Bob Zucker wrote-
"On a recent advertisement ( post card) by MoFlo they implied that digital
processing of data (DIVA) was not as good as the MO FLo type of analysis. I
thought that digital processing of Coulter and BD was superior to the older
designed electronics. Although the distributions from MoFlo do indeed look
superior to a BD Vantage ( postcard), the Cytomation people are implying
that digital electronics are inferior to their current circuitry. Any
opinions on this claim of the new BD equipment with digital electronics as
being inferior. Now I am confused as I thought digital was the new and
improved way to do flow cytometry. Is this just an advertisement from a
company that does not want to get on the digital bandwagon or is it because
they do not have it and don't want to redesign their equipment with it just
yet. I don't want to get into a debate on the virtues of the different
manufacturers but it is important to clarify this point for the flow
cytometry community."
For the record, I do consult for Cytomation and Luminex, and have consulted
for Beckman Coulter and B-D. And I have certainly been as vocal an
advocate of digital processing in flow cytometry as anybody.
The short answer to Bob's question is that, while, in principle, it is
preferable to do as much of the signal processing as possible digitally
(i.e., digital thresholding, baseline restoration, computation of pulse
peak height, area, and width), *none* of the existing electronics achieve
ideal performance in practice. Different companies have made different
tradeoffs.
Looking at Cytomation's post card ad, what was obvious was that the data
from the blank bead in an 8-peak bead set measured using B-D's DiVa
electronics were somewhat "granular" - Cytomation described the peak as a
"picket fence". This effect is also notable in the bottom half of the
bottom decade on digital electronics I have built (see Shapiro et al,
Cytometry 33:280-287, 1998, particularly Fig. 1 and associated text on p.
285). It is primarily an artifact of converter resolution. The "picket
fence" does not appear on the distribution collected using a Cytomation
MoFlo. Is this necessarily better?
Well, to tell the truth, if I had to pick a feature of the distributions to
be impressed by, it would be the distance between the blank peak and the
next highest intensity peak, which was apparently greater in the sample
collected by the MoFlo than in the sample collected by the instrument with
DiVa electronics, suggesting that the MoFlo had higher sensitivity, which
would depend more on optics and detectors than on electronics. However,
one ought never to form an impression of comparative performance from a
single sample comparison. B-D hasn't sent out its post cards yet.
In terms of the actual performance of the electronics, Mario Roederer, who
has had extensive experience with B-D optics using Cytomation electronics,
and is now using a B-D system with DiVa electronics, reported (also on this
Mailing List):
"In our preliminary evaluation of the digital electronics, we get as
good or better resolution, separation, and sensitivity using the
digital signals as compared to the analog signals on the same bench
(i.e., DiVa vs. SE). In a preliminary comparison of some 8-color
samples with those analyzed at our original machine at Stanford
(which uses the Cytomation electronics), performance was quite
similar."
The primary problem that faces the users and developers of cytometry
apparatus is this: our data values frequently span a large range -
generally not quite the four decades we take as standard, but certainly
close in many situations, particularly immunofluorescence analysis.
Immunofluorescence analysis gives rise to a second major problem; the
emission spectra of the probes or labels used overlap, necessitating that
hardware and/or software compensation be used to produce correct values for
the fluorescence of individual labels from the values of fluorescence in
particular spectral bands.
In order to display weak and much stronger fluorescence signals on the same
scale, it has become standard practice to convert from linear to
logarithmic values/scales. Historically, this was first done using
hardware, i.e., analog logarithmic amplifiers, familiarly (and familiarity
has bred contempt) known as log amps. Now, most of us have known since
high school that you can look up the logarithm of any number greater than
zero in a table and rely on the answer being as accurate and precise as the
table. Unfortunately, while, in principle, a log amp takes a voltage (or
current) as its input and delivers an output proportional to the logarithm
of its input, log amps are not usually as good as log tables. They are
typically specified as being accurate within 1/2 decibel; while this figure
sounds pretty good when you're stereo shopping, it turns out to mean
plus-or-minus 6 per cent. Most log amps get worse at the low end; some do
at the high end.
Now, facing the facts, +/- 6% is probably as good as you need for
immunofluorescence analysis; about the only place in cytometry you want
more precision is in nuclear or chromosomal DNA analysis, and we all do
that on a linear scale, eliminating any imprecision associated with the log
conversion. However, many log amps change their response characteristics
on a day-to-day basis due to temperature fluctuations, etc., so it might
make life easier to do without them. It definitely makes life easier to do
without them when you use four or more colors of fluorescence, because
compensation has to be done on linear signals, and the typical approach to
doing this in an instrument with log amps involves putting the compensation
circuit between the detector preamplifier outputs and the log amp inputs,
and the complexity of the compensation circuit goes up faster than the
number of colors used.
The way to eliminate log amps is to collect linear data in a sufficiently
precise manner to allow you to use a good old-fashioned log table to go
from a linear to a logarithmic scale. This requires the use of
analog-to-digital converters (ADC's) Until recently, most flow cytometers
used 8-bit (256-channel) or 10-bit (1024 channel) ADC's. However, to
accurately capture data with a 4 decade dynamic range, where the weakest
signal is 1/10,000 the intensity of the strongest, one needs a higher
resolution ADC. A 14-bit ADC has 16,382 channels, and will theoretically
respond, but an ADC with 16 (65,536 channels) or more bits is preferable.
Flow cytometers used to have 8- and 10-bit ADC's because higher resolution
ADC's either didn't exist or were prohibitively expensive. By the late
1980's or early 1990's, 16-bit ADC's which could convert data in a few
microseconds became available. This led to my development of the digital
electronics described in the Cytometry article cited above and to Coulter's
development of the electronics in the Epics XL. Neither of these
instruments did digital pulse processing; instead, they took analog signals
representing held values of the peak and/or integral of a pulse and
produced a single high-resolution value.
My electronics use a 16-bit converter to produce linear values between 0
and 65,535; the lowest linear value in the lowest decade on the four-decade
scale is 7, and the lowest values of the higher decades are 64, 656, and
6554. I can convert from these 16-bit linear values to a 256-channel
(8-bit) logarithmic scale, but, at the low end of the lowest decade, one
value on the linear scale corresponds to multiple values on the log scale,
and using only a single value generates the "picket fence" appearance shown
in the figure in my paper.
The XL electronics use a raw signal and an amplified signal, with a nominal
15-bit converter, to generate 20-bit linear data. This allows conversion
from 20-bit linear values to a 1,024-channel (10-bit) log scale, without
the "picket fence" effect.
Software packages which provide the facility for digital compensation must
convert log data to linear data so compensation can be applied. Data taken
from log amps via analog peak detectors or integrators, converted to only
10-bit (1,024-channel) precision, then converted to a linear scale,
compensated, and put back on a log scale, show a pronounced "picket fence"
effect; software that operates on such data usually adds random numbers to
reduce or eliminate the "picket fence" effect. This makes the data look
better, but cannot help but decrease accuracy.
High-resolution digitization of signals held in peak detectors or
integrators can be accomplished using ADC's with conversion times of 1
microsecond or more, equivalent to continuous conversion rates of less than
1 MHz.
Digital pulse processing eliminates the need for, and any inaccuracies or
limitations of, analog peak detectors or integrators (or pulse width
measurement circuits), but requires multiple samples, or "slices" of a
pulse, and thus demands faster ADC's.
My colleagues and I have calculated that 8 slices of a pulse can yield an
integral (area) nearly as accurate as can be obtained using 16 slices, and
that 32 slices are not significantly better than 16. However, peak and
width measurements get notably worse as the number of slices drops, as you
might expect, because the relevant slices are likely to be farther away
from the peak or threshold values.
The earliest digital pulse processing in flow cytometry was done by Leon
Wheeless and his colleagues in the 1970's, in "slit-scanning" apparatus,
with relatively slow flow rates and long pulse durations. They could
operate 8-bit ADC's at frequencies of several MHz, producing dozens or even
hundreds of points per pulse. Digital pulse processing was incorporated
into other instruments, but did not use ADC's with high enough resolution
to provide the 4-decade dynamic range required for immunofluorescence work.
A 12-bit converter has 4,096 channels, and produces output values between 0
and 4,095. If you calculated a pulse integral by taking 8 slices of a
pulse with a 12-bit ADC and summing the values, you would think you'd be
able to cover a range between 0 and 32,760, which should encompass a
4-decade dynamic range. However, the actual range achievable is smaller,
for two reasons. First, the signal at the lowest end of the range is 1
part in 10,000, and, to get the ADC to put out an output of 1 instead of 0,
you need about 2.5 times that, or 1 part in 4,096, so the 12-bit ADC won't
respond to signals near the bottom end of the range. Second, the highest
possible value, 32, 760, crops up only when the input pulse is flat-topped,
that is when the signal is "clipped". The maximum value for the integral
that is accurate is that which would be obtained from a pulse in which only
the peak (1 or at most 2 slices) reached the value 4,095, and, for a
Gaussian pulse, this is around 20,000.
My calculations show that, no matter whether 8, 16, or 32 slices are taken,
digital pulse integration using a 14-bit converter gives substantial
inaccuracy (close to 50 per cent) at the bottom of the range (bottom half
of the bottom decade); however, the situation may not be any better when
you use log amps because they are also almost certainly inaccurate at the
low end. B-D apparently agrees with all this. The DiVa electronics use
14-bit ADC's operating at a frequency of 10 MHz; when I have seen them in
operation, they were taking 32 slices of a 3.2 microsecond pulse. If the
pulse were shorter, the integral would have to be computed from a smaller
number of slices (e.g., for the 800 nsec pulse duration typical in a
Cytomation MoFlo, it would only be possible to take 8 slices). At the low
end of the lowest decade, the DiVa electronics come up with the "picket
fence" effect.
However, the low end is where the blanks and the noise are; the signals of
greatest interest are higher up on the scale, and either digital pulse
processing or high-resolution digitization of held peaks or integrals
should be more accurate there. In my system, accuracy seems to be within
+/- 2%; as mentioned above, accuracy with a log amp somewhere in the loop
is unlikely to be better than +/- 6%.
Cytomation does have a log amp in the loop; they do digital compensation by
performing a 16-bit conversion of held peaks or integrals of the log
amplified signal, converting to linear for the calculation, and then
converting back to log. This largely avoids the "picket fence" effect at
the low end, but probably yields lower accuracy further up the scale than
would be expected from a full digital system without a log amp. However,
Mario Roederer's comments quoted above suggest that it's hard to tell the
difference.
For now, I have to point out that neither B-D nor Cytomation has achieved
an ideal solution, which would be digital pulse processing with at least 16
slices from an 18- or 20- bit converter (even a 16-bit converter is about
14% inaccurate at the low end when doing digital pulse integration). And,
right now, there aren't any 18- or 20-bit converters fast enough to do the
job. There are 16-bit, 5- and maybe 10-MHz parts, and there are now
14-bit, 100 MHz ADC's, but, so far, nothing with higher resolution at even
2.5 MHz.
There are, however, 24-bit converters which sample as fast as 192 kHz,
which are relatively inexpensive by virtue of being used for digital audio
recording. Using these to digitize held analog peaks or integrals could
provide higher accuracy and precision than are now available, and keep up
with the data rates required for high speed sorting. This sounds good,
but, to make it work, you need analog peak detectors and/or integrators
good to 1 part in 10,000, and these are, at best, extremely difficult to
come by. The Beckman Coulter XL has integrators good to 1 part in 10,000;
the splitting and amplification of the input signal to the ADC's was
necessary when the instrument was designed, years ago, because a 20-bit
converter was unavailable. Whether the XL electronics would work in a
system running 100,000 cells/sec, I don't know. It gets easier to cover a
large dynamic range if you split signals into several intensity levels. My
colleagues and I are looking into these approaches, and encourage others to
do the same.
Note that progress in cytometry electronics depends on our industry, which
consumes economically insignificant quantities of components, being able to
use parts developed for other industries - notably the entertainment
industry. If digital audio, digital video, and games will benefit from
higher-speed, higher resolution converters, they'll become available to us;
if not, we'll have to continue to compromise.
Bottom line: If you are buying a high-speed sorter, whether or not it has
full digital electronics is probably not the most important single factor
to consider in your decision making, at least for now. Ads are ads; what
you need to do is get demos run on the samples of interest to you. At
today's prices, the manufacturers can afford to work for their money.
If you want to read more on this subject, it will be covered in great
detail in the 4th Edition of Practical Flow Cytometry, due out at next
May's ISAC meeting. Please give me some feedback on the clarity of
explanations such as this before then. Thanks.
-Howard
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