Ask The Brewmasters

 View Only

  • 1.  Cell count error

    Posted 05-26-2022 14:07

    Is there a standard way to estimate the error of a hemacytometer cell count?  We normally count four fields, and each field is considered a measurement of cell density.  If there is a lot of variation between measurements, we count an additional two fields and then take the average.  But calling each field a measurement has always seemed sort of arbitrary to me.

    I found one reference that said that for hemacytometers, the standard error = 1/sqrt(N), where N= the total number of cells counted.  But this formula gives what I find unbelievably optimistic estimates of the method's accuracy.  Any ideas?

     

    Cullen Dwyer

    Q/A Manager

    P: 978.874.9965 X1160


    Wachusett Brewing Company, Inc.
    175 State Road E.
    Westminster, MA  01473

    www.wachusettbrewingcompany.com

     



  • 2.  RE: Cell count error

    Posted 05-27-2022 14:15
    Edited by Walter Heeb 05-27-2022 18:19
    Hi Cullen, yes, there is a way to measure and determine error of hemocytometer counts. Many years ago I did a six sigma project on improving accuracy of cell counting and pitch rates at NBB. Lots to talk about, the bottom line is that at that time, after doing a measurement system analysis (MSA), we discovered high variability between operators and within the measurement itself. After we made improvements to the counting process, we decided it was still not robust enough for pitching accurately.  Finally, we threw out hemocytometer counts all together and replaced the method with spin down by % solids for day to day decision making by brewers. Happy to chat if you like, cheers,
    Jeff

    ------------------------------
    Jeff Biegert
    NBB Sponsored CSU Fermentation Science and Technology Instructor & Brewmaster
    New Belgium Brewing Co R & D, Lean Six Sigma Black Belt
    Fort Collins CO
    (970) 221-0524
    ------------------------------

    Original Message


  • 3.  RE: Cell count error

    Posted 05-31-2022 07:23
    Hi Jeff,

    Our yeast re-pitching setup is very rudimentary at the moment and we don't have the staff or equipment to do much more than viability staining on a hemocytometer and spin downs. We use a magnetic flow meter to pitch the yeast, which we have found to be reasonably accurate with the slurry thickness we work with. Would you mind sharing the approach you folks took (big picture) for day to day decisions? 

    Thanks, 
    Francesco

    ------------------------------
    Francesco Mayell
    Senior Brewer
    Brixton Brewery
    London
    02036098880
    ------------------------------

    Original Message


  • 4.  RE: Cell count error

    Posted 06-15-2022 19:55
    Jeff-
    Is there any assessment of viability along with the spin downs? 
    Thank you.
    Cheers!

    ------------------------------
    josh waldman
    brewmaster
    elysian brewing co
    seattle, wa
    ------------------------------

    Original Message


  • 5.  RE: Cell count error

    Posted 06-16-2022 15:20
    Hi Josh, no, there is no provision in spin down measurement to assess viability. When I did the six sigma project on cell count improvement, we also determined that there was high variability in methylene blue staining, so much so that we stopped doing that as well. The improvement in the concentration measurement and pitching accuracy effectively superseded any variation in viability, though eventually we had the lab give the brewers viability numbers to use in the pitch calculators. BTW, I just learned that we have finally dialed in our Aber meters and are using them plus cell counts conducted by QA for pitching decisions, spin downs were the norm for over a decade, always improving!

    ------------------------------
    Jeff Biegert
    Research and Development
    Lean Six Sigma Black Belt
    New Belgium Brewing Co
    Fort Collins CO
    (970) 221-0524
    ------------------------------

    Original Message


  • 6.  RE: Cell count error

    Posted 06-17-2022 19:58
    Hey Jeff,

    What types of variation did you see in the spin-down measurements between different strains/props/brews? I use a wide variety of different yeast strains and am looking for a quick way to calculate cell concentration dilutions for my research. And by Aber meters I am assuming you mean their conductivity probes? I haven't had a whole lot of luck with those, but that might be because of the large variations in the types of work I do. It seems like they are a good way to lock down your process and if you see variation from your baseline then you know to start troubleshooting, is that correct?

    ------------------------------
    Daniel Gusmer
    Microbiologist - Fermentation Development
    Gusmer Enterprises Inc
    Santa Rosa CA
    (707) 204-8432
    ------------------------------

    Original Message


  • 7.  RE: Cell count error

    Posted 05-27-2022 18:19
    Cullen:

    Treating each field as an estimate of the yeast abundance is the correct approach.  Infer the yeast abundance from the average estimate obtained from the different fields.  And use the field to field variation as an estimate of uncertainty associated with the average.  

    The following calculations can be done in your spreadsheet of choice. I suggest that you count 10 fields.  I'll assume that the data are in the first column, rows 1 to 10 (A1:A10).

    First, calculate the average cell count obtained from the 10 fields, =(AVERAGE A1:10).

    Second, calculate the standard deviation of the 10 fields, =(STDEV A1:A10)

    Third, calculate the coefficient of variation by dividing the standard deviation by the average and then multiply the result by 100 to yield a percentage.

    A coefficient of variation < 10% is superb., 10% to 20% is very good, 20% to 25% is good, 25% to 30% is okay but not very good, >30% is poor, so prepare a new sample and count the sample again because the uncertainty is too high to make an informed decision with these data.

    The formula that you cited for calculating the standard error is close but no quite right.  It should be: standard error = standard deviation / sqrt(n).  But in case of counting yeast with a hemocytometer the standard error is not as useful as the coefficient of variation calculated from the standard deviation and the average.

    Here are some sample (real) data:

    Cell counts in 10 fields:

    35
    41
    37
    47
    43
    45
    70
    46
    40
    29

    Average cells/field = 43
    Standard deviation = 11
    Coefficient of variation = 100*11/43 = 25%

    In this example the cell count per field is multiplied by 1.6E5 to calculate cells/mL based on  the size of the counting field (medium sized square in the hemocytometer in this case) and accounting for the sample dilution.  In this case the sample was not diluted.

    Average yeast abundance, AVG = 6.93E6 cells/mL 
    Standard deviation, SD = 1.74E6
    Coefficient of variation (100*SD/AVG) = 25% 
    Conclusion:  The sample contains about 10 million cells per mL and there is good confidence in this estimate.

    Hope that helps,
    Matt







    ------------------------------
    Matthew Cottrell
    Heavy Seas Beer
    Baltimore MD
    (302) 430-3489
    ------------------------------

    Original Message


  • 8.  RE: Cell count error

    Posted 05-28-2022 14:20
    One more thing, including a few words about the difference between standard deviation and standard error.  And a plug for the coefficient of variation.

    The term "standard deviation" is shorthand for "sample standard deviation", which is a measure of the variation between samples.  In the case of hemocytometer counts we can treat each grid square of the counting chamber as a different sample.  The sample standard deviation reflects how variable are the numbers of yeast cells in each of the different grid squares.  If the standard deviation is very high it tells us that something must have gone wrong when the sample was loaded into the sample chamber making them pile up in one area and greatly spreading out in another.   Or maybe the sample was not sufficiently homogenized to begin with.

    The term "standard error" is shorthand for "standard error of the mean", which is a measure of the variation between average counts.  Imagine if one were to load the yeast sample into 20 different hemocytometers, do the 20 cell counts and calculate the yeast abundance from each of the hemocytometers.  The standard deviation of those 20 average counts would be analogous to a standard error.  In the real world we use only one hemocytometer, but based on the way the world works we can estimate the standard error by dividing the sample standard deviation seen on the one hemocytometer by the square root of the sample size (usually 10 fields).

    The coefficient of variation is so useful because it allows the side-by-side comparison of the variability of numbers of different magnitudes.  That's accomplished by dividing the standard deviation by the mean, which re-scales the standard deviation to a magnitude that can be compared between any two data sets.  For example, notice in my previous post that the coefficient of variation for the raw cell count data and the calculated yeast abundance were both 25%.  The cell count data were of the order of magnitude 10 while the yeast abundance was of the magnitude 10^7.  The raw data ranged from 29 to 47 cells per field (a spread of 18).  The calculated yeast abundance based on those fields ranged from 4.6E6 to 7.5E6 (a spread of 2.9E6).  Naturally, big numbers of the order 10^6 will have a larger potential spread than numbers of the order 10.

    Anyway, the coefficient of variation is a convenient measure of variability because it always ranges from 0% to 100%, regardless of the underlying data ranging from 0 to 10 or 1,000,000 to 10,000,000.

    Hope that helps,
    Matt


    ------------------------------
    Matthew Cottrell
    Heavy Seas Beer
    Baltimore MD
    (302) 430-3489
    ------------------------------

    Original Message


  • 9.  RE: Cell count error

    Posted 05-31-2022 12:54
    There are 2 ways to estimate the uncertainty in cell counts. We assume that they are Poisson distributed, which is a simple approach for count data.  1.  N is the number of fields (4 or 6 in the case of the original poster), and C is average of the counts per field.  Then use a normal approximation where a 90% confidence interval is roughly plus or minus 2 * sqrt (C/N).  2.  An exact approach is simply to sum all of the counts, estimate the uncertainty in counts using an exact method (e.g.,  the below table) and then scale the lower and upper bounds by the total beer volume sampled. I suspect that with any counting procedure there is additional error in counts if one fills another slide and counts that or if other folks count.  To estimate that error I would count >5 slides and calculate as plus or minus 2 * S/sqrt (N). where N is the number of slides counted, and S is the standard deviation of the counts among the >5 slides.

    https://faculty.washington.edu/heagerty/Books/Biostatistics/TABLES/Poisson/index.html

    ------------------------------
    Robert Hall
    Board Member / Professor
    Ronan Coop Brewery
    Bigfork MT
    ------------------------------

    Original Message


Related Content