1.

Introduction

The refractive index (RI) of biological tissue is a basic material parameter that characterizes how light interacts with tissue.¹ In many optical studies, a rough estimate of RI of the tissue under study, based on the fact that the main constituent of tissue is salt water-filled cells or more precisely a mixture of salt water and proteins, is often used.^2,3 For many tissues and blood components, the data for RI in a wide spectral range and concentrations are not yet available.⁴

The study of optical properties of hemoglobin is important for the development of diagnostic and laser treatment techniques, where consideration of blood optical properties is critical. Various optical methods widely used for tissue characterization, such as visible and near-infrared (NIR) spectroscopy, optical coherence tomography, and fluorescence spectroscopy, need exact data for RI of tissue, blood, and their components to quantify properly experimental data.^5–11

At present, the usage of RI as a diagnostic marker is urgent.^5–20 Sometimes, it is a self-sufficient parameter for tissue and blood characterization. Zhernovaya et al. considered the change of RI of hemoglobin and albumin at the interaction with glucose as a possible method for studying the glycation process and determining glycated proteins, which is important for the monitoring of diabetes mellitus.⁹ The RI of tissue was used as a marker for cancer, reflecting changes of optical properties in the course of pathology development.^{10,11,14–20} An additional motivation for this study is a lot of discrepancies between the RIs reported in the literature by different research groups.

The RI is a complex value consisting of a real part $n$, which represents the ratio of the speed of light in a vacuum to the speed of light in the material $n=c/v$, and an imaginary part $k$, which represents light attenuation^21–25

Because of tissue heterogeneity, $n$ is always known as the effective or average RI.^24,26 According to the classical theory of light dispersion, the components of the complex RI of molecular structures can be written as^21–25

Over the last decades, various techniques to determine RI of biological tissues were developed; they include confocal microscopy,^1,6 optical fiber cladding method,²⁷ minimum deviation angle method,^28,29 optical coherent tomography with multiple modifications,^6,9,30–36 total internal reflection method,^26,37,38 measurement of the intensity profile of diffuse light refracted into the prism around the critical angle,³⁹ various modifications of nonlinear phase microscopy,^40–42 and quantitative phase imaging techniques.^12,43,44

Because of the strong hemoglobin absorption, direct measurements of the real part of RI using conventional refractometers (for example, an Abbe refractometer) have proven to be difficult, and data are available at a few wavelengths only. In an early study, for example, Barer measured $n$ for solutions of oxygenated hemoglobin at 589 nm only.⁴⁴ He also discussed RI dependence on the hemoglobin concentration and presented the expression

Faber et al. measured the RI of solutions of oxygenated and deoxygenated hemoglobin at 800 nm.⁴⁵ Friebel and Meinke measured directly the RI of solutions of oxygenated hemoglobin at 633 nm for several concentrations^7,8

Zhernovaya et al. also used the formula similar to Eq. (4) to describe the linear dependence of the RI of hemoglobin on the concentration

Jin et al. measured RI of hemoglobin solution at 633 and 532 nm using a total internal reflection technique.³⁷ Park et al. measured the dispersion of Hb solutions, prepared from Hb protein powder, at 440, 546, 560, 580, 600, 655, and 700 nm using spectroscopic phase microscopy.⁴¹ Deng et al. showed that, in the 400 to 750 nm range, hemoglobin solution is characterized by specific forms of dispersion and extinction spectra.⁴⁷ Yahya and Saghir measured RIs for multiple temperatures and wavelengths using the Abbemat refractometer.⁴⁸ They found linear dependences of RI on hemoglobin concentration and temperature and nonlinear on the wavelength.

Analysis of the dispersion relation in similar studies showed significant differences for oxyhemoglobin and deoxyhemoglobin, related to the difference in the imaginary part of the RI for the 500 to 600 nm region.^4,45–50 There is lack of data for RI of hemoglobin solutions for concentrations close to that in the red blood cells (RBC), especially for the NIR region.

This study is focused on the determination of the RI of hemoglobin in the visible and NIR ranges at room temperature, aiming for further quantification dispersion of hemoglobin solutions. Measurements were carried out using the multiwavelength Abbe refractometer (Atago, Japan). The hemoglobin solutions of different concentrations obtained from human whole blood were investigated. The RI of hemoglobin solutions was measured for the wavelengths: 480, 486, 546, 589, 644, 656, 680, 930, 1100, 1300, and 1550 nm, which are characteristic for different lasers widely used in biomedicine. The specific increment of RI and Sellmeier coefficients for dispersion on hemoglobin concentration were calculated based on the experimental data.

2.

Methods and Materials

Hemoglobin obtained from human whole blood was used to prepare hemoglobin specimens. Whole blood was drawn from the human vein. Immediately after collecting blood into a test tube, heparin was added in it. The sample of blood from a healthy person was taken at the State Healthcare Organization “Saratov City Clinical Hospital No. 2 named after V. I. Razumovsky” with the permission of the volunteer. To separate blood into fractions, the centrifugation for 10 min at 2000 rpm and at room temperature was provided. This resulted in separation of blood plasma, leuko-platelet layer, and RBC suspension. To conduct hemolysis and preparation of hemoglobin solutions, RBC suspension was separated and placed in a vial for freezing in a freezer at a temperature of $-15°\mathrm{C}$ for 24 h.

Actual concentration of the basic hemoglobin solution was estimated by the spectral technique and amounted to $260\mathrm{g}/\mathrm{l}$. In the experiment, we measured the RI of three specimens taken from the same sample. The RI measurements for solutions of different concentrations obtained by diluting the basic solution of hemoglobin in saline solution were also provided.

At measurements, a sample layer on the working surface of the prism had a small thickness of about 20 to $30\mu \mathrm{m}$. The time of the full oxygenation (78.4% to 94.2%) of hemoglobin in such a layer is about 6 to 10 s.⁵¹ Therefore, hemoglobin is fully saturated with oxygen, and the process of oxygenation during measurements is expected to not affect the result.

Measurements were performed using the multiwavelength Abbe refractometer (Atago, Japan) (Fig. 1). The RI was measured for samples of hemoglobin obtained from human whole blood (65, 87, 173, and $260\mathrm{g}/\mathrm{l}$) on 11 wavelengths from 480 to 1550 nm. The temperature was 23°C.

Fig. 1

General view of the multiwavelength Abbe refractometer (Atago, Japan): 1, refractometer; 2,–power supply; 3, light source; 4, the eyepiece imager for measurements in the NIR region; 5, interference filter; and 6, sample.

Multiwavelength refractometer Abbe allows one to measure the RI in the wavelength range of 450 to 1550 nm with an accuracy of $\pm 0.0002$. The working principle of the refractometer technique is based on determining the critical angle of the total reflection, where the incident light waves are completely reflected with a 90-deg angle to the normal position. The incident light waves with angles greater than the critical angle will only experience reflection at the interface surface and no refraction will be observed. The total internal reflection method is applicable to measurement of the RI of biological media, which are characterized by high light scattering and absorption. The wavelength of the light source is determined by the selection of the particular interferential filter. Available interferential filters allowed for measurements on the wavelengths $480\pm 2$, $486\pm 2$, $546\pm 2$, $589\pm 2$, $644\pm 2$, and $656\pm 2\mathrm{nm}$, $680\pm 5$, $930\pm 6$, $1100\pm 26$, $1300\pm 25$, and $1550\pm 25\mathrm{nm}$. The calibration of the device by measuring RI of distilled water at a wavelength of 589 nm (the absorption band of sodium) was used at the beginning of each experiment. The average measurement error of the RI was $\pm 0.0003$.

To approximate the dispersion dependence of the RI of the hemoglobin solution, the Sellmeier formula was used

3.

Measurement Results

The optical density spectra of a solution of hemoglobin obtained from the whole blood by hemolysis are shown in Fig. 2. The graph shows that the wavelengths available for RI measurements, i.e., 480, 486, 546, 589, 644, and 656 nm, belong to different or the same absorption bands of hemoglobin with quite different absorption abilities. Therefore, we can expect different inclusion of anomalous dispersion in RI wavelength dependence at these wavelengths. Wavelength 546 nm is the closest to the isobestic point 544 nm, where the absorption of hemoglobin does not depend on the degree of oxygenation.⁵³

Fig. 2

The optical density spectrum of a solution of hemoglobin $260\mathrm{g}/\mathrm{l}$. By the vertical lines visible working wavelengths of Atago refractometer are shown.

Table 1 presents data for Atago refractometer measurements of RI for four different concentrations of hemoglobin, i.e., 65, 87, 173, and $260\mathrm{g}/\mathrm{l}$ at room temperature, 23°C.

Table 1

RI measured for four different concentrations of hemoglobin at room temperature 23°C. SD is shown in brackets.

It is well known that the RI of proteins is nonlinearly dependent on the wavelength.^4,45–50,54 Figure 3 shows the dispersion curves for hemoglobin solutions in the visible/NIR spectral range. The symbols are experimental data from Table 1, and the lines correspond to the fit of these data to the Sellmeier formula, Eq. (7). Table 2 presents data for the decomposition of the Sellmeier formula.

Fig. 3

The dispersion curves for hemoglobin solutions: the symbols are experimental data from Table 1 and the lines correspond to the fit of these data to the Sellmeier formula, Eq. (7).

Table 2

Coefficients of Sellmeier formula for hemoglobin solutions of different concentrations.

As it follows from Table 2, for all wavelengths and hemoglobin concentrations, measured RIs are well fit to the Sellmeier formula with correlation coefficient, $R^2$, equal or better than 0.993. Specifically, there is a linear relationship between the RI and hemoglobin concentration. The RI of the hemoglobin samples is also temperature-dependent, although the temperature effect on the RI is small when compared with the hemoglobin concentration effect. Figure 4 shows the dependence of the RI of human hemoglobin solution on hemoglobin concentration for the room temperature of 23°C. These data can be used to predict the hemoglobin concentration of the blood sample based on the knowledge of the RI and using the refraction increment provided. This dependence can be described by Eqs. (4) and (5).

Fig. 4

The dependence of the RI on the concentration of hemoglobin in solution for: (a) visible and (b) NIR ranges (black symbols, experimental data; red lines, approximation of these data).

Table 3 presents data for the RI of distilled water and the specific increment of RI for hemoglobin solutions obtained by hemolysis. Approximation of the dependence of the specific increment of the RI on the wavelength was performed using the software package OriginProLab. The best fit was achieved using

4.

Discussion

The results of the measurements revealed that there is a linear relationship between the RI and hemoglobin concentration. Table 4 summarizes data on hemoglobin RI available in the literature. The comparison of received data with the literature is presented.

Table 3

The distilled water RI nH2O and the specific increment dn/dC of RI for hemoglobin solutions obtained by hemolysis, for the room temperature 23°C. SD is shown in brackets.

Table 4

The experimental data for the real part of the RI of the hemoglobin solutions.

There is lack of data on the RI measurement of hemoglobin solutions for concentrations close to that in the RBC; specifically, data for the NIR region are practically absent. The RI of hemoglobin solution of $260\mathrm{g}/\mathrm{l}$, obtained from whole blood at room temperature (23°C) for the wavelength of 480 nm, was found to be equal to $1.3879\pm 0.0002$, for 589 nm to $1.3821\pm 0.0004$, for 1100 nm to $1.3690\pm 0.0006$, and for 1550 nm to $1.3598\pm 0.0002$. The concentration increment of RI of hemoglobin was found as $0.199\pm 0.006\mathrm{ml}/\mathrm{g}$ for the wavelength 480 nm, $0.192\pm 0.005\mathrm{ml}/\mathrm{g}$ for the wavelength 589 nm, $0.183\pm 0.005\mathrm{ml}/\mathrm{g}$ for the wavelength 930 nm, and $0.179\pm 0.004\mathrm{ml}/\mathrm{g}$ for the wavelength 1550 nm.

Freibel et al. also measured the RI of a hemoglobin solution of $287\mathrm{g}/\mathrm{l}$ obtained from whole blood. According to their measurements using the spectral method and the Fresnel formula, the RI was 1.409 for the wavelength 400 nm, 1.406 for the wavelength 589 nm, 1.404 for the wavelength 700 nm, and 1.400 for the wavelength 1100 nm.^55,56 The same scientific group received at the wavelength 633 nm the $\mathrm{RI}=1.3750$ for concentration $165\mathrm{g}/\mathrm{l}$ and the $\mathrm{RI}=1.3600$ for concentration $104\mathrm{g}/\mathrm{l}$. Jin et al.,³⁷ Park et al.,⁴¹ Zhernovaya et al.,⁴⁶ Yahya et al.,⁴⁸ and Deng et al.⁴⁷ used a solution obtained from dry hemoglobin for the study of refraction. Zhernovaya et al. measured the RI of oxygenated and deoxygenated hemoglobin of $140\mathrm{g}/\mathrm{l}$ by refractometer Abbe for nine wavelengths at a temperature of 20°C. For example, the values of RI were 1.361 for the wavelength 486 nm, 1.357 for the wavelength 589 nm, and 1.352 for the wavelength 706.5 nm.⁴⁶ Yahya et al. measured RI of oxygenated human hemoglobin $150\mathrm{g}/\mathrm{l}$ as 1.36481 for the wavelength 436 nm, 1.35724 for the wavelength 589 nm, and 1.35587 for the wavelength 657.2 nm.⁴⁸ Deng et al. measured RI of 50% oxyhemoglobin $320\mathrm{g}/\mathrm{l}$ by fiber spectrometer at a temperature of 20°C. RIs were 1.3775 for the wavelength 500 nm, 1.3684 for the wavelength 600 nm, and 1.3612 for the wavelength 700 nm.⁴⁷ Jin et al. determined RI of hemoglobin for concentration of $12.97\mathrm{mmol}/\mathrm{l}$ as 1.3871 for the wavelength 532 nm and 1.3800 for the wavelength 632 nm.³⁷ Park et al. measured the dispersion of Hb solutions, prepared from Hb protein powder, at three different concentrations: 0.05, 0.15, and $0.30\mathrm{g}/\mathrm{ml}$. For example, the RI for $0.15\mathrm{g}/\mathrm{ml}$ was 1.3687 at wavelength 560 nm.

Zhernovaya et al.,⁴⁶ Freibel et al.,^55,56 Yahya et al.,⁴⁸ and Park et al.⁴¹ also calculated the specific increment of RI (20°C), which was equal to 0.147, 0.2015, and $0.151\mathrm{ml}/\mathrm{g}$ for the wavelength 589 nm and $0.183\pm 0.003\mathrm{ml}/\mathrm{g}$ for the wavelength range of 440 to 700 nm, respectively. In this study, the RI-specific increment of hemoglobin was found as $0.192\pm 0.005\mathrm{ml}/\mathrm{g}$ for the wavelength 589 nm and temperature at 23°C.

The discrepancy between literature and our data may be caused by the differences in the sample preparation protocols since the human hemoglobin may differ in content of various forms of hemoglobin of donor’s blood. The specificities of experimental setups also may play a role.

In Fig. 5, it is seen that the RI-specific increment of a solution of human hemoglobin decreases with the wavelength. This could be explained by the dispersion theory of multicomponent materials and caused by strong absorption bands of hemoglobin and water in UV, hemoglobin in the visible, and water in the NIR. The dependence of the specific RI increment $\alpha$ of hemoglobin solution on the wavelength is in a good agreement with the literature data given by Friebel et al. for whole blood using an integrating sphere spectrometer technique and by Jung et al. for an Hb solution in intact individual RBC cytoplasm.^43,55

Fig. 5

The dependence of the specific RI increment $\alpha$ of hemoglobin solution on the wavelength (black symbols, estimated data, red lines, approximation of data).

As the experimental data for the real part of RI of hemoglobin solutions differ for measurements done by alternative techniques (see Table 4), it is important for researchers to use a specific tool, such as the Kramers–Kronig relations, to analyze experimental results for discrete wavelengths and to derive the RI real part theoretically from the measurements of its imaginary part.^{4,24,49,50,53} In addition to providing quantification of the real part of the RI of hemoglobin at selected wavelengths, where no direct measurements are available, they are independent of hemoglobin concentration and thus can augment the model functions for the RI found by alternative methods.⁴ Such analysis was done early in Ref. 4 for the measurements of the real part of the RI of hemoglobin solutions at eight discrete wavelengths from 400 to 700 nm, and we received encouraging results. In this work, measurements were done in a wider wavelength range from 480 to 1550 nm at 11 discrete wavelengths, which will allow us to make a more precise Kramers–Kronig analysis, results of which we are planning to publish in the near future.

5.

Conclusion

The RI of hemoglobin solutions has been measured for visible and NIR ranges using a commercially available multiwavelength Atago refractometer. Data were approximated by the Sellmeier formula with a high accuracy in a whole wavelength range. The absolute value of the initial index of refraction $n_0$ and the specific refraction increment $\mathrm{d}n/\mathrm{d}C$ on hemoglobin concentration $C$ for room temperature at 23°C were derived from these measurements for each wavelength from 480 to 1550 nm. The data obtained are in good agreement with available data in the literature and supplementary to already measured values as done for new wavelengths, which allowed for evaluation of the specific refraction increment $\mathrm{d}n/\mathrm{d}C$ in a wide spectral range.