Broadband polarimetric glucose determination in protein containing media using characteristic optical rotatory dispersion

: One of the major challenges during polarimetric determination of glucose concentration is the spectral superposition with other optically active molecules, especially proteins like albumin. Since each of those substances has a characteristic optical rotatory dispersion (ORD), we developed a broadband polarimeter setup to distinguish between glucose and albumin. A partial least squares (PLS) regression with 5 components was applied to the polarimeter signal in the wavelength range of 380 − 680 nm. To verify the eﬃcacy of the proposed method, diﬀerent glucose levels of 0 − 500 mg/dl were spiked with varying albumin concentrations up to 1000 mg/dl. A standard error of prediction of ± 16.0 mg/dl was achieved compared to ± 128.3 mg/dl using a two-wavelength system with 532 nm and 635 nm under the same conditions.


Introduction
The proportion of people afflicted with diabetes in the adult population worldwide nearly doubled from 4.7 % in 1980 to 8.5 % in 2014 [1]. Delayed diagnosis or wrong treatments of the disease can lead to serious damage to the eyes, nerves, heart, kidneys and blood vessels [2], and in extreme cases may require limb amputation [1]. Therefore, early stage diagnosis and treatment are crucial to minimize health complications [1]. In this context, a number of research papers have reported various approaches for continuous glucose monitoring (CGM). These include optical coherence tomography (OCT), fluorescence [3], refractometry [4] and Raman spectroscopy [5,6].
A large portion of optical-based blood component analysis is represented by absorbance spectroscopy, including mid-infrared (MIR) and near-infrared (NIR) wavelength ranges. Approaches utilizing liquid nitrogen cooled Fourier transform infrared spectrometers (FTIRs) [7,8] and tunable quantum cascade lasers (QCL) [9,10] exploit the MIR absorbance spectra of glucose. However, NIR and MIR measurements suffer from the hardware's low sensitivity in this wavelength range and low absorbance, overlapped by strong absorption bands of water and other blood components such as proteins, urea or lactate [11][12][13]. Consequently, Partial least squares (PLS) regression has been widely explored and demonstrated to be able to separate overlapped absorbance spectra of several blood components [6,11,14].
Polarimetry is another optical measurement method suitable for glucose determination in fluids. This technique takes advantage of glucose's optical rotation of polarized light, that depends on the concentration, wavelength, path length, temperature and pH-value [15]. The challenges of this method are the scattering effects caused by erythrocytes and tissues [16], as well as the low optical rotation values (approximately 0.4 millidegrees per 10 mg/dl glucose at a wavelength of 670 nm for a sample cell with 10 mm path length [17]). Another big obstacle is the high protein concentration, approximately 7000 mg/dl [18], which impedes a reliable glucose prediction due to its optical activity [16]. Therefore, the aqueous humor of the eye has been repeatedly proposed for glucose measurements, as the influence of 6 mg/dl albumin [19] on the polarization signal can be neglected, and no erythrocytes are present to disturb polarization measurements by scattering. Nonetheless, time delays between 3.4 min [20] and 30 min [21] have been reported for glucose levels in blood as compared to measurements in the eye for anesthetized rabbits [22], which were under ideal laboratory conditions that prove to be unrealistic in a clinical application. A two-wavelength system with 532 nm and 635 nm was investigated by Cameron et. al [19,23] to determine glucose in the presence of varying albumin concentrations. This showed a significant improvement over single wavelength systems and enabled the polarimetric distinction of glucose and albumin for in vitro measurements. However, the authors used albumin levels between 0 − 100 mg/dl that are far below the physiological variation, which is reported to be ±540 mg/dl [18,24]. Since the optical rotatory dispersions (ORD) of different optically active blood components are quite similar, multispectral regression models have been applied to help distinguish between different analytes [15,25,26]. In this paper we show that a broadband polarimeter in combination with PLS regression is able to reliably determine glucose in the presence of physiologically varying albumin.
With the goal of a long-term stable and robust polarimetry for medical applications, we already demonstrated that our setup is able to measure independent from fluctuations in absolute light intensity and slight scattering effects [27]. Since the spectral ORD overlap of glucose with other substances remains a major source of error, we present a broadband polarimeter setup, similar to the system proposed by Cote et al. [28]. The aim is to achieve a better signal separation between glucose and the most abundant blood protein albumin, as well as a substantial improvement of the prediction accuracy. Such a system could potentially be used beyond in-vitro diagnostics. For example, an application in intensive care settings would be feasible. In this case, blood plasma could be derived from the patient using a miniaturized erythrocyte filter to implement a continuous glucose measurement. A long-term implementation might also be an implantable system for diabetes patients.

Optical activity of blood components
The optical activity of a given substance is the result of its molecules chirality, which can exist with different spatial arrangements but equal molecular weights. The ORD can be calculated for the wavelength λ using Drude's equation [15,18]: where A defines the strength and the direction of rotation, and λ c represents the absorption center wavelength [16], which is unique to each chiral component [29]. The ORD [α] T λ,pH describes the total rotation at a specific temperature T, pH-value and wavelength λ. At constant T and pH, the absolute sample rotation [Φ] T λ,pH for a given path length l is proportional to the analyte concentration c: Table 1 shows the parameters A and λ c for glucose and the most relevant blood proteins. According to the literature [18,24], the typical physiological protein concentrations are 4200 ± 540 mg/dl for albumin, 2800 ± 470 mg/dl for globulin and 300 ± 45 mg/dl for fibrinogen. Glucose exhibits the shortest absorption center wavelength at 150 nm, while the longest corresponds to albumin at 264 nm. Figure 1 shows the ORD for glucose, albumin, globulin and fibrinogen in blood as well as the ORD ratio for proteins referenced to glucose to show their linear independence. The spectral differences become larger at shorter wavelengths, especially in the UV range. (left) ORD of common blood components glucose, albumin, globulin and fibrinogen [18]. (right) Ratio of ORD for proteins referenced to glucose. The spectral differences between glucose and proteins become larger the closer the measurement approaches the UV located absorption center wavelength.
Polarization measurements in the UV region comprise several obstacles. One is a high water absorption below approximately 200 nm. Another is that most polarimeters for glucose determination usually require an optical modulation by a Faraday rotator [17,19,22,30]. The high absorption below 400 nm of most optical glasses used in these Faraday rotators as well as the strong absorption of the used Glan polarizers, which absorb strongly below 350 nm, limit the effective wavelength. The ORDs for glucose, proteins and other optically active molecules are very close to each other for wavelengths in the visible range (see Fig. 1). Therefore, ambient conditions and setup parameters need to be very stable during the measurements. Another obstacle is the additional absorbance of proteins below 500 nm, which leads to a variation in sample transmittance.

Measurement setup
To acquire the spectra of spectrally superimposed ORD, we built a broadband polarimeter as illustrated in Fig. 2 that includes a broadband light source, two crossed polarizers, a cuvette, a spectrometer and a Faraday rotator for modulation.
In order to perform highly sensitive broadband measurements, a high power light source with a continuous emission is required. In this case, a laser driven light source (EQ-99X, Energetiq Inc., USA) was chosen, providing a broad and continuous emission between 190 nm and 2100 nm with a typical output power of 80 mW. The light was linearly polarized by a Glan-Thompson Polarizer (GTH10, Thorlabs GmbH, Germany) with an extinction ratio of 100,000 : 1 over a broad wavelength range of 350 nm to 2.3 µm.
For signal improvement, the light from the first polarizer was then modulated by a Faraday rotator. The rotator consists of a 65 mm SF6-rod (Schott GmbH, Germany). The material was chosen due to its high and continuous transmission above 380 nm because commonly used terbium gallium garnet (TGG) rotators show an increased absorption around 480 nm [31]. The length of 65 mm originates from stock availability of the manufacturer. UV transparent α-BBO polarizers are available, but they are hygroscopic, which limits their long term stability. For this reason, they were not used in this setup. The rotator's solenoid has 475 turns and was driven at 2 A pp by a current driver. The reference signal for the coil driver was created by a function generator (33120A, Hewlett Packard, USA) with a frequency stability of 2 ppm/ • C and 10 ppm/90 days. A modulation frequency of 7 Hz was chosen in order to avoid any overlap with harmonics of 50 Hz. The current amplitude fluctuations were below ±100 µA (±0.005 %).
A flow-through cuvette for the sample was placed behind the Faraday rotator. Since a greater path length leads to an enhanced rotation, a path length of 50 mm was used to better resolve ORDs from glucose and albumin as already successfully used in previous studies [19,26]. A second Glan-Thompson polarizer (GTH10, Thorlabs GmbH, Germany) was placed behind the cuvette in perpendicular orientation to the first one.
Measuring a modulated multispectral signal requires a spectrometer with a low timing jitter in order to identify frequency components of the transmitted intensity. For this purpose, the light transmitted by the second polarizer was measured by a grating spectrometer (AvaSpec-ULS2048L-EVO UV-VIS, Avantes BV, Netherlands), which has a fast internal memory to ensure a proper synchronization between time stamps and intensity. The spectrometer mean timing jitter was determined to be 3 µs at an integration time of 2 ms. A partial least squares (PLS) regression was applied on the spectral data using MATLAB 2019a (Mathworks Inc., USA) to distinguish between glucose and albumin in the wavelength domain. During the measurements, the whole setup was kept inside a temperature-controlled chamber where fluctuations stayed below ±0.1 • C. An average temperature of 32 • C was chosen to maximize the protein stock solution life time.

Data processing
Based on the sinusoidal Faraday modulation at frequency ω, the detected signal has to be processed to obtain its respective frequency components. The resulting signal consists of three frequency components [23,27]. One DC-part, one at the modulation frequency ω and the last at the double frequency 2ω. Using the modulation depth Θ m , the sample rotation Φ, modulation frequency ω, incoming light intensity E 0 and transmission T, the measured intensity I(t) at a certain time t can be calculated as where the frequency component amplitudes are: 2 · E 2 0 · T As demonstrated in a previous work [27], all frequency components in Eq. (3) are proportional to the absolute light intensity. Thus, the ratio is independent from any kind of variations in light intensity. Using the ratio of Eq. (4) influences of the light source intensity, sample absorbance and slight scattering are greatly reduced, improving the reproducibility and robustness of polarimeter-setups without the need of additional hardware or reference measurements [27]. Therefore, this method was used in the present work. The spectral ORD overlap of multiple optically active substances in a sample remains as the main source of error, which is the focus of the investigation in this paper.

Sample preparation
For all measurements used in this work, samples of glucose and albumin in distilled water were prepared from stock solutions. The pH value was stabilized at 7.4 using phosphate buffer (Morphisto GmbH, Germany). 50 g of D-glucose powder (Sigma Aldrich, Germany) were weighted with a high precision balance (Kern EW 120-4NM, Kern & Sohn GmbH, Germany) with an uncertainty of ±1 mg and then diluted in 5000 ± 0.6 ml of distilled water. This resulted in a glucose concentration of 1000 mg/dl. The stock solution uncertainty was ±0.01 %. To achieve full mutarotation, the stock solution was kept at 32 • C for 24 h, which has been reported to be sufficient [25], before the measurements were carried out. In order to determine the effect of confounding proteins, albumin was chosen to model interference since it is the most abundant protein in blood [18]. Due to its similarity [29], bovine serum albumin (BSA) (Sigma Aldrich, Germany) was used for the samples and other polarimetric studies [17]. One liter of stock solution was created for each respective measurement series by adding 20 ± 0.001 g BSA to 1000 ± 0.6 ml water, which resulted in a concentration uncertainty of ±0.06 %.
Samples with different concentrations of glucose and albumin were automatically generated by mixing the stock solutions using three high precision syringe pumps (neMESYS 290N, Cetoni GmbH, Germany) with three 25 ml glass syringes (ILS GmbH, Germany). A sample volume of 25 ml was chosen in order to keep contamination with prior sample remains as small as possible. After injecting the solutions into the cuvette, the syringes were automatically refilled. Additionally, the cuvette was rinsed with 25 ml of distilled water after each measurement. Measurements were performed 30 s after the flow had stopped to ensure stationary conditions [27]. The stock solutions and syringe pumps were also maintained inside the temperature controlled chamber at 32 • C.
The syringe pump accuracy was evaluated gravimetrically using distilled water and dosing volumes of 1 ml, which was the smallest volume used in the sample generation. As result, an absolute combined uncertainty of 2.1 µl of delivered volume (bias) + 0.14 % (precision) was determined.

Measurement procedure
With the purpose to investigate the influence of albumin concentration on glucose predictability, two sets of measurements were carried out as summarized in Table 2. We used six different glucose levels (0, 100, . . . , 500 mg/dl) measured 6 times each. To evaluate the influence of albumin, each glucose solution was spiked with 0, 200, 400, . . . , 1000 mg/dl albumin, leading to a concentration matrix with 36 unique combinations. These samples were measured in a random order to avoid time-correlated effects, like for example those caused by temperature fluctuations, as described and suggested by other authors [17,25,32]. For each measurement, the broadband intensities I(ω) and I(2ω) were extracted from the raw spectra and the ratio I(ω) I(2ω) was used to obtain stabilized measurements of spectrally superimposed ORD as described in subsection 3.2. This procedure was repeated three times, resulting in three identical 6x6 matrices and a total of 108 measurements. The measurement set was later split in two groups: one for calibration and the other for validation datasets.
Previous works have shown that glucose concentration in the presence of 0 − 100 mg/dl albumin can be determined with a precision of ±20.0 mg/dl utilizing a dual-wavelength system [19]. However, the authors used an albumin concentration range representing only 10 % of the typical physiological variation (±540 mg/dl) and a maximum concentration of (100 mg/dl), which was 98 % lower than the reported blood levels (4200 ± 540 mg/dl [18,24]). Since the absolute rotation depends linearly on the concentration (see Eq. (2)), an albumin level offset introduces a constant shift of the rotation signal, which is eliminated by the regression model. As demonstrated earlier, absorption effects which may be caused by albumin or other substances are compensated for by using I(ω) I(2ω) according to Eq. (4) [27]. Consequently, we focused on the physiological variation in order to investigate the ORD interference of glucose and albumin. In this work, albumin concentrations between 0 mg/dl and 1000 mg/dl were used.
In measurement #1 the system prediction accuracy without any confounder (i.e. no albumin) was evaluated. For measurement #2 albumin concentrations of 0, 200, . . . , 1000 mg/dl were added to the matrix.
For each sample, 1000 spectra were recorded at an integration time of 2 ms and saved to the internal memory of the spectrometer. The frequency components I(ω) and I(2ω) were extracted at 7 Hz (ω) and 14 Hz (2ω) for each wavelength by applying a Fourier transform. The ratio I(ω) I(2ω) was then used to obtain the corrected ORD dependent spectra, as described in subsection 3.2.
The results were analyzed using a multivariate regression model, as suggested by other authors [15,24,26] to distinguish between different optically active molecules. For each measurement series, the data from the 3 concentration matrices (36 samples each) was split into calibration and validation data. The first 2 data sets (72 spectra) were used for calibration, while the last one (36 spectra) was used for validation. For the model calibration, a PLS regression was performed on the I(ω) I(2ω) of corresponding data sets using Matlab 2019a (statistics toolbox). The created regression model was then applied to the validation data to obtain the corresponding glucose concentrations. The deviation between predicted and reference concentration was computed as the standard error of prediction (SEP).

Glucose determination without albumin
We first evaluated the system's overall glucose prediction accuracy without albumin to later classify the results for varying confounding albumin levels in subsection 4.2. For both cases, the results for a broadband determination were compared with those obtained by a two-wavelength prediction with 532 nm and 635 nm as used by other authors [19,33,34]. For this purpose, we extracted the intensities at these wavelengths from the same data sets as used for the broadband determination.
The results for pure glucose solutions in the absence of albumin can be found in Fig. 3 for dual-wavelength analysis at 532 nm and 635 nm as well as for broad range. The best prediction accuracy was achieved with 5 PLS components and a range of 380−680 nm. Since no confounders were used in this measurement and only the glucose concentration had a major contribution to the signal, broadband and dual-wavelength range deliver similar results (±1.7 mg/dl vs. ±2.1 mg/dl), which is about one third of the ±5.4 mg/dl reported in the literature for a similar scenario [25]. The broadband data performs slightly better, probably due to the ORD being identified, which provides for distinguishing the sample signal from minor disturbance effects like drift.

Glucose determination with confounding albumin
In measurement #2, the glucose samples were spiked with albumin concentrations between 0 − 1000 mg/dl. Consequently, the ORDs of glucose and albumin are superimposed. The ratio I(ω) I(2ω) is therefore depicted in Fig. 4 for 532 nm and 635 nm as well as for broadband 380 − 680 nm wavelength data. The combination of 6 different clockwise rotating glucose concentrations with 6 different counterclockwise rotating albumin concentrations within the 6x6 matrix leads to 36 unique overlapped ORDs. As shown in Fig. 1, the broadband data provides ORD-based spectral information, which was used in the past to distinguish between glucose and albumin with a two-wavelength system [19,33,34]. The influence of confounding albumin on the prediction accuracy was then evaluated as for the pure glucose solutions. The comparison for broadband and dual-wavelength evaluation can be found in Fig. 5. Compared to the results shown in Fig. 3, the SEP increases significantly to ±128.3 mg/dl when using dual-wavelength analysis in the presence of albumin. The reason is that both, glucose and albumin, have considerable contributions to the sample's overall rotation. Dual-wavelength analysis is partially able to distinguish between them, but due to the low amount of spectral information only in a limited way. Under consideration of the albumin concentration range, the achieved accuracy of ±128.3 mg/dl for 0 − 1000 mg/dl corresponds to those of Cameron et. al, who reported ±20 mg/dl for a tenth of our albumin level (0 − 100 mg/dl) [19].
The prediction with the broadband data from 380 − 680 nm performs much better and still delivers an SEP of ±16.0 mg/dl. Since glucose and albumin have their own characteristic ORD as shown in Fig. 1, the ORD overlap of glucose and albumin generates unique combinations of their ORDs depending on their concentrations. These superimposed ORDs can then be identified by the PLS evaluated broadband data. This substantiates the results obtained by Cameron et. al [19] who achieved a prediction accuracy of ±20 mg/dl utilizing a two-wavelength system. However, the confounding albumin concentration range in our investigations was 10 times higher. A summary of the results is given in Table 3.

Conclusions
Since the fluctuations in absolute light intensity were already compensated for by using I(ω) I(2ω) [27], the spectral overlap of other optically active substances, especially proteins remained as a major source of error for glucose prediction. To overcome this obstacle, we built a broadband polarimeter as suggested by Baba, Clarke and King [15,25,26] and applied a PLS regression on the extracted spectrally superimposed ORD. In order to investigate the influence of proteins as confounder, glucose was combined with different levels of albumin, the most abundant protein in blood. To compare these results with those for dual-wavelength analysis from other studies, we extracted the intensity at 532 nm and 635 nm from the broadband data. We showed that the prediction accuracy via PLS regression and 5 components between 380 − 680 nm without albumin is similar to that obtained by the dual-wavelength analysis at 532 nm and 635 nm and is as low as ±1.7 mg/dl. By adding varying albumin concentrations in the range 0 − 1000 mg/dl, the prediction error increases to ±16.0 mg/dl for broadband data, while the dual-wavelength analysis leads to an extended SEP of ±128.3 mg/dl.
We showed, that a PLS regression applied on broadband rotation data is able to distinguish between different optically active substances by their characteristic superimposed ORD. This could be used for a substantially improved glucose prediction in the presence of confounding albumin.
Although we showed that the method leads to an improvement in glucose prediction, the influence of other optically active substances like globulin and fibrinogen must and will be investigated in the future in order to estimate how the broadband ORD based method would perform for blood plasma samples. For later application as an implantable sensor for continuous glucose monitoring the system needs to be miniaturized including a reduction of cuvette size for less sample volume and shielded from further potential interferences like mechanical torsion of the setup.