) cuts the x-axis at a particular distance away from the y-axis, and this distance represents the series resistance (R_{s}). Similarly, Figure 2e shows the Nyquist plot of a different electrical circuit model, which contains two parts connected in series, (R_{p}1||C_{p}1) and ((R_{p}2+W)||C_{p}2). Its impedance spectra contain two semi-circular arcs for two parallel circuit blocks, (R_{p}1||C_{p}1) and ((R_{p}2+W)||C_{p}2). The linear part of the spectra on the low-frequency side (right side of the graph) indicates Warburg impedance (W) [55, 56, 57, 58, 59], resulting from the diffusion effect [58, 59, 60, 61] on electrodes at low frequencies.

In some cases, the Nyquist plots are semi-circular arcs with their centers some distance below the x-axis. These depressed semi-circular Nyquist plots are complex to analyze because of the involvement of the CPE circuit. Figure 3 presents a depressed semi-circular Nyquist plot, where the equivalent circuit contains the CPE in parallel with R. The high-frequency side of the semi-circular arc cuts the x-axis at a particular distance away from the y-axis and the distance represents R_{s}.

By definition, the impedance of the CPE (Z_{CPE}) shown in Figure 3 is represented as:

where Q is the magnitude of Z_{CPE} and Y_{0}=1/Q, j=√−1 and 0<n<1.

Note that the phase angle (ϕ) of Z_{CPE} is frequency independent. It thus remains constant throughout the frequency range of EIS. The ϕ of Z_{CPE} is given by:

For an object with CPE, when n is less than 1, the CPE resembles a capacitor, but not a pure capacitor because ϕ is less than 90°. As the value of n increases, CPE gradually becomes more capacitive. At n = 1, Y_{0} becomes a pure capacitor (CCPE) for which

Nyquist plots of the circuits with a CPE are strongly influenced by circuit element combinations. When a material contains CPE and a resistive element, R_{p}, parallel to each other, the Nyquist plot (R-X plot) of the material will be a semi-circular path depressed by an angle of (1-n)*90°, as shown in Figure 3. But the R-X spectrum of a CPE alone is a straight line, generating an angle of (n*90°) with a positive x-axis (green dotted line in Figure 3).

Biological cells and tissues can be modeled by analysis of their impedance responses obtained from EIS studies conducted within a suitable frequency range. The impedance response of a biological cell is strongly influenced by cell composition [62, 63]. The individual electrical properties of each cell’s composition are thus represented by their equivalent electric circuit elements, which can be used to develop an equivalent circuit model of a single cell [6, 13, 64, 65, 66, 67, 68, 69, 70,], as described in the following sections.

Animal cells can be modeled with an equivalent circuit concept as shown in Figure 4. The resistive path created by the ICF in biological cells to an electric signal (Figure 4a) is represented as a resistive element called ICF resistance (R_{ICF}). Alternatively, the capacitance [74] offered by the protein-lipid-protein structure [62, 63] of the cell membrane is modeled as cell membrane capacitance (C_{CM}) [5, 6] (Figure 4a).

The equivalent impedance of the cell membrane and the protoplasm (which comprises cytoplasm and cell organelles) [71, 72] is called Z_{PPCM} (Figure 4b). Because the ECF is made up of conducting solution, it also creates a resistive path [6, 13, 65] (Figure 4a) that exerts an electrical resistance called ECF resistance (R_{ECF}). When cells are suspended in or by ECF, R_{ECF} becomes a resistive element connected as a parallel branch to the Z_{PPCM}. Therefore, an animal cell suspended in ECFs can be modeled as an equivalent electrical circuit [66, 67, 68, 69, 70] called the equivalent electrical impedance of an animal cell (Z_{AC}), as shown in Figure 4b.

Plant cells (Figure 5a) have cell walls made up of low-conducting materials, thus creating an additional resistive path that produces an electrical resistance called cell wall resistance (R_{CW}). Thus, as the envelope surrounding the cell membrane, R_{CW} is modeled as a resistance connected in parallel with Z_{PPCM} (Figure 5b) of the plant cell. Moreover, similar to the animal cell, ECFs in plant cells also produce resistive paths (Figure 5b). They are thus represented as R_{ECF} connected in parallel to the Z_{PPCMCW}, which is the parallel combination of Z_{PPCM} and R_{CW} (i.e., Z_{PPCM} || R_{CW}). Thus, as plant cells contain ECFs, a cell wall, a cell membrane and ICFs, they can be modeled as an equivalent electrical circuit called the equivalent electrical impedance of a plant cell (Z_{PC}), as shown in Figure 5b.

If the plant cell contains a large vacuole, the model can be modified by incorporating the impedance properties exerted by the composition of the vacuole. The vacuole of a plant cell is a cell-like structure made up of vacuole sap surrounded by a vacuole membrane, which is called a tonoplast [73, 74]. Thus, vacuole impedance can be modeled as a separate cell-like structure or a subcell inside the plant cell. The vacuole sap can be considered as the ICF of the vacuole, while the tonoplast can be considered as a membrane. Therefore, the R_{ICF} in the equivalent circuit model of a plant cell with vacuoles will be replaced by another subcellular impedance block [73, 74] in which the R_{ECF} will be the R_{ICF} because the cytoplasm could be considered the extracellular fluid of the vacuole. The equivalent circuit of biological cells can also be modeled with a number of other approaches [1, 75, 76]. The Nyquist plot, Cole-Cole plot [77, 78, 79, 80], impedance equivalent circuit [81, 82], Cole parameter estimation [75, 83, 84] of electrical bioimpedance can be suitably utilized for tissue characterization [34, 85, 86], body composition estimation [84] and disease detection [87]. It is worthwhile to note that the Cole-Cole plot is the Nyquist plot of complex permittivity [77, 78, 79, 80] whereas the Cole plot is for complex impedance or admittance.

A number of impedance data sets were generated and collected to evaluate the performance of LEBISDI. They are described in Section 2.5. Artificial impedance data were simulated and experimental impedance data were collected from various combinations of high-precision resistors and capacitors. Finally, after evaluating and calibrating LEBISDI, we collected impedance data from fruit and vegetable tissues using an impedance analyzer.

The evaluation of the performance of LEBISDI therefore included three types of impedance data: (i) computer-simulated impedance data, (ii) data generated by EIS studies conducted on real electronic circuit components with an impedance analyzer and (iii) the data collected by EIS studies conducted on fruits and vegetables with an impedance analyzer. Data sets (i) and (ii) were used to evaluate LEBISDI, whereas data set (iii) was used to calculate the equivalent circuit parameter for studying the variation in bioimpedance parameters of different tissue compositions.

Different electronic circuit combinations were simulated (Fig. 6) and a number of impedance data sets were generated using a specially developed MATLAB-based electrical impedance data-generating program. The PC-based impedance data generator mathematically calculates complex impedance and its phase angles at a number of frequency points within a particular frequency band (10 Hz to 2 MHz) for a number of circuit combinations called the simulated circuit model (SCM). Using the combinations of different circuit elements such as resistance (R), capacitance (C) and inductance (L), we could develop a capacitive circuit model (CCM) and an inductive circuit model (ICM). Figure 6 shows a few examples of the electronic circuit combinations studied; each has different values of resistance and capacitance connected in parallel and is tested to calculate the simulated impedance (Z_{S}) within a specific frequency range.

Real and imaginary parts of the simulated complex impedance obtained from all SCMs were calculated in the impedance data generator and stored in a .txt file in a desktop computer.

For a C CM made of a resistor and a capacitor connected in parallel, the real part of the impedance (R_{z}) and the imaginary part of the impedance (X_{z}) are respectively calculated as

and

The modulus of the impedance and the phase angle (θ) are respectively calculated as

and

For the ICM of a resistor and inductor connected in parallel, the real part of the impedance (R_{z}) and the imaginary part of the impedance (X_{z}) are respectively calculated as

and

The modulus of the impedance and the phase angle (θ) are calculated using the formula as shown in the equations (13) and (14).

Impedance data were also generated by conducting EIS studies on a real circuit model (RCM) developed with different circuit combinations of real electronic circuit components. A number of RCMs were developed with parallel and series-parallel combinations by high-precision resistors (1% tolerance) and capacitors (1% tolerance). EIS studies were conducted with a QuadTech7600 (QuadTech Inc., USA) impedance analyzer [88] using the four-probe technique [89, 90, 91, 92, 93, 94]. The EIS study was conducted with circuit combinations by injecting a 1 mA constant sinusoidal current at different frequencies and the impedances and phase angles were measured at 100 discrete frequency points within a frequency band of 10 Hz to 2 MHz.

The impedance responses of fruits and vegetables were studied by a four-electrode-method-based EIS using a QuadTech7600 impedance analyzer with a 1 mA constant sinusoidal applied current. The impedance variations in cucumber (_{b} and θ_{b} at 100 discrete frequency points within a frequency band of 10 Hz to 2 MHz.

Nyquist plots were obtained from R_{z} and X_{z} which were calculated from Z and θ. QuadTech 7000-04 alligator clip leads (QuadTech Inc., USA), which are generally used to connect to large multiterminal devices, were used [88] as an interface between the surface electrodes and the impedance analyzer. The QuadTech 7000-04 comprises a BNC-to-BNC cable, four banana plug adapters and four alligator clips, which easily connect to metal conductors and electrodes. Figure 7a presents a schematic of the four-probe-method-based impedance data collection, which shows the arrangement of the current and voltage electrodes used for the EIS studies we conducted on circuit combinations. Figure 7b presents an EIS data collection schematic of the four-electrode-method-based EIS studies conducted on fruit and vegetable samples with separate current and voltage electrodes. As shown in the Figure 7b, the current signal is injected through the outer driving electrodes (red rectangles) and the voltage data are measured across the inner sensing electrodes (blue rectangles).

Circuit element studies were performed by directly connecting 7000-04 alligator clips with the circuit leads. EIS for fruit and vegetable samples required that the lead set was used with an ECG electrode-based four-electrode array (EE-FEA). Four QuadTech solid gel Ag/AgCl ECG electrodes were fixed on sticky insulating tape and the EE-FEA was developed (Figure 8a). The voltage electrodes were placed between current electrodes, with a distance of 50 mm between voltage electrodes (Figure 8a). In addition, the distance between the current-electrode and the voltage-electrode was maintained by separating the voltage electrodes from the current electrodes by 25 mm (Figure 8a). Fruit and vegetable tissue health and temperature were varied in different EIS studies, whereas the amplitude (1mA r.m.s.) remained constant and the sinusoidal current varied from 10 Hz to 2 MHz (Figure 8b).

Prior to EIS studies, all fruits and vegetables were properly cleaned and marked for electrode placement using a measuring tape, and the electrode array was pasted on the skin of the cleaned samples. The QuadTech7000-04 alligator connectors of the impedance analyzer probe were connected to the electrodes by EE-FEA. During EIS studies, Z and θ were set as the primary and secondary parameters, respectively, in the impedance analyzer, and measured at 100 frequency points within 10 Hz to 2 MHz. To study the effect of storage time on vegetable bioimpedance, we conducted EIS studies every 3 days for 22 days on the same samples with the same instrumental setup. To study variation in biological tissue impedance profiles due to boiling, we conducted EIS studies on fruits and vegetables before and after boiling.

The LabVIEW-based electrical bioimpedance spectroscopic data interpreter (LEBISDI) has been developed to study the equivalent circuit parameters of biological tissues using the LabVIEW 2014 software. The NI LabVIEW is a highly productive software development environment that enables the user to obtain a graphical programing and unprecedented hardware integration facility. LabVIEW provides a rapid virtual instrumentation design facility required for the high-speed and highly sophisticated measurement and control system applications. The proposed LEBISDI has been developed with a circle-fitting algorithm and the R-X data are fit to a circular arc from which the center and radius of the circle are calculated. Using the coordinates of the circle’s center, the radius and the other impedance parameters (Z_{b}, θ_{b}, R_{z} and X_{z}) are calculated. Figures 9a and b show LabVIEW-based graphical user interface (GUI) of the LEBISDI and the Nyquist plot loaded into the LEBISDI respectively^{.}

The impedance data is fed to the LEBISDI as a matrix [M_{z}]_{100×3} having three columns: f, R_{z} and X_{z} respectively. The impedance data matrix [M_{z}] is saved in a .txt file though the program and can be easily modified to work with .xls file also. All the 100 rows are the f, R_{z} and X_{z} data obtained for a particular frequency point f_{n}. For each frequency data points (f_{n}), the real (R_{z}(f_{n})) and imaginary (X_{z}(f_{n})) parts of the impedance data are calculated from Z_{n} and θ_{n} obtained from the EIS and then are loaded through the GUI of the LEBISDI (Figure 9b) by pressing the “LOAD FILE” button. After that, the “FIT A CIRCLE” button of the LEBISDI GUI is pressed to fit the data along a circular path and the series resistance, parallel resistance, constant phase elements, X_{Max} (the maximum value of X_{z}) and X_{Max} frequency (i.e., the characteristic frequency (f_{c})) are calculated.

The real and imaginary parts of the simulated impedance data sets were calculated and Nyquist plots were drawn (Figure 10) in the Matlab-based impedance data generator. The real and imaginary parts of impedance were also stored in a .txt file for use with the LEBISDI assessment. The R-X data corresponding to each frequency point were loaded in LEBISDI (Figure 11) from the .txt file and the Nyquist plots are obtained in the GUI.

The Nyquist plots drawn from the real and imaginary parts of the simulated impedance were fitted in LEBISDI to calculate the values of the elements in the circuit combination used in the computer simulation. Impedance parameters calculated by LEBISDI were compared with the actual values of the circuit components used for impedance data simulation to assess the performance of LEBISDI.

Figure 12 shows that the LEBISDI successfully fit the Nyquist plots obtained for all four of the simulated circuit models shown in Figure 6 and accurately calculated the electronic circuit parameters (Table 1). Results from LEBISDI show that the errors found in R_{p} identification forsimulated circuit models 1, 2, 3 and 4 were 0.0027 %, 0.0187 %, 0.0188 % and 0.0030 %, respectively, and 0.937 %, 0.068 %, 0.068 % and 0.569 %, respectively, for C_{p} calculations (Table 1). Results also demonstrate that n (power in the CPE model) was equal to 1, indicating that there was no CPE in the designed models, which agrees with results for the simulated models.

Impedance parameters and errors calculated by LEBISDI for the capacitive circuit models (CCM) studied.

SCM | Frequency (f) | R_{p}(Ω) | C_{p}(F) | Error R_{p} | Error C_{p} |
---|---|---|---|---|---|

SCM 1 | 10-1kHz | 0999.97 | 1.01E-06 | 0.0027 % | 0.937 % |

SCM 2 | 10-2MHz | 0999.81 | 9.99E-10 | 0.0187 % | 0.068 % |

SCM 3 | 10-2MHz | 9998.12 | 9.99E-08 | 0.0188 % | 0.068 % |

SCM 4 | 10-10kHz | 1000.03 | 9.94E-08 | 0.0030 % | 0.569 % |

The impedance data obtained from the inductive circuit models are also analyzed with LEBISDI. The Nyquist plots obtained from the data simulator were loaded and fitted in LEBISDI and the impedance parameters used in the computer simulation, such as parallel resistance (R_{p}) and parallel inductance (L_{p}), were calculated. The results obtained from the simulated data analysis of the inductive circuit are presented in Figure 13 and Table 2.

Impedance parameters and errors calculated by LEBISDI for the inductive circuit models (ICM) studied.

SCM | Frequency (f) | R_{p}(Ω) | L_{p}(H) | Error R_{p} | Error L_{p} |
---|---|---|---|---|---|

SCM 5 | 10-2MHz | 499.98 | 09.85E-4 | 0.0032 % | 1.496 % |

SCM 6 | 10-2MHz | 999.97 | 19.70E-4 | 0.0031 % | 1.497 % |

Next, we investigated the performance of LEBISDI with the impedance data generated by the RCM developed with different circuit combinations of real electronic circuit components. Nyquist plots obtained from the real circuit data collected by an impedance analyzer were fitted by LEBISDI (Figure 14) and the impedance parameters were calculated. Figure 14a shows the impedance plots of RCM 1, which is a parallel combination of a 1 kΩ resistor and a 0.1 μF capacitor. Table 3 shows the impedance parameters calculated by LEBISDI for RCM 1 and the error obtained in the fitting. The errors were 0.348 % and 0.01% for resistance and capacitance calculations, respectively (Table 3).

Comparison of actual impedance data and the data obtained from LEBISDI for RCM 1 containing a 1 kΩ resistor and a 0.1 μF capacitor in parallel.

Values | Resistor (Ω) | Capacitor (μF) |
---|---|---|

Original | 1000.00 | 0.10 |

Calculated | 0996.52 | 0.10 |

Error | 0.348 % | 0.0885% |

Impedance data were also collected from a parallel combination of a 2 kΩ resistor and a 0.1 μF capacitor called RCM 2. Figure 14b shows the impedance plots for RCM 2 and Table 4 presents the impedance parameters calculated by LEBISDI for this circuit. The errors in the fitting process in LEBISDI were 0.335 % and 5.0 % for resistance and capacitance calculations, respectively (Table 4).

Comparison of actual impedance data and the data obtained from LEBISDI for RCM 2 containing a 2 kΩ resistor and a 0.1 μF capacitor in parallel.

Values | Resistor | Capacitor |
---|---|---|

Original | 2000.00 Ω | 0.10 μF |

Calculated | 1993.27 Ω | 0.10 μF |

Error | 0.335 % | 4.993% |

Impedance data were also collected from fruits and vegetables. Figure 15 – 17 show the impedance plots of a cucumber, a carrot and a bottle gourd, respectively. Numerical results for these configurations are reported in Table 5. To investigate the effect of boiling on impedance, data were also collected from the fruits and vegetables before and after boiling. Figures 18a and b show the impedance plots of a green banana before and after boiling, respectively. Numerical results for these configurations are reported in Table 6. After boiling, impedance parameters were lower for both series and parallel resistance, likely because boiling destroyed the structure of the cells; the CPE angle was also reduced. We investigated the role of freshness on impedance variation by collecting data from naturally stored vegetables. Impedance was measured daily and the variation over time was analyzed by LEBISDI. Figure 19 shows the impedance plots of a cucumber collected every 3 days for 22 days, and Table 7 shows the impedance parameters calculated by LEBISDI of impedance in a cucumber throughout the 22-day storage period. Over time, the impedance parameters for parallel resistance gradually increased while the impedance parameters for series resistance and parallel capacitance gradually decreased, likely due to dehydration with storage time; the CPE angle also increased slightly with time.

Impedance data obtained from LEBISDI for a cucumber, a carrot and a bottle gourd.

Parameters | Cucumber | Carrot | Bottle Gourd |
---|---|---|---|

r | 19.17 Ω | -11.68 Ω | 57.38 Ω |

R | 1437.05 Ω | 1838.85 Ω | 2115.34 Ω |

C | 0.34 μF | 0.08 μF | 0.17 μF |

X_{Max} | -463.13 Ω | -583.07 Ω | -636.83 Ω |

f_{c} | 4204.70 Hz | 14427 Hz | 6086.60 Hz |

θ_{CPE} | 19.26° | 20.16° | 20.93° |

n | 0.79 | 0.78 | 0.77 |

Comparison of the impedance parameters obtained from the impedance data estimation in LEBISDI for a green banana before and after boiling.

Parameters | Unboiled | Boiled |
---|---|---|

r | -354.08 Ω | 309.04 Ω |

R | 9382.64 Ω | 150.66 Ω |

C | 0.048 μF | 0.05 μF |

X_{Max} | -2412.03 Ω | -46.00 Ω |

f_{c} | 6896.98 Hz | 286206 Hz |

θ_{CPE} | 28.26° | 4.379° |

n | 0.69 | 0.959 |

Comparison of impedance parameters calculated from the impedance data estimation in LEBISDI for cucumber sample studied over a 22-day period.

Day | r (Ω) | R(Ω) | C (μF) | X_{Max} (Ω) | Fc (Hz) | θ_{CPE} | n |
---|---|---|---|---|---|---|---|

1 | 19.17 | 1437.05 | 0.34 | -463132 | 4204.70 | 19.26° | 0.79 |

4 | 12.43 | 1660.37 | 0.30 | -529.34 | 4204.70 | 19.94° | 0.78 |

7 | -0.26 | 1940.84 | 0.29 | -617.50 | 3717.00 | 20.27° | 0.78 |

10 | -6.14 | 2190.62 | 0.26 | -698.48 | 3717.00 | 20.34° | 0.78 |

13 | -14.74 | 2289.29 | 0.22 | -723.66 | 4204.70 | 20.81° | 0.77 |

16 | -29.27 | 2385.08 | 0.22 | -735.05 | 4204.70 | 22.09° | 0.75 |

19 | -37.05 | 2447.67 | 0.21 | -735.37 | 4204.70 | 22.98° | 0.75 |

22 | -45.29 | 2698.61 | 0.19 | -819.45 | 4204.70 | 22.76° | 0.75 |

LEBISDI software can be suitably used for analyzing the bioimpedance data for noninvasive biological tissue characterization. The present study is mainly associated with the vegetable tissues though the analysis of human tissue impedance data can be successfully conducted with the proposed software. As a future direction the proposed LEBISDI program can also be applied for human tissue characterization for health analysis and disease diagnosis. LEBISDI can also be potentially applied for multifrequency bioelectrical impedance analysis (BIA) based tissue composition assessment, electrical impedance-based tissue characterization and [95, 96] or disease diagnosis [97, 98] and EIS based tissue health characterization in biological, biomedical, medical and clinical applications [99, 100, 101, 102, 103, 104, 105, 106].

Under alternating electrical excitation, biological tissues produce a complex bioelectrical impedance that varies over a wide band of frequencies. By identifying the frequency response of a tissue’s electrical impedance, we can identify the equivalent electrical circuit model, which depicts physiological properties of the tissues that can be used later for clinical investigations. We developed a LabVIEW-based electrical bioimpedance spectroscopic data interpreter (LEBISDI) for tissue impedance analysis in medical, biomedical and biological applications by studying the equivalent circuit parameters of biological tissues from their Nyquist plots. The performance of LEBISDI was tested, calibrated and evaluated with simulated impedance data as well as with the impedance data collected from a number of high-precision resistor, capacitor and inductor circuit combinations using a standard impedance analyzer with a low amplitude sinusoidal current signal. To study the practical applicability of LEBISDI, we tested biological tissues with an impedance analyzer and the impedance data were interpreted by LEBISDI; their equivalent circuit parameters were also evaluated. Calibration studies show that LEBISDI accurately interpreted the simulated and practical electronic circuit combination data. Furthermore, experimental results show that LEBISDI successfully interpreted the bioimpedance data and estimated the capacitance and resistance of organic tissues. We also observed that LEBISDI efficiently calculated and analyzed variation in the bioimpedance parameters of different tissue compositions. Simulated data and experimental studies demonstrate that LEBISDI can be used to reveal the equivalent circuit parameters from the impedance data obtained from EIS studies. LEBISDI-based studies with a Warburg impedance element could be conducted and reported in future communications. As a future study, the proposed LEBISDI can also be used for electrical impedance-based human tissue characterization, tissue composition analysis, tissue anatomy and health studies and disease diagnosis.

#### Impedance data obtained from LEBISDI for a cucumber, a carrot and a bottle gourd.

Parameters | Cucumber | Carrot | Bottle Gourd |
---|---|---|---|

r | 19.17 Ω | -11.68 Ω | 57.38 Ω |

R | 1437.05 Ω | 1838.85 Ω | 2115.34 Ω |

C | 0.34 μF | 0.08 μF | 0.17 μF |

X_{Max} | -463.13 Ω | -583.07 Ω | -636.83 Ω |

f_{c} | 4204.70 Hz | 14427 Hz | 6086.60 Hz |

θ_{CPE} | 19.26° | 20.16° | 20.93° |

n | 0.79 | 0.78 | 0.77 |

#### Comparison of impedance parameters calculated from the impedance data estimation in LEBISDI for cucumber sample studied over a 22-day period.

Day | r (Ω) | R(Ω) | C (μF) | X_{Max} (Ω) | Fc (Hz) | θ_{CPE} | n |
---|---|---|---|---|---|---|---|

1 | 19.17 | 1437.05 | 0.34 | -463132 | 4204.70 | 19.26° | 0.79 |

4 | 12.43 | 1660.37 | 0.30 | -529.34 | 4204.70 | 19.94° | 0.78 |

7 | -0.26 | 1940.84 | 0.29 | -617.50 | 3717.00 | 20.27° | 0.78 |

10 | -6.14 | 2190.62 | 0.26 | -698.48 | 3717.00 | 20.34° | 0.78 |

13 | -14.74 | 2289.29 | 0.22 | -723.66 | 4204.70 | 20.81° | 0.77 |

16 | -29.27 | 2385.08 | 0.22 | -735.05 | 4204.70 | 22.09° | 0.75 |

19 | -37.05 | 2447.67 | 0.21 | -735.37 | 4204.70 | 22.98° | 0.75 |

22 | -45.29 | 2698.61 | 0.19 | -819.45 | 4204.70 | 22.76° | 0.75 |

#### Impedance parameters and errors calculated by LEBISDI for the inductive circuit models (ICM) studied.

SCM | Frequency (f) | R_{p}(Ω) | L_{p}(H) | Error R_{p} | Error L_{p} |
---|---|---|---|---|---|

SCM 5 | 10-2MHz | 499.98 | 09.85E-4 | 0.0032 % | 1.496 % |

SCM 6 | 10-2MHz | 999.97 | 19.70E-4 | 0.0031 % | 1.497 % |

#### Comparison of actual impedance data and the data obtained from LEBISDI for RCM 1 containing a 1 kΩ resistor and a 0.1 μF capacitor in parallel.

Values | Resistor (Ω) | Capacitor (μF) |
---|---|---|

Original | 1000.00 | 0.10 |

Calculated | 0996.52 | 0.10 |

Error | 0.348 % | 0.0885% |

#### Impedance parameters and errors calculated by LEBISDI for the capacitive circuit models (CCM) studied.

SCM | Frequency (f) | R_{p}(Ω) | C_{p}(F) | Error R_{p} | Error C_{p} |
---|---|---|---|---|---|

SCM 1 | 10-1kHz | 0999.97 | 1.01E-06 | 0.0027 % | 0.937 % |

SCM 2 | 10-2MHz | 0999.81 | 9.99E-10 | 0.0187 % | 0.068 % |

SCM 3 | 10-2MHz | 9998.12 | 9.99E-08 | 0.0188 % | 0.068 % |

SCM 4 | 10-10kHz | 1000.03 | 9.94E-08 | 0.0030 % | 0.569 % |

#### Comparison of actual impedance data and the data obtained from LEBISDI for RCM 2 containing a 2 kΩ resistor and a 0.1 μF capacitor in parallel.

Values | Resistor | Capacitor |
---|---|---|

Original | 2000.00 Ω | 0.10 μF |

Calculated | 1993.27 Ω | 0.10 μF |

Error | 0.335 % | 4.993% |

#### Comparison of the impedance parameters obtained from the impedance data estimation in LEBISDI for a green banana before and after boiling.

Parameters | Unboiled | Boiled |
---|---|---|

r | -354.08 Ω | 309.04 Ω |

R | 9382.64 Ω | 150.66 Ω |

C | 0.048 μF | 0.05 μF |

X_{Max} | -2412.03 Ω | -46.00 Ω |

f_{c} | 6896.98 Hz | 286206 Hz |

θ_{CPE} | 28.26° | 4.379° |

n | 0.69 | 0.959 |

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