1.

Introduction

It is known that the optical parameters ${\mu }_a$ , ${\mu }_s$ , and $g$ of blood depend on various physiological parameters. The frequently investigated parameters are oxygen saturation and hematocrit.^{1, 2, 3, 4, 5, 6} These parameters change, among other things, the concentration of the red blood cells or the absorption behavior of the hemoglobin. If these two main parameters remain constant, the parameters cell shape and volume of physiological red blood cells can cause changes in the optical properties.

The variations in osmolarity not only change the shape and the volume of the cells but also the inner cell hemoglobin concentration. Due to an increase in the hemoglobin concentration, the complex refractive index increases.⁷ A hyperosmolar medium causes a shrinking of the cells due to water outflow, resulting in characteristically shaped cells called spinocytes. In low-osmolarity media, the cells start to swell by diffusion of water into the cell, leading to spherically formed cells, which become full to the point of bursting.

Osmolarity changes can be caused as the result of diagnostic measurements in extracorporal blood circulations and during in vitro investigations on blood, e.g., immersion optical clearing.^{8, 9, 10} Data concerning the influence of osmolarity on the optical properties are not readily available.

In this study, the influence of the osmolarity was investigated on the optical parameters of red blood cells in physio-logical saline solution. Using the integrating sphere technique combined with an inverse Monte Carlo simulation¹¹ (iMCS), three optical parameters (absorption coefficient ${\mu }_a$ , scattering coefficient ${\mu }_s$ , and anisotropy factor $g$ ) of undiluted, flowing red blood cells (RBCs) could be determined, dependent on osmolarity in the spectral range of $250\text{to}1100\mathrm{nm}$ , including the spectral areas of high hemoglobin absorption.

2.

Materials and Methods

3.

Results

The optical properties of red blood cells depend on the biological variability of the size and shape of the RBCs and the hemoglobin (Hb) content. To exclude the optical influence of this biological variability of RBC samples with identical Hcts taken from different donors, all intrinsic optical parameters given in this paper are relative values related to those determined at an osmolarity of $300\mathrm{mosmol}∕\mathrm{L}$ .

The investigated RBC samples with RBC concentration (RBCc) of $5\times {10}^6∕\mu \mathrm{l}$ had an Hct of 42.1%, a mean corpuscular volume (MCV) of $89.3\mu {\mathrm{m}}^3$ , and a mean corpuscular hemoglobin concentration (MCHC) of $34.4\mathrm{g}∕\mathrm{dL}$ . An increase in osmolarity to $400\mathrm{mosmol}∕\mathrm{L}$ resulted, via cell shrinking, in a reduced Hct of 37%; a decrease to $225\mathrm{mosmol}∕\mathrm{L}$ resulted, via cell swelling, in an increased Hct of 45.5%. The MCV can be calculated by Hct $[\%]=\mathrm{MCV}\times \mathrm{RBCc}\times 100\%$ . Changes in cell volume lead to a reciprocal change in hemoglobin concentration within the cell (MCHC) and therefore also in the refractive index.¹⁴ The changes in the relative cell volume (MCV) and the refractive index with different osmolarities are shown in Fig. 1 .

Fig. 1

(a) Osmolarity dependent relative mean cell volume (MCV̱rel) measured and calculated according to the empirical formula of Zhestkov ¹⁰ (circles), and (b) the mean refractive index $\left(n\right)$ at $600\mathrm{nm}$ of the RBC dependent on osmolarity, calculated according to Ref. 14.

The measured MCV changes are in agreement with calculated values, based on a formula presented by Zhestkov ¹⁰ and measurements of Roggan ⁵ The swelling of the cells resulted in a higher MCV and a lower refractive index and vice versa. The refractive index was estimated using the formulas of Friebel and Meinke.¹⁴ At $600\mathrm{nm}$ , for example, a refractive index of $n_{300}=1.423\pm 0.003$ can be calculated under isotonic conditions $(300\mathrm{mosmol}∕\mathrm{L})$ . According to the reciprocal changes in the MCHC the refractive index decreases to $n_{225}=1.416\pm 0.003$ at $225\mathrm{mosmol}∕\mathrm{L}$ and increases to $n_{400}=1.436\pm 0.003$ at $400\mathrm{mosmol}∕\mathrm{L}$ . For comparison, effects on the absorption and scattering cross sections and the anisotropy factor were estimated from these refractive index changes via Mie theory for spheres of the same volume, which is used as a simplified RBC model. In special cases, Mie theory can also be used^{4, 11} to calculate absorption and scattering cross section of RBCs. It is known from recent investigations that calculation of the absorption coefficient is possible in the wavelength range $600\text{to}1100\mathrm{nm}$ , where ${\mu }_a$ is low, ${\mu }_s$ may only be estimated for highly diluted blood $(⪡\mathrm{Hct}1\%)$ , and the anisotropy factor can only be predicted for diluted blood $(\mathrm{Hct}\approx 1\%)$ in the spectral range of low absorption. Nevertheless, Mie theory may be useful for calculating effects on the optical parameters induced by small relative volume and refractive index changes. These expected relative changes of the optical parameters at 225 and $400\mathrm{mosmol}∕\mathrm{L}$ relative to $300\mathrm{mosmol}∕\mathrm{L}$ were determined and averaged over all 171 wavelengths in the range $250\text{to}1100\mathrm{nm}$ .

3.1.

Absorption Coefficient

The relative absorption spectra show no significant dependence on wavelength. Therefore, mean values over the whole spectrum could be established. The influence of the osmolarity on the relative absorption coefficient is shown in Fig. 2 .

Fig. 2

Mean values of ${\mu }_a\text{\_}\mathrm{rel}$ of the spectral range $250\text{to}1100\mathrm{nm}$ of RBCs in saline solution dependent on osmolarity and values for 225 and $400\mathrm{mosmol}∕\mathrm{L}$ calculated by Mie theory relative to $300\mathrm{mosmol}∕\mathrm{L}$ .

The absorption coefficient increases with increasing osmolarity. This means shrinking of the cells increases and swelling decreases ${\mu }_a$ . At $225\mathrm{mosmol}∕\mathrm{L}$ , the value of ${\mu }_a$ is $1.95\pm 0.01$ , and at $400\mathrm{mosmol}∕\mathrm{L}$ , it is $1.05\pm 0.02$ . The values calculated with Mie theory show a comparable increase to $1.04\pm 0.04$ (the error describes the statistical distribution of cell volume and refractive index within the cell) at $400\mathrm{mosmol}∕\mathrm{L}$ , whereas the decrease of the osmolarity to $225\mathrm{mosmol}∕\mathrm{L}$ does not lead to a significant change with $1.00\pm 0.04$ .

3.2.

Scattering Coefficient

As observed for the absorption, ${\mu }_s\text{\_}\mathrm{rel}$ of RBC solutions show no significant dependence on wavelength but are significantly influenced by changes in osmolarity. Figure 3 shows the mean relative values of ${\mu }_s$ dependent on osmolarity.

Fig. 3

Mean values of ${\mu }_s\text{\_}\mathrm{rel}$ in the spectral range $250\text{to}1100\mathrm{nm}$ of RBCs in saline solution dependent on osmolarity and values for 225 and $400\mathrm{mosmol}∕\mathrm{L}$ calculated by Mie theory relative to $300\mathrm{mosmol}∕\mathrm{L}$ .

As found for ${\mu }_a\text{\_}\mathrm{rel}$ , the relative scattering coefficient also increases with increasing osmolarity with values of $0.87\pm 0.04$ at $225\mathrm{mosmol}∕\mathrm{L}$ and $1.11\pm 0.04$ at $400\mathrm{mosmol}∕\mathrm{L}$ . Induced by the change in volume and refractive index, Mie theory shows an inverse change in the scattering cross section of 1.1 at $225\mathrm{mosmol}∕\mathrm{L}$ and 0.9 at $400\mathrm{mosmol}∕\mathrm{L}$ .

3.3.

Anisotropy

In contrast to ${\mu }_a\text{\_}\mathrm{rel}$ and ${\mu }_s\text{\_}\mathrm{rel}$ , $g\text{\_}\mathrm{rel}$ shows distinct wavelength dependence below $600\mathrm{nm}$ . Figure 4 shows the relative values of the anisotropy factor $g$ of RBCs suspended in saline solution for different osmolarity values, dependent on wavelength. Therefore, a mean $g\text{\_}\mathrm{rel}$ only averaged over the spectral range $600\text{to}1100\mathrm{nm}$ was calculated for each osmolarity. In addition, the osmolarity dependence at $415\mathrm{nm}$ was determined to characterize the wavelength dependence in the range of high absorption. The averaged relative changes of $g$ are depicted versus the osmolarity in Fig. 5 , including $g\text{\_}\mathrm{rel}$ at $415\mathrm{nm}$ . The decrease with increasing osmolarity is more pronounced in the high absorption region of hemoglobin and has its maximum at $415\mathrm{nm}$ .

Fig. 4

Mean values of $g\text{\_}\mathrm{rel}$ dependent on wavelength for six different osmolarity values (relative to $300\mathrm{mosmol}∕\mathrm{L}$ ).

Fig. 5

Mean values of $g\text{\_}\mathrm{rel}$ at $415\mathrm{nm}$ and of the spectral range $600\text{to}1100\mathrm{nm}$ of RBCs in saline solution dependent on osmolarity and values for 225 and $400\mathrm{mosmol}∕\mathrm{L}$ calculated by Mie theory relative to $300\mathrm{mosmol}∕\mathrm{L}$ .

In the wavelength range above $600\mathrm{nm}$ , the mean relative $g$ value is linearly dependent on osmolarity. At $225\mathrm{mosmol}∕\mathrm{L}$ , $g\text{\_}\mathrm{rel}$ has the value $1.007\pm 0.001$ , and at $400\mathrm{mosmol}∕\mathrm{L}$ , only $0.991\pm 0.002$ . This is within the error tolerance in the range of the values calculated with the Mie theory.

As already could be observed in Fig. 4, the influence of the osmolarity on $g$ is significantly more pronounced at $415\mathrm{nm}$ , where the hemoglobin absorption is high than in the wavelength region above $600\mathrm{nm}$ where there is low absorption. The $g\text{\_}\mathrm{rel}$ values for $415\mathrm{nm}$ results in $1.080\pm \mathrm{0,007}$ at $225\mathrm{mosmol}∕\mathrm{L}$ and $0.950\pm 0.008$ at $400\mathrm{mosmol}∕\mathrm{L}$ .

3.4.

Effective Scattering Coefficient

Corresponding to the anisotropy factor, ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ shows slightly different behavior below and above $600\mathrm{nm}$ . Therefore mean values of ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ in the wavelength range $600\text{to}1100\mathrm{nm}$ were calculated for the osmolarity dependence as well as for $415\mathrm{nm}$ to characterize the wavelength dependence in the range of high absorption (Fig. 6 ).

Fig. 6

Mean values of ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ of RBCs in saline solution in the spectral range $600\text{to}1100\mathrm{nm}$ and at $415\mathrm{nm}$ dependent on osmolarity and values for 225 and $400\mathrm{mosmol}∕\mathrm{L}$ calculated by Mie theory relative to $300\mathrm{mosmol}∕\mathrm{L}$ .

In the spectral range $600\text{to}1100\mathrm{nm}$ ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ increases linear with increasing osmolarity. At $400\mathrm{mosmol}∕\mathrm{L}$ ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ is $1.39\pm 0.06$ , twice as high as at $225\mathrm{mosmol}∕\mathrm{L}$ with $0.65\pm 0.06$ . At $415\mathrm{nm}$ , ${\mu }_s^{\prime }\text{\_}\mathrm{rel}$ shows a lower increase with values of $0.73\pm 0.06$ at $225\mathrm{mosmol}∕\mathrm{L}$ and $1.27\pm 0.05$ at $400\mathrm{mosmol}∕\mathrm{L}$ . The Mie theory agrees with an increase with the osmolarity but the extent of the increase is only half of that in the range $600\text{to}1100\mathrm{nm}$ with values of $0.85\pm 0.03$ at $225\mathrm{mosmol}∕\mathrm{L}$ and $1.18\pm 0.03$ at $400\mathrm{mosmol}∕\mathrm{L}$ .

4.

Discussion

All optical parameters are influenced by osmolarity changes. Moreover, dependence was found to exist between the osmolarity-dependent effects and the Hb absorption. An osmotically induced decrease in the cell volume by approx. 10% with an identical increase in Hb concentration within the cell leads to an increase in the absorption coefficient by approx. 5% and vice versa. This is, in principle, in agreement with the results of Roggan, ⁵ who also found a ${\mu }_a$ increase with increasing osmolarity at $633\mathrm{nm}$ and Hct 7.5% but with a higher steepness. This may be explained by the very low Hb absorption at this wavelength and the relatively high blood dilution. At a constant RBCc, the absorption coefficient, and therefore the absorption cross section, increases continuously with the osmolarity, i.e., cell shrinking leads to an increase of ${\mu }_a$ , cell swelling to a decrease. According to this, the absorption cross section is mainly determined by the Hb concentration, which changes inversely to the cell volume and determines the complex refractive index within the cell, whereas the geometric cross section of the cells is of minor importance. This is partly confirmed by Mie theory, predicting a comparable increase of the absorption cross section at the increasing imaginary and real parts of the refractive index within the cell by decreasing volume. However, the Mie theory does not show a decrease of the absorption cross section for a decreasing refractive index.

Averaged over the investigated spectral range, the increase in the refractive index induced by osmotic cell shrinking leads to an increase of the scattering coefficient for increasing osmolarity, in spite of the decreased geometric cross section and vice versa. In principle, this dependence is in agreement with the theoretical results of Bashkatov ⁸ using Mie theory and quantifier of the scattering cross section by the often used^{9, 15, 16} “packing factor” 1-(Hct/100%). He showed that increasing the osmolarity from $300\text{to}580\mathrm{mosmol}∕\mathrm{L}$ resulted in an increase of ${\mu }_s$ for seven investigated wavelengths in the range $415\text{to}900\mathrm{nm}$ , with the exception of $415\mathrm{nm}$ , where ${\mu }_s$ decreased slightly. A linear interpolation of the relative ${\mu }_s$ increase at an osmolarity increase from $300\text{to}400\mathrm{mosmol}∕\mathrm{L}$ averaged over all seven wavelengths resulted in a relative ${\mu }_s$ increase of approximately 3%. This indicates an attenuated dependence and is in contradiction to the presented Mie calculations based on our own refractive index measurements.^{7, 14} Following this theory, the scattering cross section of a sphere is determined mainly by the sphere size and the difference in the refractive indices and predicts a decrease of the scattering cross section with increasing osmolarity and vice versa. As shown in experiments for the hematocrit dependence of the scattering coefficient,^{4, 11} the scattering cross section per cell is not constant at increasing Hct, but continuously decreasing. The cause of this phenomenon is the decreasing distance between the cells, leading to an increasing superposition and interference of the single scattering events¹⁷ (“collective scattering”) The osmolarity-induced change in Hct influences analogously the distance between the cells, not by changing the cell concentration, but the cell volume.

Based on these data, an interpolation of the relative scattering cross section per cell for the osmotically changed Hct values 37 and 45.5% leads, without consideration of the refractive index change within the cell, to a scattering cross section decrease to 0.92 at $225\mathrm{mosmol}∕\mathrm{L}$ and an increase to 1.12 at $400\mathrm{mosmol}∕\mathrm{L}$ . The correction of the calculated relative ${\mu }_s$ changes with values of $1.01\pm 0.09$ at $225\mathrm{mosmol}∕\mathrm{L}$ and $1.02\pm 0.1$ at $400\mathrm{mosmol}∕\mathrm{L}$ leads to an almost complete compensation of the ${\mu }_s$ changes predicted by Mie theory without correction. Within the error tolerances, the corrected values are comparable to the results of Bashkatov but still disagree with the experimentally determined distinct increase of ${\mu }_s$ with increasing osmolarity. Therefore, the change of the cell shape must be considered, which is not considered by the Mie theory. It is possibly the change in cell shape from the sphere via the normal discoid shape to the star-shaped spinocyte shape that leads to an additional increase in the scattering cross section.

The inverse dependence of ${\mu }_s$ on osmolarity presented by Roggan ⁵ can be explained by the use of another scattering phase function in the MCS used, since in combination with the lower increase of $g$ with osmolarity, the changes in the resulting effective scattering coefficient ${\mu }_s^{\prime }$ are comparable to the osmotically induced changes already presented.

In spectral ranges where the absorption is low, the anisotropy factor seems to be mainly determined by the difference between the real parts of the refractive index within the cell and in the surrounding medium. An osmolarity-induced decrease in volume by approx. 12 to 13% leads¹¹ via refractive index increase to a decrease in $g$ of approx. 0.01 at wavelengths $>600\mathrm{nm}$ . In principle, this is in agreement with the theoretical results of Bashkatov, ⁸ who also found that $g$ decreased with increasing osmolarity from $300\text{to}580\mathrm{mosmol}∕\mathrm{L}$ , but by much lower relative values between 0.001 and 0.002. Similar to these values, our own calculated theoretical values of $0.005\pm 0.003$ at $400\mathrm{mosmol}∕\mathrm{L}$ in the wavelength range above $600\mathrm{nm}$ are lower than the measured values but with overlapping error tolerances. However, Mie theory fails to describe the strong osmolarity-dependent decrease of $g$ at $415\mathrm{nm}$ . This osmolarity dependence seems to increase significantly with the absorption. Induced by this phenomenon of swelling of the RBCs to a spherical shape, the marked decrease of $g$ with increasing absorption, which was shown to be not explainable by Mie theory,^{4, 11} will be diminished. Possibly, this absorption-dependent decrease of $g$ is connected to the nonspherical shape of the erythrocyte.

The relative changes in the effective scattering coefficient for the wavelength range $250\text{to}1100\mathrm{nm}$ are qualitatively in agreement with the predictions of Mie theory. However, the ${\mu }_s^{\prime }$ increase when the osmolarity increases is underestimated by Mie theory. When correcting the ${\mu }_s^{\prime }$ values with the Hct-dependent scattering cross section, as was already done for the scattering coefficient, the predicted relative osmolarity-induced changes in ${\mu }_s^{\prime }$ are with values of 0.75 at $250\mathrm{mosmol}∕\mathrm{L}$ and 1.3 at $400\mathrm{mosmol}∕\mathrm{L}$ within the error tolerances of the measured values. This may be also connected with the changes in the geometric shape. According to this, the ideal spherical shape may result in a lower effective scattering effect compared to the discoid erythrocyte shape; deformation in the direction of a spinocyte would increase the effective scattering effect.

5.

Conclusion

The investigation on osmolarity-dependent optical effects of RBCs showed that changes in cell volume and shape and the inversely related Hb concentration lead to significant changes in all the optical parameters. The maximal absorption and scattering cross sections were found for shrunken RBCs. For the anisotropy as well as for the effective scattering coefficient it was found that the osmolarity-dependent effects are different in wavelength ranges of high and low Hb absorption.

Apart from concentration- and absorption-induced changes in optical parameters due to Hct and oxygen saturation changes, the optical parameters can be drastically influenced by cell volume and cell shape changes due to osmolarity variations. Therefore, osmolarity-induced changes must be considered when optical measurements for the determination of blood properties are used.¹⁸