2.1.

Blood Cell Preparation

In order to measure native RBCs in saline solution, three samples of fresh human erythrocytes from a healthy blood donor were centrifuged three times $\left(250\mathrm{g}\right)$ and washed with isotonic phosphate buffer ( $300\mathrm{mosmol}∕\mathrm{L}$ , pH 7.4) to remove the blood plasma and free hemoglobin. This procedure does not influence the biological function of the RBCs but inhibits the formation of aggregates. The hematocrit was determined using a red blood cell counter (Micros 60 OT 18, ABX Diagnostics, Montpellier, France). To investigate the influence of the oxygen saturation, the blood sample was adjusted to a Hct of 32.2% and the sample was divided in half. One part was equilibrated with a gas mixture of 96% ${\mathrm{O}}_2$ and 4% $\mathrm{C}{\mathrm{O}}_2$ to keep the sample in the fully oxygenated state; the other part was equilibrated with a gas mixture of 96% ${\mathrm{N}}_2$ and 4% $\mathrm{C}{\mathrm{O}}_2$ , after addition of 0.3% sodium dithionite $\left({\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4\right)$ to ensure complete deoxygenation.⁹ The oxygen saturation was determined with a blood gas analyzer (OPTI Care, AVL Medizintechnik GmbH, Bad Homburg). A miniaturized blood circulation setup was used with a roller pump (Sorin Group, Germany) and a blood cell reservoir, which was constantly aerated with the gas mixture. The temperature was kept constant at $20°\mathrm{C}$ . The red blood cell suspension was gently stirred to avoid uncontrolled sedimentation or cell aggregation within the reservoir. The cell suspension was kept flowing by a customized turbulence-free cuvette with laminar flow and a sample thickness of $116\mu \mathrm{m}$ . A cuvette thickness of approximately $100\mu \mathrm{m}$ ensures multiple scattering and significant light transmission as well as avoiding obstruction phenomena. The flow was adjusted for each sample to keep constant wall shear rates of $600{\mathrm{s}}^{-1}$ at the inner cuvette surfaces, avoiding aggregation or sedimentation at flow stop and shear-rate-induced deformation of the cells at high shear rates above $1000{\mathrm{s}}^{-1}$ (Refs. 11, 14).

2.2.

Spectral Measurements

The diffuse reflectance $R_d$ , the total transmission $T_t$ , and the diffuse transmission $T_d$ ( $=T_t-\text{transmission}$ within an aperture angle of $5.3\mathrm{deg}$ ) of all blood cell samples were measured using an integrating sphere spectrometer (Lambda 900, Perkin Elmer, Rodgau-Jügesheim, Germany) in the spectral range of $250\text{to}2000\mathrm{nm}$ at $5\text{-}\mathrm{nm}$ intervals in the range $250\text{to}1200\mathrm{nm}$ and at $10\text{-}\mathrm{nm}$ intervals above $1200\mathrm{nm}$ . The optical arrangement of a sample and a reference beam compensates for light intensity shifts and changes in the inner sphere reflectivity by positioning the glass cuvette in front of or behind the sphere. For the measurement of $T_t$ , the reflectance port of the sphere is closed with a diffuse reflecting Spectralon standard. $T_d$ is measured after the standard is removed so that nonscattered and scattered transmitted light leaves the sphere within an angle of $5.3\mathrm{deg}$ . $R_d$ is measured relative to a certified reflectance standard, and the Fresnel reflectance of the cuvette glass leaves the sphere. The experimental setup allowed measurement of the macroscopic radiation distribution with an error of less than 0.1% and has already been described by Friebel ⁴ A special inverse Monte Carlo simulation (iMCS) program was used, including forward Monte Carlo simulations to calculate the parameters ${\mu }_a$ , ${\mu }_s$ , and $g$ iteratively on the basis of a given phase function and the measured values for reflection and transmission. It considers all kinds of radiation losses by simulating the exact geometry of the illuminating light beam and of the sample, the cuvette, and the integrating sphere, including all diaphragms and apertures. As starting values, the parameters ${\mu }_a$ , ${\mu }_s$ , and $g$ were estimated from the Kubelka-Munk theory, and the approximation to the measured values was carried out by calculating a gradient matrix.⁴ Hct-dependent effective phase functions for RBCs flowing with a shear rate of $600{\mathrm{s}}^{-1}$ were evaluated previously using the double integrating sphere technique.⁴ The iMCS was carried out using the Reynolds-McCormick phase¹⁵ function with $\alpha =1.7$ for Hct 33.2%. An error threshold of 0.1%, i.e., the difference between measured and simulated macroscopic radiation distribution, was used for the calculation of the intrinsic optical parameters of the red blood cells. A total of three independent measurement series were carried out for all three samples, and independently simulated, using ${10}^7\text{photons}$ for each simulation. Due to the strong interindividual differences of RBCs, standard data can be obtained only by taking the mean values of many different samples. In order to exclude the optical influence due to this biological variability of the RBCs, all measured changes in the optical properties induced by reducing the oxygen saturation in the wavelength range $250\text{to}1100\mathrm{nm}$ were calculated as relative values related to those determined at 100% oxygen saturation. The absolute values were obtained by multiplication with the averaged parameters of a standard RBC suspension with the same Hct 33.2% (Ref. 12). As standard data are available only in the spectral range $250\text{to}1100\mathrm{nm}$ , the optical parameters determined in this experiment for the wavelength range $1100\text{to}2000\mathrm{nm}$ were linearly adapted to the standardized data in the range $250\text{to}1100\mathrm{nm}$ to reach a smooth junction in the region of $1100\mathrm{nm}$ .

3.1.

Absorption

Figure 1 shows the absorption spectrum of red blood cells of Hct 33.2% with an oxygen saturation of 100% and 0% in the wavelength range $250\text{to}2000\mathrm{nm}$ . For comparison with data from the literature, the absorption spectra of pure water and of hemoglobin solutions extrapolated to a hemoglobin concentration of $96.5\mathrm{g}∕\mathrm{L}$ (Ref. 16), are also depicted in the wavelength range $250\text{to}1100\mathrm{nm}$ .¹⁷ At complete oxygenation, the absorption spectrum shows the characteristic peaks at $415\mathrm{nm}$ $\left(87{\mathrm{mm}}^{-1}\right)$ and the double peak at $540∕575\mathrm{nm}$ with values of $20.8{\mathrm{mm}}^{-1}$ . The extrapolated hemoglobin curve is between 250 and $1000\mathrm{nm}$ , within the error tolerance identical to the RBC absorption spectrum, with the exception of the maximum of $174{\mathrm{mm}}^{-1}$ at $415\mathrm{nm}$ . This difference results from the phenomenon of absorption flattening and can be explained by the Sieve effect.¹⁸ Above $1100\mathrm{nm}$ , the ${\mu }_a$ curve increasingly approximates that of water absorption. Above $1360\mathrm{nm}$ , the RBC absorption follows exactly the shape of the water curve but with values 20 to 30% below the water absorption values. This can be explained by the absence of significant hemoglobin absorption in this spectral area leading to a ${\mu }_a$ decrease due to the reduced water content in the cells as a result of the replacement by the hemoglobin molecules. The curve of the deoxygenated sample shows characteristic changes in the absorption behavior with a wavelength shift of the maximum peak of $117{\mathrm{mm}}^{-1}\text{to}430\mathrm{nm}$ and a unique peak at $550\mathrm{nm}$ $\left(19.2{\mathrm{mm}}^{-1}\right)$ . This result also corresponds to the absorption curve of deoxygenated hemoglobin from the literature, taking into account that the Sieve effect induces a lower absorption of the red blood cell suspension compared to the hemoglobin solution with $195{\mathrm{mm}}^{-1}$ at $430\mathrm{nm}$ . In the spectral range above $1150\mathrm{nm}$ , ${\mu }_a$ is independent of the hemoglobin oxygen saturation.

Fig. 1

${\mu }_a$ of RBCs in saline solution with a Hct 33.2% dependent on wavelength with an oxygen saturation of 100% and 0% compared with a hemoglobin solution with a corresponding hemoglobin concentration of $96.5\mathrm{g}∕\mathrm{dL}$ .

3.2.

Scattering

Figure 2 shows the spectrum of the scattering coefficient ${\mu }_s$ of red blood cells of Hct 33.2% with an oxygen saturation of 100% and 0% in the wavelength range $250\text{to}2000\mathrm{nm}$ . In the spectral range up to $600\mathrm{nm}$ , the ${\mu }_s$ spectrum shows the characteristic decreases correlated with the absorption peaks at $415\mathrm{nm}$ and $540∕575\mathrm{nm}$ as described earlier.⁴ According to the phenomenon of the absorption-induced decrease in $\mu _s{}_{,}$ the curve of completely deoxygenated RBCs shows the corresponding changes. The wavelength of the local minimum shifts from $415\mathrm{nm}\text{to}430\mathrm{nm}$ , and the double peak at $540∕575$ is replaced by the single peak at $550\mathrm{nm}$ . After reaching the maximum in the region of $600\mathrm{nm}$ , with ${\mu }_s$ values between 83 and $88{\mathrm{mm}}^{-1}$ , ${\mu }_s$ decreases continuously with increasing wavelength to values of about $30{\mathrm{mm}}^{-1}$ at $2000\mathrm{nm}$ , independent of the oxygen saturation. This decrease is with ${\lambda }^{-0.93}$ and near to the theoretically expected value of ${\lambda }^{-1}$ according to Mie theory when the sphere size is large compared to the wavelength.¹⁹

Fig. 2

${\mu }_s$ of RBCs in saline solution with Hct 33.2% dependent on wavelength with an oxygen saturation of 100% and 0%.

3.3.

Anisotropy

Figure 3 shows the values of the anisotropy factor $g$ of RBCs suspended in saline solution for two different oxygen saturation states, dependent on wavelength. The anisotropy factor follows the absorption spectrum inversely with the distinct minimum of 0.72 at $415\mathrm{nm}$ at an oxygen saturation of 100%, as described earlier.⁴ In the completely deoxygenated state, the minimum shifts to $430\mathrm{nm}$ . The local absorption minimum in the oxygenated state at $370\mathrm{nm}$ results in a relative $g$ maximum, whereas this $g$ maximum disappears as expected in the deoxygenated state. The double minimum at $540∕575\mathrm{nm}$ in the oxygenated state turns into a single minimum at $550\mathrm{nm}$ with complete deoxygenation. Above $600\mathrm{nm}$ , where $g$ is at the maximum level of 0.977, the $g$ spectrum of the oxygenated RBCs and the deoxygenated RBCs are equal. The value of $g$ decreases continuously to about 0.96 at $1800\mathrm{nm}$ , with the exception of a slight minimum at $1480\mathrm{nm}$ and a distinct local minimum at $1900\mathrm{nm}$ with a value of 0.87. In contrast to the scattering parameter ${\mu }_s$ , $g$ appears to be influenced not only by the hemoglobin absorption in the wavelength range below $600\mathrm{nm}$ , i.e., absorption within the scattering cells, but also by the absorption maxima of water in the region of $1480\mathrm{nm}$ and $1900\mathrm{nm}$ , i.e., absorption within the medium and a reduced absorption within the scatterer.

Fig. 3

$g$ of RBCs in saline solution with Hct 33.2% dependent on wavelength with an oxygen saturation of 100% and 0%.

3.4.

Effective Scattering Coefficient

Figure 4 gives the calculated values of the effective scattering coefficient ${\mu }_s^{\prime }={\mu }_s(1-g)$ for both oxygen saturation states in the wavelength range $250\text{to}2000\mathrm{nm}$ . If compared to the anisotropy factor, ${\mu }_s^{\prime }$ shows inverse spectra for both 100% and 0% oxygen saturation, which reflects the absorption spectrum. The maximum for the deoxygenated state is $13.9{\mathrm{mm}}^{-1}$ at $250\mathrm{nm}$ in the observed spectral range. The other distinct maximum is $8.3{\mathrm{mm}}^{-1}$ at $380\mathrm{nm}$ . At $530\mathrm{nm}$ , the characteristic relative single maximum is about $3{\mathrm{mm}}^{-1}$ . At complete oxygen saturation, the respective relative maxima are $12.5{\mathrm{mm}}^{-1}$ at $250\mathrm{nm}$ , $11.5{\mathrm{mm}}^{-1}$ at $360\mathrm{nm}$ , and the double peak at $530∕575\mathrm{nm}$ with values in the region of $3{\mathrm{mm}}^{-1}$ . Above $600\mathrm{nm}$ , ${\mu }_s^{\prime }$ is in the range of $1.8{\mathrm{mm}}^{-1}$ and decreases continuously and independently of oxygen saturation to values of about $1.0{\mathrm{mm}}^{-1}$ at $1880\mathrm{nm}$ . At $1950\mathrm{nm}$ , ${\mu }_s^{\prime }$ shows the water-absorption-induced maximum with values of $3.3{\mathrm{mm}}^{-1}$ . Corresponding to the minimum value of $g$ at $1480\mathrm{nm}$ , a local maximum is visible but not significant.

Fig. 4

${\mu }_s^{\prime }$ of RBCs in saline solution with Hct 33.2% dependent on wavelength with an oxygen saturation of 100% and 0%.

4.1.

Oxygenation-Induced Effects

It could be shown that differences in the oxygen saturation induce changes not only in absorption but also in the optical scattering parameters ${\mu }_s$ , $g$ and ${\mu }_s^{\prime }$ . This is due to the characteristic change in the absorption behavior of hemoglobin. As the hemoglobin absorption is invariant against the oxygen saturation between 1300 and $2000\mathrm{nm}$ but exhibits strong saturation dependence in the range $250\text{to}600\mathrm{nm}$ , the induced changes of the scattering parameter ${\mu }_s$ occur mainly between 250 and $1100\mathrm{nm}$ , whereas the saturation-induced changes of $g$ and ${\mu }_s^{\prime }$ occur only between 250 and $600\mathrm{nm}$ .

The strongest oxygen saturation dependence of $g$ , in relation to the oxygenated state, is at wavelengths $250\mathrm{nm}$ and $375\mathrm{nm}$ , with a decrease of 4.5%, and in the range $410\text{to}430\mathrm{nm}$ , with a maximal decrease of 12%. Due to changes in saturation, the maximum change in ${\mu }_s$ is 15% at $400\mathrm{nm}$ and 5% at $570\mathrm{nm}$ . In the range $700\text{to}850\mathrm{nm}$ , ${\mu }_s$ decreases by about 2%. Above $750\text{to}800\mathrm{nm}$ , the induced changes in ${\mu }_s$ are not significant. Apart from absorption, ${\mu }_s^{\prime }$ shows the strongest oxygen dependence at the same wavelength regions as $g$ . The maximum change in ${\mu }_s^{\prime }$ of about 35% is at $375\mathrm{nm}$ , up to 25% in the range $410\text{to}430\mathrm{nm}$ and 15% at $575\mathrm{nm}$ At $250\mathrm{nm},$ ${\mu }_s^{\prime }$ increases by 10%, which means that significant changes have to be considered when the scattering behaviour of RBCs is investigated and there are changes in the oxygen saturation.

The results partly contradict earlier results published by our group⁹ because the scattering has now been shown to be influenced by the absorption properties. This has been shown using a commercially available spectrometer, which offers a much higher degree of accuracy and considerably shorter measurement times, leading to a reduction in the influence of hemolysis-induced optical effects.

These results are partly in agreement with the data presented by Faber,¹⁰ who calculated the optical parameters in the wavelength range $250\text{to}1000\mathrm{nm}$ via Mie theory from the complex refractive indices of oxygenated and deoxygenated hemoglobin solutions taken from porcine blood. In that paper, ${\mu }_s$ shows similar characteristic differences between deoxygenated RBCs and fully oxygenated RBCs. The difference in the absolute values are of minor importance since Faber’s values are linearly calculated from the scattering cross sections for a hematocrit of 50%, assuming independent scattering of the cells, which is not obvious at such high cell concentrations. The minimum value at $410\mathrm{nm}$ shifts to $430\mathrm{nm}$ , and the maximum value in the area of $500\mathrm{nm}$ shifts to a more pronounced peak at $470\mathrm{nm}$ . The double minimum at $540∕575\mathrm{nm}$ changes into a single minimum at $560\mathrm{nm}$ , and in the range $600\text{to}1000\mathrm{nm}$ , the curve of the deoxygenated RBCs runs below the curve of oxygenated RBCs. It is only in the spectral range $250\text{to}400\mathrm{nm}$ that the data do not fit with the data presented here. This is possibly due to differences in the calculated complex refractive index of hemoglobin by Faber, which is quite different from other measured index values in this spectral range.¹⁶ The anisotropy factor of oxygenated RBCs shows also a minimum near $420\mathrm{nm}$ , which shifts to longer wavelengths when deoxygenated. In the same way, the double minimum at $540∕575\mathrm{nm}$ vanishes. The constant higher level of the deoxygenation curve compared to the oxygenation curve above $500\mathrm{nm}$ together with the behavior of $g$ in the wavelength range $250\text{to}400\mathrm{nm}$ could not be observed in the experiments presented here. Also, the absolute $g$ values of Faber are higher than the ones presented here, which can also be explained by assuming independent scattering within the calculation.

Even though Mie theory fails to predict the absolute values of the scattering parameters ${\mu }_s$ and $g$ at physiological hematocrit values,⁴ special phenomena can be recognized in the spectra that could be calculated according to Mie theory. For example, the relative minima of ${\mu }_s$ at 540 and $575\mathrm{nm}$ induced by the relative absorption maxima at the same wavelengths can also be seen in Mie calculations. With this in mind, the influence of the absorption on ${\mu }_s$ is also explainable in principle by the Mie theory.⁴ However, the phenomenon of the significant decrease of the anisotropy factor $g$ when ${\mu }_a$ is increased is more difficult. This behavior shows Mie theory only if ${\mu }_a$ were to be 100 times greater. Since the decrease of $g$ tended to become smaller when the RBCs were changed to a more spherical shape, it can be assumed that the nonspherical shape is responsible for this discrepancy.⁴ Independent of this, it seems to be feasible that an increase in the complex refractive index results in an increase in the reflection and a decrease in transmittance, resulting in increased backscattering of the photons, which means a smaller $g$ .

There are further indications in the literature that absorption peaks in light scattering media may lead to a reduction of ${\mu }_s$ and $g$ and an increase in ${\mu }_s^{\prime }$ (Refs. 8, 10, 13).

It is of considerable interest that the changes in water absorption at 1450 and $1900\mathrm{nm}$ induce changes in $g$ in the same way as the strong changes in hemoglobin absorption do. In both cases, absorption is increased within the scatterer. In the case of water absorption, there is an additional and stronger absorption increase within the surrounding medium. ${\mu }_s$ shows no comparable change at the spectral regions of high water absorption, whereas $g$ and ${\mu }_s^{\prime }$ are influenced by the kind of absorption peaks described earlier. Classical Mie theory does not describe the scattering behavior of spheres in an absorbing medium. However, by using a modified Mie theory, it could be shown that under special conditions, similar to the blood situation for spheres and cylinders absorption within the surrounding medium, a decrease in ${\mu }_s$ and $g$ , could be induced.^{20, 21} These results at least partly correspond to the data presented in this study and the results of other previous studies.^{4, 11, 18}