4.1.

Lymphocyte Models and Calculated Light Scattering Patterns

We model lymphocytes by two-layer concentric spheres (Fig. 1 ). Such a model, unlike the simplest ones,²³ is more informative and, as distinct from complex models,²⁷ is suitable for rapid calculation in real time. The model ignores some structure features of lymphocytes. We will revert to reasonableness of our approximation later; for the moment, we proceed by describing the model. The nonsmooth surface of the cell is modeled by us as a homogeneous equivolume surface layer [see Fig. 1]. Different thickness ranges of this layer simulate surface features of different kinds, such as, for example, folds and microvilli. The parameters of the cell model in our calculation are presented in Table 1 on the basis of our data^{26, 27} and known data.^{50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61} Since surface changes of immunocompetent cells under persistent virus infections in question are nonspecific,⁴⁷ we suggest that cell and nucleus sizes and refractive indexes are the same for the healthy and afflicted individuals in question. The known models (cytoplasm–membrane and cytoplasm–nucleus) for a lymphocyte with smooth surface^{50, 51} are shown in Figs. 1 and 1. It is worth noting that our designations “nonsmooth” and “smooth” are related to the cells rather than to the cell models.

Fig. 1

Models of the lymphocytes with (a) nonsmooth and (b, c) smooth surfaces. Model (a) is developed in this paper for the cell with near-surface texture. Figures (b) and (c) display the known lymphocyte models with membrane (b) and nucleus (c). The cytoplasm, nucleus, and layer simulating cell texture are homogeneous. Cell parameters are indicated in Table 1.

Table 1

Cell parameters in our calculation of light scattered by the lymphocyte being in surrounding media with refractive index 1.35. Wavelength of the incident light is 0.63μm .

The results of calculations for light-scattering patterns of model lymphocytes with nonsmooth and smooth surfaces [Figs. 1, 1, 1] are presented in Figs. 2 and 3 , respectively. We used reliable high-accuracy, up-to-date code⁶² to calculate intensities $i^{*}$ . The value of $i^{*}=i_1^{*}+i_2^{*}$ , where $i_1^{*}$ and $i_2^{*}$ are nondimensional intensities for light polarized parallel and orthogonal to the plane of scattering. Sometimes, $i_1^{*}$ and $i_2^{*}$ are referred as the Mie intensities. We averaged the calculated intensities $i^{*}$ within a collection angle, taken as $7\mathrm{deg}$ . The intensities averaged within this angle are denoted as $i$ . (The same collection angle is used in the results displayed in Figs. 4, 5, 6, 7 ). Comparison of the light-scattering patterns in Figs. 2 and 3 demonstrates that lymphocytes with surface features could be discriminated from smooth lymphocytes by the intensity differences. The intensity differences of light-scattering patterns for nonsmooth and smooth lymphocytes are mostly observed in the backward-scattered light, although some similar differences are seen in the forward-scattering pattern as well. An angle range of scattering for finding the maximum intensity differences to distinguish the cells involved is $80\text{to}180\mathrm{deg}$ . This angular range is traceable with a scanning flow-cytometer; part of the range near $90\mathrm{deg}$ is traceable with the SSC-channel of a conventional flow-cytometer. Within the indicated angle range, the nonsmooth cells scatter light more strongly than the smooth cells, and the intensity of scattered light for nonsmooth and smooth lymphocytes roughly differs by at least a 1.1 order of magnitude. This difference is sufficient to be revealed, for instance, by light-scattering channels of a flow-cytometer, and in particular, by the SSC channel of a conventional flow-cytometer. On the basis of our calculations, we can anticipate comparative changes of SSC signal distributions for lymphocytes of infected and healthy individuals. Assume that the percentage of smooth lymphocytes is decreased and the percentage of nonsmooth lymphocytes is increased, as happens with the cells of infected patients as compared to healthy individuals.⁴⁷ In this case, according to our calculations, the distribution will be shifted to large SSC signals for the infected individuals as compared with the healthy ones. Note that for near-backward directions, smooth cells scatter light more weakly than nonsmooth cells (see Figs. 2 and 3). This observation is in accordance with data.^{34, 43}

Fig. 2

Angular dependences of light-scattering intensity $i$ calculated for a nonsmooth lymphocyte. Lymphocyte with microvilli (curve 1) and folds (curves 2, 3, and 4); thicknesses of the layers mimicking folds are $0.15\mu \mathrm{m}$ , $0.25\mu \mathrm{m}$ , and $0.35\mu \mathrm{m}$ , respectively; 40.7%, 69.6%, and 100% of fold volume is filled with membrane, respectively. Lymphocyte diameter corresponding to the typical value of lymphocyte size is $7.5\mu \mathrm{m}$ . Other cell parameters are indicated in Table 1.

Fig. 3

Angular dependences of light-scattering intensity $i$ calculated for the smooth lymphocyte; cell without (curve 1) and with (curve 2) nucleus. Lymphocyte diameter, membrane thickness, and refractive index are $7.5\mu \mathrm{m}$ , $10\mathrm{nm}$ , and 1.52, respectively. Other cell and nucleus parameters are indicated in Table 1.

Fig. 4

Angular dependences of light-scattering intensity $i$ calculated for a lymphocyte at the left wing of the size distribution of the cells. Smooth lymphocyte (curve 1), nonsmooth lymphocyte with microvilli (curve 2) and folds (curves 3, 4, and 5); thicknesses of the layers mimicking folds are $0.15\mu \mathrm{m}$ , $0.25\mu \mathrm{m}$ , and $0.35\mu \mathrm{m}$ , respectively; 40.7%, 69.6%, and 100% of fold volume is filled with membrane, respectively. Lymphocyte diameter is $6.7\mu \mathrm{m}$ . Other cell parameters are indicated in Table 1.

Fig. 5

Angular dependences of light-scattering intensity $i$ calculated for a lymphocyte at the right wing of the size distribution of the cells. Smooth lymphocyte (curve 1), nonsmooth lymphocyte with microvilli (curve 2) and folds (curves 3, 4, and 5); thicknesses of the layers mimicking folds are $0.15\mu \mathrm{m}$ , $0.25\mu \mathrm{m}$ , and $0.35\mu \mathrm{m}$ , respectively; 40.7%, 69.6%, and 100% of fold volume is filled with membrane, respectively. Lymphocyte diameter is $8.25\mu \mathrm{m}$ . Other cell parameters are indicated in Table 1.

Fig. 6

Angular dependences of light-scattering intensity $i$ calculated for a lymphocyte with membrane thickness of $11\mathrm{nm}$ . Smooth lymphocyte (curve 1), nonsmooth lymphocyte with microvilli (curve 2) and folds (curves 3, 4, and 5); thicknesses of the layers mimicking folds are $0.15\mu \mathrm{m}$ , $0.25\mu \mathrm{m}$ , and $0.35\mu \mathrm{m}$ , respectively; 40.7%, 69.6%, and 100% of fold volume is filled with membrane, respectively. Lymphocyte diameter is $7.5\mu \mathrm{m}$ . Other cell parameters are indicated in Table 1.

Fig. 7

Angular dependences of light-scattering intensity $i$ calculated for a lymphocyte with membrane thickness of $9\mathrm{nm}$ . Smooth lymphocyte (curve 1), nonsmooth lymphocyte with microvilli (curve 2) and folds (curves 3, 4, and 5); thicknesses of the layers mimicking folds are $0.15\mu \mathrm{m}$ , $0.25\mu \mathrm{m}$ , and $0.35\mu \mathrm{m}$ , respectively; 40.7%, 69.6%, and 100% of fold volume is filled with membrane, respectively. Lymphocyte diameter is $7.5\mu \mathrm{m}$ . Other cell parameters are indicated in Table 1.

Therefore, smooth and nonsmooth lymphocytes are separated by differences in light-scattering intensity (see Figs. 2 and 3). Figures 2 and 3 show the results for typical values of lymphocyte size and membrane thickness. But the cells and their membranes have size variability, which can reduce the separation. Results of calculations taking into account the variability both of cell size and cell membrane thickness are presented in Figs. 4, 5, 6, 7. One can see that there are still clear separations between the smooth and nonsmooth lymphocytes.

Aiming at a simple cell model, we neglect some structure features of the cells. In particular, we replace a slightly rough cell surface by an ideal spherical one. To determine the effect of such a replacement on particle light-scattering, we use the known literature data. The authors of paper in Ref. 34 compare calculated scattering patterns for the ideal sphere and a rough particle. The scattering patterns are computed by the FDTD method.³⁴ For these computations, (1) the optical parameters of the particles as well as the particle surroundings are similar to the ones in our calculations for lymphocytes, namely, diameters of the ideal and rough scatterers are $6\mu \mathrm{m}$ , scatterer refractive indices are 1.3675, and surrounding refractive index is 1.35; (2) the shape and roughness of the particle with rough surface are reconstructed from the 3-D confocal microscopy images of polystyrene particles. Now, assume that the roughness of the particle is analogous to one for the lymphocyte surface. Then, the rough particle and the ideal particle can be considered as an optical analog of the nonsmooth and smooth cell, respectively. The comparison of the scattering patterns for the ideal sphere and the rough particle shows that the mean intensity differences for these scatterers at the sideward and backward directions are less than 0.4 order of magnitude, while the differences of scattered light for models of nonsmooth and smooth lymphocytes are at least 1.1 order of magnitude. Hence, local roughness of the particle surface generating scatter in the fashion of very small Rayleigh scatterers does not move a central impact on the scattered intensity. It is worth noting that the authors of Ref. 34 also compare FDTD-calculated scattering patterns for the ideal sphere and a rough B-cell. Its shape and roughness is reconstructed from the 3-D confocal microscopy images for scattering pattern computation. Analysis of comparison data shows that the mean intensity differences for these scatterers are less than 0.5 order of the magnitude. These differences, in general, are large. Nevertheless, they are rather small in the context of the problem in question. Note that the small effect of roughness on angular scattering is also evident when comparing the light-scattering patterns calculated in paper Ref. 43 for the ideal sphere and Chebyshev particle being analog of rough particle. Thus, local roughness of the cell surface generating scatter in the fashion of very small Rayleigh scatterers does not have a dominant impact on scattered intensity. For the folded and villoused cells, the dominant impact for increased scattering is the thickness of the equivalent coated sphere.

Our lymphocyte model takes no notice of cell nucleus. Light-scattering patterns for cell models with and without a nucleus (Fig. 3) demonstrate that the maximal mean intensity difference is 0.4 order of magnitude. In the scattering angle range of about $85\text{to}95\mathrm{deg}$ , the difference is about 0.1 order of magnitude. Therefore, it is acceptable to ignore the nucleus in the lymphocyte model in the context of the problem involved. Generally speaking, a fairer comparison of cells with and without nucleus would be to correlate a membrane–cytoplasm in one case and a membrane–cytoplasm–nucleus in the other case. Nevertheless, provided that light-scattering-intensity is averaged in a large collection angle, the estimation being based on the results of Ref. 26 shows that the membrane contribution to the intensity for the sideward $\left(80\text{to}100\mathrm{deg}\right)$ and backward $\left(160\text{to}170\mathrm{deg}\right)$ directions of scattered light for lymphocytes is a rather small value (in the context of the problem). So, a nucleus-free model of lymphocytes is adequate in the frame of our biomedical task.

Our lymphocyte model takes no notice of such organelles as mitochondria and lysosomes, which can potentially contribute to the cell light scattering. The relative importance of organelles in light scattering is different in various cell types. Mitochondria play a significant role in light scattering for cells with high mitochondrial volume fraction,⁶³ especially for hepatocytes and some other cells, for instance, mammary tumor cell line EMT6.³⁶ Some types of cells have a significantly smaller volume fraction of mitochondria. As to lymphocytes, data on the number of mitochondria in these cells differ in various sources. It seems likely that the authors give data for different lymphocyte populations, including rare ones that are small in number. Data for the mitochondria contribution to lymphocyte light scattering are absent to our knowledge. For these cells one should, however, expect substantially smaller mitochondria contribution to light scattering than for hepatocytes or for other cells with high content of the mentioned organelles. The fact is that the number of mitochondria in lymphocytes is about 110 to 150 times smaller than in hepatocytes.⁶⁴ Lymphocytes contain a few mitochondria.⁶⁵ The mean amount of mitochondria in lymphocytes is 3.2 per cell.⁶⁶ So, it is reasonable to ignore mitochondria in the lymphocyte model. As for lysosomes, their contribution to cellular light scattering is noticeable for some сells with high content of these organelles. For EMT6, as an example of such cells, intensity of light scattered in the sideward direction for cells with lysosomes and cells without lysosomes (they are ablated by some procedure) is different by a 0.25 order of the value.³⁶ This difference being quite noticeable is nevertheless rather small in the context of the present paper. Lysosome contribution to lymphocyte light scattering will be even less than the previously mentioned value, because lymphocytes, excluding their small subpopulation as NK-cells, contain few lysosomes. For example, from the data in Refs. 67, 68, lymphocytes contain only several lysosomes. Note, in our on-line task with millisecond calculations, we ignore the light-scattering influence of some organelles—in other words, we ignore certain homogeneity details of cell refractive index distribution. If long they computation is acceptable (off-line tasks with calculations, for example, by the DDA method), then the more realistic distribution of cell refractive index can be taken into account. The 3-D distributions of this kind are recently developed for some cells.⁵ Calculations of the cell light-scattering patterns for large particles such as lymphocytes by DDA and similar methods is a separate complex task. Still, such methods give no opportunity to decrease time computation to obtain the real-time cell-distinguishing that is one of the main problem of scanning flow cytometry.

4.2.

Experimental Data on Light-Scattering for Lymphocytes of Healthy and Infected Individuals

As mentioned earlier, intensity differerences in light-scattering patterns calculated in the frame of the constructed model are sufficient to see contrast between the lymphocytes of healthy and infected individuals in the scattering angle range of $80\text{to}180\mathrm{deg}$ . Light scattered near the $90\text{-}\mathrm{deg}$ scattering angle can be measured by the side-scattering (SSC) channel of a conventional flow-cytometer. We compare SSC signal distributions measured with a conventional flow-cytometer for cells of lymphocyte populations of healthy and infected individuals. The comparison, as exemplified in Figs. 8 and 9 , shows that for infected individuals as compared with healthy ones, the distribution is shifted to large SSC intensities. (The distribution modification detected by the experiment reflects the lymphocyte population changes for infected individuals.) The experimental data support the results of our calculations for smooth and nonsmooth lymphocytes of healthy and infected individuals. To understand the quantitative discrepancy between experimental and calculated data, one should take into account the following. Experimental data show scattering of cells for lymphocyte populations from healthy versus infected individuals. Calculated data show scattering of single smooth versus nonsmooth lymphocytes. Since both lymphocyte populations (of healthy and infected individuals) include both smooth and nonsmooth lymphocytes (and differ in their proportions; see Sec. 2), the discrepancy should exist. The less distinction in the proportion of smooth and nonsmooth cells between healthy and infected individuals, the more the discrepancy. It is worth noting that the shift of scattered intensity distribution for infected individuals as compared with healthy ones will be larger when measuring scattered light by scanning flow cytometer rather than by conventional instrument used in our experiment. The fact is that scattering intensity differences between smooth and nonsmooth lymphocytes are larger in the backward direction than in the sideward one. (Recall that measuring of scattering in the backward direction is accessible for the scanning instrument and inaccessible for the conventional one.) For example, the difference near the scattering angle $165\mathrm{deg}$ is about 4.5 times larger than the difference near the scattering angle $90\mathrm{deg}$ . Along with theoretical calculation, experimental results show that the indicated changes of the SSC signal distributions can be used as an additional parameter to be alert to a disease under primary detection of individuals infected with hepatitis B and C viruses. So our analysis demonstrates that scanning wide-angle flow-cytometers, being a new type of flow device, have a considerable quantitative advantage over the classic flow apparatus for the task we considered (distinguishing the lymphocyte populations of healthy and infected individuals without using cell CD markers).

Fig. 8

Normalized histograms of the side-scattering signal distributions measured with FACScan flow cytometer and analyzed using CellQuest software (Becton Dickinson) for lymphocytes of a healthy individual (gray) and a patient with persistent hepatitis C (black).

Fig. 9

Normalized histograms of the side-scattering signal distributions measured with FACScan flow cytometer and analyzed using CellQuest software (Becton Dickinson) for lymphocytes of a healthy individual (gray) and a patient with virus hepatitis B and hepatic cirrhosis (black).

As discussed earlier, flow-cytometers could detect infected individuals directly on the basis of the experimental data exemplified in Figs. 8 and 9. To solve the task of this detection, we propose also a different mediated procedure with advanced facilities. It requires the lymphocyte model and involves solving the inverse problem on the basis of flow-cytometry light-scattering data. Solving the inverse problem enables one to distinguish (and to count the proportion of) smooth and nonsmooth cells in the lymphocyte population of an individual studied. For healthy versus infected individuals, the proportions are known to differ substantially. Additionally, for individuals infected by different viruses, the proportions also show marked distinctions.⁴⁷ Consequently, the individual proportions determined on the basis of solving the inverse light-scattering problem have potential importance as diagnostic and even differential diagnostic criterion. Note that the experimental data exemplified in Figs. 8 and 9 are best suited to screening rather than diagnostics. The proposed procedure based on the solution of the inverse light-scattering problem needs experimental validation. This is beyond the scope of this paper.

Thus, the findings show that the concentric homogeneous layer simulating lymphocyte surface texture (for example, cell surface folds) is necessary as the important constituent of the simple lymphocyte model with reference to the particular biomedical task involved. The layer simulating surface texture is applicable also as the constituent of our complex lymphocyte model²⁷ to extend and further develop it. As for the simple lymphocyte model in question, it can be used for rapid (in the real-time scale) solution of the inverse light-scattering problem on the basis of optical data measured by label-free flow cytometry. The proposed approach has another important application. It could be utilized to screen individuals of risk groups, by conventional or wide-angle flow-cytometer under the real-time mode, for detecting persons suspected as infected with some viruses.