Glucose Concentration Measurement in Human Blood Plasma Solutions with Microwave Sensors

Three microwave sensors are used to track the glucose level of different human blood plasma solutions. In this paper, the sensors are evaluated as glucose trackers in a context close to real human blood. Different plasma solutions sets were prepared from a human blood sample at several added glucose concentrations up to 10 wt%, adding also ascorbic acid and lactic acid at different concentrations. The experimental results for the different sensors/solutions combinations are presented in this work. The sensors show good performance and linearity as glucose level retrievers, although the sensitivities change as the rest of components vary. Different sensor behaviors depending upon the concentrations of glucose and other components are identified and characterized. The results obtained in terms of sensitivity are coherent with previous works, highlighting the contribution of glucose to the dielectric losses of the solution. The results are also consistent with the frequency evolution of the electromagnetic signature of glucose found in the literature, and are helpful for selecting frequency bands for sensing purposes and envisioning future approaches to the challenging measurement in real biological contexts. Discussion of the implications of the results and guidelines for further research and development of more accurate sensors is offered.


Introduction
In the last years, many efforts have been devoted to develop non-invasive blood glucose monitoring (NIBGM) technology. People with diabetes need to self-measure their blood glucose level (glycemia) several times every day, as a means to control the excursion of the glycemia out of the healthy range. The usual ways to make these measurements are invasive and painful, involving the pricking of the skin with a lancet in order to collect a drop of blood on a test strip [1]. Given the comfortless of the process, the frequency and effectivity of the measurements throughout the day is often reduced, thus yielding a poorer management of the disease.
Hence, NIBGM technology that is able to measure glycemia in a non-invasive, comfortable way would produce a remarkable enhancement in diabetes treatment. NIBGM technology could incrementally increase the number of measurements per day and provide a quicker detection of undesired events. It could even lead to continuous glucose monitoring (CGM), making it possible to detect almost instantaneously any glycemia change, and allow the individual or other devices to perform the right correction at the moment, noticeably enhancing the treatment of diabetes [2]. as well as their interpretation and implications, are shown in Section 4. Finally, the main conclusions and the most important aspects inferred from this study are gathered in Section 5.

Sensors Description
Three microwave sensors were used for measuring human plasma solutions [43]. The aim was to provide characterization and useful information about the behavior of the sensors when more realistic biological solutions are concerned. Hence, as sensors, three microstrip open-loop half-wave resonators were employed, hereinafter named R1, R2, and R3, having as resonant frequencies (without measuring any sample) 2 GHz, 5.7 GHz, and 8 GHz, respectively.
In the design, an open-loop geometry was chosen to exploit the high electric field region created between the open ends of the resonator for the first resonant mode. At resonance, there are voltage maxima of opposite signs in the open ends; therefore, this is the place where the electric interaction with the immediate upper space is the highest. For this reason, tracking the electrical response of each resonator when the sample is placed onto its open-end gap enables characterizing the sample, as illustrated in Figure 1. The convenience of having highly capacitive sensors (sensors exploiting high electric field zones) has recently been remarked by other authors [45]. In order to optimize the field-sample interaction, the gap length was chosen as a trade-off to avoid too weak intensity (long gap) and excessive field concentration in the interface between the substrate and the sample holder (short gap). This criterion led to gap lengths of 1600 µm for R1 and R2, and 1200 µm for R3. its open-end gap enables characterizing the sample, as illustrated in Figure 1. The convenience of having highly capacitive sensors (sensors exploiting high electric field zones) has recently been remarked by other authors [45].
In order to optimize the field-sample interaction, the gap length was chosen as a trade-off to avoid too weak intensity (long gap) and excessive field concentration in the interface between the substrate and the sample holder (short gap). This criterion led to gap lengths of 1600 µm for R1 and R2, and 1200 µm for R3. A low-permittivity substrate (Taconic TLX-8, ɛr = 2.55, tan δ = 0.0017) was selected to reduce the influence of the substrate in the measurements. Within the available options, thick substrates were preferred to give a higher weight to the upper space than to the substrate in the energy distribution, having final substrate thicknesses of 1200 µm for R1 and 800 µm for R2 and R3. This avoids the fields being confined into the substrate, and hence they can be more affected by the media upon the circuit. Also, relatively high characteristic impedances were chosen in order to increase the field intensity at the open ends, since it is easy to show that the field intensity becomes greater as the characteristic impedance increases. To do it, narrow strip widths (within fabrication limitations) of 600 µm were selected, producing characteristic impedances of 117 Ω for R1 and 100 Ω for R2 and R3. Finally, the resonators were coupled to two 50 Ω I/O lines through coupled-line sections to conform a transmission configuration. The coupling strength was designed as a trade-off between too strong coupling (which would worsen the resolution of the unloaded Q factor of the resonators) and too weak coupling (which would lead to a too low resonant peak, unsuitable for measurement purposes), resulting in a coupling slot width of 500 µm for the three sensors.
Special sample holders with an approximately hemispherical inner shape were designed and placed on the gap between the open ends of each resonator. These sample holders were glued onto the gap with a very thin layer (~50 µm) of epoxy resin (with roughly ɛr = 3.55, tan δ = 0.01). The chosen material was polytetrafluoroethylene (PTFE) because of its low permittivity, low losses, and low chemical reactivity, so that the influence of the sample holder in the measurements was minimum. A 25-µL inner volume PTFE sample holder was used for R1 and R2, and a 5-µL one was used for R3 (due to its smaller open-end gap), thus allowing for the characterization of very small samples. After gluing the sample holders and filling them with a reference A low-permittivity substrate (Taconic TLX-8, ε r = 2.55, tan δ = 0.0017) was selected to reduce the influence of the substrate in the measurements. Within the available options, thick substrates were preferred to give a higher weight to the upper space than to the substrate in the energy distribution, having final substrate thicknesses of 1200 µm for R1 and 800 µm for R2 and R3. This avoids the fields being confined into the substrate, and hence they can be more affected by the media upon the circuit. Also, relatively high characteristic impedances were chosen in order to increase the field intensity at the open ends, since it is easy to show that the field intensity becomes greater as the characteristic impedance increases. To do it, narrow strip widths (within fabrication limitations) of 600 µm were selected, producing characteristic impedances of 117 Ω for R1 and 100 Ω for R2 and R3. Finally, the resonators were coupled to two 50 Ω I/O lines through coupled-line sections to conform a transmission configuration. The coupling strength was designed as a trade-off between too strong coupling (which would worsen the resolution of the unloaded Q factor of the resonators) and too weak coupling (which would lead to a too low resonant peak, unsuitable for measurement purposes), resulting in a coupling slot width of 500 µm for the three sensors.
Special sample holders with an approximately hemispherical inner shape were designed and placed on the gap between the open ends of each resonator. These sample holders were glued onto the gap with a very thin layer (~50 µm) of epoxy resin (with roughly ε r = 3.55, tan δ = 0.01). The chosen material was polytetrafluoroethylene (PTFE) because of its low permittivity, low losses, and low chemical reactivity, so that the influence of the sample holder in the measurements was minimum. A 25-µL inner volume PTFE sample holder was used for R1 and R2, and a 5-µL one was used for R3 (due to its smaller open-end gap), thus allowing for the characterization of very small samples. After gluing the sample holders and filling them with a reference sample of the human plasma used in this study, the resonant frequencies dropped to 1.92 GHz, 5.17 GHz, and 7.16 GHz, which were three frequency points within an interesting frequency range for biological sensing purposes, according to [37]. A picture of the sensors used in this study can be seen in Figure 2.

Experimental Procedure
The experimental study consisted of measuring the frequency response of the sensors R1, R2, and R3, having their sample holders filled with various blood plasma solutions with different concentrations of glucose and other substances (see Figures S1, S2 and S3 in Supplementary Materials section). For this purpose, O+ blood plasma from an unknown healthy donor (provided by Hospital General Universitario de Alicante, Alicante, Spain) was used. In this regard, the donors were informed, and the procedures were in accordance with the ethical standards of the Ethics Committee of the Hospital General Universitario de Alicante. The plasma was mixed with several additional substances, namely glucose, lactic acid (hereinafter labeled LA), and ascorbic acid (hereinafter labeled AA). Five sets of plasma solutions were prepared with different concentrations of AA and LA in each one. Each set consisted of five solutions with added glucose concentrations of 0%, 2.5%, 5%, 7.5%, and 10% in mass, thus yielding 25 solutions in aggregate. These concentrations are convenient to allow for comparison with other works and identify different behaviors of the sensors with biological solutions.
The concentrations of AA or LA in each set are shown in Table 1. The solutions were prepared by directly adding the solutes to the plasma samples, not mixing the plasma with previously diluted substances. The two values of AA and LA concentrations correspond to their respective low and high physiological limits [46]. It should be noted that the initial glucose content in the plasma sample was unknown, and the glucose concentrations expressed in this paper refer to the added glucose. However, the initial glucose concentration is supposed to be within the normal physiological range, and hence it may be deemed negligible in comparison with the added glucose amounts. In addition, all the solutions were prepared from the same plasma sample, and no variations in this parameter are expected. Also, as will be shown later, the measurements in this study are differential; the initial glucose concentration has no effect on the concentration raises. On the other hand, initial AA and LA concentrations were unknown as well, and they can be considered as concentration offsets, which can be roughly estimated as the mean of their normal physiological ranges (13 × 10 −6 g/cm 3 for AA, and 12.15 ×

Experimental Procedure
The experimental study consisted of measuring the frequency response of the sensors R1, R2, and R3, having their sample holders filled with various blood plasma solutions with different concentrations of glucose and other substances (see Figures S1-S3 in Supplementary Materials section). For this purpose, O+ blood plasma from an unknown healthy donor (provided by Hospital General Universitario de Alicante, Alicante, Spain) was used. In this regard, the donors were informed, and the procedures were in accordance with the ethical standards of the Ethics Committee of the Hospital General Universitario de Alicante. The plasma was mixed with several additional substances, namely glucose, lactic acid (hereinafter labeled LA), and ascorbic acid (hereinafter labeled AA). Five sets of plasma solutions were prepared with different concentrations of AA and LA in each one. Each set consisted of five solutions with added glucose concentrations of 0%, 2.5%, 5%, 7.5%, and 10% in mass, thus yielding 25 solutions in aggregate. These concentrations are convenient to allow for comparison with other works and identify different behaviors of the sensors with biological solutions.
The concentrations of AA or LA in each set are shown in Table 1. The solutions were prepared by directly adding the solutes to the plasma samples, not mixing the plasma with previously diluted substances. The two values of AA and LA concentrations correspond to their respective low and high physiological limits [46]. Table 1. Solutions sets used in the study. AA: ascorbic acid, LA: lactic acid.

Label
Concentrations of AA or LA Added to Plasma P No additional components AAL AA at low limit (6 × 10 −6 g/cm 3 ) AAH AA at high limit (20 × 10 −6 g/cm 3 ) LAL LA at low limit (4.5 × 10 −5 g/cm 3 ) LAH LA at high limit (19.8 × 10 −5 g/cm 3 ) It should be noted that the initial glucose content in the plasma sample was unknown, and the glucose concentrations expressed in this paper refer to the added glucose. However, the initial glucose concentration is supposed to be within the normal physiological range, and hence it may be deemed negligible in comparison with the added glucose amounts. In addition, all the solutions were prepared from the same plasma sample, and no variations in this parameter are expected. Also, as will be shown later, the measurements in this study are differential; the initial glucose concentration has no effect on the concentration raises. On the other hand, initial AA and LA concentrations were unknown as well, and they can be considered as concentration offsets, which can be roughly estimated as the mean of their normal physiological ranges (13 × 10 −6 g/cm 3 for AA, and 12.15 × 10 −5 g/cm 3 for LA).
Additionally, a sixth set was prepared by adding AA and LA to the plasma, both at half their high limit concentration, i.e., AA at 10 × 10 −6 g/cm 3 and LA at 9.9 × 10 −5 g/cm 3 . This set was prepared to see the aggregate effects of the simultaneous presence of both acids, and it is labeled 'Mix' on what follows. All the solutions were characterized with the three microwave sensors (R1 to R3), thus performing 90 measurements. The frequency responses of the sensors (S-parameters) were measured with a vector network analyzer (VNA), previously calibrated with a Short-Open-Load-Through (SOLT) calibration kit. Special focus was placed on the transmission coefficient (S21). For each sensor, the frequency response with an empty holder was saved, frozen, and held in the VNA screen. For each solution, the sample holder was filled with a fixed volume (5 µL or 25 µL, depending on the sample holder) using a micropipette. After measuring the corresponding S-parameters, the sample holder was carefully cleaned with ethanol until the empty-case S-parameters frozen in the VNA screen were perfectly matched again, and hence the system was ready for a new measurement. The measurement setup can be seen in Figure 1. The sets were measured in the following order: P, AAL, AAH, LAL, LAH, and Mix. For each set, the measurements were performed in order from the lowest (0%) to the highest (10%) added glucose concentration. All the measurements were made at 25 • C room temperature. Deionized water and an unaltered sample of the blood plasma were measured at the beginning and at the end of the measurement session for each sensor, to account for repeatability. Identical frequency responses were obtained for all these control measurements.

Results
The measurements for each set with each sensor were plotted together, in order to identify the possible behavior. As an example, Figure 3 shows the S21 parameters for the measurements of the plasma set (P) with the three sensors. The solutions are labeled as Px.x, where x.x indicates the added glucose mass percentage in the plasma solution. The rest of sets presented similar behaviors. All the data are freely available in [47].
As it can be seen, these graphs show the relationship between the measured frequency response and the sample glucose concentration. By paying attention to the plots in Figure 3a-c, one can note that the variations due to the glucose level are not seen in the resonant frequency (f r ), but in the resonance 3-dB bandwidth (∆f 3dB ) and in the maximum amplitude of the S21 parameter (S21 max , expressed in dB). The ∆f 3dB is the frequency range between the two frequencies for which the S21 magnitude falls 3 dB from S21 max , at both sides of the resonance. These magnitudes are related to the resonator loaded (Q L ) and unloaded (Q u ) quality factors, which are given by: While Q L depends on the coupling strength between the resonator and the VNA ports, Q u depends only on the resonator properties. Thus, on what follows, we will use Q u as the magnitude determined by the resonance bandwidth.
due to the glucose level are not seen in the resonant frequency (fr), but in the resonance 3-dB bandwidth (∆f3dB) and in the maximum amplitude of the S21 parameter (S21max, expressed in dB). The ∆f3dB is the frequency range between the two frequencies for which the S21 magnitude falls 3 dB from S21max, at both sides of the resonance. These magnitudes are related to the resonator loaded (QL) and unloaded (Qu) quality factors, which are given by: While QL depends on the coupling strength between the resonator and the VNA ports, Qu depends only on the resonator properties. Thus, on what follows, we will use Qu as the magnitude determined by the resonance bandwidth.
(a) (b)  The variations of the glucose concentration are expected to change the value of the dielectric permittivity, which is a complex, frequency-dependent parameter [31]: where f is the frequency. As a matter of fact, the variations of ɛ' are expected to induce changes in the resonant frequency of the resonators, whilst the variations of ɛ″ are related to dielectric losses in the medium, and shall be noticed in the Qu factor. The parameter S21max depends on the resonator-VNA coupling and on Qu; therefore, it is indirectly affected by the losses. Thus, the very small variations in fr, along with the significant changes in S21max and Qu indicate that in the studied frequency range, the glucose concentration affects ɛ″ more than ɛ′. This is consistent with the data reported in [34] and with the results presented in [43] for water-glucose solutions in the present frequency range. Therefore, a comprehensive analysis of the data was carried out in order to compute and plot these parameters, which can be seen in Tables S1, S2 and S3 in Supplementary Materials section. All the resonant frequencies were obtained and plotted, but no conclusive results were achieved, which was expected, since the variations were random and comparable to the VNA frequency resolution.
The parameters S21max and Qu were computed for all the sets and added glucose concentrations. The results, grouped for each sensor, are shown in Figures 4-6, without considering the Mix set. These figures represent for each set the absolute difference in the S21max and the percentage change in the Qu, both with respect to their respective 0% added glucose measurement. These parameters are plotted against the added glucose concentration in mass percentage, thus allowing for the identification of glucose contribution to the changes of the measuring parameters. As it can be seen, clear relationships between the tracking parameters and the glucose level were obtained, which also showed a certain dependence on the acid content. While roughly the same tendencies of the responses concerning the added glucose concentration were obtained for all sets, the sensibility  The variations of the glucose concentration are expected to change the value of the dielectric permittivity, which is a complex, frequency-dependent parameter [31]: where f is the frequency. As a matter of fact, the variations of ε are expected to induce changes in the resonant frequency of the resonators, whilst the variations of ε" are related to dielectric losses in the medium, and shall be noticed in the Q u factor. The parameter S21 max depends on the resonator-VNA coupling and on Q u ; therefore, it is indirectly affected by the losses. Thus, the very small variations in f r , along with the significant changes in S21 max and Q u indicate that in the studied frequency range, the glucose concentration affects ε" more than ε . This is consistent with the data reported in [34] and with the results presented in [43] for water-glucose solutions in the present frequency range. Therefore, a comprehensive analysis of the data was carried out in order to compute and plot these parameters, which can be seen in Tables S1-S3 in Supplementary Materials section. All the resonant frequencies were obtained and plotted, but no conclusive results were achieved, which was expected, since the variations were random and comparable to the VNA frequency resolution.
The parameters S21 max and Q u were computed for all the sets and added glucose concentrations. The results, grouped for each sensor, are shown in Figures 4-6, without considering the Mix set. These figures represent for each set the absolute difference in the S21 max and the percentage change in the Q u , both with respect to their respective 0% added glucose measurement. These parameters are plotted against the added glucose concentration in mass percentage, thus allowing for the identification of glucose contribution to the changes of the measuring parameters. As it can be seen, clear relationships between the tracking parameters and the glucose level were obtained, which also showed a certain dependence on the acid content. While roughly the same tendencies of the responses concerning the added glucose concentration were obtained for all sets, the sensibility (in terms of the slope) seems to change for each one, having the greatest for the P set and the lowest for the LAH set for the unloaded Q factor, and the other way round for the S21 max , in the general case.
is consistent with the data reported in [34] and with the results presented in [43] for water-glucose solutions in the present frequency range.
Therefore, a comprehensive analysis of the data was carried out in order to compute and plot these parameters, which can be seen in Tables S1, S2 and S3 in Supplementary Materials section. All the resonant frequencies were obtained and plotted, but no conclusive results were achieved, which was expected, since the variations were random and comparable to the VNA frequency resolution.
The parameters S21max and Qu were computed for all the sets and added glucose concentrations. The results, grouped for each sensor, are shown in Figures 4-6, without considering the Mix set. These figures represent for each set the absolute difference in the S21max and the percentage change in the Qu, both with respect to their respective 0% added glucose measurement. These parameters are plotted against the added glucose concentration in mass percentage, thus allowing for the identification of glucose contribution to the changes of the measuring parameters. As it can be seen, clear relationships between the tracking parameters and the glucose level were obtained, which also showed a certain dependence on the acid content. While roughly the same tendencies of the responses concerning the added glucose concentration were obtained for all sets, the sensibility (in terms of the slope) seems to change for each one, having the greatest for the P set and the lowest for the LAH set for the unloaded Q factor, and the other way round for the S21max, in the general case.    Finally, the results for Mix set showed an intermediate behavior between AAH and LAH. This is a logical result, since the samples of this set have half the concentrations of the AAH and LAH samples. This also points out that their effects are additive. As an example, Figure 7 shows the unloaded Q factors percentage changes obtained for Mix set in comparison with those for AAH and LAH with the sensor R2. The rest of measurements for the Mix set resulted always in similar behaviors.

Discussion
In this section, the main focus will be on Qu as sensing magnitude for the glucose concentration (Cg). Although the parameter S21max provides an alternative measurement of Cg, they both are related, as it can be seen in Equations (1) and (2), and they therefore give essentially the same information regarding Cg. Moreover, Qu has the advantage of not depending upon the external coupling, since it is an intrinsic property of the resonator.
Within the added glucose concentration range of the solutions measured in this study (0-10% mass content), the variation of Qu with respect to Cg is approximately linear for all the solution sets. The addition of other solutes alters the slope, but the behavior remains linear. In this discussion, we are not considering the possible chemical reactions between the added components and plasma, and it is assumed that the only component with a remarkably higher concentration than the physiological ones is glucose.
The Qu sensitivities (SQ) obtained for all the sets with a simple least squares method can be seen in Table 2. Comparison with measurements with distilled water-glucose solutions (WG) is also presented. It is worthy to note that a glucose concentration increment leads to a Qu decrement, but the corresponding negative sign is not included in SQ as the changes were computed in relation to percentage difference. The Qu values obtained for the 0% added glucose measurement (denoted as Qu0) in each set are shown in Table 3. These are the values that are used as reference for computing the percentage differences.  Figure 7. Results for Q u measurements for the Mix, AAH, and LAH sets with R2.

Discussion
In this section, the main focus will be on Q u as sensing magnitude for the glucose concentration (C g ). Although the parameter S21 max provides an alternative measurement of C g , they both are related, as it can be seen in Equations (1) and (2), and they therefore give essentially the same information regarding C g . Moreover, Q u has the advantage of not depending upon the external coupling, since it is an intrinsic property of the resonator.
Within the added glucose concentration range of the solutions measured in this study (0-10% mass content), the variation of Q u with respect to C g is approximately linear for all the solution sets. The addition of other solutes alters the slope, but the behavior remains linear. In this discussion, we are not considering the possible chemical reactions between the added components and plasma, and it is assumed that the only component with a remarkably higher concentration than the physiological ones is glucose.
The Q u sensitivities (S Q ) obtained for all the sets with a simple least squares method can be seen in Table 2. Comparison with measurements with distilled water-glucose solutions (WG) is also presented. It is worthy to note that a glucose concentration increment leads to a Q u decrement, but the corresponding negative sign is not included in S Q as the changes were computed in relation to percentage difference. The Q u values obtained for the 0% added glucose measurement (denoted as Q u0 ) in each set are shown in Table 3. These are the values that are used as reference for computing the percentage differences. In general, the linearity of the measurements results is good, with adjusted R 2 values over 0.98 for the least squares approximation with sensors R2 and R3. Regarding R1, the behavior is less linear, with adjusted R 2 values of 0.90 for the P set and 0.94 for the AAL set. The tracking parameter (Q u ) presents in general a good correlation with the target magnitude (C g ), as it can be inferred from the correlation coefficients (R) obtained for the three sensors when measuring all the solutions sets, as shown in Table 4. The correlation coefficients obtained in this work compare well with the ones obtained with WG solutions. This means that the measurement principle seems right, and the differences are not found in the linearity, but rather in the sensitivity. In all the sets, and for the three sensors, the sensitivity is lower than the one obtained for water-glucose solutions. This result can be explained by estimating the resonator unloaded quality factor considering the sample as the only loss factor, i.e., disregarding the ohmic or radiation losses in the microstrip line, as well as the substrate dielectric losses. With these assumptions, it is easy to express the Q u sensitivity with respect to C g as: This expression clearly shows that an increase in the dielectric losses yields to a decrease in the sensitivity. In blood plasma, there are at least two additional loss factors in comparison to water for the same glucose concentration: a greater ionic conductivity, due to the presence of electrolytes, and a greater viscosity, associated with the presence of several organic molecules. A viscosity rise moves the frequency at which the ε" is maximum, which is roughly 20 GHz for pure water [48], toward lower frequencies. This is due to the proportional relationship between the dielectric relaxation time and the viscosity [49]. For the frequencies considered in this study (within the 2-7 GHz range), the final effect results in dielectric losses increment. This effect can be seen in a clear manner in Figure 1 of [50] (p. 3). The losses associated to the ionic conductivity, which are greater for low frequencies, might also explain why the sensitivity of sensor R1 is lower (see Table 2).
The experimental values of S Q obtained for plasma are coherent with the values that can be expected from Equation (4). For our measurements, it can be assumed that the Q u /Q u0 ratio is slightly lower than 1 (see Tables 2 and 3) and ε"∼20 (a usual value for water in the considered frequency range), whereas ∆ε"/∆C g can be set from the references shown in Table 5 (some of these data were obtained from the original plots by means of a graphic data extraction software, and must be therefore considered as approximate): Table 5. Values of ∆ε"/∆C g obtained from the scientific literature.
The sensitivities for the AA and LA sets are always lower than those for the P sets, as shown in Figure 8 (where the sensitivities of the P sets are the dots at 0 added acid concentration). Specifically, the sensitivities for AAL with respect to P decrease to 88.11%, 82.39%, and 71.45% for R1, R2, and R3, respectively, whereas those for LAL with respect to P decrease to 69.95%, 43.43%, and 55.17%. In this figure, due to the unknown prior concentrations of the acids, all the points could be displaced in the x-axis by a certain offset, with the behavior remaining unaltered. An approximation for this offset can be taken as the mean value for the physiological range of each acid. Besides, the increase of AA or LA concentration leads in both cases to a decrease in the sensitivity, as it is clearly seen in Figure 8. This decrease is not linear, and it seems to be more related to a saturation effect; that is to say, the sensitivity seems to trend toward a limit value at high concentrations (at least within the physiological ranges). In the case of LA sets measured with R1, this saturation state seems to have been reached, and the small sensitivity increase from LAL to LAH might be due to instrumental errors. It should be noted that the sensitivity reduction regarding LA sets is only slightly greater than the sensitivity reduction regarding AA sets, even though the AA concentrations are one order of magnitude smaller. This could be due to a greater influence, in relative terms, of ascorbic acid because of its greater molecular size (six carbon atoms in the AA molecule, C6H8O6, for three in the LA molecule, C3H6O3). Concerning the results for the Mix set, the sensitivity is quite approximately the mean of the AAH and LAH sensitivities (see Figure 7).
To the best of our knowledge, very few data are available concerning the dielectric properties of these acids. The relative permittivity of water-LA solutions was studied in [53]. At 2.45 GHz and ∼25 °C, the effective relative permittivity of a solution at 14.6% in mass was shown to be ɛr,eff * ∼9-j5.5. The relative permittivity of deionized water at the same temperature and frequency is ∼77-j10 [48]. Therefore, the relative dielectric permittivity of LA can be estimated by means of the Maxwell-Garnett formula: where ɛ1 and ɛ2 are the relative permittivities of the solvent (water) and the solute (LA), respectively, and v is the volume fraction of the solvent. Approximating v as the mass fraction (which induces low error in aqueous solutions), the above-mentioned data can be used to solve Equation (5) for ɛ2, giving ɛ2 (LA) ≈ 1.18-j4.75. This estimation, specifically regarding the imaginary part of the relative permittivity, accounts for the noticeable contribution of LA to the overall dielectric losses of the solution, relative to its concentration. This is consistent with the data reported in Table 2.
Although our attention has been focused upon Qu as a sensing magnitude for Cg, the experimental results Besides, the increase of AA or LA concentration leads in both cases to a decrease in the sensitivity, as it is clearly seen in Figure 8. This decrease is not linear, and it seems to be more related to a saturation effect; that is to say, the sensitivity seems to trend toward a limit value at high concentrations (at least within the physiological ranges). In the case of LA sets measured with R1, this saturation state seems to have been reached, and the small sensitivity increase from LAL to LAH might be due to instrumental errors. It should be noted that the sensitivity reduction regarding LA sets is only slightly greater than the sensitivity reduction regarding AA sets, even though the AA concentrations are one order of magnitude smaller. This could be due to a greater influence, in relative terms, of ascorbic acid because of its greater molecular size (six carbon atoms in the AA molecule, C 6 H 8 O 6 , for three in the LA molecule, C 3 H 6 O 3 ). Concerning the results for the Mix set, the sensitivity is quite approximately the mean of the AAH and LAH sensitivities (see Figure 7).
To the best of our knowledge, very few data are available concerning the dielectric properties of these acids. The relative permittivity of water-LA solutions was studied in [53]. At 2.45 GHz and ∼25 • C, the effective relative permittivity of a solution at 14.6% in mass was shown to be ε r,eff * ∼9-j5.5. The relative permittivity of deionized water at the same temperature and frequency is ∼77-j10 [48]. Therefore, the relative dielectric permittivity of LA can be estimated by means of the Maxwell-Garnett formula: where ε 1 and ε 2 are the relative permittivities of the solvent (water) and the solute (LA), respectively, and v is the volume fraction of the solvent. Approximating v as the mass fraction (which induces low error in aqueous solutions), the above-mentioned data can be used to solve Equation (5) for ε 2 , giving ε 2 (LA) ≈ 1.18-j4.75. This estimation, specifically regarding the imaginary part of the relative permittivity, accounts for the noticeable contribution of LA to the overall dielectric losses of the solution, relative to its concentration. This is consistent with the data reported in Table 2.
Although our attention has been focused upon Q u as a sensing magnitude for C g , the experimental results for the sensitivity of S21 max with respect to the added glucose concentration (∆S21 max /∆C g ) are shown in Table 6. Provided the existing relationship between Q u and S21 max [see Equations (1) and (2)], it is easy to obtain the relationship between ∆S21 max /∆C g and S Q . The theoretical estimations thereby calculated from the experimental values of S Q in Tables 2 and 3 are similar to the experimental values in Table 6, except for small differences that can be put down to experimental errors. For microwave resonators in the frequency range concerned in this work, the sensitivity reduction for complex solutions, such as in blood plasma, in comparison to that for pure water, shows the need for further research before application for future non-invasive sensors. New designs should be studied, aimed at maximizing the interaction of the electromagnetic fields with the sample and thereby gaining sensitivity. In this sense, the study of new options for placing the sample with strategic structures to amplify the field seems advisable. The results in this work also suggest broadening the study of the glucose influence in the dielectric behavior of plasma to other frequency bands.

Conclusions
The performance of three microwave sensors for glucose concentration has been analyzed when human blood plasma solutions are concerned. The assessment included, in addition to glucose, the use of ascorbic acid and lactic acid. The results have shown how the three sensors are able to track the glucose variations in all the considered situations, provided that the rest of the components in the solution are known. This entails a step forward toward the development of a NIBGM device in a real, complex environment, as this study allows identifying and characterizing the behavior of this kind of sensors when biological solutions are regarded, as well as when the concentrations of other components different from glucose are changing.
The results have revealed a better performance in terms of the sensitivity for R2 and R3 than that for R1, thus pointing to higher frequencies as desirable for future designs. They have also underlined the importance of individual calibration (as it was pointed out by other authors [54]), as well as the need for multicomponent tracking. In this sense, the comprehensive modeling of the real environment of application is deemed as essential for the success of future NIBGM proposals. Due to these reasons, further research on new sensors based on the principles discussed in this work is advised, which should include different frequencies and measuring parameters, and should involve several technologies and physical principles. The information gathered from them all will serve to feed machine learning algorithms devoted to building complex, trustable models of the real environment in order to understand all the phenomena occurring from an electromagnetic point of view. Once such a device will be ready, and the algorithms will provide accurate models for each individual, the composition of the main parameters, including glucose level, should be retrievable from new measurements of the sensors. Research on real biological conditions, such as the ones presented in this paper, is essential for advancing toward these future systems.
As to future scope, new techniques to gain sensitivity will be investigated, based on the principles seen in this work, trying to maximize the interaction of the fields with the sample. The conclusions reached in this paper suggest involving higher frequencies for future attempts. In addition, it seems important to consider different measurement principles, frequencies, or devices benefiting from the different behaviors shown in this paper to gain selectivity and discern the glucose level from the measurements, regardless the rest of the components.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript:

CGM
Continuous Glucose Monitoring NIBGM Non-Invasive Blood Glucose Monitoring PTFE Polytetrafluoroethylene SOLT Short-Open-Load-Through VNA Vector Network Analyzer WG Water-Glucose