RE: Cell size and FSC

Howard Shapiro wrote:
" The most accurate measurement of the mean volume of a large number of
cells can be obtained from the "cellocrit" (hematocrit in the case of 
erythrocytes). Spin the cells down, determine the fraction of the total 
volume of sample comprised of cells (correcting for suspending medium 
trapped in the column of cells), and divide by the cell count. This remains 
the best way of calibrating Coulter volume measurements."

I suspect that it is precise in terms of being reproducible; unfortunately,
the hydrostatic head produced by the centrifugal force will have an osmotic
effect and should slightly shrink the cells.

Mie theory for simple spheres provides a Bessel function.  As much as one
would like to measure the forward lobe of this function, the profile of the
laser for fluorescence excitation interferes with this.

I should note that there are two Coulter effects. The first is conventional
DC impedance, which measures cell volume. The second is radiofrequency
impedance (20 to 30 MegaHz) which I believe measures total solids. The ratio
of these two impedance measurements, opacity, is a measure of the buoyant
density (1), the concentration of solids. Opacity is thus inversely related
to water content, which is a measure of physiological status.

Both impedance measurements, fluorescence, and light-scattering have been
measured simultaneously with what was essentially an enhanced Coulter Corp.
white cell system (2).

(1) R. C. Leif, S. Schwartz, C. M. Rodriguez, L. Pell-Fernandez, M. Groves,
S. B. Leif, M. Cayer, H. Crews; "Two Dimensional Impedance Studies of BSA
Buoyant Density Separated Human Erythrocytes". Cytometry 6 pp. 13-21 (1985).

(2) R. C. Leif, M. L. Cayer, W. Dailey, T. Stribling, and K. Gordon, "The
use of a Spherical Multiparameter Transducer for Flow Cytometry". Cytometry
20, pp 185-190 (1995).

Bob Leif

-----Original Message-----
From: Howard Shapiro [mailto:hms@shapirolab.com] 
Sent: Wednesday, March 17, 2004 6:33 PM
To: cyto-inbox
Subject: Re: Cell size and FSC

Ramy Arnaout wrote-

>I am relatively new to flow and have a question about how forward scatter 
>relates to cell size. From some of the previous postings, I can imagine 
>the short answer is "poorly," but I would be grateful if someone out there 
>could tell me more. Specifically:
>
>I have read that FSC is a (rough) measure of cell diameter, but also that 
>it is a (rough) measure of volume. Presumably if one treats the cell as 
>light-impermeable, it's closer to area, while if it's light permeable, 
>it's closer to volume. Is this right? Assuming constant density (not a 
>very good assumption, I know), is there a plot of this relationship 
>somewhere that anyone can point me to? Or an explication of the theory? I 
>would be happy enough if someone could say at least whether FSC scales 
>(roughly) as area or volume.

On p. 5 of the 4th Edition of Practical Flow Cytometry, I note that "It 
is...wise to avoid thinking of the small angle scatter signal [FSC] as an 
accurate measure of cell size. The gory details appear on pp. 275-6, 279-81 
and 517.

FSC measurement is a reasonably cheap way of determining whether or not a 
cell is present in the observation volume of a flow cytometer. However, 
different instruments use different optical configurations to make FSC 
measurements. As Fig. 7-1 on p. 275 illustrates (using data from Kevin 
Becker et al), the FSC signal from a BD Biosciences FACSCalibur is bigger 
for 3 um diameter beads than for 4 um beads, bigger for 5 um beads than for 
6 um beads, and bigger for 7 um beads than for 8 um beads. The beads all 
have the same refractive index, so we can safely conclude that this FSC 
signal is not terribly useful as a size measurement. The FSC signal 
amplitudes from a Beckman Coulter EPICS XL are in the proper ascending 
order for 3, 4, 5, 6, 7, and 8 um beads, but you won't get a very good fit 
of a plot of FSC amplitude against either diameter, cross-section (diameter 
squared) or volume (diameter cubed), limiting the utility of the signal for 
sizing.

If you subject erythrocytes to isovolumetric sphering, you can calculate 
both size and refractive index from multiangle scatter measurements (at 
angles different from those used in most fluorescence flow cytometers) 
using relatively complex math. This measurement is incorporated in Bayer 
Diagnostics' hematology analyzers, and allows them to measure hemoglobin 
content of individual red cells, a gory detail if ever there was one. 
However, the method doesn't work for any other cell types, not even 
lymphocytes, which are pretty spherical, as cells go. You can also get a 
predictable, if complicated, relationship between FSC signal amplitudes (in 
some instruments) and size of bacteria. If you really wanted to learn about 
scatter signals in depth, you could get sent to Siberia, where Valery 
Maltsev has built and works with the fanciest flow cytometric scatter 
measurement system now in operation.

>Also, and this is perhaps naive, I assume that the voltage readout 
>attached to FSC is actually a delta-V. Otherwise, I have trouble seeing 
>how a larger FSC means a larger (generally speaking) cell, and not a 
>smaller cell. Unless it is the case that the smaller the cell, the more 
>light goes straight through but is *not* figured into the FSC because the 
>intensity of this light is subtracted out/ignored in the measure of FSC?

Yes, it is naive. Not even close. But FSC is counterintuitive.

The blocker [bar] in a scatter measurement system prevents light that goes 
through the cell from reaching the FSC detector. If you measure the light 
going through the cell, you get an extinction signal, which is opposite in 
polarity to scatter and fluorescence signals. Provided the measurement is 
set up right, extinction signals can do a fair job of sizing cells, but, as 
far as I know, no current commercial fluorescence flow cytometer or sorter 
makes extinction measurements.

Mie's theory does a reasonably good job of relating FSC to size, but what 
it gives us is a wiggly curve, predicting that although, in general, bigger 
particles will have bigger FSC signals, there will be points on the curve 
at which the FSC signal from a smaller particle is bigger than the FSC 
signal from a larger one. And that is what we find when we make the 
measurements.

It must be the proper phase of the moon for thinking about cell size 
measurements, because Volker Eckstein posted a question about measuring 
cell volume almost immediately following Ramy Arnaout's posting. David 
Galbraith suggested measuring cell diameter from a pulse width signal and 
cubing the result to get a quantity proportional to volume. The pulse width 
size measurements available from most commercial instruments aren't all 
that good, but the idea is sound.

Also note that DC impedance measurements (using the Coulter principle), 
made in a properly designed instrument, provide a good indicator of volume, 
used in many hematology instruments, but in few fluorescence flow
cytometers.

The most accurate measurement of the mean volume of a large number of cells 
can be obtained from the "cellocrit" (hematocrit in the case of 
erythrocytes). Spin the cells down, determine the fraction of the total 
volume of sample comprised of cells (correcting for suspending medium 
trapped in the column of cells), and divide by the cell count. This remains 
the best way of calibrating Coulter volume measurements.

-Howard