With rising obesity levels around the world, diabetes has emerged as a major medical concern with significant health and economic implications. If left untreated, diabetes can result in blindness, kidney failure, loss of limbs, heart attacks, strokes, and even death.1 Consequently, effective methods for diagnosing and monitoring diabetes are urgently required. Typically, such methods are based on measuring the glucose concentration in human blood or tissue. Noninvasive methods for glucose concentration determination either track an intrinsic molecular property of the glucose directly or the effects of glucose on the optical properties of the tissue or blood.2 Methods of the former type typically track the optical rotation angle, near-infrared (NIR)/midinfrared absorption coefficient, Raman shift, or NIR photoacoustic absorption.34.–5 By contrast, methods of the latter type generally measure parameters such as the light scattering coefficient of tissue, the refractive index of interstitial fluid, and the acoustic propagation speed in tissue.67.8.–9 The optical measurements required for glucose determination are commonly performed using optical coherence tomography (OCT).10,11 For noninvasive glucose monitoring based on measurement of coherently scattered light from specific layers of tissues and slopes of OCT signals, Esenaliev et al.12 showed that the slope of the OCT signal reduced substantially and linearly with increases in the blood glucose concentration. Larin et al.13,14 found that a good correlation exists between the OCT signal slope and the blood glucose concentration under normal physiological conditions. Kirillin et al.15 showed that the addition of glucose to 2% and 5% Intralipid suspension increased the refractive index and decreased the scattering coefficient, thereby leading to a reduction in the OCT signal slope. Additionally, various polarization-sensitive (PS) OCT structures have been developed for measuring the depth-resolved optical birefringence properties of biological tissues using a Jones calculus formulation.1617.–18 Yao and Wang19 developed an enhanced PS-OCT system for measuring the full depth-resolved Mueller matrix of biological tissue. In a later study,20 the same group used the PS-OCT system to measure the degree of polarization and backscattering coefficient of liquid and solid scattering samples. It was shown that the proposed system made possible the observation of several tissue structures that could not be visualized using a standard (nonpolarization) OCT setup. Liao and Lo21 proposed an OCT system based on a hybrid Mueller matrix formalism for extracting full-range measurements of the linear birefringence (LB) and linear dichroism (LD) properties of anisotropic optical samples. The results revealed that the proposed method was both more reliable and more accurate than traditional Mueller matrix decomposition methods.
Stokes–Mueller matrix polarimetry is a well-known technique for noninvasive diagnosis of cancerous tissue and turbid tissue-like scattering media.22 Phan and Lo23 recently proposed a differential Mueller matrix polarimetry technique for performing noninvasive glucose monitoring on the human fingertip. In Ref. 23, samples were treated as a black box for simplicity. The circular birefringence (CB) and depolarization index of the human fingertip tissue were both found to vary with changes in the glucose concentration. Accordingly, the present study proposes a technique for extracting the CB and depolarization properties of glucose aqueous solutions using a Mueller OCT system. The feasibility of the proposed technique is demonstrated by measuring the CB and depolarization properties of glucose aqueous solutions with low scattering properties (i.e., 0.02% Lipofundin addition) and high scattering properties (i.e., 2% Lipofundin addition), respectively. Finally, the practical applicability of the proposed method is demonstrated by measuring the optical rotation angle and depolarization index of the tissue on the fingertip of healthy human volunteers under various glucose conditions.
Mueller Optical Coherence Tomography System for Extraction of Circular Birefringence and Depolarization Properties of Optical Sample
Figure 1 shows the Mueller OCT measurement system used in the present study to extract the CB and depolarization (Dep) properties of aqueous glucose solutions with scattering properties. (Note that full details of the OCT setup are presented in Ref. 21.) Briefly, however, a low-coherence interferometric signal is obtained at detectors 1 and 2 as the scanning stage is driven at a constant velocity. The signal at detector 1 is obtained by locating the peak of the envelope of the signal for extracting the thickness and refractive index of the samples, whereas the signals obtained at detector 2 are employed to determine the anisotropic properties of the sample by calculating the amplitude of the interferometric signal.
In general, the Mueller matrix of an optical sample has the form21
As shown in Fig. 2, the measurement beam passes through the beam splitter and is then incident on the sample. It is noted that the samples were stored in a 1-mm thickness quartz cuvette with an inside width of 40 mm. Following transmission through the sample, it is reflected from the mirror, transmitted back through the sample, and then reflected from the beam splitter. In this study, the sample with only CB/depolarization properties is studied for simplicity as associated with the glucose detection application. The optical arrangement shown in Fig. 2 can be modeled using the following Mueller matrix representation:21.) Meanwhile, is the Mueller matrices of the sample with CB and depolarization effects and can be expressed as 21
The depolarization index can then be calculated as
Notably, the proposed analytical model of the sample/OCT system given in Eq. (2) allows the unknown CB and depolarization parameters of the sample to be determined over the full range, i.e., and , respectively. In this proposed method, the sample is treated as a black box; thus, the physical properties of samples in a complete homogeneity are assumed. For the sake of simplicity in the signal process, only optical rotation angle and depolarization index properties of the samples were extracted. The optical rotation angle represents the CB property of glucose, whereas the depolarization index describes the scattering effect caused by scattering particles.
Analytical Model for Extraction of Circular Birefringence and Depolarization Properties of Turbid Media
The CB and depolarization properties of the sample can be obtained by simply equating the Mueller matrix in Eq. (1) with that given in Eq. (2). However, in practice, is highly complex; hence, obtaining a closed-form analytical solution is extremely difficult. Accordingly, in the present study, the CB and depolarization properties of the sample are inversely derived using a genetic algorithm (GA)24 with the Mueller matrix given in Eq. (1) as the target function.
The ability of the proposed model to yield full-range measurements of the sample parameters was investigated by simulating the measured Mueller matrix using an inverse differential calculation approach given assumed parameter values for a hypothetical sample. In particular, the assumed values were input into the measured Mueller matrix, and the GA method was then used to obtain the input values inversely using the proposed analytical model.24 The extracted values obtained using the GA were then compared with the theoretical input values. In other words, the accuracy of the GA extraction results was evaluated using the following fitness function:
In performing the simulations, one of the considered parameters ( or ) was varied over the full range, whereas the other parameters were assigned a constant default value. The simulations commenced by setting the depolarization index equal to and extracting the values of given input values in the range of to 180 deg. It is noted that the value of was set randomly in the range of 0 to 1 to demonstrate the extraction of depolarization index. The optical rotation angle was then set as a constant , and the depolarization index was extracted for input values in the range of to 1. It is noted that the value of was set randomly in the range of 0 deg to 180 deg for demonstrating the extraction of depolarization index. To minimize the fitness function in Eq. (8), run a loop 100 times and calculate the loop 20 times. The results of the fitness function should be set under . It is noted that the error function in Eq. (8) is set as . The extracted values of the two optical parameters with the input values in every case are shown in Fig. 3. In general, the results confirm that the CB and depolarization parameters can both be extracted over the full range, i.e., and , respectively. Moreover, a good agreement is obtained between the extracted values of the optical parameters and the input values. From inspection, the standard deviations of the extracted values of and are found to be and , respectively. In other words, the validity and accuracy of the GA-based analytical model are confirmed.
Experimental Setup and Results
As shown in Fig. 1, the OCT system consisted of a halogen lamp (R150-BM1, Techniquip, USA), two photo-detectors (2001, New Focus Corporation), a scanning stage (SGSP 20-85, Sigma Koki, Japan), a scanning stage driver (Mark-204MS, Sigma Koki, Japan), a dispersion compensator consisting of D263T glass plate and a waveplate (5540, New Focus Corporation), an oscilloscope (6050, LeCroy Corporation), and two nonideal beam splitters (BS010, Thorlab) conducting the experiments. Compensation for the polarization distortion was performed using a composite polarizer component comprising a quarter-wave plate, half-wave plate, and second quarter-wave plate (Q/H/Q). (Note that full details of the compensation process are provided in Ref. 21.)
Parameter Extraction for Aqueous Glucose Samples with Low Scattering Effects
Aqueous glucose samples were prepared comprising deionized (DI) water mixed with glucose powder in concentrations ranging from 0 to (in increments of ) and 0.02% Lipofundin (Lipofundin MCT/LC1 20%, B|Braun, Germany, particle size: 150 to 230 nm). The tissue phantom samples were stored in a 1-mm thickness quartz cuvette with an inside width of 40 mm. Figures 4(a) and 4(b) show the experimental results obtained for the variations of the optical rotation angle and depolarization index, respectively, with the glucose concentration. Note that, in compiling the results presented in Fig. 4, the optical rotation angle and depolarization index values obtained for an empty container were first subtracted such that the plotted results correspond to the sample only. The dash line in Fig. 4(a) shows the variation of the extracted optical rotation angle of the samples with the glucose concentration when performing the measurement process using the OCT system. As shown in Fig. 4(a), the optical rotation angle () system increases approximately linearly with increases in the glucose concentration. The correlation coefficient has a value of , indicating a linearity between two variables. Furthermore, the standard deviations of the measured values of obtained over four repeated extractions are shown in Table 1, and the average deviation is found around 0.125 deg. Sun et al.25 obtained a measurement sensitivity of approximately when measuring the glucose concentration of polystyrene sphere suspensions. Similarly, Malik and Coté26 detected glucose concentration with a sensitivity of over a concentration range of 0 to . The results presented in Fig. 4(a) indicate that the proposed OCT system has a measurement sensitivity of . In other words, the system achieves a good sensitivity in measuring the glucose concentration. The dash line in Fig. 4(b) shows the variation of the extracted depolarization index with the glucose concentration when performing the measurement process using the OCT system. The correlation coefficient has a low value of , and it still can be seen that the depolarization index slightly reduces with increases in the glucose concentration. The present results are thus consistent with those of previous studies,56.–7 which showed that the depolarization index reduces with increases in the glucose concentration as a result of a corresponding increase in the refractive index and reduction in the refractive-index mismatch between the glucose solution and the Lipofundin powder. Furthermore, the standard deviations of the measured values of obtained over four repeated extractions are shown in Table 2, and the average deviation is found around 0.027.
The standard deviations of the measured values of γ obtained on four repeated extractions over the measured concentration range of aqueous glucose samples with 0.02% Lipofundin using OCT system.
|Glucose concentration||0 mg/dL||1000 mg/dL||2000 mg/dL||3000 mg/dL||4000 mg/dL||Average|
|Standard deviation (deg)||0.106||0.123||0.142||0.074||0.178||0.125|
The standard deviations of the measured values of Δ obtained on four repeated extractions over the measured concentration range of aqueous glucose samples with 0.02% Lipofundin using OCT system.
|Glucose concentration||0 mg/dL||1000 mg/dL||2000 mg/dL||3000 mg/dL||4000 mg/dL||Average|
The red dots shown in Figs. 4(a) and 4(b) indicate the optical rotation angle and depolarization index, respectively, for a pure water sample obtained using the OCT system. The two parameters have values of 0.546 deg and 0.227, respectively. In theory, both parameters have a value equal to zero for pure water. Thus, it is speculated that the OCT system contains a small degree of experimental error due to component misalignments and imperfections of the optical elements themselves.
The solid-line in Fig. 4 shows the results obtained for the variation of the optical rotation angle and depolarization index of the samples with the glucose concentration when performing the measurement process using a transmission-mode Stokes–Mueller polarimetry system.27 As for the case of the OCT, the optical rotation angle increases linearly with increases in the glucose concentration with a correlation coefficient of , whereas the depolarization index slightly reduces with increases in the glucose concentration with a correlation of . The difference between the two sets of results can be attributed to a difference in the optical path length (OPL) in the two systems. Specifically, the OPL in the Stokes–Mueller polarimetry system is much shorter than that in the OCT system. From an inspection of Fig. 4, the sensitivity of the Stokes–Mueller polarimetry system is around . By contrast, that of the OCT system is . It is noted that the large deviations and the nonlinearity of the measured results could be attributed to the misalignment of the system, the imperfections of the optic components themselves, and the noise environment.
Parameter Extraction for Tissue Phantom Samples with High Scattering Effects
Biotissue phantom samples were prepared by mixing DI water with 10-ml glucose solutions (-Merck Ltd.) with concentrations 0 to (in increments) and 2% Lipofundin (Lipofundin MCT/LC1 20%, B|Braun, Germany, particle size 150 to 230 nm). Note that previous studies28,29 have shown that 2% of Lipofundin in solution accurately reproduces the scattering effect of human skin and tissue. Figure 5 shows the experimental results obtained for the variation of the optical rotation angle and depolarization index with the glucose concentration. As shown in Fig. 5(a), although the correlation coefficient has a value of , the optical rotation angle still slightly increases with increases in the glucose concentration. The extracted optical rotation angles for the six samples have standard deviation values of 0.327, 0.268, 0.125, 0.562, 0.344, and 0.203, respectively. Figure 5(b) shows the variation of the extracted depolarization index with the glucose concentration. It is found that the depolarization index decreases approximately linearly with increases in the glucose concentration with a value of . The standard deviation values for the six samples are 0.081, 0.191, 0.134, 0.102, 0.168, and 0.236, respectively. The results are, therefore, in good qualitative agreement with those presented in Ref. 19. The reduction in the depolarization index with increases in the glucose concentration is to be expected as a higher glucose concentration results in a higher refractive index. As a consequence, the velocity at which light travels through the aqueous sample is reduced and, hence, the scattering effect is also reduced.
In general, the results shown in Fig. 5 confirm the feasibility of the proposed OCT system for performing glucose sensing based on just two optical parameters. The optical rotation angle represents the CB property of the glucose sample, whereas the depolarization index represents the scattering effects caused by particles within the sample. In general, the depolarization index reduces as a result of the OPL traversed by the light in passing through the sample. Therefore, both parameters (i.e., the optical rotation angle and the depolarization index) are required to obtain reliable estimates of the glucose concentration.
Glucose Extraction on Human Fingertip
The practical feasibility of the proposed optical system was evaluated by measuring the optical rotation angle and depolarization index of the tissue on the fingertips of healthy human volunteers. The experiments commenced by measuring the optical rotation angle and depolarization index of four volunteers under two glucose conditions, namely before and after an enhanced glucose condition induced by drinking 700 mL of sugared water. Note that in the latter case, glucose detection was performed 15 min after the drink was consumed to allow sufficient time for the sugar to enter the bloodstream. In performing the experiments, the volunteer’s fingertip was pressed against a 1-mm-thickness glass plate as shown in Fig. 6.
Furthermore, for both glucose conditions for each subject, four glucose measurements were obtained over a period of 20 min. The experimental results obtained for the four subjects are shown in Figs. 7Fig. 8Fig. 9–10. For all of the subjects other than subject #3, the average optical rotation angle increased following ingestion of the sugared water. Moreover, the average depolarization index reduced in every case. In other words, the results are in good agreement with those presented in Fig. 5(a) for the tissue phantom samples. It is noted that the strict preparation of volunteers for glucose testing is extremely necessary due to the different results obtained for subject #3.
A second series of experiments was performed in which the fingertip glucose concentration was measured for three volunteers at five different times over an 8-h period. The times were chosen in such a way as to track natural variations in the glucose concentration due to ingestion of food and drink at mealtimes, i.e., 9:00 AM (before breakfast), 10:00 AM (after breakfast), 11:00 AM (before lunch), 13:00 PM (after lunch), and 17:00 (before dinner). As in the previous experiments, the measurement process was performed using a 1-mm-thick glass attached to the fingertip. Four glucose measurements were obtained over a 20-min period in each case. Figures 11(a) and 11(b) show the extraction results obtained for the optical rotation angle and depolarization index of the three volunteers at the five different measurement times. As shown in Fig. 11(a), the optical rotation angle increased following breakfast (except for the case of volunteer 1) and, following a slight dip at 11:00 AM, increased to a peak value after lunch before decreasing continuously until 17:00 PM. Conversely, Fig. 11(b) shows that the depolarization index increased before meal times (indicating a lower glucose concentration) and decreased after the meal times (indicating a higher glucose concentration). In other words, the results are again in good qualitative agreement with those obtained for the tissue phantom sample [Fig. 5(b)]. Moreover, the standard deviations of the and measurements obtained at five different times over an 8-h daytime period are equal to 0.302 deg and 0.045, respectively.
This study has presented a Mueller OCT system for evaluating the glucose concentration of aqueous samples by means of two optical parameters (the optical rotation angle and the depolarization index) extracted using a differential Mueller model. The basic feasibility of the proposed method has been demonstrated by extracting the optical rotation angle and depolarization index of aqueous glucose solutions containing glucose with concentrations of 0 to and 0.02% Lipofundin powder. The results have shown that the optical rotation angle increases, whereas the depolarization index decreases, with increases in the glucose concentration. A similar tendency has been found for tissue phantom samples containing 2% Lipofundin powder. The practical applicability of the proposed method has been demonstrated by measuring the optical rotation angle and depolarization index of the human tissue on the fingertips of three healthy volunteers before and after the ingestion of sugared water, respectively. Moreover, the standard deviations of the and measurements obtained at five different times over an 8-h daytime period are equal to 0.302 deg and 0.045, respectively. The results obtained for human tissue are in a good qualitative agreement with those obtained for phantom tissue samples. Hence, the basic feasibility of the proposed OCT system for noninvasive glucose monitoring is confirmed. In the future, Monte Carlo theory will be implemented into the model to obtain the quantitative predictions of the glucose concentration from the experimentally extracted values of the optical rotation angle and depolarization index. Thus, the scattering properties of different people with different ages, race, and skin color will be investigated and studied in more detail to achieve trustable results for glucose concentration extraction.
No conflicts of interest, financial or otherwise, are declared by the authors. The current study has followed our institutional policies for the use of human subjects in our research. The informed consent was waived by the oversight body.
The authors gratefully acknowledge the financial support provided to this study by the Ministry of Science and Technology (MOST) of Taiwan under Grant No. NSC 106-2221-E-006-020-MY2. This research was also supported in part by the Ministry of Education, Taiwan, under the “Aim for Top University Project” of National Cheng Kung University.
Tseng-Lin Chen received his BS degree in mechanical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C. His research interests include OCT for biosensing.
Yu-Lung Lo received his BS degree from National Cheng Kung University, Tainan, Taiwan, ROC, in 1985, and his MS degree and PhD in mechanical engineering from the Smart Materials and Structures Research Center, University of Maryland, USA, in 1992 and 1995, respectively. Currently, he is the chairman of the Asian Society of Experimental Mechanics (ASEM) and the Steering Committee in International Symposium on Optomechatronics Technology (ISOT). His research interests include experimental mechanics, fiber-optic sensors, optical techniques in precision measurements, biophotonics, and additive manufacturing. He has authored over 150 journal publications, and one article was included in Spotlight on Optics by OSA in 2015.
Chia-Chi Liao received his PhD in mechanical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C. His research interests include OCT for biosensing.
Quoc-Hung Phan received his BS degree in mechanical engineering from HCM University of Technology, Viet Nam in 2004 and his MS degree in Department of Mechanical Engineering at Southern Taiwan University, Tainan, Taiwan, R.O.C. In 2016, he received his doctor’s degree in the Department of Mechanical Engineering, National Cheng Kung University. His research interests include subwavelength sensors, polarimetry, and optical biosensing.