SEARCH

SEARCH BY CITATION

Keywords:

  • microfluidics;
  • microchip;
  • flow cytometry;
  • immunofluorescence;
  • immune status

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

In this article, we demonstrate the potential of a microfluidic chip for the differentiation of immunologically stained blood cells. To this end, white blood cells stained with antibodies typically applied for the determination of the immune status were measured in the micro-device. Relative concentrations of lymphocytes and subpopulations of lymphocytes are compared to those obtained with a conventional flow cytometer. The stability of the hydrodynamic focusing and the optical setup was determined by measuring the variation of the signal pulse height of fluorescence calibration beads, being about 2% for the micro-device. This value and the overall performance of the micro-device are similar to conventional flow cytometers. It follows from our results that such microfluidic structures are well suited as modules in a compact, portable read-out instrument. The production process of the microflow cytometers, which we exploited for immunological cell differentiation, is compatible with mass production technology like injection molding and, hence, low cost disposable chips could be available in the future. © 2011 International Society for Advancement of Cytometry

Microflow cytometry is an emerging field because of its potential to provide low cost, disposable chips for complex cellular-based analyses. Such technology could provide the basis for simple and robust analytical systems being of particular relevance for point-of-care in-vitro diagnostics with applications in intensive care and emergency medicine. The main challenge here, is to design micro-devices featuring functionality which is at least similar, if not superior to their large frame conventional equivalents.

Research in the field of microflow cytometry concentrates on four main areas (1–5): focusing of particles in microfluidic channels, miniaturized fluid handling (6–9), integration of optical elements into the chip (10–14), and applications development, e.g., for biomedical purposes. When analyzing micro particles, focusing of the sample stream is usually applied to restrict their trajectories inside the flow channel (1, 3, 5, 6, 8–11, 15–26). This positioning serves to increase signal stability when measuring particle properties and to avoid surface fouling in microfluidic channels. The latter is of particular importance in hematology since the samples typically contain high concentrations of blood cells. For this purpose, the micro-device studied here uses hydrodynamic focusing as described in the next section.

Differentiation of blood cells is considered as one of the most promising applications of microflow cytometers (9, 20, 27–29). The prospects of high-throughput analysis and separation of blood cells using micro-devices were reviewed by Toner and Irimia (6). In the present article, we explore the potential of a microfluidic chip for differentiation of immunologically stained leukocytes. Our study is based on comparison of the results obtained for the same sample material with the micro-device and a routine instrument. In order to facilitate such a comparison, we implemented a fluid handling similar to commercial flow cytometers and used corresponding detection electronics for the micro-device.

The aim of this article is to demonstrate the equivalence of microflow cytometry and conventional flow cytometry for immunologically, fluorescence-based leukocyte differentiation. Although the signal-to-noise ratio in the microfluidic device is somewhat smaller, we will demonstrate that it is just as well applicable for the reliable identification of cells and the determination of relative blood cell concentrations as conventional flow cytometers. In addition, the performance of the microfluidic device was quantitatively characterized by measuring the dependence of the coefficient of variation (CV) on the relative sample flow rate and as a function of fluorescence intensity. We demonstrate a CV of pulse height distribution of less than 2% for the micro-device, being in the range of conventional flow cytometer. These results open up a broader perspective for future developments of complex microflow systems which integrate, besides the presented analysis chip, sample preparation, and cell sorting modules.

MATERIALSAND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

Microflow Cell Design

The microfluidic structure used to investigate cells is depicted in Figure 1a and a photograph is shown in Figure 1b. Details of the chip design were described in a previous paper (10). Briefly, the micro-device is composed of an upper plate and a lower plate, both being produced by hot embossing in transparent thermoplastic (polycarbonate). Optical fibers were inserted before laser welding was applied to join both parts of the microstructure. The fluidic channels of this chip are shown in blue in Figure 1a. The sample stream is hydrodynamically focused in the vertical, i.e., perpendicular to the joining plane, as well as in the horizontal direction in a cascade of two steps. For hydrodynamic focusing in the vertical direction, we utilized a high aspect ratio, which can be achieved by ultra-precision milling of the embossing tool. The height of the channels of the sheath flow is 1 mm in the cascade. The sample stream is injected into the first focusing stage using a channel of 125 μm height. In addition to a cascaded channel system with high aspect ratio between the focusing stages and the flow channel for cell analysis (10), we tested spin focusing for the positioning of cells (30). Both focusing stages show robust and reliable operation and allow the variation of the sample to sheath flow rate of approximately three decades between 0.002% and 2%. This allows easy adaptation of the count rate for cell suspensions of different concentrations. Typically, the sheath flow was set to 1200 μL min−1 and the sample flow rate varied between 0.2 μL min−1 and 24 μL min−1. Varying the sample flow rate in this range resulted in a change of the sample stream width between 4 μm and 15 μm within the detection channel (cross-section 125 μm × 125 μm) as measured with fluorescence microscopy (10).

thumbnail image

Figure 1. (a) Layout of the microfluidic prototype chip with cascaded hydrodynamic focusing. Grooves to insert optical fibers are indicated in yellow and integrated mirrors in green color (ALL: axial light loss, FLS: forward light scatter; SSC: side scatter). Fluorescence is measured in parallel to orthogonal light scatter (OLS). (b) Photograph of the micro-device shown above. (c) Arrangement used for leukocyte differentiation; the microscope objective serves for laser excitation and fluorescence detection in epi-illumination mode. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

Optical Setup and Data Acquisition

The detection of optical and electrical signals in microfluidic applications was recently reviewed by Zhang et al. (2). In the micro-device considered here, optical excitation can be performed in two ways. Figure 1a shows the geometry for excitation through a polarization maintaining monomode source fiber, and Figure 1c shows the arrangement for excitation through the microscope objective (epifluorescence). Epifluorescence was also used by Wolff et al. and it is a convenient approach for particle counting (24). However, in our system, a laser beam rather than the light of the mercury lamp of the microscope was used to excite fluorescence. Epifluorescence provided superior signal stability compared to excitation by the monomode fiber in the chip shown in Figure 1. Therefore, it was used in the measurements discussed here.

Fluorescence of stained cells was excited at a wavelength of (488 ± 2) nm in the measurements with the micro-device, employing a solid-state laser (Sapphire 488–200, Coherent, Santa Clara, CA). The output power of the laser was set to 80 mW. The laser beam was elliptically shaped in the detection channel to minimize the influence of light intensity reduction for cells not passing the center of the Gaussian distribution of the laser beam. The sensitivity for detecting dim fluorescence signals can be improved using optics with high numerical aperture. Usually microscope objectives are applied for this purpose although appropriate lenses could be integrated into the chip (31). We use a 40× microscope objective (Olympus, CDPlan 40 ulwd) with a numerical aperture of NA = 0.5 to focus the laser beam to an elliptical spot size of 7 μm by 87 μm, the smaller axis being parallel to the direction of the particle flow. Both values refer to the full width at half maximum.

Besides the laser-induced fluorescence of cells collected by the same microscope objective, orthogonal light scatter (OLS) was collected with optical fibers. These optical fibers exhibit a numerical aperture of 0.22 and a core diameter of 105 μm. Fluorescence and scattered light were detected by photomultipliers (Hamamatsu R3896). Following amplification, the signal pulse heights were detected and converted by analogue-to-digital converters (CyFlow ML electronics; Partec GmbH, Muenster, Germany). The fluorescence signals from different dyes used for labeling were measured simultaneously using combinations of long pass and band pass filters (Fig. 2). The OLS served as trigger. Fluorescence was measured orthogonal to the incident laser light in the MoFlo cell sorter (Beckman Coulter, Brea, CA), while reflection geometry was used for the micro-device. The chip was mounted on a microscope stand (Zeiss, Axiovert 200M), which provides an intermediate image of the epifluorescence at the exit of the side port. The fluorescence was selected from this image with a pinhole and collimated by a lens. The arrangement in the MoFlo cell sorter was similar. The laser power at 488 nm (Ar+-laser) was set to 220 mW for the MoFlo. It should be noted that it was not possible to collimate the fluorescence collected by the microscope objective in this case, since the jet in air geometry produced astigmatic beams. Hence, a second lens was introduced into the optical pathway to re-collimate the fluorescence light (Fig. 2, lower diagram).

thumbnail image

Figure 2. Optical arrangements for detection using the micro-device (top) and the MoFlo cell sorter (bottom). The spectral detection characteristics are closely matched to facilitate direct comparison of the two settings.

Download figure to PowerPoint

Preparation of Blood Sample

Fresh venous blood, treated with EDTA-anticoagulant, was mixed with different solutions of fluorescently labeled antibodies of a kit used for the determination of the immune status (Simultest IMK-lymphocyte, BD Biosciences, San Jose, CA). This kit is designed for enumerating percentages of various human leukocyte subsets by double or triple staining: T (CD3+) lymphocytes, B (CD19+) lymphocytes, helper/inducer Th/i (CD3+, CD4+) lymphocytes, suppressor/cytotoxic TS (CD3+, CD8+) lymphocytes, and natural killer (NK) cells (CD3, CD8+) (32). The kit also allows the direct measurement of the CD4/CD8 concentration ratio, which is considered to be a more robust marker for HIV disease progression than the concentration of Th/i lymphocytes (33). The amount of blood (100 μL), antibody reagents (between 5 μL and 20 μL), and the incubation time of 900 s at room temperature were chosen as recommended by the manufacturer. Staining at a lower temperature (4°C) was tested but showed no improvement on labeling specificity. Subsequent to the staining of the respective target cells, red blood cells were lysed and white blood cells were stabilized (Cell Kit C05, Cellset AG, Giffers, Switzerland). The total volume of the three different reagents added for lysis amounted to 965 μL; thus the resulting volume fraction of blood in the suspension used for measurement corresponded to approximately 9% and was used without further dilution.

Measurement Procedure and Fluorescence Calibration

For analysis, each diluted blood sample was divided into two parts. The first aliquot was drawn in a 1 mL polypropylene syringe and fed into the sample inlet port of the microfluidic device. The volume flow rate of the blood sample was set between 10 μL min−1 to 16 μL min−1 using a programmable syringe pump. The sheath flow rate was controlled with a flow meter (ASL 1430-24, Sensirion AG, Staefa ZH, Switzerland) and set to approximately 1200 μL min−1 by adjusting the pressure in the reservoir. Using these conditions for the flow rates, typical count rates of blood cells were 400 Hz and the particle velocity was about 3 m/s. Higher count rates could easily be achieved with increased blood cell concentration. However, to keep counting loss due to coincidences low, the vendor of the electronic detection system recommends to limit the count rate to less than 500 Hz when quantitatively measuring particle concentrations.

The performance of the microflow cytometer was evaluated by means of comparison experiments employing the MoFlo cell sorter. For this purpose, the second aliquot of the diluted blood sample was analyzed at the same time as the first one. The instrument was operated with a nozzle of a 70 μm diameter and a setting of 4 bar to drive the sheath flow. The pressure difference to maintain the sample flow was chosen to obtain a count rate of 200 Hz for blood cells.

The calibration of the fluorescence intensity of the micro-device as well as the MoFlo was achieved using a set of calibration beads with eight different fluorescence intensities (Sphero™ Rainbow Calibration Particles RCP-30-5A, 8 peaks, 3.0–3.4 μm, Spherotech, Lake Forest, IL). In addition, a suspension of calibration spheres (Sphero™ Rainbow Fluorescent Particles RFP-30-5, 1 peak, 3.0–3.4 μm) exclusively exhibiting particles with intensity similar to the highest intensity of the set was sampled to facilitate the quantification of the pulse height resolution in the microflow cytometer. In both instruments, the fluorescence (in MESF units, molecules of equivalent soluble fluorochrome) of the calibration particles and as of the immunologically stained blood cells was observed in the fluorescein isothiocyanate (FITC, in MEFL units) and phycoerythrin (PE, in MEPE units) detection paths (cf. Fig. 2). Differentiation of leukocytes was supported in some cases by triple staining including labeling with anti-CD45-PerCP. It should be noted that for PerCP calibration of the fluorescence in terms of MESF units was not accomplished.

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

Microflow Cell and Fluorescence Detection

To characterize the stability of flow cytometric measurements employing the micro-device, fluorescence signals of the single intensity calibration spheres were determined for different sample flow rates. As indicator of the stability and the reproducibility the CV of the pulse height distribution was analyzed, an approach commonly used in flow cytometry (34). The pulse height distributions were recorded using linear amplification and measured in the FITC detection path. The results are depicted in Figure 3, where the measured CV (dots) is plotted against the width ws (full width at half maximum) of the sample stream. To derive the CV, we fitted Gaussian curves to the pulse height distribution. The fluorescence intensity of the single intensity calibration spheres of (32,3000 ± 8,000) MEFL units was derived by the comparison with the intensities measured for the calibrated set of eight intensity calibration beads. In Figure 3, the abscissa ranges from 4 μm to 13 μm, corresponding to a change of the sample flow rate from 0.5 μL min−1 to 15 μL min−1 at a constant sheath flow rate of 1180 μL min−1. The influence of the sample stream width on the signal stability is evident from Figure 3. The CV is reduced from about 5% to 2% when decreasing the sample flow rate. The dependence of the CV on the sample stream width may be analyzed as the sum of two different contributions according to

  • equation image(1)
thumbnail image

Figure 3. Coefficient of variation (CV) of the pulse height distribution as function of the sample stream width. To derive the CV, the fluorescence of single peak calibration spheres (Sphero™ Rainbow Fluorescent Particles) of 323,000 MEFS was measured in micro-device employing linear amplification. The solid line describes modeling with Eq. (1).

Download figure to PowerPoint

 The first term CVmath image is attributed to the intrinsic variation of the fluorescence of the calibration particles and noise caused by laser intensity fluctuations. Detector noise can be neglected, because particles of high fluorescence intensity were used in this experiment. The second term accounts for the influence of the particle trajectory, since with increasing distance from the maximum of the Gaussian intensity distribution the power incident on the particle decreases. It is reasonable to assume that CVinst varies quadratically with the sample stream width ws (see Appendix). Our data are consistent with this simple approach, i.e., CVinst = β·wmath image. The solid line was obtained by fitting Eq. (1) to the measured CV, yielding the value CV0 = (1.76 ± 0.06)% and the device parameter β = (2.77 ± 0.08) × 10−4 μm−2. The value derived for CV0 is slightly larger than indicated by the manufacturer (1.64%), probably because of additional contributions like laser noise.

The sensitivity of the microflow cell was evaluated by the measurement of calibration beads featuring eight (1 ≤ i ≤ 8) populations of different fluorescence intensities. The histogram, shown in Figure 4a, was measured with the micro-device at a constant flow rate of 15 μL min−1 resulting in a sample stream width of approximately 9.5 μm. The corresponding result for the MoFlo cell sorter is shown in Figure 4b. The fluorescence was recorded using logarithmic amplification prior to pulse height detection. Both distributions were fitted with eight Gaussian peaks, respectively. The resulting curves are included in the figure as solid lines (green) and the sum of all distributions is illustrated as the area under the curve. The Gaussian peaks correspond to log-normal distributions of the fluorescence measured for the eight individual particle fractions. Besides the centers of gravity, Pci, we calculate the CV δPci of the log-normal distributions from the parameters of the Gaussian peaks. The results are plotted in Figure 4c demonstrating that the CV decreases with increasing fluorescence intensity. This behavior was modeled for the micro-device by the variance function (35)

  • equation image(2)
thumbnail image

Figure 4. (a) Pulse height distribution of fluorescence signals of calibration beads measured with the micro-device (Sphero™ Rainbow Calibration Particles, eight different fluorescence intensities). The histogram was obtained observing the fluorescence in the FITC detection channel. Calculated pulse height distributions are included as solid lines (green) for each of the eight intensity distributions. The sum of all calculated distributions is illustrated as filled area (orange) under the curve. (b) Result measured with MoFlo cell sorter. (c) Up triangles: coefficient of variation as function of the fluorescence intensity derived from the histogram in (a); down triangles: results from (b). Solid line represents values modeled by the variance function (see Eq. (2)). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

 The parameters for the solid line included in Figure 4c are β1 = 634, β2 = 0.07, and J = 1.81, respectively. The intercept equation image corresponds to a standard deviation of s ≈ 340 MEFL and represents the minimal line width achievable with the microflow cytometer. At higher fluorescence intensities the CV drops to 2.7% in the same manner as for the MoFlo cell sorter (Fig. 4c). The results obtained for the micro-device can also be compared directly with values reported by Chase and Hoffman (34). The CV of the micro-device is always smaller than the CV obtained by Chase and Hoffman (on average by a factor of 1.7). Therefore, we conclude that despite its smaller sensitivity compared to the MoFlo cell sorter the micro-device allows the reliable differentiation of immunologically stained cells against negative populations. This application is analyzed in the following paragraph in more detail.

Microflow Cytometer for Immunofluorescence Detection

Detecting monocytes and subpopulations of lymphocytes is a typical example of an immunologically based cell differentiation. The performance of the microflow device applied to immunological cell differentiation was tested by comparison measurements with the MoFlo cell sorter. The LeukoGATE reagent (Simultest IMK-Lymphocyte, BD Biosciences) was utilized to evaluate the light scatter and fluorescence gating of leukocytes through double staining with anti-CD14-PE and anti-CD45-FITC. This procedure is often used to differentiate monocytes, lymphocytes, and granulocytes from each other and from other cells and noise (32).

Scatterplots of leukocytes using fluorescence and orthogonal light scatter detection are depicted in Figure 5. The LeukoGATE allows to delineate all leukocytes and to distinguish lymphocytes (Ly), monocytes (M), and granulocytes (G) based on the scatterplot of the fluorescence measured in the FITC channel versus orthogonal light scatter (Fig. 5a). The leukocyte subsets in Figure 5 were distinguished using elliptical borderlines and marked with colors. Granulocytes are clearly separated from non-lysed red blood cells (RBC), cell debris, and noise because of their high orthogonal light scatter. The population of monocytes (CD14+, gated green in Fig. 5a) is accessible in Figure 5b, where the fluorescence intensity measured for PE is displayed versus the intensity of FITC. Spectral compensation to correct the crosstalk was not used in order to simplify direct comparison of the results. The effect of spectral crosstalk caused by FITC-fluorescence emissions overlapping with the spectral window selected for detecting the PE fluorescence is noticeable in the scatterplots, since the clusters are arranged along straight lines featuring a positive slope. The broader distributions of clusters observed for the micro-device is related to increased noise in the measurements with the micro-device.

thumbnail image

Figure 5. Leukocyte differentiation employing anti-CD45-FITC, anti-CD14-PE and orthogonal light scattering at 488 nm obtained with the micro-device and the MoFlo cell sorter. The scatter plot (a), anti-CD45-FITC fluorescence versus orthogonal light scatter, illustrates the setting of elliptical gates to border particular subpopulation of leukocytes (Ly: lymphocytes, M: monocytes, G: granulocytes, RBC: red blood cells). (b) LeukoGATE test used to evaluate the light scatter gate with anti-CD14-PE that differentiates the majority of normal peripheral blood monocytes (32). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

In Figure 6, results of fluorescence measurements of cells are depicted. The data were obtained using staining reagents usually applied for cell differentiation when determining part of the immune status. In this case, a two-color direct immunofluorescence reagent kit (Simultest IMK-Lymphocyte, BD Biosciences) for the identification of mature human leukocyte subsets in erythrocyte-lysed whole blood was exploited (32). The appropriate reagents were selected for differentiation of T, B, Th/i, and TS lymphocytes. Although a supplementary leukocyte labeling with anti-CD45-PerCP stain was used here for verification purpose, the applied gating strategy was solely based on two-parameter scatterplots shown in Figures 6a–6c. The detailed gating protocols and specification of applied monoclonal antibodies are specified in the literature (32, 36). For clarity of presentation the distinguished cell subsets were marked with colors (no borderlines shown).

thumbnail image

Figure 6. Comparison of results obtained with the micro-device and the MoFlo cell sorter for immunological differentiation of leukocytes. Fluorescence scatterplot for (a) anti-CD4-PE/anti-CD3-FITC, (b) anti-CD8-PE/anti-CD3-FITC, and (c) anti-CD19-PE/anti-CD3-FITC staining. (Ly-B: B lymphocytes, NK: natural killer cells, WBC: white blood cells). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

The scatterplots of fluorescence signals obtained by anti-CD4-PE and anti-CD3-FITC staining, shown in Figure 6a, aim at the detection of helper/inducer Th/i lymphocytes. It should be noted that the CD4 negative population of TS lymphocytes exhibits weak signals in the PE-detection channel, because the original, non-compensated data are presented as in Figure 5. In Figure 6b, TS lymphocytes are identified as being positively labeled with anti-CD8 and anti-CD3 antibodies. Natural killer (NK) (CD3, CD8+) cells can also be indirectly differentiated in this plot. B lymphocytes are discerned in Figure 6c by means of labeling with anti-CD19-PE.

The pulse height distributions of fluorescent calibration beads shown in Figure 4 clearly demonstrated that the micro-device has inferior resolution at low fluorescence level. Thus for target cells featuring dim antibody staining, differentiation between negative and dim cell clusters is somewhat easier in fluorescence diagrams obtained with the MoFlo cell sorter than with the micro-device (see, e.g., Fig. 6c, Ly-B). On the other hand, the pulse height resolution of both cytometers for calibration beads is equivalent for high intensity fluorescence signals. Hence, for highly fluorescent populations the observed cluster sizes of cells reacting positively with two different antibodies reflect the biological variance. It follows that discrimination is alike in the micro-device and the MoFlo cell sorter.

The calibration of the fluorescence detection channels using rainbow particles can be exploited to compare the fluorescence of labeled cells as measured in flow cytometers. The fluorescence intensities of the cells assigned to subpopulations gated in Figures 5 and 6 were plotted in respective histograms and analyzed by fitting with log-normal distributions. The centers of gravity obtained when measuring with the MoFlo and the micro-device are plotted in Figure 7. Since both devices were calibrated with the same set of rainbow particles, one might expect to find equal values when expressing the fluorescence of stained cells in MESF units (straight lines in Fig. 7). While this is true for the signal heights measured in the FITC detection channel (Fig. 7a), the micro-device systematically records higher fluorescence for PE (Fig. 7b). Such discrepancies between the fluorescence brightness recorded by flow cytometers from different manufacturers are observed frequently. The point is that the rainbow particles cannot be used for quantifying the number of fluorophores present on the cells, since they have photophysical properties significantly different from dyes used for immunostaining purposes. Most important are the spectral emission characteristics. The rainbow particles emit over a broad spectral range, whereas dyes like PE have a pronounced fluorescence band. The deviation of the data points in Figure 7b could thus be explained by a different spectral match of the PE fluorescence detection in the microflow cytometer than in the MoFlo cell sorter (Fig. 2).

thumbnail image

Figure 7. Comparison of results obtained with a microflow cytometer and a conventional MoFlo instrument. The centers of gravity for the respective cell populations in Figure 6 are plotted: (a) detection of fluorescence in FITC channel and (b) for PE-channel. The error bars indicate the standard deviation of the log-normal distribution fitted to the fluorescence histogram. The diagonals represent straight lines of slope unity and indicate equal readings for calibrated instruments.

Download figure to PowerPoint

In Table 1, we compare relative cell concentrations determined with both flow cytometers. The concentrations were derived from measurements shown in Figures 5 and 6 and are related to the concentration of all leukocytes. The uncertainties were derived from typically five repeat measurements and include contributions of counting statistics. Uncertainties were estimated according to the guidelines published by JCGM (37). The respective coverage factor was chosen on the basis of the level of confidence of 95% and determined from the effective number of degrees of freedom truncated to the next lower integer. Since the uncertainties were derived from repeat measurements they represent the imprecision and not the inaccuracy, which also includes the bias, e.g., as result of specific settings for triggering.

Table 1. Comparison of relative cell concentrations measured with the micro-device and the MoFlo cell sorter (from Figs.5 and 6)
PopulationMoFlo cell sorterMicro-device
νeffcrνeffcr
  1. Relative concentrations cr are given with respect to all leukocytes and represent the average of 2–8 repeat measurements. Effective degrees of freedom νeff were determined by the Welch–Satterthwaite equation and the uncertainties of cr represent the imprecisions at a level of confidence of 95% (37).

Ly6.2(30.1 ± 4.5)%6.3(35.9 ± 7.2)%
M7.4(10.8 ± 1.9)%7.5(9.8 ± 3.3)%
Ly-T5.3(21.6 ± 2.1)%5.3(28.6 ± 7.0)%
Ly-B1.1(3.2 ± 1.1)%1.1(2.5 ± 1.3)%
NK1.0(1.7 ± 0.7)%1.0(1.4 ± 1.4)%
Ly-Th/i5.3(11.8 ± 0.5)%3.5(18.9 ± 1.1)%
Ly-Ts3.1(9.8 ± 3.2)%3.7(11.0 ± 2.3)%

DISCUSSIONAND PERSPECTIVES

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

Most modern instruments can achieve CVs between 1% and 2% in fluorescence measurements of beads (38), although commercial flow cytometers are typically specified with a CV between 2% and 5%. Apart from DNA content measurements for cell cycle analysis to identify different tumor cell lines (39) such a pulse height resolution is sufficient due to significantly larger biologically based variations for light scattering experiments and immunofluorescence detection. This targeted range is achieved exploiting the cascaded hydrodynamic focusing built in the micro-device introduced here.

Several methods have been used to achieve particle focusing in micro-chips. Most commercially available optical flow cytometers use hydrodynamic focusing. The notation regarding the dimension of hydrodynamic focusing is not consistent in literature (18, 19). Most simple arrangements for hydrodynamic focusing in micro-chips enclose the sample only in one lateral dimension and we call this one-dimensional focusing here (3, 8, 9, 11, 20–22). This geometry is frequently used when lithography is applied in chip production. However, such systems will be prone to fouling in the microfluidic channels and it has been argued that this geometry will produce data with relatively large variance (1, 11, 23). Two-dimensional focusing requires to ensheath the sample stream in both lateral dimensions. Previous designs of two-dimensional hydrodynamic focusing used up to six inlets to ensheath the sample flow (1, 18, 24, 25). Such a system was demonstrated by Simonnet and Groisman where the relative sheath flow values of the six inlets were used to fully control the position and size of the sample stream (18). This device achieved a CV of 2.7% in fluorescence measurements at particle count rates up to 1 kHz for the brightest particles tested, which is marginally worse than the CV achieved with the micro-device presented here (Fig. 4c). The possibility to position the sample flow inside the flow channel is an interesting option. However, the sensitive adjustment of all sheath flows can cause some inconvenience in daily use.

A unique feature of the design used in our work is that only a single inlet for the sheath flow is used to achieve two-dimensional (2D) hydrodynamic focusing (10). The micro-device we employed has a robust and reliable hydrodynamic focusing stage for 2D positioning of particles in both directions perpendicular to the direction of the flow. This attribute could turn out to be indispensable for practical flow cytometric analysis to obtain a pulse height resolution significantly lower than the biological variation, for example, in cell size or antibody expression.

The design of hydrodynamic focusing used depends on the technique applied for chip production. Simple one-step lithography is typically used to create 2[1/2]D fluidic structures (i.e. 2D layout and [1/2]D for the channel height). However, such microchips are limited to 1D hydrodynamic focusing only. A distinct advantage of lithography is that it offers smooth surface walls which can be used to create low loss optical waveguides. Such waveguides are sometimes applied to collect optical signals (8, 12). Lithography can also be used to create V-shaped grooves (3). Altendorf et al. used a V-shaped groove to align blood cells by cell adhesion (40). This allowed them to differentiate platelets, lymphocytes, monocytes, and neutrophils in blood samples (depleted of erythrocytes) by small angle and large angle light scattering. More elaborate structures can be built by stacking 2[1/2]D fluidic structures, which permit implementation of 2D hydrodynamic focusing. An example is the chip used by Kim et al., who used sequential lithographic steps to create a master on a silicon wafer featuring flow channels and chevron-shaped grooves (23). This device used two inlets for sheath flow and was applied for detecting bacteria with fluorescent coded microspheres. In contrast to sequential lithography, we exploited ultra-precision milling technique to manufacture the master. This approach, as reported in details in Ref.10, offers higher flexibility in design of fluidics and integrated optical elements.

In hydrodynamic focusing, the sample stream is confined by a sheath stream and focusing is achieved by squeezing the combined stream through a narrowing channel (1, 5, 17). Alternatively, acoustic focusing (15) can be used to analyze particles and cells (16). Dron et al. demonstrated acoustic focusing of particles in a planar microchannel using a standing acoustic wave (41). The aim was to improve imaging of particles for particle image velocimetry (PIV). Shi et al. used a combination of sheath flow and acoustic focusing for particle separation (42). Smaller particles are focused substantially slower by the acoustic field (15). This effect was used by Shi et al. to demonstrate the continuous separation of particles with different sizes. Focusing can also be achieved with dielectrophoretic forces (DEP) and is widely used in microfluidics (1, 3, 6, 19, 26). The advantage of using DEP or acoustic focusing is that the forces exerted can also be used for other purposes in a coherent approach, in particular for particle sorting (7, 19, 42).

Notably a high signal stability can potentially be achieved without focusing the sample stream at all, if the complete fluid channel is measured with sufficiently high spatial resolution, e.g., using a camera or laser scanning (21, 43–45). Bang et al. achieved a CV as low as 1.4% using one-dimensional hydrodynamic focusing applying camera detection. Alternatively, the excitation light for fluorescence detection can be adjusted to be homogenous across the whole microfluidic channel. Recently, Joo et al. used excitation by light emitting diodes to detect fluorescence from beads and cells (46). They demonstrated high signal stability without using particle focusing in their portable flow cytometer. However, the count rate for fluorescent particles demonstrated was limited to about 2 Hz. Such comparatively low count rates are expected for approaches using extended detection regions and may limit their usefulness for application in hematology and immunology.

In hematology, cell concentrations in the original samples are typically high so that the maximum useful particle count rate is usually not limited by sample throughput but by coincidence loss (47, 48). The number of particles counted Nc is approximately given by

  • equation image(3)

where N is the number of particles passing the detection region and τ is the mean dead time of the detection system (Tc: counting time). Thus, the useful count rate is approximately inversely proportional to the mean dead time at a given level of coincidence loss. The mean dead time is ultimately limited by the time needed for the particle to cross the detection region although there might be an additional contribution from electronic signal processing. The basic consequence is that high count rates require high linear particle velocity in the detection region. In this context, a potential drawback of using dielectric focusing (DEP) is that the maximum flow speed may be limited to about 1 cm s−1 (8), whereas with microfluidic hydrodynamic focusing particle velocities above 1 m s−1 have been demonstrated (7, 10, 18).

The required particle count rates depend on the application. For instance, a critical threshold in HIV disease progression is a concentration of CD4 positive T lymphocytes of 200 cells per μL (49). About 10,000 leukocytes should be counted to adequately reduce the contribution of the statistical uncertainty to the overall accuracy when determining this concentration. Conventional optical flow cytometers are specified for maximum count rates ranging from 500 Hz to 100 kHz, which would allow to carry out such measurements in less than a minute.

Recently, blood cell counting using microflow cytometers started to appear in commercial systems. Cheung et al. used a combination of DC and AC impedance counting to measure the concentration of erythrocytes (20). This combination allows to measure cellular properties in addition to size (50, 51). A readout system using this chip is now commercially available from Axetris (Switzerland). However, most applications of microflow cytometers for blood cell counting have not reached that level yet. Holmes et al. demonstrated 3-part differential count in a microfluidic device detecting lymphocytes, monocytes, and neutrophils using AC impedance counting in combination with fluorescence detection (27). Four-part differential blood count was demonstrated by Shi et al. exploiting fluorescence staining with FITC and PI (28). They succeeded in differentiating lymphocytes, monocytes, neutrophils, and eosinophils with particle count rates around 10 Hz. Wang et al. applied a microfluidic system for staining and counting CD4 positive and CD8 positive T lymphocytes (9). They combined a vortex-type micromixer for antibody staining of T lymphocytes with a microfluidic flow cytometer with 1D hydrodynamic focusing and bivariate fluorescence detection demonstrating count rates of a few hertz. On chip staining of T lymphocytes has been reported before by Chan et al. (29), however, without using an integrated micromixer. Chan et al. used chips from Agilent Technologies which were vortexed to achieve mixing of the cell suspension and antibody reagent in the sample wells of the chip.

The micro-device presented in this article was used to determine relative concentrations of fluorescently labeled subpopulations of lymphocytes and other leukocytes at a high count rate. Although the signal-to-noise ratio achieved was smaller compared to MoFlo cell sorter, the performance of the micro-device was similar to the large frame flow cytometer when detecting cells with a high level of fluorescence. Furthermore, the sensitivity was sufficient to identify cells exhibiting moderate fluorescence intensity, e.g., anti-CD4-PE labeling of monocytes. The comparison between conventional instruments and microfabricated devices presented here proves the applicability of adequately designed microflow cytometers for cell-based assays for biomedical research, and also for routine applications. The development of a system composed of a compact read-out instrument to accommodate disposable cartridges with integrated microfluidic chips is underway, although such a combination of optimized microfabricated subunits has not been demonstrated yet.

The results listed in Table 1 are to our knowledge the first comparison of measurements of relative blood cell concentrations using microfluidic and conventional flow cytometry. It indicates the capability of microfluidic devices for immunological cell differentiation and the determination of cell concentrations. However, improved accuracy for measuring cell concentrations is highly desirable. At present, both set-ups used were not optimized to allow precise determination of (relative) cell concentrations. The performance of both instruments could be improved by modifying the sample transport to the flow cell, in particular by reducing tubing length and selecting a material to prevent cell specific adhesion. It should be noted that the occurrence of large inter-platform differences (up to 25%) is sometimes also observed in interlaboratory comparisons for the measurands of the immune status, regularly organized in Germany by the Reference Institute for Bioanalytics (RfB) and the Society for Promotion of Quality Assurance in Medical Laboratories (INSTAND).

Within this limit there is an overall good agreement between the measurements compared here. A deviation below 20% was observed for the relative concentrations of lymphocytes, monocytes, and TS lymphocytes. The values for the relative concentrations of B lymphocytes and NK cells also agree within 25%, but in both cases the uncertainties are large due to the low number of repeat measurements and poor counting statistics. On the other hand, larger deviations are found for the relative concentrations of T lymphocytes as well as for the T-helper/inducer cells. In this context, it is noticeable that the relative concentrations of lymphocytes and lymphocyte subsets determined with the MoFlo cell sorter systematically deviate to smaller values.

At present, conventional flow cytometers using quartz flow cells still offer superior signal-to-noise ratios in fluorescence detection. Although this does not limit the application of micro-devices for counting fluorescently labeled cells as considered in this article, the fluorescence background in micro-device could be reduced using other thermoplastics; e.g., cyclic olefin copolymers are known to allow the production of high quality optical components. Adding optical components for laser beam shaping or more efficient integrated light collection might also help to resolve this issue and make disposable plastic flow cells the better choice even for general purpose flow cytometers. Further developments would aim at the integration of different subassemblies into a compact disposable cartridge mounted in fully automated sample-handling and readout device.

Acknowledgements

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

The authors would like to thank Peter Pawlak, Klaus Witt, Stephan Reitz, and Markus Malcher for providing technical assistance and Christine Werner, Mesrure Baydaroglu, and Amin Chebbo for their support in sample preparation and the optimization of the data acquisition.

LITERATURE CITED

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix
  • 1
    Ateya DA,Erickson JS,Howell PBJr,Hilliard LR,Golden JP,Ligler FS. The good, the bad, and the tiny: A review of microflow cytometry. Anal Bioanal Chem 2008; 391: 14851498.
  • 2
    Zhang H,Chon CH,Pan X,Li D. Methods for counting particles in microfluidic applications. Microfluid Nanofluid 2009; 7: 739749.
  • 3
    Huh D,Gu W,Kamotani Y,Grotberg JB,Takayama S. Microfuidics for flow cytometric analysis of cells and particles. Physiol Meas 2005; 26: R73R98.
  • 4
    Motamedi ME. MOEMS: Micro-Opto-Electro-Mechanical Systems. Bellingham: SPIE-The International Society for Optical Engineering; 2005.
  • 5
    Ligler FS,Kim JS. The Microflow Cytometer. Singapore: Pan Stanford Publishing Pte. Ltd.; 2010.
  • 6
    Toner M,Irimia D. Blood-on-a-chip. Annu Rev Biomed Eng 2005; 7: 77103.
  • 7
    Ahn K,Kerbage C,Hunt TP,Westervelt RM,Link DR,Weitz DA. Dielectrophoretic manipulation of drops for high-speed microfluidic sorting devices. Appl Phys Lett 2006; 88: 024104.
  • 8
    Yang SY,Hsiung SK,Hung YC,Chang CM,Liao TL,Lee GB. A cell counting/sorting system incorporated with a microfabricated flow cytometer chip. Meas Sci Technol 2006; 17: 20012009.
  • 9
    Wang JH,Wang CH,Lin CC,Lei HY,Lee GB. An integrated microfluidic system for counting of CD4+/CD8+ T lymphocytes. Microfluid Nanofluid 2011; 10: 531541.
  • 10
    Kummrow A,Theisen J,Frankowski M,Tuchscheerer A,Yildirim H,Brattke K,Schmidt M,Neukammer J. Microfluidic structures for flow cytometric analysis of hydrodynamically focussed blood cells fabricated by ultraprecision micromachining. Lab Chip 2009; 9: 972981.
  • 11
    Wang Z,El-Ali J,Engelund M,Gotsaed T,Perch-Nielsen IR,Mogensen KB,Snakenborg D,Kutter JP,Wolff A. Measurement of scattered light on a microchip flow cytometer with integrated polymer based optical elements. Lab chip 2004; 4: 372377.
  • 12
    Godin J,Lo YH. Two-parameter angular light scatter collection for micro-fluidic flow cytometry by unique waveguide structures. Biomed Opt Expr 2010; 1: 14721479.
  • 13
    Rosenauer M,Buchegger W,Finoulst I,Verhaert P,Vellekoop M. Minaturized flow cytometer with 3D hydrodynamic particle focusing and integrated optical elements applying silicon photodiodes. Microfluid Nanofluid 2011; 10: 761771.
  • 14
    Merenda F,Rohner J,Fournier JM,Salathé RP. Minaturized high-NA focusing-mirror multiple optical tweezers. Opt Expr 200715: 60756086.
  • 15
    Ward M,Turner P,DeJohn,Kaduchak G. Fundamentals of acoustic cytometry. Curr Protoc Cytom 2009; 49: unit 1.22:11.22.12.
  • 16
    Goddard GR,Sanders CK,Martin JC,Kaduchak G,Graves SW. Analytical performance of an ultrasonic particle focusing flow cytometer. Anal Chem 2007; 79: 87408746.
  • 17
    Chung TD,Kim HC. Recent advances in miniaturized microfluidic flow cytometry for clinical use. Electrophoresis 2007; 28: 45114520.
  • 18
    Simmonet C,Groisman A. High-throughput and high-resolution flow cytometry in molded microfluidic devices. Anal Chem 2006; 78: 56535663.
  • 19
    Holmes D,Sandison ME,Green NG,Morgan H. On-chip high-speed sorting of micron-sized particles for high-throughput analysis. IEE Proc Nanobiotechnol 2005; 152: 129135.
  • 20
    Cheung K,Gawad S,Renaud P. Impedance spectroscopy flow cytometry: On-chip label-free cell differentiation. Cytometry Part A 2005; 65A: 124132.
  • 21
    Bang H,Yun H,Lee HY,Park J,Lee J,Chung S,Cho K,Chung C,Han DC,Chang JK. Expansion channel for microchip flow cytometers. Lab Chip 2006; 6: 13811383.
  • 22
    Lee GB,Chang CC,Huang SB,Yang RJ. The hydrodynamic focusing effect inside rectangular microchannels. J Micromech Microeng 2006; 16: 10241032.
  • 23
    Kim JS,Anderson GP,Erickson JS,Golden JP,Nasir M,Ligler FS. Multiplexed detection of bacteria and toxins using a microflow cytometer. Anal Chem 2009; 81: 54265432.
  • 24
    Wolff A,Perch-Nielsen IR,Larsen UD,Friis P,Goranovic G,Poulsen CR,Kutter JP,Telleman P. Integrated advanced functionality in a microfabricated high-throughput fluorescent-activated cell sorter. Lab Chip 2003; 3: 2227.
  • 25
    Hairer G,Vellekoop MJ. An integrated flow-cell for full sample stream control. Microfluid Nanofluid 2009; 7: 647658.
  • 26
    Holmes D,Morgan H,Green NG. High throughput particle analysis: Combining dielectrophoretic particle focussing with confocal detection. Biosens Bioelectr 2006; 21: 16211630.
  • 27
    Holmes D,Pettigrew D,Reccius CH,Gwyer JD,van Berkel C,Holloway J,Davies DE,Morgan H. Leukocyte analysis and differentiation using high speed microfluidic single cell impedance cytometry. Lab Chip 2009; 9: 28812889.
  • 28
    Shi W,Kasdan HL,Fridge A,Tai YC. Four-part differential leukocyte count using μflow cytometer. Wan Chai, Hong Kong, People's Republic of China: 2010 IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS); 2010. pp 10191022.
  • 29
    Chan SDH,Luedke G,Valer M,Buhlmann C,Preckel T. Cytometric analysis of protein expression and apoptosis in human primary cells with a novel microfluidic chip-based system. Cytometry Part A 2003; 55A: 119125.
  • 30
    Theisen J,Schmidt M. Method for the hydrodynamic focusing of a fluid and associated assembly. Patent applications DE 10,017,318 A1; 2007 and WO125081 A1;2008.
  • 31
    Singh K,Su X,Liu C,Capjack C,Rozmus W,Backhouse CJ. A miniaturized wide-angle 2D cytometer. Cytometry Part A 2006; 69A: 307315.
  • 32
    Becton Dickinson Simultest™ IMK-Lymphocyte, Datasheet, Catalog No. 340182; and references cited therein.
  • 33
    Li X,Breukers C,Ymeti A,Lunter B,Terstappen LWMM,Greve J. CD4 and CD8 enumeration for HIV in resource-constrained settings. Cytometry Part B 2009; 76B: 118126.
  • 34
    Chase ES,Hoffman RA. Resolution of dimly fluorescent particles: A practical measure of fluorescence sensitivity. Cytometry 1998; 33: 267279.
  • 35
    Sadler WA,Murray LM,Turner JG. Minimum distinguishable difference in concentration: A clinically oriented translation of assay precision summaries. Clin Chem 1992; 38: 17711778.
  • 36
    Jackson A. Basic phenotyping of lymphocytes: Selection and testing of reagents and interpretation of data. Clin Immunol Newslett 1990; 10: 4355.
  • 37
    JCGM. Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement. Paris: JCGM; 2008, AnnexG.
  • 38
    Shapiro HM. How flow cytometers work; Performance: Precision, sensitivity, and accuracy. In: ShapiroHM, editor. Practical Flow Cytometry,4th ed. Hoboken, NJ: Wiley-Liss; 2003. Chapter 4.10.
  • 39
    Otto FJ. High-resolution analysis of nuclear DNA employing the fluorochrome DAPI. Methods Cell Biol 1994; 41: 211217.
  • 40
    Altendorf E,Zebert D,Holl M,Yager P. Differential blood counts obtained using a microchannel based flow cytometer. Chicago, IL, USA: IEEE International Conference on Solid State Sensors Actuators, Transducers; 1997. pp 531534.
  • 41
    Dron O,Ratier C,Hoyos M,Aider JL. Parametric study of acoustic focusing of particles to improve micro PIV-measurements. Microfluid Nanofluid 2009; 7: 857867.
  • 42
    Shi J,Huang H,Stratton Z,Huang Y,Huang TJ. Continous particle separation in a microfluidic channel via standing surface acoustic waves (SSAW). Lab Chip 2009; 9: 33543359.
  • 43
    McKenna BK,Selim AA,Bringhurst FR,Ehrlich DJ. 384-Channel parallel microfluidic cytometer for rare-cell screening. Lab Chip 2009; 9: 305310.
  • 44
    Furuki M,Imanishi S,Shinoda M. Optical detection of a sample in a channel. Patent EP 2078950A2; 2009.
  • 45
    Tarnok A,Gerstner AOH. Clinical applications of laser scanning cytometry. Cytometry 2002; 50: 133143.
  • 46
    Joo S,Kim KH,Kim HC,Chung TD. A portable microfluidic flow cytometer based on simultaneous detection of impedance and fluorescence. Biosens Bioelectr 2010; 25: 15091515.
  • 47
    Strackee J. Coincidence loss in bloodcounters. Med Biol Eng 1966; 4: 9799.
  • 48
    Helleman PW. Quality control in blood cell analysis. Comp Hematol Int 1991; 1: 2128.
  • 49
    Crowe S,Turnbull S,Oelrichs R,Dunne A Monitoring of human immunodeficiency virus infections in resource-constrained countries. Clin Infect Dis 2003; 37( Suppl 1): S25S35.
  • 50
    Gawad S,Cheung K,Seger U,Bertsch A,Renaud P. Dielectric spectroscopy in a micromachined flow cytometer: Theoretical and practical considerations. Lab Chip 2004; 4: 241251.
  • 51
    Gawad S,Schild L,Renaud P. Micromachined impedance spectroscopy flow cytometer for cell analysis and particle sizing. Lab Chip 2001; 1: 7682.

Appendix

  1. Top of page
  2. Abstract
  3. MATERIALSAND METHODS
  4. RESULTS
  5. DISCUSSIONAND PERSPECTIVES
  6. Acknowledgements
  7. LITERATURE CITED
  8. Appendix

In the micro-device considered here the exciting laser light is incident perpendicular to the particle stream. The variation of laser intensity along the light propagation direction will be neglected compared to the variation of laser intensity transverse to the laser beam. In a situation where high signal stability is of primary concern, the laser beam is much wider than the width of the sample stream or the size of the particles investigated. In properly configured arrangements the signal is maximized, so that the transverse beam profile, i.e., the radial dependence of the irradiance, is well approximated by the Taylor expansion

  • equation image(A1)

where r is the distance measured from the center of the sample flow. To be more precise, Eq. (A1) should be viewed as the convolution of the light field and the geometrical cross-sections of the particles used to probe signal stability. To simplify discussion, we can safely neglect the particle size since the particles are much smaller than the laser beam width as this would change only the numerical values of the parameters I2 and I0, which are not needed in the following. Thus, the Gaussian intensity profile of the laser beam can be reliably approximated by its quadratic dependence on r in the range accessible by the sample stream. Only measurement of pulse height distributions are considered so that only the intensity distribution orthogonal to the sample flow has to be considered in Eq. (A1). Pulse area measurements may require to consider the spatial distribution in more detail.

The sample stream is characterized by a distribution of potential particle positions crossing the laser beam equation image which is parameterized by the “width” ws of the sample stream. We assume that the shape of this distribution does not change with sample stream width, so that we can describe the general distribution with the one describing the case ws = 1:

  • equation image(A2)

with the normalization

  • equation image(A3)

 The coefficient of variation (CV) is the ratio of the standard deviation σ and the average peak intensity sampled, which is

  • equation image(A4)

where we introduced the constant

  • equation image(A5)

 Equation (A4) describes the reduction of the average signal intensity (pulse height) with increasing sample flow width, a feature usually considered negligible in discussing the influence of high sample throughput on measurement performance. Indeed, for the estimation of the CV targeted here, this provides a higher order correction only. The variance σ2 is calculated as

  • equation image(A6)

where we introduced the constant

  • equation image(A7)

 The CV of the pulse height distribution is thus given by

  • equation image(A8)

 This demonstrates that the CV will generally vary quadratically with sample stream width. Changes are expected for wide sample streams which could easily violate the assumptions underlying Eq. (A1), particularly if tight focusing of laser light is used to increase signal level.