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An experimental setup capable of measuring simultaneous 2D scattered light angular distribution from two directions to study cell morphology without the use of bio-labels was developed. Experiments with hematopoietic stem cells (CD34+ cells) show good agreement with detailed numerical simulations of light scattering. Numerical simulations and computer models of cells are used to identify physical features of cells with the largest scattering cross sections. This allows for determination of size, geometry of the nucleus and distribution of mitochondria in hematopoietic stem cells by means of our label-free method.
© 2016 Optical Society of America
1. Introduction
Hematopoietic stem cells (HSCs) are stem cells that mature and produce other blood cells like monocytes, erythrocytes, platelets, T cells (both myeloid and lymphoid) through the process of hematopoiesis. HSCs are obtained from bone marrow, mobilized peripheral blood or umbilical cord blood (UCB) and are used in HSC transplantation. UCB is normally used if suitable donors of bone marrow or peripheral blood cannot be found. HSC research has shown that they can used to treat certain types of cancers and immune system disorders through transplant. The transplant involves the intravenous infusion of the HSCs, which is performed to treat patients with hematologic cancers (e.g., leukemia, lymphomas, multiple myeloma), certain non-malignant hematologic disorders (e.g., aplastic anemia, thalassemia major, sickle cell anemia), and some solid tumors (e.g., germ-cell tumors, ovarian cancer, neuroblastoma) [1].
UCB harbors greater primitive HSC content than either bone marrow or mobilized peripheral blood [2,3]. The number of HSCs can be estimated using the cell-surface antigen CD34 as a marker. Label free noninvasive techniques like light scattering detection can be used to detect these types of cells. The techniques used in this research can directly be applied towards a path of label free detection for counting the number of HSCs
For years, conventional flow cytometry has been used to identify and sort biological cells. In this technique, a unique combination of biomarkers that attaches only to a particular cell lineage is used to label it. Laser light hits the flow of the labeled cell sample and excites the biomarkers as the cells pass through. The intensity levels of excited biomarkers are measured in two directions (forward and side directions). Depending on the ratio of these two intensity values, the cells are identified and categorized for further use.
In recent years, label-free techniques for cell analysis have become increasingly employed by the life science and medical communities. Laser light scattering has been demonstrated to provide effective label-free analysis of biological cells [4–10]. The laser light-scattering technique has been applied to study several types of blood cells [4, 5], including platelets, lymphocytes, myeloid precursor cells, and CD34+ cells as well as leukemic (Jurkat and THP-1) cells. In these studies, angular distribution of scattered light from single cells at side-scattering angles, from 79 to 101 degrees, were captured by a Charged-Couple-Device (CCD) camera. We observed that these blood cells have distinct two-dimensional scattered light patterns [4, 5] which can be used as fingerprints for identification and potentially for purification of these cell samples. The different biochemical makeup of cells and their components contribute to a spatially varying index of refraction on a scale length on the order of, or smaller than, the laser wavelength in the visible range. The close proximity of the laser wavelength to the size of features constitutes the main difficulty in optical imaging of the cells. However the information about the internal structure of cells [4, 5, 12] can be gained from the scattered light angular distribution, provided the accurate theoretical description is obtained of the scattered light angular spectra. This can be achieved by solving the 3D Maxwell equations using the finite-difference time-domain (FDTD) code [8]. By comparing the experimental and two-dimensional scattered light patterns from numerical simulations, one can identify the dominant scattering centers and obtain information about the internal cell structure [4, 5, 9]. In our previous studies [4,5] we discovered that the patterns from laser scattering light of single cells at side-scattering angles of 79 to 101 degrees are sensitive to the distribution of the cell mitochondria. Speckle analysis was used as a quantitative calculation to illustrate the similarities and differences of side-scattered patterns [4].
In this paper, we report our label-free light scattering analyses in two directions of human UCB HSCs. Adopting the similar idea of conventional flow cytometer machines (FACS), we have designed a new setup to capture simultaneous two-directional patterns experimentally. Our method is label-free and is based on simultaneous scattered patterns collected from a range of viewing angles in different directions. Each direction carries information about the cell’s internal structures. FDTD numerical modeling is implemented to investigate and decode the buried information of scattered experimental results. Combinations of this information and numerical results lead to accurate cell models that produce similar patterns to those of experimental results. Speckle analysis was implemented to compare the side scattered patterns of the experimental results and the numerical model’s simulated results. Our proposed numerical models are similar to confocal and microscope images of UCB HSCs.
2. Methods
We begin with the description of UCB CD34+ cell collection. UCB samples were obtained from healthy full-term neonates with the mothers’ informed consent, in accordance with the guidelines approved by the University of Alberta Health Research Ethics Board. Light-density mononuclear cells (MNCs) were separated by centrifugation using a 60% Percoll density gradient (1.077 g/mL, Amersham, Uppsala, Sweden). CD34+ cells were isolated from the light-density MNC interphase using the Miltenyi MACS system (Miltenyi Biotech, Auburn, California) as described previously in work [13].
The experimental setup used in the light scattering experiment has three major components: the probing laser, the sample holder, and the CCD cameras with microscope objectives. A schematic diagram of our experimental device is shown in Fig. 1. This design allows us to collect the scattered light from the specific target cell simultaneously from two different directions. As shown in Fig. 1, the overlap of the focused laser beam and the observation regions of the two CCD cameras with microscope objectives defines a small collection volume of scattered light of about 0.002 mm3 [14]. A 10 ml CD34+ cell solution of 1000 cells/ml was prepared for each experiment. The cells move freely inside the solution due to Brownian motion and occasionally a cell enters the collection region for scattered light leading to its 2D light scattered patterns being recorded simultaneously in the forward and side directions. As illustrated in Fig. 1, the laser light (632.8 nm, HeNe laser, Melles Griot, USA) is aligned perpendicular to one side of the sample holder. A biconvex lens of one-inch diameter and focal length of one inch is used to focus the laser beam to a focal spot of a few hundred micrometers’ diameter. The laser focal plane is approximately at the center of the sample holder. In our setup, a ~1 mW input laser power is used. Each imaging system consists of a microscope objective and a CCD sensor (ICX445, Sony, Japan) which are placed on the side and forward directions with respect to laser beam direction. The resultant viewing region is defined by two optical systems that are focused at the center of the sample holder. In the forward direction there is a 10x Mitutoyo infinity-corrected long working distance objective with a numerical aperture (NA) of 0.28; in the side direction, there is a 10x microscope objective with a NA of 0.25. The forward direction CCD camera measured scattered light from 18°≤θ≤ 42° with a central angle of θ = 30° and the side direction CCD camera measured scattered light from 79°≤θ≤ 101° with a central angle of θ = 90°. The laser beam is in the θ = 0° direction. To ensure the two cameras have same observation point, we first optimize the optical system so that clear images of an optical fiber (105/125μm, Thorlabs, New Jersey) illuminated by the laser can be seen by both cameras. After this procedure the optical systems are defocused 200μm in the side direction and 300μm in the forward direction prior to collecting scattered light from the cells.
Fig. 1 Schematic diagram of experimental setup. The setup consists of HeNe laser on the right, 2 CCD cameras at two different locations for measuring forward and side scattering lights and sample holder in the middle. Cell is located inside the sample holder and can be observed when it passes through a common observation region defined by illuminating laser beam, the 2 microscope objects and the 2 CCD cameras.
We compared experimental observations with the 2D simulation results that were obtained by using AETHER, our finite difference time domain (FDTD) numerical code [11], based on Yee’s algorithm [4, 5]. This code solves Maxwell’s equations and generates numerical solutions for light scattering from computer models of single cells with different geometries, internal structures and inhomogeneities [4–7]. Yee’s discretization scheme separates six components of electric and magnetic fields from one another by equal grid spacing. Maxwell’s discrete curl equations will be solved for each component using Yee’s algorithm. The Courant condition is tested to check the stability of results and to prevent error divergence. Liao boundary conditions terminated the 3D grid where a scatterer is located [15]. The total field/scattered field (TF/SF) technique was used to extract the scattered field from the input field. As we are interested in scattering patterns far from the cells, the Near-To-Far (NTF) field transformation was applied at the boundaries of the scattering volume. Numerical simulations of light scattering are important for cell identification and subsequent development of sorting criteria. Cell identification from the angular distribution of the scattered light is achieved by comparison of measured radiation with the calculated scattering from computer generated models of the cells. Such models make it possible to identify the dominant physical, light scattering features of the cells.
3. Results and discussion
We have applied our experimental setup to measure 2D scattered light angular distributions from spherical beads and UCB HSCs. Light scattering from spherical beads has been performed to verify the observed angular spectra and accuracy of AETHER numerical simulations by comparing with Mie theory results for spherical beads. The experimentally measured scattered light angular spectra from UCB HSC contain a wealth of information about the cell’s physical properties. These properties, such as dimensions and shape of the cell, or internal distribution of mitochondria, can be identified by comparing calculated light scattering angular distributions from the computer models of cells with experimental results. We have found that the simulated patterns reproduce well the experimental results.
3.1 Spherical beads
Figure 2(a) shows the experimental 2D scattered light patterns from 6μm diameter spherical polystyrene latex beads in the forward direction (top image) and the side direction (bottom image). FDTD light scattering simulations were also performed for a 6μm diameter dielectric sphere with a refractive index n = 1.59 in a medium with nm = 1.334. Figure 2(b) shows the AETHER simulated 2D scattered light patterns from a 6μm diameter dielectric sphere (n = 1.59, nm = 1.334) for the polar angles of 18° to 42° in the forward direction with respect to the laser axis (top image) and from 79° to 101° degrees in the side direction with respect to the laser axis (bottom image). AETHER generates 3D scattered radiation patterns from a scatter in the far field. The 3D scattered radiation patterns for forward and side directions from a 6μm diameter dielectric sphere are shown in Fig. 3. In the simulations, the laser light propagates along the z-axis. Because beads are uniform spheres, the scattered light displays a cylindrical symmetry (independent of azimuth angle, φ) about the z-axis. Good agreement is found between the experimental and simulation results. Both the experimental and simulation 2D scattered light patterns show five and four fringes in the forward and side directions, respectively. The 2D scattered light patterns for a dielectric sphere are expected to consist of vertical fringes as predicted by the Mie theory [16, 17]. Figure 2(c) shows the simulation results from the Mie theory calculations and from AETHER for a 6μm diameter dielectric sphere (n = 1.59, nm = 1.334). Our two light collection windows in the forward and side directions are highlighted with red background. We used the same experimental setup to study UCB HSCs.
Fig. 2 Scattering light pattern of a 3μm radius bead: (a) Experimental and (b) simulated by AETHER (c) Compares simulation results for AETHER and Mie theory in 1D spectrum. The two viewing range of angles are shown in forward and side directions.
3.2 UCB HSC experimental and simulation results
We have focused our studies on HSCs. These cells are used in transplantation for various diseases, their roles and morphology are well understood. Thus, they are a good choice for validating our method, and their internal structure is relatively simple, making them conducive to non-invasive probing and sorting.
The experimental 2D scattered light patterns from UCB HSCs [CD34+ cells] are shown in Fig. 4(a)-4(e). The top images in Fig. 4(a)-4(e) are measurements of scattered light in the forward direction and the images in the bottom row are observed in the side direction. The well-defined fringes in the 2D scattered light patterns of UCB HSCs in the forward direction are due to scattering from the nucleus which is the largest internal component of a cell, contributing to the majority of scattering in the forward direction because it has a higher refractive index compared to cytoplasm [18]. We can also observe randomly distributed speckles of relatively large sizes in the side direction scattering (bottom row in Fig. 4A-E). The speckles in the 2D scattered light patterns of UCB CD34+ cells in the side direction have been characterized by us before [4, 5]. These speckle patterns are produced by interference of the light scattered from the mitochondria [4, 5, 16]. As the number and size of mitochondria increases, the speckle size in the side direction becomes smaller. Additionally, it has been shown that different aggregations of mitochondria inside the cell change the number of speckles and their average cross-sectional area in 2D light scattering patterns recorded in the side direction [4, 10].
Fig. 4 Experimental forward-scattering and side-scattering patterns for UCB HSCs, A-E UCB HSC cells observed in pairs of forward and side direction for each cell.
Information about the cells being studied can be extracted by comparison with scattered light patterns from numerical models of cells. The effects of the nucleus and mitochondria will be discussed separately in more detail, and the numerical results are shown below.
3.3 Scattering from a nucleus
The scattering pattern in the forward direction is strongly dependent on the size, optical density and shape of the cell nucleus. We have illustrated an effect of the nucleus on the angular distribution of scattered radiation by performing FDTD simulations of scattering from three different cell models. Figure 5 shows scattered light patterns in the forward direction (from left to right respectively) for stand-alone cytoplasm with n = 1.35 and a radius of 3.3μm, stand-alone nucleus with n = 1.39 and radius of 2μm, and both cytoplasm and nucleus, the whole cell model. In all our simulations, the surrounding medium has a refractive index of 1.334. The refractive index values of cytoplasm and nucleus are based on publications [7, 13, 20]. The well-defined diffraction fringes in Fig. 5 can be analyzed by using one dimensional Fast Fourier Transform (1D-FFT) to examine the intensity distribution along the z-axis. The 1D-FFT-based method was successfully applied before for the size determination of spherical polystyrene beads in Ref [6, 21, 22]. 1D-FFT spectra of scattered light patterns from Fig. 5 are shown in Fig. 6. Two pronounced frequency peaks can be found in the 1D-FFT spectrum of the whole cell model in Fig. 6 (top curve). By examining 1D-FFT spectra of scattered light patterns from stand-alone cytoplasm and stand-alone nucleus (bottom curves), we found that the first dominant peak in the whole cell spectrum is due to periodic diffraction fringes produced by scattering from the nucleus and the second peak of lower amplitude is due to scattering from the cytoplasm. Here we can see the dominant effect of the nucleus peak in this range of viewing angle. The cytoplasm's small peak may be seen, but its effect is smaller than that of the nucleus.
Fig. 5 This figure shows the simulated forward direction patterns for A) standalone cytoplasm, B) standalone nucleus and C) cytoplasm and nucleus as whole cell.
Fig. 6 1D 1D FFT analysis of forward patterns obtained from different cytoplasm and nucleus simulations as shown in Fig. 5. The analysis indicates two pronounced peaks one due to the cytoplasm and the other one due to the nucleus. It is also observed shown in the upper panel that the effect from the cytoplasm is smaller than that of the nucleus.
In the absence of mitochondria, the scattered light patterns in the forward direction are mainly due to the nucleus. Next we will add mitochondria to our numerical models.
3.4 Effect of the mitochondria on the scattered radiation
Simulations have been performed to study the effect of the distribution of mitochondria on both forward and side directions in the scattered light distribution. To this end we have developed several numerical models of cells with different mitochondrial distributions, cf. Figure 7(b)-7(e). In all models, there are 80 randomly distributed spherical mitochondria (n = 1.42) of 250nm radius, and nucleus (n = 1.39) and cytoplasm (n = 1.35) of radius 2μm and 3.3μm, respectively. The refractive index value of mitochondria is based on Ref [7, 23–25]. Models consist of A) no mitochondria, B) mitochondria distributed randomly inside the cytoplasm, C) mitochondria concentrated close to the outer membrane of the cytoplasm, and D) mitochondria concentrated close to nucleus. These models were used in simulations of scattered light and to calculate the intensity distributions in the forward and side directions and are presented in Fig. 7. These patterns illustrate the effect of mitochondrial distribution and in particular their different spatial separations from the nucleus.
Fig. 7 This picture shows the simulated models for A) UCB HSC cell with no mitochondria, B) UCB HSC cell with mitochondria distributed randomly between the cytoplasm and nucleus gap, C) UCB HSC cell with mitochondria distributed randomly close to cytoplasm, D) UCB HSC cell with mitochondria distributed randomly close to nucleus E) UCB CD34 + previous model. Speckles size changes from model B-D in side direction patterns. Fringes similar patterns exist in forward direction as the effect of spherical shape nucleus.
The scattered light patterns in the forward direction are slightly distorted in the presence of mitochondria but the number of fringes and their periodicity are maintained (cf. Figure 7, middle row). The scattered light patterns in the side direction vary with mitochondrial distribution (Fig. 7 bottom row). For example, by moving mitochondria further from the nucleus, smaller speckles are produced. This is seen in the scattered light patterns from models “B” and “C” as compared to that of the model “D” which has bigger size speckles.
The insights gained from the last two subsections could help us to understand the experimental results of the UCB HSCs and perform proper numerical modeling simulations to confirm them. Two proposed numerical models for UCB HSCs will be discussed in the next subsection.
3.5 Numerical model for UCB HSCs
To understand the experimental scattered light patterns from UCB HSCs, two numerical models that provide the best fits were closely examined. The first model has the same mitochondrial distribution, close to the nucleus, as presented in Fig. 7(d). This model represents a normal cell which has a mitochondrial distribution aggregated to the periphery of the nucleus [16, 24]. This model was considered previously in Ref [4]. and is based on the confocal microscopy of UCB CD34+ cells. In the second model, the cell is assumed to be spherical and its internal structure consists of a spherical nucleus and aggregated mitochondria [4, 5]. In each model we assumed 80 spherical mitochondria with a radius of 250nm and n = 1.42. We also assumed that cytoplasm has n = 1.35 and a radius of 3.3μm and the nucleus has n = 1.39 and a radius of 2μm. The laser propagation was assumed to be along the z-axis.
The scattered patterns from simulations are shown in the second and third rows of Fig. 7(d) and 7(e). The similarity of vertical fringes in the simulated forward direction and speckle size in simulated side directions in Fig. 7(d)-7(e) shows a good agreement with those patterns in the equivalent directions of the experimental results presented in Fig. 4(a)-4(e). The forward direction in that range of angles is strongly dependent on the cell nucleus. The vertical fringes in the forward direction are due to scattering on the nucleus of the cell. Sizes of speckles in the side direction are related to mitochondrial distributions. The calculated scattered light patterns from our two proposed numerical models show good agreement with the experimental scattered light patterns of UCB HSCs. Based on this agreement it would suggest that the nucleus of the UCB HSCs has a diameter of 4μm and their mitochondrial distributions are close to the nucleus or aggregated inside the cell. The above suggested value for the diameter of the nucleus of a UCB HSC is consistent with observed values [27].
3.6 Analysis of 2D light scattering patterns
The statistical analysis of speckle distributions proposed in Ref [4]. is applied to study the experimental and stimulated scattered light patterns in the side direction. We proceed by identifying local intensity maxima and counting them. The size of each speckle is characterized by calculating an area corresponding to half the value of its maximum intensity. The averages of all areas that are calculated in this way characterize each scattering image in Fig. 7. We use the number of speckles and the average area to construct the 2D plot in Fig. 8 that includes the results of measurements and simulations from Fig. 4 and Fig. 7.
Fig. 8 As the figure shows, the average area ratio over the number of speckle peaks for numerical model “D” and “E”, red points, fits in the range for experimental results shown in black. Two other numerical models, “B”-“C”(green and blue), have other distinguishable values far from experimental results and two other numerical models “D” and “E”.
The number of speckles and their average area for experimental scattered light patterns of UCB HSCs in the side direction from Fig. 4 are shown as a black diamond in Fig. 8 and on average there are 4 speckles with an area of pixels. The red circle (4 speckles, pixels) and red diamond (5 speckles, pixels) are data for numerical models “D” (Fig. 7(d)) and “E” (Fig. 7(e)) respectively. As can be seen in Fig. 8, clearly the experimental data are consistent with those of numerical models “D” and “E”. The green diamond (10 speckles, pixels) and blue diamond (13 speckles, pixels) are data for numerical models “B” (Fig. 7(b)) and “C” (Fig. 7(c)), respectively. There is a significant difference between the number of speckles and the average area between green and blue points and red and black points. This statistical value can be used for quantitative analysis of 2D scattered patterns for further applications such as cell sorting.
4. Summary and conclusions
We have discussed experimental set-up that is based on the standard cell cytometers as far as scattered light collection optics is concerned. Mainly the scattered laser light from a single cell is collected simultaneously in the forward direction (18°≤θ≤ 42° with a central angle of θ = 30°) and the side direction (79°≤θ≤ 101° with a central angle of θ = 90°). The main emphasis in our work has been on the physical analysis of the angular distribution of the scattered light. The cell identification and characterization are aided by the following numerical procedure. First we have developed computer models of cells in which different cell components of varying geometries are assigned different sizes and different indices of refraction. Next the scattered light is calculated using Maxwell equation solver AETHER and compared with experiments. The quantitative analysis which contributes to these comparisons includes fast Fourier transform and speckle distribution statistical analysis of the numerical and experimental results. We have applied these noninvasive procedures to the UCB HSCs. These cells are important because they are used in transplantation for various diseases, their roles and morphology are well understood so they have been a good choice for validating our method.
We found that the scattered light patterns of cells in the forward direction could be used to deduce their nucleus sizes and the scattered light patterns of cells in the side direction are sensitive to their mitochondrial distributions. The measurements and analysis of scattered light patterns from cells discussed in our paper can find application in the label-free characterization and sorting of cells.
Funding
Natural Sciences and Engineering Research Council of Canada (NSERC); Canadian Blood Services (CBS); and Canadian Institute of Health Research (CIHR).
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