2.1.

Diffuse Reflectance Theory

Light propagation in a turbid medium, such as ES, is generally expressed by the radiative transfer equation.¹² A simpler exponential model was introduced by Zonios et al. for modeling diffuse reflectance from a homogeneous semi-infinite turbid medium.¹³ In the exponential model, the integral term of the radiative transfer equation was neglected and it was assumed that light is attenuated in the medium according to absorption and reduced scattering coefficients. Based on this model, a semiempirical equation was developed for relating measured diffuse reflectance ($R_m$) with the optical properties:¹³

Here, ${\mu }_{\mathrm{a},\mathrm{ES}}$ and ${\mu }_{\mathrm{s},\mathrm{ES}}^{\prime }$ correspond to absorption and reduced scattering coefficients of ES, respectively, and $c_1$, $c_2$, and $c_3$ are the empirical parameters. The parameter $c_1$ was added to the semiempirical model in this study. It depends mostly on the optical properties of the blood bag. Other parameters $c_2$ and $c_3$ are related to the measurement geometry in addition to the optical properties of the blood bag. This semiempirical expression [Eq. (1)] shows two fundamental characteristics of the reflectance: inverse dependence on the absorption coefficient and linear dependence on the reduced scattering coefficient.¹⁴ The reflectance model has been tested on many biological studies.^15–18

2.2.

Erythrocyte Suspensions and Their Optical Properties

In the general preparation process of ES, blood is collected into a multibag system prefilled with an anticoagulant containing citrate, phosphate, and dextrose solution. The collected whole blood is centrifuged and then plasma is transferred into another bag. A 100-mL preserving solution containing saline, adenine, guanine, and mannitol (SAGM) is added to the remaining erythrocytes to replace plasma.

Erythrocytes are densely packed in ES; the hematocrit (HCT) of ES is around 55% to 70%, while the lowest HCT of healthy women is 36% and the highest HCT of healthy men is 54%. Consequently, concentration of red blood cells (RBCs) and hemoglobin are higher in ES than in the body. The count of RBCs in ES is around 5.5 to $7.0\times {10}^{12}(1/\mathrm{L})$. With recent developments, the leukocytes are filtrated in ES and the number of residual white blood cells (WBCs) is decreased to $<{10}^6/\mathrm{L}$. In addition, the number of platelets (PLTs) is reduced, but their counts remain about ${10}^{10}/\mathrm{L}$. The normal range of single erythrocyte volume is about 80 to $100\mu {\mathrm{m}}^3$, and cellular hemoglobin concentration is in the range of 320 and $360\mathrm{g}/\mathrm{L}$.

Optical properties of ES are very similar to those of whole blood, which have been extensively studied^19–23 and reviewed^24–26 in the literature. The absorption coefficient of ES is proportional to mean cell hemoglobin concentration (MCHC),²⁷ and the forms of hemoglobin such as oxy- and deoxyhemoglobin characterize this absorption. The absorption coefficient of ES (${\mu }_{\mathrm{a},\mathrm{ES}}$) is equal to

Leukocytes, platelets, and FHB do not have much influence on the absorption properties of ES.^22,28 Although FHB absorbs light, the light absorption of cellular hemoglobin is much higher since MCHC is at least 20 times denser than FHB concentration. It was also shown by Roggan et al.²⁸ that FHB concentration has a very small effect on the absorption coefficient of whole blood. Therefore, MCHC sufficiently describes the absorption characteristics of whole blood.

The scattering properties of ES may be different from the scattering properties of whole blood since in ES the plasma is substituted with SAGM of which the refractive index is possibly different from the plasma.

The scattering properties are related to cell volumes and counts.²⁹ Concentrations ($C_n$), volumes ($V_n$), and scattering cross-sections (${\sigma }_{s,n}$) of different cell types determine the scattering coefficient of ES (${\mu }_{\mathrm{s},\mathrm{ES}}^{\prime }$):

The contribution of different cells, RBCs, WBCs, and PLTs, on the scattering coefficient can be expressed as

${\mu }_{\mathrm{s},\mathrm{EXT}}$ represents the light scattering coefficient, due to the particles in the extracellular medium. For example, scattering contributed by the platelets, ${\mu }_{\mathrm{s},\mathrm{PLT}}$, would be proportional to the ratio of platelet concentrations in ES to mean platelet volume (MPV):

Here, MCV is mean cell volume of RBCs, ${\sigma }_{\mathrm{s},\mathrm{RBC}}$ is the scattering cross section of RBCs, and $\gamma (\mathrm{HCT})$ is HCT-dependent correction factor. (1–HCT), ${(1-\mathrm{HCT})}^2$, and (1–HCT)(1.4–HCT) were suggested by several authors for this empirical factor.^26,30–33

The reduced scattering coefficient of ES is proportional to the scattering coefficient but additionally depends on the anisotropy factor $g$:

2.3.

Storage Lesions and Their Effects on Optical Properties

During storage, erythrocytes undergo serious morphological and biochemical changes triggered by an inadequate adenosine triphosphate (ATP) production due to slowing down of glycolysis reactions in the refrigerated conditions. The lack of ATP inactivates the sodium-potassium pumps, and potassium ions leave RBCs, while sodium and calcium ions accumulate inside. The ionic exchanges between the intracellular and extracellular media alter their refractive indices and light scattering from cells at the interface between cell membrane and the extracellular space. Although glycolysis reactions slow down in low temperatures, RBCs continue to metabolize and the products of glycolysis make the media more acidic. The fall in pH reduces 2,3-diphosphoglycerate, which regulates binding of oxygen to hemoglobin and the hemoglobin oxygen affinity increases.³⁴ The hemoglobin oxygenation process changes the absorption characteristics of the ES unit. Free radicals derived from oxygenation cause RBC injury by damaging membrane phospholipids and cytoskeletal proteins. These oxidative damages and the loss of intracellular water and ions result in crenation of erythrocytes. Subsequently, the erythrocytes swell and form a sphere shape with multiple long spicules. These shape changes would definitely affect the scattering cross-section of RBCs. Erythrocytes eventually loose these spicules as microvesicles into supernatant.³⁵ Microvesicles carry cytoplasmic particles from their originated cells. The size of the microvesicles range from 100 nm to $1\mu \mathrm{m}$, and their concentration progressively increases during storage.³⁶ The accumulation of these micro-sized membrane particles in supernatant would increase the number of scattering events in the extracellular medium. The decreasing surface-to-volume ratio of cells with the membrane fragmentation decreases the deformability, and oxidative damages to structural components of RBCs make them susceptible to hemolysis. Erythrocytes finally rupture and release cytoplasmic particles and hemoglobin into the cell suspending medium. This leads to an increase of scattering in the extracellular medium of ES.

2.4.

Modeling of FHB Concentration

Storage lesions modify both absorption and reduced scattering coefficient of ES as described in Sec. 2.3. However, FHB concentration, which is a substantial element for quality assessment of blood products, is expected to be in correlation with the increase of scattering from the extracellular medium. The combined effect of storage lesions on the overall reduced scattering coefficient of ES is unpredictable, but accumulation of microvesicles, cellular particles, and FHB into the extracellular medium would increase the contribution of scattering from the extracellular medium. For investigating the reduced scattering coefficient of extracellular medium (${\mu }_{\mathrm{s},\mathrm{EXT}}^{\prime }$), Eq. (1) is rewritten as

After partitioning ${\mu }_{\mathrm{s},\mathrm{ES}}^{\prime }$ as in Eq. (4) and omitting ${\mu }_{\mathrm{s},\mathrm{WBC}}^{\prime }$, ${\mu }_{\mathrm{s},\mathrm{EXT}}^{\prime }$ can be expressed as

Since the FHB concentration is associated with the increase in ${\mu }_{\mathrm{s},\mathrm{EXT}}^{\prime }$, Eq. (9) can be used to model the FHB concentration. After substituting ${\mu }_{\mathrm{a},\mathrm{ES}}$, ${\mu }_{\mathrm{s},\mathrm{PLT}}^{\prime }$, and ${\mu }_{\mathrm{s},\mathrm{RBC}}^{\prime }$ according to Eq. (2), Eqs. (5) and (6), respectively, the FHB concentration can be modeled with regressors depending on only diffuse reflectance and hematological parameters. Immeasurable covariates such as scattering cross-sections and anisotropy factor can be covered by the regression coefficients. The details and results of modeling are given in Secs. 3.4 and 4.5.

3.1.

Measurement of Optical Properties of Blood Bag

Optical properties of blood bags (Macopharma, Fr) were measured for investigating their contribution to diffuse reflectance data. Reflectance and transmittance of the blood bag were measured using two integrating spheres (Labsphere Inc.). In the measurement setup, an optical fiber, connected to the white light source (Ocean Optics, HL-2000), was directed to the entrance port of the first sphere and through the lens and diaphragm (Fig. 1). The incident light beam was focused on the blood bag, which was placed between the spheres. The reflected light and the transmitted light were integrated in first and second spheres, respectively. A fiber was connected to the detector ports of the spheres for transferring the light to the spectrometer (Ocean Optics, USB4000-VIS-NIR). During the measurements, air inside the bag was discharged with a vacuum pump because air may form an additional layer between two plastic sheets and produce errors in the measurements. The measured reflectance and transmittance were normalized with reference and dark measurements of both spheres. Finally, the inverse-adding-doubling (IAD) method³⁷ was used to compute absorption and reduced scattering coefficients from the normalized reflectance and transmittance. The IAD program was run three times for different estimated anisotropy factors, $g=0.7$, 0.8, and 0.9. The refractive index of the blood bag was assumed to be 1.5. The IAD method requires additional inputs such as the dimensions of measurement geometry to calculate the optical properties. Input values are listed in Table 1.

Fig. 1

Measurement setup of reflectance and transmittance of empty blood bag with two integrating spheres.

Table 1

The input parameters of the IAD method.

3.2.

Monte Carlo Multilayer Simulations

Effects of the optical properties of ES on the intensity of diffuse reflected light were simulated with the Monte Carlo multilayer code.³⁸ Three layers were structured for the ES unit; the first and the last layers were the blood bag (thicknesses of 0.03 cm). ES was in the mid-layer with a thickness of 1.54 cm. The simulation was run 196 times, for 14 absorption coefficients of ES, logarithmically increasing from 1 to $3000{\mathrm{cm}}^{-1}$, and 14 scattering coefficients of ES ranged from 250 to $900{\mathrm{cm}}^{-1}$ in $50{\mathrm{cm}}^{-1}$ increments. The refractive index and anisotropy factor of ES were assumed to be 1.37 and 0.95, respectively. The Henry–Greenstein phase function was used for the random scattering process. ${10}^6$ photons were launched in each run, and the angle of incidence was set as 45 deg to limit the optical depth. The total diffuse reflectance (${\mathrm{DR}}_{\text{total}}$) was considered for analysis. Changes in ${\mathrm{DR}}_{\text{total}}$, according to optical properties of ES, were recorded for testing the validity of the semiempirical model [Eq. (1)].

3.3.

Experiments

This study was approved by the Ethics Committee of Institutional Review Board for Research with Human Subjects of Bogazici University, Istanbul, Turkey, and realized in cooperation with Turkish Red Crescent, Northern Marmara Regional Blood Center. Leukocyte-depleted 40 ES units supplied by the blood bank were used in the measurements. The ES units were stored at 4°C in blood bank refrigerators for 70 days. Their diffuse reflectance, hematological parameters, and reference FHB concentrations were measured on the 1st, 42nd, 49th, 56th, 63rd, and 70th days of storage. These days were chosen for observing higher FHB concentrations. In statistical analysis, ES units were divided into two groups: 28 units were used for training and the remaining 12 units for validation.

3.3.1.

Diffuse reflectance measurements

A reflection probe (Thorlabs, RP20) was used in diffuse reflectance measurements. The probe has six-around-one fibers with 0.2-mm core diameters. The central fiber was used for transmitting the incident light from the optical source to the ES unit, and the fibers around the central one were used for transmitting the reflected light from the ES unit to the spectrometer. The spectrometer (Ocean Optics, USB4000-VIS-NIR) covers a wide range of the spectrum from 344 to 1038 nm, and its optical resolution is about 1.5 to 2.3 nm. The optical source was a tungsten halogen lamp (Ocean Optics, HL-2000). White diffuse reflectance standard (Ocean Optics, WS-1) was used to record the intensity of the incident light. Data acquisition was controlled by the software Oceanview (Ocean Optics Inc.).

Before starting each measurement, the optical source was warmed up for 20 min. The ES unit was gently agitated to assess homogeneity inside the bag. Aggregated cells were separated, and the sedimented cells were mixed in this way. For the diffuse reflectance measurement, the ES unit was laid on a probe stand (Thorlabs, RPH-SMA). The probe holder was placed over the ES unit and tightened to an optical post. The probe was placed into the 45 deg mount of the probe holder to avoid specular reflection. The setup was enclosed with black hardboard (Thorlabs, XE25C5D/M) to eliminate the interference of the ambient light on the measurements (Fig. 2).

Fig. 2

Diffuse reflectance measurement of ES unit inside the dark box. The reflection probe was placed in the 45-deg aperture of the probe holder. The probe holder was tightened at the point where the probe connects the surface of the blood bag.

The integration time for the spectrometer to count reflected photons was set to 5 ms. The software was averaged over 100 scans before recording the data, and boxcar averaging width was adjusted to 25 for smoothing the collected data. After recording of the first measurement, the ES unit was removed and placed again under the probe and the measurements were repeated at least three times. The repeated measurements were averaged to minimize positioning and placement errors.

3.4.

Generalized Linear Model for Predicting FHB Concentration

GLM was used to relate the FHB concentration with the reduced scattering coefficient of extracellular medium. The general expression of GLM is

Indices $p$, $n$, and $k$ represent the number of predictors, the number of ES units, and the number of repeated measurements during storage, respectively. GLM was applied to 28 ES units in the training set for all wavelengths from 344 to 1000 nm with 2-nm increments. The goodness of fits, RMS errors, and statistical significance of the regression coefficients were analyzed, and the models were tested on 12 ES units in the validation set. Matlab 2017b (Mathworks Inc.) was used for statistical analysis; the results are given in Secs. 4.5 and 4.6.

4.1.

Storage Effects on Hematology of ES

During the 70 days of storage, ES units underwent storage lesions and a gradual increase in FHB concentration was observed. The standard deviations between the FHB concentrations of 40 samples also increased with the storage period. The critical level of FHB concentration in blood bags is about 3 to $6.5\mathrm{g}/\mathrm{L}$. FHB concentration of all ES units was measured below the critical level for the first 42 days, but it became critical on the 56th day of storage and thereafter. On the 70th day, almost all ES units were beyond the acceptable quality limits. Hematological parameters that directly affecting the optical properties have also changed significantly with prolonged storage. An increase in HCT and MCV was observed while there was a fall in MCHC (Fig. 3). Repeated measures-ANOVA results showed that storage had a significant effect on these hematological variables ($p<0.001$). Changes in PCT and MPV were not statistically significant. The correlation coefficient between FHB concentration and MCHC, HCT, and MCV were 0.734, 0.6863, and 0.5524, respectively.

Fig. 3

Effect of storage on (a) HCT, (b) MCV, and (c) MCHC, measured with the hematology analyzer after sampling blood from ES units.

4.2.

Diffuse Reflectance Spectra of ES Units and Effects of Storage on Them

The diffuse reflectance spectrum of an arbitrarily chosen ES unit is plotted in Fig. 4, for the first day of storage. The diffuse reflectance spectrum exhibited the absorption characteristics of hemoglobin dominantly. The inverse relationship between absorption and measured diffuse reflectance, as in Eq. (1), can be seen in Fig. 4. A valley in a particular region of diffuse reflectance spectrum corresponded to the peak molar extinction coefficient of hemoglobin at that wavelength. However, this inverse proportionality was broken in the 400- to 450-nm region [Fig. 4(b)], where the absorption of hemoglobin molecules is highest, but it was not the region having lowest reflected light intensity, in diffuse reflectance spectra [Fig. 4(a)]. The diffuse reflectance spectrum had a constant base level in the region where the absorption of ES was higher. In this region, the detected light mostly contained the reflections from the blood bag.

Fig. 4

(a) The diffuse reflectance of an ES unit, measured on the first day and (b) oxy- and deoxyhemoglobin absorption curves (data are from Ref. 45) are shown.

The first day measurements of the diffuse reflectance spectra of ES units showed large deviation among them (Fig. 5). It is likely that variations in their hematological parameters caused such difference in their optical properties, i.e., in their diffuse reflectance spectra.

Fig. 5

Diffuse reflectance spectra of 40 ES, on the first day of storage.

With storage time, it was observed that diffuse reflectance of ES units generally increased between 600 and 750 nm and decreased beyond 800 nm. The peak wavelength of the spectrum shifted to the left. The two peaks around 725 and 790 nm turned into a single peak around 670 to 680 nm, and the valley around 760 nm diminished in some of the ES units. These changes were associated with the changes in the hemoglobin oxygenation level, calculated with Eq. (10). The oxygenation levels of ES units increased with storage time (Fig. 6). The direction of the shift in diffuse reflectance spectra due to increasing oxygenation [Fig. 7(b)] could be estimated from the reciprocal of hemoglobin molar extinction spectra [Fig. 7(a)].

Fig. 6

Percent change of oxygenation during storage.

Fig. 7

Shifts in diffuse reflectance spectra with increasing oxygenation and its correlation with the reciprocal of molar extinction coefficient of hemoglobin. (a) Reciprocal of the molar extinction coefficient of reduced and fully oxygenated hemoglobin,⁴⁵ (b) the diffuse reflectance spectra of different ES units measured at different storage times.

There was no strong correlation between the changes at any wavelength of the diffuse reflectance spectra and FHB concentration. The most powerful correlation was observed in the range of 800 to 1000 nm, and it was a negative correlation of around 0.6.

4.3.

Optical Properties of Blood Bag

The absorption and reduced scattering coefficients of the blood bag were computed with the IAD method. Between 550 and 900 nm, the absorption coefficient of the blood bag was between 0.5 and $0.7{\mathrm{cm}}^{-1}$, and the reduced scattering coefficient was around $7{\mathrm{cm}}^{-1}$ (Fig. 8). Beyond this region, higher fluctuations were observed as the power of the halogen source decreased and the measurement signal-to-noise ratio became poor. The blood bags were semitransparent; the inner surface was generally modified to provide an appropriate contact with erythrocytes and minimize hemolysis. These textures lead to high scattering and absorption coefficients.⁴⁶ Even higher scattering coefficients were presumed in Ref. 47. The anisotropy factor had very little influence on the computations of the reduced scattering and absorption coefficients.

Fig. 8

Spectra of absorption (left axis) and reduced scattering coefficients (right axis) of the blood bag. Actual measurements were smoothed for both spectra. The error bars in the absorption spectra represent the standard deviations of measurements with different anisotropy factors ($g=0.7$, 0.8, and 0.9).

4.4.

Validity of Exponential Model

The measured optical properties of the blood bag were used as inputs to Monte Carlo multilayer (MCML) simulations to investigate the semiempirical reflectance model [Eq. (1)]. The absorption coefficient of the blood bag was set to $0.6{\mathrm{cm}}^{-1}$ and the scattering coefficient of the blood bag was calculated as $35{\mathrm{cm}}^{-1}$ while the anisotropy factor was selected as 0.8 and the reduced scattering coefficient of the blood bag was set to $7{\mathrm{cm}}^{-1}$.

The simulated data were in a good agreement with Eq. (1), when the data were divided into two parts according to absorption levels of ES. The goodness of fits were 0.9287 and 0.992, respectively, for low and high absorption levels (Fig. 9). The model seemed to be slightly better when ${\mu }_{\mathrm{a},\mathrm{ES}}$ was higher. Nevertheless, the fitness of the model for low ${\mu }_{\mathrm{a},\mathrm{ES}}$ was also acceptable. At low absorption levels of ES (${\mu }_{\mathrm{a},\mathrm{ES}}\le 5{\mathrm{cm}}^{-1}$), the relationship between the reduced scattering coefficient and diffuse reflectance became nonlinear. At very high absorption levels of ES, however, total diffuse reflectance converged to $c_1$ as in Eq. (1).

Fig. 9

MCML simulations: the diffuse reflectance behavior according to the absorption and the reduced scattering coefficients of ES. The model fit to data with (a) low absorption levels and (b) high absorption levels of ES.

The validity of Eq. (1) was also tested with the experimental data of the training set. Initially, diffuse reflectance at 570 nm was used for normalization, where the intensity of measured reflectance was minimum, to eliminate the empirical coefficient $c_1$, which is asymptotically equal to the measured diffuse reflectance at higher absorption levels of ES. The normalized diffuse reflectance spectra $R_{\text{norm}}(\lambda )$ was acquired by subtracting the reflectance at 570 nm from the spectra:

Following normalization, the optical properties ${\mu }_{\mathrm{a},\mathrm{ES}}$ and ${\mu }_{\mathrm{s},\mathrm{ES}}^{\prime }$ in Eq. (1) were replaced with the hematological parameters MCHC, HCT, MCV, and Sat (${\mathrm{O}}_2$) according to Eqs. (2) and (6), respectively. Then, with these hematological parameters, the normalized reflectance values were predicted according to Eq. (1). The predicted values were in good agreement with the actual normalized diffuse reflectance values (Fig. 10). The best goodness of fit was 0.8922, obtained at 658 and 660 nm. Nonetheless, the goodness of fits were greater than 0.8 in all wavelengths from 590 to 700 nm.

Fig. 10

The fitness of the model on experimental data, at 568 nm, with the highest goodness of fit. One outlier data at (0.119 and 0.1513) although included is not visible in the plot range.

4.5.

Results of GLM for FHB Predictions

For estimating the response variable FHB concentration, the selected predictors of GLM were

The GLM of each wavelength gave statistically significant regression coefficients, except for a few side wavelengths of the spectrum. The significance of the regression coefficients is shown in Table 2 by their ranges of $p$-values through the wavelengths. The correlation coefficient between the reference and predicted FHB concentration ranged from 0.77 to 0.83 for the GLM of each wavelength. The goodness of fits of the models was in a similar range ($0.66<R^2<0.70$), and the RMS error was around 2.52 to $2.65\mathrm{g}/\mathrm{L}$. It was observed that no particular wavelength had a priority for estimating FHB concentration.

Table 2

Significance of regression coefficients.

Although there was no physical meaning of the regression coefficients individually, some interpretations could be made with their ratios. The ratio of the regression coefficient $b_5$($\lambda$) to $b_6$($\lambda$) informed us about the $\gamma$(HCT) because $b_5$($\lambda$) and $b_6$($\lambda$) are both related to ${\mu }_{\mathrm{s},\mathrm{RBC}}^{\prime }$. This ratio was expected to be around $-1$ or around $-1.4$, for consistency with suggested empirical factors in the literature. For most of the spectrum, the ratio was calculated around $-1$ (mean of wavelengths: $-0.9396$, standard deviation 0.0420) [Fig. 11(a)]. Second, the ratio of the regression coefficients $b_3(\lambda )$ and $b_4(\lambda )$ was expected to be proportional to the ratio of molar extinction coefficients of oxy- and deoxyhemoglobin because they were sample independent factors. The ratio $b_3(\lambda )/b_4(\lambda )$, plotted in Fig. 11(b), resulted in a good fit with the assumption. In addition, $b_5(\lambda )/b_7(\lambda )$ or $b_6(\lambda )/b_7(\lambda )$ should have been consistent with ${\sigma }_{\mathrm{s},\mathrm{RBC}}^{\prime }(\lambda )/{\sigma }_{\mathrm{s},\mathrm{PLT}}^{\prime }(\lambda )$, which is the ratio of the reduced scattering cross-sections of RBCs and PLTs. According to ratios of these regression coefficients, it was found that ${\sigma }_{\mathrm{s},\mathrm{PLT}}^{\prime }>{\sigma }_{\mathrm{s},\mathrm{RBC}}^{\prime }$, although the size of PLT is lower than RBC. This result can be explained by the lower anisotropy factor of PLTs compared with RBCs. The ratio of the reduced scattering cross-sections is equal to

Fig. 11

Ratios of some regression coefficients: (a) $b_5(\lambda )/b_6(\lambda )$, and (b) $b_3(\lambda )/b_4(\lambda )$.

4.6.

Accuracy of GLM on Validation Set for Predicting FHB

The FHB concentrations of the ES units in the validation set were predicted with the regression coefficients computed from the training set. The predictions were compared with the actual FHB concentrations. The optimum results for validation were observed at 568 nm. At this wavelength, the goodness of fit was 0.7999 (Fig. 12) and the correlation coefficient between reference and predicted FHB concentrations was 0.8943. The RMS error was computed as $1.5347\mathrm{g}/\mathrm{L}$.

Fig. 12

Estimation accuracy of FHB concentrations of 12 ES units of the validation set, with the model at 568 nm: reference versus predicted FHB concentrations.

Although predicting the exact value of the FHB could not be achieved with the proposed model, the model predicted and actual FHB concentrations were highly correlated, suggesting that the model could give accurate information about the quality of the blood under storage. The hemolysis levels of ES units were calculated from the following equation after predicting FHB concentrations with the proposed model:

The ES units having hemolysis levels higher than the limit levels were judged as low quality units. The true condition was compared with the assignments according to these predictions. For the threshold of 0.8% hemolysis, the maximum accuracy was observed as 64/72 ($\sim 89\%$) for the model at 568 nm, and, for the threshold of 1.0% hemolysis, the maximum accuracy was observed as 66/72 ($\sim 92\%$) for the model at 562 nm.