2.1.

Dual-Wavelength Probing of Blood-Serum Mixture

Let us demonstrate the principle of RBC agglutination registration by two-wavelength probing of blood-serum mixture. The PRBC of blood layer is assumed to be probed by two monochromatic light beams with different wavelengths of the visible range ${\lambda }_1$ and ${\lambda }_2$. Hemoglobin spectrum (one of the constituents of RBC content) is presented in Fig. 2 (curve 1).

Fig. 2

Spectral characteristics: 1—hemoglobin, 2—optical filter.

Wavelengths ${\lambda }_1$ and ${\lambda }_2$ are chosen according to hemoglobin spectrum: ${\lambda }_1=540\mathrm{nm}$ corresponds to one of the maxima of absorption in green range of spectrum and ${\lambda }_2=640\mathrm{nm}$ corresponds to that when light absorption is much lower. Estimations based on the Twersky formula²⁶ show that the attenuations of light beams at ${\lambda }_1$ and ${\lambda }_2$ due to scattering phenomenon should be quite close to each other because scattering cross-sections for erythrocytes for both wavelengths are nearly equal. At the same time, the attenuation of light beams at ${\lambda }_1$ and ${\lambda }_2$ differs, and this difference increases when RBC concentration and/or blood layer thickness increases. This allows one to assume that light beams at ${\lambda }_1$ and ${\lambda }_2$, which pass through the sample, are attenuated mostly due to absorption phenomenon; this may be described by Bouguer’s law:

The absorption coefficient ${\mu }_a(\lambda )$ may be defined as follows:²⁷

Taking into account that the PRBC sample has a higher concentration of erythrocytes related to the whole blood, it is necessary to correct Eq. (3) in respect to Ref. 27 by introducing hematocrit $H$ (assuming that when plasma is totally deleted from blood after blood centrifugation, $H=1$). In addition, in order to account for PRBC sample dilution, parameter $N$ was introduced. Correspondingly, Eq. (3) is transformed to

The estimations using Eq. (4) for $C=150$, $e({\lambda }_1)=\mathrm{53,236}$, $e({\lambda }_2)=4$ [oxyhemoglobin, $(\mathrm{l}/\mathrm{cm})/{(\mathrm{mole}/\mathrm{l})}^{27}$], $H=1/2$, and $N=1$ (no dilution) give the following results: ${\mu }_a({\lambda }_1)=575({\mathrm{cm}}^{-1})и{\mu }_a({\lambda }_2)=4({\mathrm{cm}}^{-1})$. The calculated dependences for ${\mu }_a({\lambda }_1)$ and ${\mu }_a({\lambda }_2)$ are presented in Fig. 3 (curve 1 corresponds to ${\lambda }_1=540\mathrm{nm}$ and curve2 to ${\lambda }_2=640\mathrm{nm}$); the ratio of intensities $K=I_0({\lambda }_1)/I_0({\lambda }_2)$ was chosen as $K>1$. It is important to notice that the curves 1 and 2 are crossing in the point $l_0$, which corresponds to such a PRBC layer thickness when $I({\lambda }_1)=I({\lambda }_2)$. From the graphs, it is obvious that for $K=4.3$ (the $K$ value will be discussed in Sec. 3), the layer thickness is $l_0=26\mu \text{m}$. A similar result can be obtained analytically.

Fig. 3

The intensity of light flux at the output of blood layer as a function of its thickness: erythrocyte mass—1 corresponds to ${\lambda }_1=540\mathrm{nm}$ and 2 to ${\lambda }_2=640\mathrm{nm}$; erythrocyte mass solution—3 corresponds to ${\lambda }_1=540\mathrm{nm}$ and 4 to ${\lambda }_2=640\mathrm{nm}$. The level of erythrocyte mass dilution was $1:150$.

Notice that Eq. (5) is derived from Eqs. (1) and (2) taking into account $I({\lambda }_1)=I({\lambda }_2)$.

From Fig. 3 it is easy to see (curves 1 and 2) that for sample layer thickness $l<l_0$, the relation between intensities is $I({\lambda }_1)>I({\lambda }_2)$—the green spectrum component prevails over red one when PRBC sample is probed by dual-wavelength beams. Otherwise, for $l>l_0$, the blood layer thickness becomes so large that in spite of the accepted condition $K>1$, the relation between intensities is $I({\lambda }_1)<I({\lambda }_2)$, i.e., the red spectral component dominates. This result may be related to the case of positive reaction of agglutination when erythrocytes are glued by serum, and this clot is similar to PRBC blood sample.

These estimations and data presented in Fig. 3 permit to formulate the following approach for registration of immune RBC complexes. If in blood-serum mixture being tested by dual-wavelength optical probe large erythrocyte formations of red color are visualized $(l>l_0)$, then they may be treated as RBC agglutinates (positive reaction).

Let us consider the model of negative reaction of agglutination. In this case, there are no agglutinates; sample is a suspension of erythrocytes in saline. For the experimental blood dilutions from ($1:300$) to ($1:50$), the level of $N$ was varying within the limits $50\le N\le 300$ (will be discussed in Sec. 3). The calculations using Eqs. (4) and (5) give the following values $1.3\le l_0\le 7.8(\mathrm{mm})$. In the experiments the blood layer thickness $l$ was 0.3 mm (Sec. 3), i.e., $l<l_0$; hence, $I({\lambda }_1)>I({\lambda }_2)$ and the blood layer image will be always green. It is easy to see the same from Fig. 3: the curves 3 and 4 do not intersect. Then it is possible to state that if sample image is green then agglutination has not been taken place (negative reaction).

On the whole, the generalization of the cases for positive and negative reactions of agglutination leads to the following criterion:

2.2.

Sample Testing by a Spectrally Filtered Light Beam

The difference between the problems studied here and in Sec. 2.1 lies in the fact that the probing light beam is not the combination of two monochromatic waves now, but a light beam with a continuous spectrum passed through an optical filter. Furthermore, if in Sec. 2.1 in order to find the critical thickness of blood layer $l_0$, two intensities of light beams compared at the wavelengths ${\lambda }_1$ and ${\lambda }_2$ were equalized [$I({\lambda }_1)=I({\lambda }_2)$], in this section the same parameter $l_0$ will be estimated by the comparison of R and G components of RGB decomposition of sample image $[\mathrm{B}(\mathrm{R})=\mathrm{B}(\mathrm{G})]$. Hereinafter, the following designations are accepted: B(B), B(R), and B(G) are the brightness of blue/red/green components of the image.

In the experiments, the source of light illumination of a sample was a filament lamp (Biomed microscope, Sec. 3), the spectrum of which is close to the spectrum of ideal black body at a temperature 3000 K. This light was transported through optical green filter. Its spectrum is presented in Fig. 2. One should pay attention to the fact that maximum of its light transmittance is very close to one of light absorption spectrum maxima for hemoglobin in the green range ($\lambda \approx 540\mathrm{nm}$).

To find erythrocyte layer thickness $l_0$, when brightness of red component B(R) and green one B(G) become equal, a rigorous approach is used: it is based on the calculation of XYZ coordinates of the sample in a linear color coordinate system and then on color transformation from XYZ to RGB. To estimate X,Y,Z color components, the spectral characteristics of the following were used: light source spectrum, $S(\lambda )$, optical filter spectrum, $F(\lambda )$, and spectral coefficient of transmission of PRBC of blood dependence, $T(\lambda )$, which were calculated on the basis of data for ${\mu }_a(\lambda )$ from Sec. 2.1. Still, as in Sec. 2.1, it is assumed that light beam attenuation is caused by light absorption only; the wavelength-dependent changes of light scattering in the sample in the visible range are not significant. Thus, the final formula to calculate color coordinates $X$, $Y$, and $Z$ for the sample is as follows:

Equations (6) and (7) allow one to estimate R, G, and B color components of RGB decomposition of image by varying the wavelength of light $\lambda$ in the limits $360\le \lambda \le 830\mathrm{nm}$ for a chosen thickness of blood layer $l$. Taking different values of $l$ and fulfilling the same calculations for each $l$, one may get the critical blood layer thickness $l_0$ when brightness of B(R) and B(G) components are equal $[\mathrm{B}(\mathrm{R})=\mathrm{B}(\mathrm{G})]$. The calculations showed that $l_0=27.2\mu \text{m}$, which is very close to the result obtained in Sec. 2.1.

Comparison of the results obtained in Secs. 2.1 and 2.2 shows that the criterion suggested to register RBC agglutinates may be realized in practice in two modes of light beam probing of blood-serum mixture:

3.1.

Sample Preparation Technique

As noted in Sec. 2.1, the sample under study is erythrocyte mass of donor blood for all four groups in ABO system. In this paper, such a sample will be named as erythrocyte mass or the sample of blood or simply blood.

Blood was diluted by saline and then agglutinating serum was added. Taking into account the serum volume, the blood (PRBC) dilution was $1:25$ and the ratio of blood-serum was $1:10$, which is the standard proportion for medical diagnostic practice when whole blood is investigated, but not for PRBC blood samples. As an example, let us recall that the combination blood A(II)-serum ${\mathrm{A}}_{\beta }(\mathrm{II})$ does not lead to RBC agglutination (negative reaction), but the same blood sample mixed with serum ${\mathrm{B}}_{\alpha }(\mathrm{III})$ leads to immune erythrocyte complexes formation (agglutinates)—positive reaction of agglutination.

It was shown in Refs. 17, 22, and 23 that ultrasonic standing wave (USW) action upon blood-serum mixture leads to agglutination reaction intensification, which increases the quantity of immune erythrocytes complexes and, most important, their sizes. The tested blood-serum mixture was poured into the cuvette of 6 ml in volume and then it was placed on piezoceramic transducer. Ultrasonic frequency was 2.25 МHz and voltage not more than 15 V in order to avoid RBC hemolysis. To optimize sample preparation technique, time duration of ultrasonic action upon sample was varied discretely in the limits from 15 s up to 2 min.

USW oriented in vertical direction grouped erythrocytes in its nodal zones. That led to the cell stratification in liquid with a period equal to a half of ultrasonic wavelength (${\lambda }_{\mathrm{us}}/2$). The erythrocyte convergence in the nodal zones of USW increased the probability of their induced aggregation (agglutination). In the presence of immunologically adequate serum, erythrocytes were gluing (agglutinating) and large immune RBC complexes were forming—positive reaction of agglutination. These complexes and free (not glued) erythrocytes were levitating—they remained weightless due to USW action. When ultrasound was switched off, large and rather stable RBC agglutinates were sedimenting quickly.

At the same time, when blood sample tested was not immunologically adequate to the type of serum (negative reaction), the formation of agglutinates in the nodal zones of USW did not occur. Under this condition, unstable RBC aggregates were formed: they fell into individual cells when ultrasound was switched off. It is necessary to notice that the rate of RBC sedimentation was much lower than that for agglutinates. USW action upon the mixture blood-serum was analyzed in Refs. 22 and 23.

So after some time (the duration of sample incubation) due to the difference in the rates of sedimentation, the agglutinates for positive reaction or free erythrocytes for negative one accumulate on the bottom of the cuvette. It should be noticed that blood-serum mixture incubation is an interval of time from the moment of ultrasound switching off up to the moment when sediment of liquid under test is sampled. Then sediment was diluted by saline. The process of incubation was necessary to form the sediment enriched by agglutinates for positive reaction as the negative one did not lead to the formation of agglutinates. To find the optimal time of incubation, it was varied in experiments discretely in the limits from 15 s up to 4 min. After incubation for both types of reactions, equal volumes of liquid investigated (2 ml) being taken from the cuvette bottom were diluted in such a proportion to provide the final blood dilution discretely from $1:300$ to $1:50$. These solutions of agglutinates (positive reaction) or erythrocytes (negative reaction) were transported through a capillary with cross-section $0.3\times 1.5{\mathrm{mm}}^2$ and analyzed by a digital microscopy method.

3.2.

Experimental Device, Imaging of the Sample

The experimental device was based on optical microscope Biomed, WEB-camera Logitect-QuickCam connected to computer. All the settings of WEB-camera were fixed; they were not changed during the series of experiments. Hereinafter, WEB-camera used will be named as digital camera. Light beam from filament lamp (microscope illuminator) passed through green glass filter (supplied microscope); its spectral characteristic measurement is presented in Fig. 2 (curve line 2). From Fig. 2, it is easy to see that for the filter used and for the wavelengths chosen in Sec. 2 (${\lambda }_1=540\mathrm{nm}$ and ${\lambda }_2=640\mathrm{nm}$), the ratio $K=I_0({\lambda }_1)/I_0({\lambda }_2)$ is 4.3.

Then light beam being filtered was directed on the glass capillary with a rectangular cross-section of $0.3\times 1.5{\mathrm{mm}}^2$ through which the liquid under investigation was pumping. In contrast to Ref. 12, microscope objective was changed from $40\times$ to $20\times$ and ocular from $10\times$ to $15\times$ because it was revealed experimentally that in the tested liquid flow heavy large immune erythrocyte complexes were moving along the bottom of microcapillary. The application of objective with a longer working distance (magnification $20\times$) allowed for focusing microscope optical system on the bottom of capillary and to detect large agglutinates. The ocular change was necessary to keep the level of microscope magnification.

The digital camera Logitect-QuickCam was able to make 15 shots per second. For each sample, the liquid flow was registered: video-clip of 150 frames was made. It is very important to notice that on the computer monitor large immune erythrocyte complexes were red in color [Fig. 1(c)], but free erythrocytes and small complexes were dark green [Figs. 1(a) and 1(b)], as it was predicted in Sec. 2. Naturally, the color cannot be seen in the black-and-white images (Fig. 1): erythrocytes and their small agglutinates appear black with respect to the background; they can be differentiated from each other in size only.

4.1.

Binarization of RBCs and Their Immune Complex Images

The first step in the experimental results processing was the procedure of video images binarization: it simplifies the agglutinates area calculation by the computer program. Binarization of the raw digital images was fulfilled by RGB analysis. Two digital matrixes B(R) and B(G) corresponding to the image were compared pixel by pixel programmatically. If brightness B(G) corresponding to a definite pixel of the image was higher than B(R) in the same point of image frame, then B(R) was zeroed $[\mathrm{B}(\mathrm{R})=0]$. Otherwise brightness B(R) was assigned to the definite numerical value, for example, 255.

For negative reaction when the sample contains free erythrocytes only, the condition $\mathrm{B}(\mathrm{G})>\mathrm{B}(\mathrm{R})$ (according to Sec. 2) for each pixel leads to $\mathrm{B}(\mathrm{R})=0$ in every point of the binarized image, i.e., the image is black completely.

For positive reaction in the areas of the image frame corresponding to intracellular space, free erythrocytes, or small RBC immune complexes, the condition $\mathrm{B}(\mathrm{G})>\mathrm{B}(\mathrm{R})$ is fulfilled, and thus, these zones were formatted as black. However, in other areas of the frame, where large RBC immune complexes are placed, it appears $\mathrm{B}(\mathrm{G})<\mathrm{B}(\mathrm{R})$ and the brightness B(R) is assigned to a number, for example, 255. This area in monitor is colored in red (hereinafter on the black-and-white illustration this zone is marked as gray).

As a result, the comparison of components of image brightness B(G) and B(R) allows one to transform the raw sample image into a binary one. We have to note that

But (as will be illustrated later in Sec. 5) such an approach is quite acceptable to register RBC agglutinates.

For clarity, quantitative confirmation of the effect observed, and illustration of the binarization result, Fig. 4 is presented. In Fig. 4(a), one can see the images of a single erythrocyte (I) and four RBC immune complexes of different sizes (II to V).

Fig. 4

The set of images and brightness distribution: (a) the raw images of erythrocyte (I) and RBC immune complexes of different sizes (II to V); (b) the distribution of brightness: solid line 1—B(G) as a function of coordinate X; dash line 2—B(R) as a function of X; (c) binary images of the raw images (a), the line M-M’ corresponds to the line L-L’ in raw images (a).

For agglutinates III to V, white outline selects the zones of red color; the rest of the external to the outline is of dark green color. In the selected areas of agglutinates, the thickness of the agglutinates (perpendicular to the picture plane) is high enough to provide light beam at ${\lambda }_1=540\mathrm{nm}$ to be absorbed completely, while the beam at ${\lambda }_2=640\mathrm{nm}$ due to small absorption coefficient is passing through this agglutinate freely. That is why agglutinate looks red. At the same time, a single erythrocyte (I, its thickness is 2 μm only) and a small RBC immune complex (II) have dark green color.

Brightness as a function of coordinate $X$ along the line L-L’ is presented in Fig. 4(b) for five raw images (I to V) of Fig. 4(a). From Fig. 4(b), it is easy to observe that there are regions (marked by crosses) where $\mathrm{B}(\mathrm{R})>\mathrm{B}(\mathrm{G})$, only for the cases III to V. It is important to note that for these regions only [Fig. 4(b)], there are red zones in Fig. 4(a). It is interesting that brightness distribution B(X) corresponds not only to the size of erythrocyte, but to its shape as well.

4.2.

Calculation of RBC Agglutinate Area

To obtain data on the number of agglutinates and their areas from binary images of raw microimage, the procedure of image segmentation was used on the basis of principles of splitting and merging. As a result of such an approach, the location and area of each agglutinate were determined. In calculations, in order to take into account the areas of agglutinates, only selection of sample image structures by areas was carried out. If the area of the structure is less than the threshold $S_0$ [$S_0$ corresponded to the maximal size (area) of a single erythrocyte], the blood structure element was assumed as an RBC and information about it was not taken into consideration. But when the area of the blood structure was greater than or equal to $S_0$, this element was prescribed as an agglutinate and its area was written down in file. It is important to note that in the case of negative reaction, erythrocytes in flow may become located occasionally close to each other; we named such RBC groups as RBC-formations. They may be accepted by blood typing apparatus as agglutinates. Let us introduce the following notations: $S_{ai}$—the area of $i$’th agglutinate, where $i$ is its number (positive reaction of agglutination) and $S_{fj}$—the area of $j$’th RBC-formation, $j$ is its number (negative reaction). The computer program developed allowed us not only to estimate the areas $S_{ai}$ and $S_{fj}$, but also to calculate the quantity of agglutinates and RBC formations of different sizes. Hence, it was possible to define the distribution of agglutinates and RBC formations in sizes (areas). The same program provided summation of the agglutinate areas $S_a=\mathrm{\Sigma }{S}_{ai}$ or the areas of RBC formations $S_f=\mathrm{\Sigma }{S}_{fj}$ for a specified number of snapshots for each sample probe. The comparison of $S_a$ and $S_f$ allows to determine the resolving power of the method (device) from $r=S_a/S_f$.