r 1998 Wiley-Liss, Inc.
Cytometry 33:267–279 (1998)
Resolution of Dimly Fluorescent Particles: A Practical
Measure of Fluorescence Sensitivity
Eric S. Chase1 and Robert A. Hoffman2*
2Becton
1Cytek Development, Inc., Fremont, California
Dickinson Immunocytometry Systems, San Jose, California
Received 9 June 1998; Accepted 16 June 1998
Flow cytometry is usually used to analyze subpopulations of cells, not simply to measure the mean
fluorescence level of a mixture. Thus, resolution or
coefficient of variation (CV) of dimly stained populations is the most appropriate measure of fluorescence ‘‘sensitivity.’’ Methods used to measure sensitivity that are in routine use do not unambiguously
and completely determine the ability of a flow
cytometer to resolve dimly fluorescent populations
from each other. Since fluorescence sensitivity depends on two factors, background light (B) and
detection efficiency (Q, the detected photoelectrons
per fluorochrome molecule on an analyzed particle), one cannot uniquely define the operating
condition of a flow cytometer with just one of these
factors. In general, it is not possible to define the
ability of a flow cytometer to resolve dim subpopulations by using a single number such as ‘‘noise level’’
or ‘‘detection threshold’’—the description requires a
‘‘two-parameter’’ measure. A carefully characterized
flow cytometer was used to determine the inherent
fluorescent CV of dimly fluorescing beads. The fluorescence from the beads is also calibrated in terms of
molecules of equivalent soluble fluorophore (MESF).
The beads with known inherent CV and MESF provide a standard against which the instrument contribution to the CV of dim fluorescence can be measured. By measuring the standard deviation (SD) of
the fluorescence histogram from unstained beads
(noise) we obtain a second measure of instrument
performance. The bead CV and noise SD are a
sufficient pair of factors to determine the optical
capability of a flow cytometer to resolve dim subpopulations of particles. It is also possible to use the
measurements to calculate B and Q and use this
information to predict the shapes of fluorescence
histogram distributions of dim particles. Cytometry 33:267–279, 1998. r 1998 Wiley-Liss, Inc.
Fluorescence sensitivity has two different definitions in
the cytometry literature. One of the authors (3) has
summarized the definitions as:
fluorescent ‘‘sensitivity’’ for most of the applications for
which cytometry is currently used. It is rare that one is
trying to resolve a homogenous particle population from
background.
Unfortunately, the current methods (2,6) routinely used
to assess the fluorescence ‘‘sensitivity’’ of a cytometer
measure the detection threshold appropriate for definition
1 above. The threshold definition of ‘‘sensitivity’’ can fail
to distinguish instruments with different ability to resolve
dim subpopulations (3,8).
In this report we focus on three essential characteristics
of a measure of ‘‘sensitivity.’’ The measure should be able
to 1) quantitatively measure and distinguish the ability to
resolve dimly fluorescent subpopulations; 2) be practical
to implement and use; and 3) be able to predict perfor-
‘‘1. Degree to which a flow cytometer can measure
dimly stained particles and distinguish them from a particlefree background (threshold). Threshold is important when
the mean fluorescence of a dimly fluorescent population is
measured. The greater the number of particles analyzed,
the more . . . precisely will the mean fluorescence be
measured.
2. Degree to which a flow cytometer can distinguish
unstained and dimly stained populations in a mixture of
particles (resolution). Resolution is important for immunofluorescence analysis of subpopulations and is strongly
affected by the measurement CVs for dim and unstained
particles.’’
The ability of a cytometer to resolve subpopulations of
dimly fluorescent particles is the appropriate definition of
Key terms: particles; fluorescence sensitivity; CV;
MESF; background light; optical efficiency
*Correspondence to: Robert A. Hoffman, Becton Dickinson Immunocytometry Systems, 2350 Qume Drive, San Jose, CA 95131–1807.
E-mail: bhoffman@bdis.com
268
CHASE AND HOFFMAN
mance of an instrument and the effect of sensitivity
differences on analytical results.
Previous studies by Pinkel and Steen (4) and Steen (7)
and by Gaucher et al. (1) provide a rigorous theoretical and
empirical basis for thoroughly analyzing the fluorescence
sensitivity of a flow cytometer. This report builds on their
work, analyzes the factors that most affect practical
measurement of Q and B, and describes simple methods
for determining Q and B. A simple theoretical model is
described that provides calculation of fluorescence histograms reflecting the effect of Q and B on the widths and
overlap of fluorescence distributions.
This report emphasizes practical issues and development of a generally useful method for estimating the
essential factors, background light and efficiency of fluorochrome to photoelectron conversion, that affect fluorescence sensitivity. Some theoretical rigor and complexity is
neglected in order to focus on the essential issues in this
paradigm shift in assessment of fluorescence sensitivity.
COMPARISON WITH PREVIOUS WORK
Two previous reports by Gaucher et al. (1) and Steen (7)
carefully characterized flow cytometers in terms of Q and
B and discussed measures of sensitivity. Both investigations used dim light flashes from an LED to measure the
optical noise contribution from photoelectron statistics.
And both used fluorescein stained beads calibrated in
terms of molecules of equivalent soluble fluorophore
(MESF) to measure Q. Gaucher et al. also cross-calibrated
stable fluorescent beads to their MESF calibrators as a
secondary reference particle. The stable beads were very
brightly fluorescent, however, and were not useful in
measuring the effect of photoelectron statistics a low
signal levels. Gaucher et al considered the intrinsic CV of
the sample to be variable and unpredictable and do not
seem to have considered using dimly fluorescent beads
whose intrinsic CV was determined.
Since the LED calibration method is not available on
commercial instruments we have investigated using relatively uniform, dimly fluorescing beads as substitutes for
LED flashes used by Gaucher et al. and Steen. Under
practical conditions it is possible to use such beads as
nearly ideal light sources and to obtain the same measurements of Q and B which Gaucher et al and Steen made.
The practical issues that must be considered in using the
beads are the bead intrinsic CV and the contribution of
illumination variability to the CV. An upper limit to the
intrinsic CV can be estimated by comparing bead CVs with
the CVs from LED flashes. The contribution to the measured CV from illumination variability can be estimated
from the CV obtained with uniform, brightly fluorescent
beads where background light and photoelectron statistic
contributions are minimal. Commercially available beads
with sufficiently dim and uniform fluorescence can be
used to make these measurements on typical benchtop
flow cytometers.
THEORETICAL CONSIDERATIONS
Fluorescent light generated from fluorochrome molecules produces photoelectrons in the detector—usually a
photomultiplier (PMT). The photoelectrons are then processed by electronics and software to become linear
fluorescence units in a histogram or dot plot. The signal
processing may include transformation of the signal to a
logarithmic scale. In a well designed cytometer, all the
noise introduced in the processing of the fluorescence
light is due to photoelectron statistics—the statistical
fluctuations due to the random physical process of light-toelectron conversion.
The theory described below applies to signal processing
that uses pulse integration and baseline restoration. Ideal
performance of the detectors and electronics is assumed
and minor factors such as photomultiplier (PMT) dynode
noise (1,7) are ignored. The theory will also be used to
evaluate data from instruments that use peak detection of
bandwidth limited pulses, which produce nearly the same
result as pulse integration.
The photoelectron generation follows Poisson statistics
at the photocathode. If the average number of photoelectrons is n, then the standard deviation SDe at the photocathode is
SDe 5 În
(1)
The signal processing converts photoelectrons to a
linear channel in a histogram with a gain factor G. Note
that the gain defined here includes all aspects of the signal
conversion process not simply PMT and amplifier gain. In
the process of amplification by the amount G, the noise is
smoothed to a normal distribution with standard deviation
still determined by the original Poisson statistics.
SDp 5 G · În
(2)
We let F represent the number of fluorochrome molecules (usually expressed in MESF) and B the equivalent
number of fluorochrome molecules required to produce
background light. The conversion of fluorochrome molecules to photoelectrons is done with an efficiency, Q.
Q has units of photoelectrons per fluorochrome molecule
or MESF. The number of signal photoelectrons is Q 3 F,
and the number of background photoelectrons is Q 3 B.
The final measured signal has mean value of
Signal 5 G 3 Q 3 F.
(3)
Steen (7) and Gaucher (1) describe the factors affecting
variation in fluorescence signal measurements. The measured standard deviation due to photoelectron statistics in
the process of optical detection is
SDoptical 5 G · ÎQF 1 QB 5 GÎQ · ÎF 1 B
(4)
PRACTICAL MEASURES OF SENSITIVITY
269
FIG. 1. Compare log and linear displays of the same distributions. In
each case the mean of the lowest population (noise distribution) is zero
linear fluorescence units. The populations are calculated for particle MESF
of 0 (noise), 500, 2,000, and 10,000. The background B is 200 MESF, and
the efficiency Q is 0.01 photoelectrons/fluorochrome molecule. Perfect
baseline restoration circuitry is assumed so that the mean channel of the
noise distribution is zero in linear fluorescence units. Note the artifactual
peak of the noise distribution on the log display due to the increasing bin
width (in linear fluorescence units) of the log histogram channels.
If we are measuring particle fluorescence, there is
additional variation in the measurement due to the inherent variation of the number of fluorochrome molecules
per particle, SDintrinsic, and uniformity of excitation illumination, SDillumination.
The total measurement SD is
tion. The mean of the distribution is given by Equation 3,
and the standard deviation is given by Equation 5. The
instrument contribution to the standard deviation includes
only the factors due to photoelectron statistics, SDoptical,
and uniformity of particle illumination, SDillumination.
A simple spreadsheet is described in the Appendix that
allows calculation of histogram distributions based on this
model.
SD 5
ÎSD
2
optical
2
2
1 SDinherent
1 SDillumination
(5)
The coefficient of variation, CV, of the final measurement is
CV 5 SD/Signal 5 SD/(G 3 Q 3 F).
(6)
A simple model for calculating the fluorescence histogram distributions assumes a normal (Gaussian) distribu-
DEFINITIONS OF ‘‘SENSITIVITY’’ COMPARED
WITH THE MODEL
The simple model for calculating fluorescence histograms assumes perfect instrument performance—including pulse integration and baseline restoration of any offset
at the detector due to background light. Figure 1 shows
the effect logarithmic and linear amplification have on
identical distributions-i.e. with the same mean and stan-
270
CHASE AND HOFFMAN
FIG. 2. Detection threshold definition of fluorescence sensitivity. The
lowest population in each panel is
from a non-fluorescent particle and
is due only to background noise. The
other three populations represent
fluorescent populations with the low,
middle and high fluorescent populations having the same MESF in each
panel. Individual populations are
shown on the left and the sum of
individual distributions is shown on
the right. The top and bottom panels
are results with the same sensitivity
defined by the mean or other metric
of the noise (nonfluorescent particle) distribution. The noise distributions for the top and bottom panels
are identical.
dard deviation. Although the type of amplification does
not affect the resolution of dim populations, the type of
amplification does affect the shape of the distributions. In
particular it is important to notice that the logarithmic
display of the histogram has an apparent peak for the
unstained particles even though the mean of the distribution is zero. This is due to the way data are binned in the
log histogram channels. Larger channel numbers include a
wider range of signal values.
Figures 2 and 3 illustrate how commonly used definitions of sensitivity are not adequate to determine how well
dimly fluorescent particles are resolved either from background (unstained particles) or one dimly fluorescent
population from a second. The theoretical model is used to
calculate histograms of non-fluorescent particles and three
different populations of particles with different MESF
values.
Figure 2 illustrates the detection threshold (2,5,6) definition of ‘‘sensitivity’’. Figure 3 illustrates the ‘‘signal/
noise 5 1’’ definition used by Steen (7). Neither of these
definitions that uses a single number or feature of the data
to describe ‘‘sensitivity’’ can uniquely describe the ability
of an instrument to resolve dimly fluorescent populations.
Only a 2-dimensional characterization of ‘‘sensitivity’’
describes the full range of performance.
To simplify slightly, if background is low, one can have
good resolution of a dimly stained population from noise
but unless the efficiency, Q, is also high the population
that is resolved well from noise will not be well resolved
from a slightly brighter population. As a practical example
consider a hypothetical case where lymphocyte autofluorescence is 5,000 MESF. We could have a situation where
the autofluorescence is well resolved from background
noise, but where cells stained with 5,000 MESF (10,000
MESF total fluorescence) are not resolved from autofluorescence.
PRACTICAL PROBLEMS
Any routine method to measure Q and B must be rapid
and sufficiently accurate to provide useful results. The
most accurate determination of Q would use LED light
pulses of varying intensities. However, most instruments
are not equipped with LEDs able to generate variable
intensity signals. In addition, the logarithmic amplifiers
used to generate histograms may not have a uniform
transfer function across the range of signal levels.
Lastly, if dim distributions are truncated at histogram
channel 0, incorrect CVs will be given by the analysis
software. Any routine method to determine Q and B must
minimize or eliminate these problems.
PRACTICAL APPROACHES TO DETERMINE
Q AND B
It is possible to use fluorescent beads instead of LED
light pulses to determine the photoelectrons/pulse. However, it must be verified that the measured CVs are
primarily due to photoelectron statistics and are not
broadened by background, intrinsic CVs, and illumination
CVs. It is possible to correct the observed CVs for these
factors, but this requires more calculations, and is not
convenient. To provide a rapid method, it is desirable to
run a bead sample that is bright enough so its CV is not
increased by background light, but not bright enough such
that its observed CV is broadened by illumination and/or
instrinsic CVs.
Figure 4 shows the theoretical effect of background and
intrinsic plus illumination CVs on observed CVs. Beads
with about 10,000 MESFs have an observed CV mostly
PRACTICAL MEASURES OF SENSITIVITY
271
FIG. 3. Illustration of the definition of signal/noise 5 1 for fluorescence sensitivity. In the top and
bottom panels the S/N 5 1 for a
particle with MESF 5 100. In both
cases the lowest peak in each case is
from nonfluorescent (0 MESF) particles, and the low (200 MESF),
middle (500 MESF) and high (9,600
MESF) fluorescence peaks in each
panel have the same MESF. In the
top panels B 5 900 MESF, Q 5 0.1
and G 5 0.5. In the lower panels
B 5 2, Q 5 0.01, and G 5 5.
FIG. 4. Calculated CVs as a function of mean equivalent soluble fluorochrome. The CV was
calculated using typical values of Q 5 0.005, b 5 1,000, and CVinherent1illumination 5 3.0%.
dominated by photoelectron statistics, and least affected
by background and intrinsic plus illumination effects.
To confirm the observed CV of the moderately bright
bead is indeed dominated by photoelectron statistics, an
extremely bright bead with a CV dominated by the
intrinsic plus illumination CV should have a CV less than
one third of the moderately bright bead. A blank bead
should have a standard deviation less than one third of the
CHASE AND HOFFMAN
272
moderately bright bead to ensure that the background CV
can be ignored.
Ideally, the moderately bright bead would have a known
number of MESFs. However, beads with known MESFs
may have intrinsic CVs large enough to broaden observed
CVs. Consequently, a second bead with known MESFs can
be used to convert the moderately bright bead mean into
MESFs. So with one bead sample with a known MESF, one
moderately bright bead sample with a low intrinsic CV,
one blank bead sample, and one bright bead sample, it is
possible determine the Q factor and verify the measurement is accurate.
In the case where illumination and intrinsic CVs can be
ignored, the standard deviation of a bead population is
given by Equation 4). If the observed SD of the moderately
bright bead is at least 3 times greater than the blank bead
SD, and the observed CV of the moderately bright bead is 3
times greater than the bright bead, then the observed SD
of the moderately bright bead is given approximately by
SDparticle 5 G · ÎQF 5 GÎQ · ÎF
(7)
Using Equation 3 and 7,
CVparticle 5 SDparticle/Mean 5 1/ÎQF
and so
and signal processing electronics from a FACScan. A green
LED was mounted on a stage so that it could be moved
different distances from the flow cell. The LED was driven
by a square wave signal generator with a 3.0 µs duration.
Laser power was 15 mW for all measurements. A constant
amplitude square wave pulse from the pulse generator was
used to drive an LED in the Forward Scatter channel to
trigger the signal processing. Linear gain was used to
record the mean and CV of the LED pulses obtained in the
green fluorescence channel, designated FL1. A background distribution was obtained by triggering the instrument without any green LED output but with the laser on
as if analyzing particles.
Four different intensity fluorescein calibration beads
with MESF range, 5,334–82,151 were run (Quantum 24
kit, Flow Cytometry Standards Corporation, San Juan, PR)
to calibrate the means of the LED generated distributions
in MESF.
Background corrections were made to the observed
LED distributions. The median (50% cumulative) channel
of the background (blank bead) histogram channel was
assumed to represent the mean of the background distribution, and this mean was subtracted from observed means
to obtain a background corrected mean. The background
standard deviation was obtained by assuming the distribution was normal and using the observed 50% and 90%
cumulative distribution channels
SDbackground 5
(8)
· (90% Cumulative Ch 2 50% Cumulative Ch)/1.30.
Equation 8 also applies if the measured CV has been
corrected for factors other than the photoelectron statistics from the particle signal.
When there is no particle signal F, the SD of the noise or
blank bead distribution is
Use of this equation assumes the median channel is greater
than zero.
The background SD was geometrically subtracted from
the observed SD to obtain the background corrected SD.
The corrected SD was divided by the corrected mean to
obtain the background corrected CV. For LED flashes, this
corrected CV was the photon statistical CV, since LED
flashes have little or no illumination or intrinsic CV. The
photoelectron statistical CVs were plotted against
1/ÎMean, and the best slope J was determined. J2 is a best
fit measure of Channels/photoelectron. The MESF of the
Quantum 24 beads was plotted against Mean, and the best
slope K was determined. K is a best fit measure of the
MESF/channel. Then according to Equation 8, the optical
efficiency Q is
Q 5 1/(CV2 p F).
SDbackground 5 G · ÎQB 5 GÎQ · ÎB
(9)
Furthermore, the right side of the blank bead distribution
can be used to determine the background standard deviation. Then according to Equation 9, the square of the ratio
of the standard deviations times the MESF of the moderately bright bead will give B.
B 5 (SDbackground/SDparticle)2 3 (MESFparticle),
(10)
Q 5 1/(CV2F) 5 1/(J2K)
where SDbackground and SDparticle are measured in linear
histogram channel numbers.
This proposed method of determining Q and B avoids
the use of LEDs, avoids the use of log gains, and avoids the
use of truncated distributions to determine means or CVs.
Using Equations 3, 8, and 9, B was determined from
2
B 5 (SDbackground
) p K/J2.
MATERIALS AND METHODS
Measuring Q and B with LED Light Flashes
Measuring Q and B With Multiple Levels
of Fluorescent Beads
Q and B were determined using LED flashes on an
experimental flow cytometer that used optics, flow cell,
Five different intensity Rainbow beads (nos. 2–6) from a
7-bead kit (Catalog number RFP-30–5K, Spherotech Inc.,
PRACTICAL MEASURES OF SENSITIVITY
Libertyville, IL) were run on an experimental flow cytometer using log or linear gain, and means and CVs were
obtained in the green fluorescence channel, designated
FL1. Four different intensity FCSC beads were run (Quantum 24 kit; MESF range, 5,334–82,151) to translate the
means of the Spherotech bead distributions into MESFs.
Spherotech bead no. 1 (nonfluorescent blank) was used to
determine the background distribution.
The observed CVs were then corrected for background
broadening as described above. The background corrected CVs were then corrected for illumination and
intrinsic broadening using
2
2
2
CVPhoton
Statistical 5 CVBackground Corrected 2 CVIllumination1Instrinsic
where the no. 8 Spherotech bead was used to estimate an
upper limit on Illumination 1 Intrinsic CV. Again, the
slope of the photon statistical CVs was plotted against
1/Sqrt(Mean), and the best slope J was determined. Q and
B were then determined as described for the LED method.
Excess background light was introduced into the optics
using an incandescent lamp, and the Spherotech bead CVs
were measured using log gain. Q and B were then
determined as described above. A 0.5ND filter was placed
in the emission path of the FL1 detector. Again, Spherotech bead CVs were measured using log gain. Q and B
were again determined as described above.
Measuring Q and B With a Minimal
Bead Set—A Rapid Method
Blank beads (Spherotech no. 1 Rainbow Bead), moderately bright beads (Spherotech no. 4 Rainbow Bead),
bright beads (Spherotech no. 8 Rainbow Bead), and a bead
with known MESFs (15,472 MESF bead in Quantum 24 set)
was run. Linear gain was used and Forward Scatter was
used as a trigger. A Forward Scatter gate was set around
bead singlets.
If the CV of the moderately bright bead was more than 3
times the CV of the bright bead, and the SD of the
moderately bright bead was more than 3 times the SD of
the blank bead, then the CV of the moderately bright bead
was assumed to be dominated by photon statistics, and the
observed CV was used to determined the number of
photoelectrons per pulse using
Photoelectrons 5 1/CV .
2
A 1-point calibration factor, MESF/channel, was determined from the bead with known MESF. The MESF of the
moderately bright bead was determined by multiplying its
mean channel by the calibration factor.
The optical efficiency Q was then calculated from the
photoelectrons and MESF corresponding to the moderately bright bead.
Q 5 (Moderately Bright Photoelectrons)/
· (Moderately Bright MESF)
273
Then the 50% and 90% cumulative distribution channels
were determined for the blank bead. The standard deviation was determined from
SDbackground 5 (90% Channel 2 50% Channel)/1.30,
assuming a normal distribution and a median channel
greater than zero.
The standard deviation of the Moderately Bright Bead
was determined from
SDbead 5 CV p Mean
The background MESF was then determined from Equation 10.
RESULTS
Comparison of LED Flashes and Fluorescent Beads
The observed CVs of the brightest Spherotech beads
tended to be greater than the CVs of the LED pulses of the
same signal level. The brightest Spherotech bead had an
observed CV 5 3.05%, whereas an LED flash would have a
1.90% CV at this intensity. According to Equation 5, the
geometrical difference is an estimate of the illumination
plus intrinsic CV of the bright Spherotech bead. The
estimated illumination plus intrinsic CV of 2.39% was used
to correct the observed Spherotech bead CVs. Dimly
fluorescent Spherotech Rainbow beads used to estimate Q
(e.g. Rainbow bead no. 4) had CVs indistinguishable from
LED pulses in our tests. Rainbow bead no. 4 gave a CV of
15%, the same as LED pulses.
Figure 5 shows examples of the histograms used to
estimate intrinsic bead CV and to calibrate Spherotech
Rainbow beads and LED light pulses in units of fluorescein
MESF.
Figure 6 shows the corrected CVs obtained with the
LED flashes and the Spherotech beads using Log and Linear
Gain. The slopes J from this graph were used with the
calibration factor (K 5 66.2 MESF/channel) determined
using Quantum 24 beads to calculate Q as described
earlier. Standard deviations of the background distributions were used to calculate B.
Comparison of Methods on a Single Flow Cytometer
The moderately bright bead (Spherotech no. 4) gave a
CV of 15.2% with linear gain. The SD of this bead was 29
channels, whereas the SD of the blank bead (Spherotech
no. 1) was 8.2 channels. Since the SD of the moderately
bright bead was 3.53 the blank bead SD, background
broadening of the CV could be ignored for the rapid
method. The CV of the bright bead (Spherotech no. 8) was
3.0%. Because the CV of the moderately bright bead was
5.0 times the bright bead, illumination plus intrinsic
broadening of the CV could be ignored for the rapid
method. The photoelectrons/pulse was calculated as 43.3.
The MESF of the moderately bright bead was calculated as
11,400, giving a Q of 0.0038. B was calculated from the
data to be 925 MESF.
274
CHASE AND HOFFMAN
FIG. 5. Raw data histograms for LED flashes, Spherotech Rainbow beads or FCSC Quantum 24 FITC
beads. Bead data were acquired with both linear and logarithmic amplification. Maximum instrument
gain was used for linear histogram display.
The square of the ratio of the blank SD to the moderately
bright bead SD was 0.0077. This times the moderately
bright bead MESF gave B 5 925. A similar analysis was
performed for the log data.
Results from the LED method, rapid method, and
multiple bead method are shown in Table 1. To confirm
the accuracy of the B estimate, the baseline restorer
circuitry was disabled, and the mean of the background
was measured using an electronic trigger. This gave B 5
962.
A 0.50ND filter was placed between the collection lens
and the PMT. This should reduce the optical efficiency, but
should not affect the background. Using log amplification,
the rapid method gave Q 5 0.00078 and B 5 1,047 MESF;
the multiple bead method gave Q 5 0.00086 and B 5
1,476 MESF. Both the rapid and multiple bead methods
gave a reduced Q, however, the multiple bead method
came closest to the expected value of 0.00090.
A low-intensity incandescent lamp was placed near the
PMT housing. This should increase the background, but
not affect the optical efficiency. Using log amplification,
the rapid method gave Q 5 0.0022 and B 5 2,138 MESF;
the multiple bead method gave Q 5 0.0031 and B 5 3,753
MESF. This indicates the rapid and multiple bead methods
can distinguish changes in optical efficiency from changes
in optical background. Because the rapid method made no
corrections for background broadening, the photon statistical CV was overestimated, and the Q was underestimated.
Overall, the results tend to indicate the rapid method is
sensitive to changes in optical efficiency and optical
background, but not as accurate as the multiple bead
method. The data suggests some of the inaccuracy of
determining the optical background is due to using log
amplification.
Determination of Q and B on Multiple Flow
Cytometers Using the Rapid Method
The rapid method was used to measure Q and B on
several instruments using linear gain. Results are shown in
Table 2.
Use of Q and B to Predict Analytical Performance
Figure 7 shows Blank Beads and dim Spherotech no. 2
beads (1,505 MESF) acquired on FACScan 81169 and
FACSCalibur E0634. There is better resolution of the dim
beads on the cytometer with the higher Q value. The
panels to the right show model results for the corresponding experimental data. The mean of the noise distribution
was modeled as equal to the standard deviation—an
empirically derived approximation based on investigation
of the peak detection electronics response to calibrated
noise sources (data not shown).
As a measure of the resolution of the noise and dim
fluorescence peaks, we defined an overlap ratio as
Overlap Ratio 5 (10% Cumulative Dim Bead Channel)/
· (90% Cumulative Noise Channel).
PRACTICAL MEASURES OF SENSITIVITY
275
FIG. 6. A: Corrected CV’s for LED light flashes
and Spherotech Rainbow beads versus Mean
Channel using data acquired with linear amplification. B: Corrected CV’s for Spherotech Rainbow
beads versus Mean Channel using data acquired
with logarithmic amplification.
Table 1
Multiple Method Results
Method
Rapid
Rapid
Multiple LED
Multiple bead
Multiple bead
Q
0.0024
0.0038
0.0033
0.0027
0.0028
B
1,586
925
1,010
806
1,508
Table 2
Multiple Instrument Results
Amplifier
Log
Linear
Linear
Linear
Log
The overlap ratio gives a measure of the ability of a
cytometer to resolve dim populations from noise. A larger
Overlap Ratio means the peaks in the histogram are better
resolved.
Instrument
FACSorty B0375
FACSCalibury E0344
FACSCalibur E0634
FACScany 81871
FACScan 81169
Q
0.0052
0.0088
0.015
0.011
0.0059
B
1,016
1,300
895
994
1,042
The overlap ratio was determined on 5 instruments
using Spherotech no. 2 beads as the dim bead.
Because the flow cytometers used in these experiments
used peak detection rather than pulse integration, the
CHASE AND HOFFMAN
276
FIG. 7. Comparison of fluorescence histograms from instruments with different measured Q and B
values. Data were acquired using linear amplification and are displayed as linear channel numbers.
Corresponding calculated histograms are shown in the panels on the right.
histogram of a noise distribution had a non-zero mean. The
Noise MESF (equivalent to the detection threshold in some
definitions of ‘‘sensitivity’’) was determined on several
cytometers using
(50% Cumulative Distribution Noise Channel)/
· (Mean Channel of MESF Calibration bead)
p MESF value of Calibration bead
As shown in Figure 8, Q was well correlated with the
Overlap Ratio, but the Noise MESF was not well correlated
with the Overlap Ratio. The value of Q was a good
predictor of the ability of an instrument to resolve a dimly
fluorescent particle from background noise, but the Noise
MESF provided almost no information on the ability to
resolve these distributions.
Figure 9 compares experimental fluorescence distributions of Spherotech Rainbow beads with model calculations. The FL1 (green fluorescence) data are from a
normally operating experimental flow cytometer (upper
panel A) or from the same instrument with a neutral
density filter in front of the PMT (upper panel B). The
measured reduction in signal intensity with the neutral
density filter in place was a factor of 3.7. The efficiency, Q,
and background, B were determined for the unperturbed
condition to be Q 5 0.0028 and B 5 1,508 MESF. For the
unperturbed condition these values of Q and B were used
to calculate the background (noise) histogram distribution
and histograms of populations with MESF values assigned
to the Spherotech beads through cross calibration to FCSC
Quantum 24 beads. The calculated model data are shown
in the corresponding lower left panel. For the perturbed
condition with 3.7-fold reduction in light reaching the
PMT, the model was recalculated with both Q and B
reduced by a factor of 3.7. Results are shown in the lower
right panel.
The observed histograms and histograms calculated
from the simple model compare well at least to the level of
visual inspection. Considering that the logarithmic amplifier used to acquire the data is not perfect and the
theoretical model does not take into account any differences between pulse integration and bandwidth limited
peak detection, the agreement is very encouraging. Quantitative use of this or a more sophisticated model should be
useful for determining errors in analyzing dim and poorly
resolved subpopulations and could possibly provide more
accurate answers for such data.
PRACTICAL MEASURES OF SENSITIVITY
FIG. 8. A: Overlap Ratio versus optical efficiency, Q, for 5 cytometers of
Table 2. B: Noise MESF versus Overlap Ratio for the same 5 cytometers.
DISCUSSION
We have described an approach to determine the
fundamental factors, Q and B, that affect the ability of a
flow cytometer to resolve subpopulations of dimly fluorescing particles. The approach chosen uses commercially
available particles and requires no special apparatus or any
alteration to the normal operation of a flow cytometer.
Although the method may use data acquired with logarithmic amplification, it is preferable to avoid potential errors
introduce by log amplifiers and collect the data with linear
amplification. Changes in PMT voltage between that needed
for linear and log amplification should introduce minor, if
any, change in the CVs of the distributions.
Spherotech Rainbow beads were chosen for the experiments for convenience, but beads from other manufacturers may work as well. The primary requirements are adequately uniform fluorescence at a low
enough fluorescence level for the instrument type being
evaluated.
We did not attempt to carefully evaluate the factors that
affected Q in the instruments tested in this study. Laser
power and laser focus spot size were the same in all the
instruments we tested as were the specifications for the
speed of particles through the laser beam, light collection
optics, filters, and PMTs. The greatest variability was
277
probably in the subtle differences in optical alignment and
photocathode efficiency of the PMTs. In our experience,
PMT photocathode sensitivity can vary by as much as a
factor of three for a given type of PMT. Side window PMTs
used in our instruments also have variable sensitivity
across the photocathode, which allows for some variability in sensitivity due to location of the light beam
on the photocathode. Variation of Q by a factor of 3 in
the small number of instruments surveyed was not surprising.
Sources of background light could in general include
luminescence of optical components, Raman scatter, and
fluorochrome in the sample stream. Raman scatter from
the 488-nm laser excitation we used is primarily at 585 nm
and should not be detected in the 515–545-nm pass band
of the filter used for green fluorescence. We did not
intentionally have fluorescent material in our samples
other than particles, but unbound fluorescent reagent
(e.g., unbound fluorescent antibody) will be a serious
source of background light when particles or cells are not
washed from a staining solution.
A final, subtle but important source of background light
can come from spectral overlap of ‘‘out of band’’ fluorochromes used in multicolor staining. For example, a
particle double stained with fluorescein isothiocyanate
(FITC) and phycoerythrin (PE) will have FITC fluorescence in the detector used for (PE). Although electronic
subtraction of the overlapping spectral signal can compensate for the average FITC signal that is detected in the
yellow fluorescence detector used for PE, the noise in the
PE measurement will be increased due to increased
FITC background light during the measurement of the
particle.
When the Q and B factors are known for an instrument it
is possible to predict histogram distributions for dim
signals. Even the simple model use in this work was able to
predict the shape and approximate degree of overlap of
particle distributions. The additional information about
the fluorescence histograms provided by knowledge of Q
and B should be valuable in improving models and
algorithms for analyzing data from dimly fluorescing
samples.
CONCLUSIONS
We have shown that dim, uniformly fluorescent beads
can be used to measure the optical efficiency Q and
background light B in a flow cytometer. When the brightness level of the beads is matched to instruments such that
the primary contribution to the fluorescence CV of the
bead is due to photoelectron statistics, a simple method
that ignores other instrumental factors is possible. In the
present study we have examined the green fluorescence
channel of benchtop flow cytometers that are widely used.
The same approach described here can be used for other
types of flow cytometers and other fluorescence detection
channels. The method should also be applicable to scan-
278
CHASE AND HOFFMAN
FIG. 9. Compare experimental data with theory. Green fluorescence
(FL1) histograms of Spherotech Rainbow beads were obtained for a
normally operating instrument (panel A) and the same instrument with a
neutral density filter in the FL1 optics path (panel B). The efficiency, Q,
and background, B, were determined for the unperturbed condition to be
Q 5 0.0028 and B 5 1508 MESF. Predicted Q for the perturbed instrument
was 0.00076, and perturbed B 5 1508 MESF. These Q and B values along
with know MESF per particle were used to calculate the corresponding
histograms shown in the lower panels.
ning cytometers and may be of use in quantitative image
analysis.
Sample Spreadsheet for Histogram Calculations*
APPENDIX: SPREADSHEET MODEL FOR
FLUORESCENCE DISTRIBUTION HISTOGRAMS
To model the fluorescence histograms resulting from
various values of F, Q and B a spreadsheet program was
written for Microsoft EXCEL. Mean and standard deviation
for the probability distribution were calculated from
equations 3) and 4) above. In order to plot log histograms
as log channel number, the primary independent value
column in the spreadsheet was log channel number. A
second column of corresponding linear channel numbers
was calculated, and the linear channel numbers were used
as input to the cumulative probability function for a
normal distribution. Events per channel were calculated as
the cumulative probability for linear values from the
previous channel linear value to the linear value for the
channel being calculated. In order to plot histograms in
terms of MESF, a spreadsheet column was calculated for
MESF corresponding to the linear channel value. Spreadsheet was tested with Microsoft EXCEL versions 5.0
and 97.
A sample spreadsheet and the relevant functions are
shown below. For the example shown, MESF/particle F 5
0, Background B 5 30 MESF, Q 5 0.030, Gain 5 1.667,
scale 5 2,400, and 64 channels/decade.
Row n
0
A
Log
CH #
B
Lin
Value
C
MESF/
lin_value
D
Events/
channel
E
Cumulative
1
0
0.00
20.00
1785.511
2
1
1.04
20.73
18.40127
0.743963
3
2
1.07
21.49
18.76081
0.75163
4
3
1.11
22.28
19.10367
0.759447
5
4
1.15
23.10
19.42688
0.767407
6
5
1.20
23.94
19.72728
0.775501
7
6
1.24
24.82
20.00152
0.783721
0.5
*Lin Value 5 EXP(LN(10)*An/channels_per_decade),
note lin value 5 0.0000001 for log ch 0.
MESF/Linvalue 5 LogCH#/((photoelectrons/MESF)*Gain)
For log channel 0,
events/channel 5 Scale*(NORMDIST(B1,mean,SD,TRUE)).
For log channels other than 0,
events/channel 5 Scale*(NORMDIST(Bn,mean,SD,TRUE)
2 NORMDIST(B(n 2 1), mean,SD,TRUE)).
Cumulative 5 NORMDIST(Bn, mean,SD,TRUE)
Definition of function NORMDIST: Returns the normal
cumulative distribution for the specified mean and standard deviation.
PRACTICAL MEASURES OF SENSITIVITY
Syntax: NORMDIST(x,mean,standard_dev,cumulative),
where X is the value for which you want the distribution.
Mean is the arithmetic mean of the distribution. Standard_dev is the standard deviation of the distribution. Cumulative is a logical value that determines the form of the
function. If cumulative is TRUE, NORMDIST returns the
cumulative distribution function; if FALSE, it returns the
probability mass function.
The inverse function NORMINV(probability,mean,standard_dev) is useful for determining the channel number
that includes a certain fraction (the probability) of a
distribution.
LITERATURE CITED
1. Gaucher JC, Grunwald D, Frelat G: Fluorescence response and sensitivity determination for ATC 3000 flow cytometer. Cytometry 9:557–565,
1988.
279
2. Gratama JW, Kraan J, Adriaansen H, Hooibrink B, Levering W, Reinders
P, Van den Beemd MW, Van der Holt B, Bolhuis RL: Reduction of
interlaboratory variability in flow cytometric immunophenotyping by
standardization of instrument set-up and calibration, and standard list
mode data analysis. Cytometry 30:10–22, 1997.
3. Hoffman RA: Standardization, Calibration, and Control in Flow Cytometry. In: Current Protocols in Cytometry, Robinson JP (ed). Unit 1.3.
John Wiley & Sons, Inc., New York, 1997.
4. Pinkel D, Steen HB: Simple methods to determine and compare the
sensitivity of flow cytometers. Cytometry 3:220–223, 1982.
5. Schwartz A, Fernández Repollet E, Vogt R, Gratama JW: Standardizing
flow cytometry: construction of a standardized fluorescence calibration
plot using matching spectral calibrators. Cytometry 26:22–31, 1996.
6. Schwartz A, Fernández-Repollet E: Development of clinical standards
for flow cytometry. Ann NY Acad Sci 677:28–39, 1993.
7. Steen HB: Noise, sensitivity, and resolution of flow cytometers.
Cytometry 13:822–830, 1992.
8. Wood JCS, Hoffman RA: Evaluating fluorescence sensitivity on flow
cytometers: An overview. Cytometry 33:256–259, 1998.