1.

Introduction

Noninvasive sensing methods for determining glucose concentration in biological fluids have been under investigation for more than 30 years.¹ These approaches include the glucose absorption measurement with near infrared (NIR) spectroscopy,² photoacoustic spectroscopy,^{3, 4} and tissue scattering measurement with optical coherence tomography (OCT).⁵ As most measurement sites are blood-containing tissue on external body (e.g., skin, finger, earlobe, lip),^{5, 6, 7} these techniques face problems such as the complexity of human tissue, pulsatile nature of blood flow, unstable temperature^{8, 9} and effect of skin pressure¹⁰ etc. Up to now, few repeatable and quantifiable results have been reported in vivo. It is well known that there is a good correlation between glucose levels in aqueous humor and in blood.¹¹ Because aqueous humor in the anterior chamber of the eye is, optically, a more accessible glucose-containing body fluid, it is suggested that aqueous humor could be served as a surrogate for blood for noninvasive analysis of glucose concentration.

Several research groups have proposed and studied approaches to monitor glucose concentration in the aqueous humor. These techniques include polarization changes, Raman spectroscopy, and iris imaging analysis. In 1999, Cameron ¹² used polarization rotation of light through the eye to measure glucose concentration. Recently, Malik ^{13, 14} achieved a resolution of 12.8 mg/dL in the curette experiments with real-time closed-loop dual-wavelength optical polarimetry. In 2005, Lambert ¹⁵ and Pelletier ¹⁶ utilized Raman spectroscopy in combination with partial least squares (PLS) analysis to quantify glucose concentration and achieved a root-mean-square error of 22 mg/dL in artificial aqueous humor experiment. In 2010, Webb ¹⁷ reported a multivariate image processing technique for noninvasive glucose sensing. Based on the refractive index change of aqueous humor induced by glucose concentration,¹⁸ they created a calibration model to predict glucose concentration by analyzing iris images.

Since it was introduced in 1991,¹⁹ OCT has been proven to be an important modality for micrometer-scale imaging. In recent years, many groups have worked on expanding OCT to functional imaging. Promising results have been reported in Doppler flow imaging, polarization sensitive OCT, and spectroscopic OCT. Several authors have addressed the challenge of extracting quantitative information on optical properties using low coherence interferometry (LCI) and OCT. Michael Pircher reported differential absorption OCT to measure water concentration in human cornea.²⁰ It was also reported the measurement of dye diffusion in scattering tissue phantoms using dual-wavelength LCI.²¹

The motivation of this work is to monitor glucose concentration in the anterior chamber of eye with a differential absorption low-coherent interferometry (DALCI) technique. We selectively obtain the signals scattered from the iris by LCI technique. The light scattered from the other parts can therefore be eliminated, especially the strong light reflected from the cornea. As a result, the LCI technique has a relatively high signal-to-noise ratio, as well as a relatively high resolution in quantification measurement. In addition, since aqueous humor can be treated as non-scattering medium in the wavelengths that we used in this work, the influence due to scattering can be ignored.²² According to the absorption band of glucose and water,²³ we developed a DALCI using two different light sources, one centered within (1625 nm) and one centered outside (1310 nm) of a glucose absorption band, to measure glucose level in the anterior chamber of a pig eye ex vivo.

2.

Principle

The anterior chamber is located between the cornea and the lens, with the thickness of 3.13 ± 0.50 mm.²⁴ It is filled with transparent liquid–aqueous humor, with a total volume about 250 μL.²⁵

Figure 1 shows the structure of a typical anterior chamber. A light beam with intensity I₀ passes through the aqueous humor in the anterior chamber of the eye. Since the cornea and aqueous humor are nearly optically transparent, the iris could be treated as a natural reflector to scatter the beam back. The intensity I of the scattered beam from the iris after propagating through twice of thickness z of the aqueous humor can be described by Beer's law

Fig. 1

The structure of anterior chamber. An incident light I₀ gets into the anterior chamber. After passing through the aqueous humor, the emergent light I is scattered back from the iris. Being absorbed twice by glucose in the aqueous humor, the emergent light I carries the information of glucose concentration.

The theory of differential absorption LCI was established in Ref. 20. The relation between signals of two wavelengths LCI and the differential absorption coefficient Δ μ_a and scattering coefficient Δμ_s can be expressed as

where S_LCI(z, λ₁) is the LCI signal of 1625 nm light, S_LCI(z, λ₂) is the LCI signal of 1310 nm light, and z is the thickness of the aqueous humor.

In our experiments, the cornea and aqueous humor can be treated as nearly non-scattering substance. The difference in the absorption coefficient is much larger than the difference in the scattering coefficient, thus the influence of scattering can be neglected. The differential absorption cross section Δσ_a can be measured by the conventional spectroscopy. Equation 2.2 can be reduced to

3.

Materials and Methods

The DALCI setup, shown in Fig. 2, is a fiber based Michelson interferometer. Two different low coherence light sources were coupled by a wavelength division multiplexer (WDM) at the interferometer entrance. For this work we used two fiber pigtailed SLDs (Denselight Inc., Singapore) with center wavelengths at 1310 nm (FWHM bandwidth Δλ = 50 nm) and at 1625 nm (FWHM bandwidth Δλ = 50 nm), respectively. The emission powers and coherence length were 5 mW, 15.1 μm for the 1310 nm light source and 10 mW, 23.3 μm for the 1625 nm light source in the air, respectively. These two wavelengths were separated by a WDM into two reference beams. To eliminate the two wavelengths cross interaction in the WDM, two optical bandpass filters and two optical switches were placed in the corresponding reference beam. The reference mirror was driven by a servo motor, which was well controlled and synchronized by a personal computer. When the motor moved forward and backward, the beam of 1310 and 1625 nm switched on separately, allowing the same detector to record the coherence signals of the interferometer of such two wavelengths separately. The spectra responses of the detector to light with center wavelengths at 1310 and 1625 nm were 0.94 and 1.01 A/W, respectively. Normalization was conducted during calculation of the ratio R. An objective lens (10/0.25, 160/0.17) was used in sample arm to focus light on the sample. The electronic filter of the detector was set to be 2 kHz to improve signal-to-noise ratio. This required that the motor moved forth and back with different velocity. When we recorded interferometric signals with center wavelengths at 1310 and 1625 nm, the scanning speeds of the reference mirror were set to 0.91 and 0.74 mm/s, respectively.

Fig. 2

Schematic diagram of the differential absorption LCI system with two wavelengths (SLD1, λ₁ = 1310 nm; SLD2, λ₂ = 1625 nm; FC, 2X2 fiber coupler; OF, optical filter; WDM1, wavelength division multiplexer; WDM2, wavelength demultiplexer; M, vibratile mirror; L, lens).

In the experiments, we prepared a set of glucose water solution with concentrations of 0, 100, 200, 300, 400, 500, and 600 (mg/dL). To reduce the speckle noise, we took an average value by recording 30 coherence signal ratios (R) from the DALCI for each sample measurement. Every sample was measured four times to take the effect of the external environment into account. A weighted average of these four measurements was used as the final results.²⁶ In the pig eye experiments, we used the fresh native pig eyes which had been ex vivo for less than 4 hours. The fluid in the anterior chamber with glucose solution was replaced by home-made infusion device including an eye clamp to maintain the structure of the anterior chamber and the depth z unchanged throughout the experiments to minimize motion influence.

4.

Results and Discussions

The LCI signals of the iris were shown in Fig. 3 to prove the feasibility of our experiment. The sample was a pig eye which had been ex vivo less than 4 hours. We recorded 30 signals in each measurement and averaged these signals over four measurements. In Fig. 3, the vertical and lateral axis represent the intensity of LCI signals (A-scans) and position of the scanning mirror in the reference arm, respectively, which corresponds to the real position of sample. As is shown in Fig. 3a, due to the absorption by glucose, the intensity of LCI signal in 1625 nm is becoming smaller with the increase of glucose concentration. The signal attenuation is obvious where x-coordinate is 50 μm. We integrated the signals from 40 μm to 110 μm of x-coordinate in the experiment. By contrast, as is shown in Fig. 3b, the signal intensity of 1310 nm is basically unchanged when glucose concentration is increased. The difference of refractive index resulting from the two wavelengths is about 1.408 × 10⁻³, while the relationship between the change of refractive index and glucose concentration is Δn = 1.52 × 10⁻⁶ per 1 mg/dL glucose.²⁷ Thus, the optical path length induced by the difference of refractive index is negligible, which is also shown in Fig. 3 that the signals’ position remains almost the same whatever the wavelengths and the glucose concentrations are.

Fig. 3

The sample was a pig eye which had been ex vivo less than 4 hours. (a) The different intensity of interference signals of the wavelength 1625 nm; (b) The basically unchanged intensity of interference signals of the wavelength 1310 nm.

With the goal to measure glucose concentration in aqueous humor, we made an eye model to simulate the structure of anterior chamber. As shown in Figs. 4a and 4b, the model was composed of a glass hemispherical shell and the scattering background which was a piece of white paper pasted on the shell. The glass hemispherical shell we used was similar to the anterior chamber in structure. Figure 4c shows the sample arm in these experiments. The light was focused on the center of the model. The thickness z in this experiment was 5 mm.

Fig. 4

The eye model experiment. (a) The photo of eye model. (b) The structure of eye model. (c) The diagram of the optical path in the sample arm.

The resolution δC can be expressed as

After we measured a series of glucose water solution, seven groups of data were recorded. Taking a weighted average over each group, R was plotted in Fig. 5a. As shown in Fig. 5a, the resolution calculated by Eq. 4.1 in the shell experiment was 26.8 mg/dL and the root-mean-squared error of prediction (RMSEP) was 28.45 mg/dL. We also plotted –ln R in Fig. 5b. After linear fitting of the data points, the correlation coefficient was 0.9944.

Fig. 5

The measurement results for the eye model experiment. (a) The R is shown versus glucose concentration. An average of thirty R within two minutes was recorded as a sample measurement. In order to reduce the impact of the external environment, the weighted average of four times measurement was calculated as the final results. The resolution was 26.8 mg/dL, and the RMSEP was 28.45 mg/dL. (b) The -lnR is shown versus glucose concentration. The linear correlation between C and -lnR was 0.9944.

We used a fresh pig eye as the test sample which had been ex vivo less than 4 hours [Fig. 6a]. The biodiversity was not taken into account in the result. Fig. 6b shows the sample arm in this experiment and the light was focused on the edge of iris. A commercial OCT system (OSE-1400, Moptim Inc., China) was used to measure the thickness z of the pig eye in our experiment. The OCT image of pig eye is shown in Fig. 6c. The axial spatial resolution of the commercial OCT system was about 8 μm. The thickness z was about 1.65 mm. The error in concentration resulting from the error in z was about 0.5% of the absolute concentration value. We exchanged the fluid in the anterior chamber with an infusion device [Fig. 6d]. Each of the glucose water solution was measured once in 2 min.

Fig. 6

The pig eye experiments: (a) The photo of sample we used in this experiment. (b) The diagram of the optical path in the sample arm. (c) The OCT image of the pig eye we use. The thickness z is about 1.65 mm. (d) The diagram of liquid replacement setup in the pig eye experiments. It is made by an infusion device and two needles. We made 50mL glucose solution flow through the anterior chamber each time.

After we measured a series of glucose water solution, we still recorded seven groups of data. The average R of each group was plotted in Fig. 7a. As shown in Fig. 7a, the resolution we calculated in this experiment was 69.6 mg/dL and the RMSEP was 65.62 mg/dL. We also plotted –ln R in Fig. 7b, after linear fitting of the data points, the correlation coefficient was 0.9931.

Fig. 7

The measurement results for the pig eye experiment: (a) The R is shown versus glucose concentration. We recorded 30 R within 2 min for a sample measurement. We took an average for these 30 R we got each time. Due to the limitation of the eyes ex vivo, each of the concentration was only measured once. The resolution was 69.6 mg/dL, and the RMSEP was 65.62 mg/dL. (b) The -lnR is shown versus glucose concentration. The black line represents the fit of the data points. The linear correlation between C and -lnR was 0.9931.

The influence induced by other materials, such as water, proteins, ascorbic acid, and melanin in the aqueous humor, were not taken into account. Among such interferents, the impact of water is the most significant, as it has a higher absorption than other materials. Moreover, it is the main constitute of aqueous humor, which is as high as 99%.²⁸ To minimize the influence of water, we used two light sources with center wavelengths at 1310 and 1625 nm where the absorption of water is relatively equal and low, while the absorption difference of glucose is relatively high.^{29, 30} It has been proved that the glucose concentration in the aqueous humor is two orders of magnitude higher than other optically active substances.³¹ Meanwhile, the absorption coefficient of glucose at these wavelengths is larger than other substances.^{30, 32, 33, 34, 35} In order to reduce the remaining little influence of water and other materials, two possible methods can be considered to solve this problem. One is multivariate calibration techniques^{36, 37, 38}; the other is to use a closed-loop system.³⁹ Both of them have been demonstrated to be able to compensate for the interference due to other materials potentially.

The absorption coefficients of water and glucose solution do not remain the same under different temperatures. In our experiment, each sample was used in the experiment until they reached the same temperature. Located deep in the eyes, the change of temperature of iris is much smaller than that of the external bodies, such as skin, earlobe, etc., which are often used in current detection. Another vital influence of the measurement is the flowing status of liquid. According to the observation and calculation in the experiment, we observed significant difference in the absorption coefficient if the flowing status of solution was different. Generally, the solution would become static in 2 min after every replacement of new solution. In our future experiments in vivo, since the producing rate of aqueous humor is about 3.1 μl/min in the daytime,⁴⁰ it keeps a dynamic equilibrium and the flowing status basically stays unchanged. As a result, the errors introduced by the liquid flowing can be ignored.

Because of the different scattering properties of different scattering locations, the focusing position of incident light should keep unmoved especially in the pig eye experiment to maintain the deepness z unchanged. To reduce the errors induced by the movement of imaging spot, all experiment equipments were fastened tightly on the optical table and a non-touching replacing solution trick is very important in the ex vivo experiment. To reduce the impact of the movement of focusing position further, the incident light should not focus exactly on the iris. If we exclude the limitation of intensity detection, the best choice is to use parallel mode in the in vivo experiments. Another efficient solution to reduce the influence of the movement of imaging spot is to utilize rapid scanning optical delay (RSOD) instead of a mirror driven by motor as the reference arm. Currently, a total 120 s are needed to acquire 30 signals. We can reduce measurement time by using RSOD to obtain hundreds of signals within a second.

We use calibration curves to measure glucose concentration currently. According to Eq. 2.2, the slope of the curve is determined by z. Since z is different in the shell and pig eye experiment, the slopes in Figs. 5b and 7b are different. From the calibration curves, we can obtain the relationship between –InR and glucose concentration C. The value of z does not exert influence on the final results while it produces impact on the theoretical resolution in our experiments. We can calculate such curves with the absolute values of Δμ_a and z instead of obtaining a calibration one for each patient. The only step required is to measure every patient's anterior chamber structure by OCT to obtain the absolute value of z.

According to the Eq. 2.2, the resolution is determined by Δμ_a and z and may increase if we have a higher value of Δμ_a or z. Based on the experiments we have done, two ways can be introduced to improve the resolution. (1) We can select other light sources to get a higher value of Δμ_a. For example, the light source with wavelength at 1625 nm can be replaced by the light source with wavelength at 2100 nm, where glucose has a three times higher absorption.³⁰ (2) The light incidence position can be changed to obtain a larger value of z. One possible solution is using a high intensity light to shine on eyes to make the pupil smaller before experiment. Then we could make the incident light closer to the center and obtain a larger value of z. The resolution can thus be enhanced with the larger depth z. Moreover, the depth z can be enhanced if we utilize obliquely incident light instead of current normally incident mode. As a conclusion, the resolution may be potentially improved to meet the clinical application.

5.

Conclusion

We developed a differential absorption low-coherent interferometry (DALCI) technique to measure the glucose concentration in the anterior chamber of eye model. The results demonstrated that the intensity of emergent light of wavelength 1625 nm was declined whereas the intensity of emergent light of wavelength 1310 nm was unchanged with the glucose concentration increasing. In the pig eye experiment, we proved that a resolution glucose level of 69.6 mg/dL can be potentially obtained ex vivo. The results showed an excellent linearity of lnR and glucose concentration within a range of 0–600 mg/dL. This method for measurement of glucose concentration in aqueous humor is potential to calculate the blood sugar level according to the steady relationship between the glucose concentration in aqueous humor and in blood.