I go once a year, SO, I pig out.  Now, I DO take more insulin than
usual, but I figure that once in a while I can go wild.  After a fried
chicken dinner and platters of fresh roasted corn, We stopped at
Hoffman’s –  a small rural market which makes its own ice cream – I had
a DOUBLE scoop (probably as much ice cream as I had in the last YEAR),
after all that corn, what difference does it make?

Two hours later I took my BG, and it was…..
75 !!!!!

about 100 points less than I was expecting.  And, yes, it WAS 75, I
retested to verify

–
"…in addition to being foreign territory the past is, as history, a
hall of mirrors that reflect the needs of souls observing from the present"
Glen Cook

- Hide quoted text — Show quoted text -

JC wrote:
> Regarding the calculation of HbA1c I have seen references to 4 week and 90
> day periods of BSL
> readings as contributing factors to the figure.  I have not seen any
> references as yet that give definitive factors to apply to the BSL
> averages (whichever is used) over the 4 weeks or 90 days to come up with
> the final HbA1c guesstimate.

> From what I have seen so far there doesn’t seem to be any agreement on
> either the base data, the number of days readings to consider or the
> factors applicable over that period.

> I am currently using the daily average but have no real reason for this
> over the night/morning
> average.   I am currently using the 90 day model applying factors of 1 for
> days 1 – 50 and then reducing this factor by 2.5% over the next 40 days so
> that on day 90 the factor is 0.

> Given the variability of the times when we take our BSL readings and the
> number of readings taken
> per day this seems to me to be a reasonable approximation.   I agree that
> it is a rather simplistic model and could be improved and am open to
> suggestions on improvements to the model.

> Given the variability of the number, and time when taken, of the BSL
> readings do we need to be any more accurate?

Hi JC,

First, I don’t want to get into the calculus of time averaging over the 160
days of BG data I keep.  I just don’t have the memory or horsepower in the
HP-48 to do this.  Moreover, it becomes a nighhtmare to calculate this over
160 days, instead of just 24 hours as done on the DCCT, when the data
points are irregularly sampled.  It also becomes a burden to make all these
BG measurements when you’re busy trying to make your mortgage payment.  So
I decided to use the fasting and bedtime BG average and call it the
nocturnal BG, NBG=(fastingBG + bedtimeBG)/2.

As a simple test for the model, Dr Goldstein (DCCT lab MD), mentions that
HbA1c drops 1% in a week when average BG goes from 300 mg/dl to 120 mg/dl
abruptly.  My NBG model with curve fit specific to my body starts at a 7.4%
HbA1c when all 160 days of data are (300+300)/2=300 mean NBG.  (So my body
under glycates relative to the DCCT data and this has always been my
problem.  My time average BG has always been much higher than 150 mg/dl to
get a typical 7% HbA1c.)

After a week of (120+120)/2 NBG data, my HbA1c drops to 6.3% for a total
change of 7.4-6.3 = 1.1%.  This is pretty good in my book (for a model that
ignores the reverse reaction, it also suggests that new red blood cells
entering the bloodstream with low mean BG will have a major impact on HbA1c
in a short period of time: my model handles these daily RBC cohorts
individually and yours does not).

Another Goldstein data point is 3% (or more) lower HbA1c in 1 month of 120
mg/dl mean daily BG from a starting point of 300 mg/dl time average.  But
obviously this is impossible for me with 7.4-3=4.4% which is a number I’ve
never seen (4.8%, ref <6.1% normal, is as low as I’ve ever seen for my
body).  But my model, at 30 days, gives 4.89% for 7.4-4.9 = 2.5% change in
HbA1c.  These are all winter values so they are the maximum HbA1c values I
will see.

These test points were published in "Glycated Hemoglobin: Methodologies and
Clinical Applications," Goldstein et al., Clinical Chemistry, vol 32, No
10B, 1986, pp B64-B70.  See page B69 for these numbers.

Next, I don’t publish the RBC cohort weighted average to HbA1c formula
because it’s specific to my body and it will not be applicable to the
majority of DMs, since I’m one of those low numbers in the DCCT data.  But
it is semi-log HbA1c so:

HbA1c = b * exp(m * BG)  or

ln( HbA1c ) = BG * m + b   (m is the slope and b the y-intercept of a line)

This gave the best curve fit specific to the statistical model I use for the
RBC turnover with mean lifespan of 120 days and SD of 10 days.  This may
change as I gather more data.  But this will give you some idea of what
works.

Lastly, if your model has much more than the expected 1% lower HbA1c for the
300 to 120 mg/dl mean BGs, then I would say your model has an error and/or
you need to improve your model’s accuracy.

HTH,
—
Jim Dumas
T1 4/86, background retinopathy, rarely hypoglycemic: <1/mo.
lispro+R+U+NPH daily, moderate exercise, typically <6% HbA1c

- Hide quoted text — Show quoted text -

On Sun, 08 Aug 2004 14:43:52 GMT, Jim Dumas <j-dumas@.no.SPAM!mindspring.com> wrote:
> ~Reference 4: Mortensen HB, Volund A, Christophersen C: Glucosylation of
> ~human haemoglobin A. Dynamic variation in HbA1c described by a
> ~biokinetic model. Clinica Chimica Acta 136:75-81, 16 January 1984.

> The reaction kinetics for the reversible condensation of D-glucose and
> haemoglobin A through a labile haemoglobin A-aldimine adduct to HbA1c have
> been investigated using a biokinetic model. The specific rate constants
> obtained from in vitro experiments were included in the model which also
> took into account the removal of HbA1c by decay of erythrocytes. Using a
> sinusoidal variation in blood glucose a phase delay of about 2 hours was
> observed between the maximum blood glucose concentration and the maximum
> aldimine concentration. The mean haemoglobin A-aldimine concentration was
> independent of both the amplitude and frequency of the blood glucose
> oscillations and reached equilibrium concentration within 24 hours. The
> steady state relation between mean blood glucose and HbA1c was similar to
> the corresponding relation based on an irreversible formation of HbA1c.
> However, contrary to the irreversible model the steady state HbA1c
> concentration with the reversible model was reached 3 to 4 weeks after a
> change in blood glucose level. This finding is in agreement with clinical
> experience and indicates that in assessing continuous glycaemic control in
> diabetic patients haemoglobin A1c should be measured approximately every 3
> to 4 weeks.
> ——

> This is an interesting model.  But I take issue with a sinusoidal variation
> in BG.  This driving (or forcing) function is nonphysiological and
> therefore the results are in question.  But I’m impressed that this model
> accounts for the red blood cell turnover with an exponential decay.  This
> is an old compartmental model approach that I also used before I switched
> to the statistical model for RBC destruction.

> Next, I now think the reversal half-life for HbA1c is longer than the 31
> days that Ed Reid is using in the FAQ-#2.  I think it’s twice as large as
> this.  This is based on "Nonenzymatic Glucosylation of Lysine Residues in
> Albumin," Baynes JW, Thorpe SR and Murtiashaw MH, Methods in Enzymology
> v.106, pp 88-98, 1984.  This paper compares the albumin and hemoglobin
> rates of association/dissociation with glucose.  If this is true, then we
> don’t have to bother with the reverse chemical reaction, as it’s on the
> order of the lifespan of the RBCs.  But I need to find another reference on
> this to make sure.
> ——

Jim,

Given that we don’t have meters permanently attached to our arms to give us readings over the day we
have to rely on measurements taken at various times during the day to estimate the HbA1c.   Some
people use the average of previous night bed time reading and this morning’s pre breakfast reading
while others simply average the readings taken during the day as the base data.   It may well be a
heads or tails situation in that one ignores the day while the other ignores the night.

Regarding the calculation of HbA1c I have seen references to 4 week and 90 day periods of BSL
readings as contributing factors to the figure.  I have not seen any references as yet that give
definitive factors to apply to the BSL averages (whichever is used) over the 4 weeks or 90 days to
come up with the final HbA1c guesstimate.

From what I have seen so far there doesn’t seem to be any agreement on either the base data, the
number of days readings to consider or the factors applicable over that period.

I am currently using the daily average but have no real reason for this over the night/morning
average.   I am currently using the 90 day model applying factors of 1 for days 1 – 50 and then
reducing this factor by 2.5% over the next 40 days so that on day 90 the factor is 0.

Given the variability of the times when we take our BSL readings and the number of readings taken
per day this seems to me to be a reasonable approximation.   I agree that it is a rather simplistic
model and could be improved and am open to suggestions on improvements to the model.

Given the variability of the number, and time when taken, of the BSL readings do we need to be any
more accurate?

Cheers . . . JC

- Hide quoted text — Show quoted text -

Thad O wrote:
> On Sun, 01 Aug 2004 14:46:10 GMT, Jim Dumas
> <j-dumas@.no.SPAM!mindspring.com> wrote:

>>Last year someone else asked the same question.  I have an HbA1c model
>>that mimicks the death rate (turnover) of red blood cells based on the
>>fact that
>>the average lifespan of RBCs is 120 days.  This means that a daily cohort
>>of RBCs still have 50% left at 120 days!  So my model weights daily
>>cohorts of RBCs with a normal (Gaussian) curve with a guess at the death
>>rate
>>standard deviation of 10 days.  This basically says: "What is the
>>probability that a daily cohort of RBCs is still circulating in the body,"
>>is the weighting used on the daily BG data.  This RBC cohort weighted
>>average is summed and this value is curve fit to my HbA1c data.

> Except for one thing, The level of A1C and it’s "lifetime" is not
> determined by the rate of decay of RBC. So RBC lifetime forms
> an upper bound. What is more relevant is the rate of A1C production
> and the rate of A1C decay. Check the references in the FAQ
> in particular reference 2. A1C is an exponentially weighted one month
> average.

Hi Thad,

First, FAQ ref 2 has nothing to do with the exponential decay you mention:

~Reference 2: Kilpatrick ES, Maylor PW, Keevil BG:  Biological Variation
~of Glycated Hemoglobin. Diabetes Care 21:261-264, February 1998.
~Abstract available on the web at
~ http://care.diabetesjournals.org/cgi/content/abstract/21/2/261.

I have this issue of Diabetes Care and read the full article.  The objective
was: "To assess the inherent potential of glycated hemoglobin as a
screening test for type 2 diabetes by determining the biological variation
in nondiabetic subjects."

Conclusions: "This fundamental characteristic of HbA1c means that even if
analytical methods improve, glycated hemoglobin measurements will always be
of limited value when screening for type 2 diabetes.  If similar
interindividual differences also exist in diabetic subjects, then patients
with the same glycemic control may vary by at least 1-2%, which has
implications in setting glycated hemoglobin targets."

The conclusion at the end of the paper suggests DMs will have more than 1-2%
variation for higher values of HbA1c, (4% was the normal mean for this
instrument used in the UK, the US uses 5.1% as the DCCT mean HbA1c for
normals), typically seen with DMs.  So it speculates DMs at a mean of 7%
will have more than 2% variation about this average of 7% with identical BG
control for each of these DMs.

The paper has a graph of the Normal (Gaussian) curve for outlying
individuals and total sample of these normals.  The point being that there
is a large range of HbA1c values for identical BG control in normals.
——

Next, FAQ refs 3-5 of Mortensen are just a computer model:

~Reference 3: Mortensen HB, Christophersen C: Glucosylation of human
~haemoglobin a in red blood cells studied in vitro. Kinetics of the
~formation and dissociation of haemoglobin A1c. Clinica Chimica Acta
~134:317-326, 15 November 1983.

~Reference 4: Mortensen HB, Volund A, Christophersen C: Glucosylation of
~human haemoglobin A. Dynamic variation in HbA1c described by a
~biokinetic model. Clinica Chimica Acta 136:75-81, 16 January 1984.

~Reference 5: Mortensen HB, Volund A: Application of a biokinetic model
~for prediction and assessment of glycated haemoglobins in diabetic
~patients. Scandinavian Journal of Clinical and Laboratory Investigation
~48:595-602, October 1988.

The Abstract for ref 4 above is:

Glucosylation of human haemoglobin A. Dynamic variation in HbA1c described
by a biokinetic model.

Mortensen HB, Volund A, Christophersen C.

The reaction kinetics for the reversible condensation of D-glucose and
haemoglobin A through a labile haemoglobin A-aldimine adduct to HbA1c have
been investigated using a biokinetic model. The specific rate constants
obtained from in vitro experiments were included in the model which also
took into account the removal of HbA1c by decay of erythrocytes. Using a
sinusoidal variation in blood glucose a phase delay of about 2 hours was
observed between the maximum blood glucose concentration and the maximum
aldimine concentration. The mean haemoglobin A-aldimine concentration was
independent of both the amplitude and frequency of the blood glucose
oscillations and reached equilibrium concentration within 24 hours. The
steady state relation between mean blood glucose and HbA1c was similar to
the corresponding relation based on an irreversible formation of HbA1c.
However, contrary to the irreversible model the steady state HbA1c
concentration with the reversible model was reached 3 to 4 weeks after a
change in blood glucose level. This finding is in agreement with clinical
experience and indicates that in assessing continuous glycaemic control in
diabetic patients haemoglobin A1c should be measured approximately every 3
to 4 weeks.
——

This is an interesting model.  But I take issue with a sinusoidal variation
in BG.  This driving (or forcing) function is nonphysiological and
therefore the results are in question.  But I’m impressed that this model
accounts for the red blood cell turnover with an exponential decay.  This
is an old compartmental model approach that I also used before I switched
to the statistical model for RBC destruction.

Next, I now think the reversal half-life for HbA1c is longer than the 31
days that Ed Reid is using in the FAQ-#2.  I think it’s twice as large as
this.  This is based on "Nonenzymatic Glucosylation of Lysine Residues in
Albumin," Baynes JW, Thorpe SR and Murtiashaw MH, Methods in Enzymology
v.106, pp 88-98, 1984.  This paper compares the albumin and hemoglobin
rates of association/dissociation with glucose.  If this is true, then we
don’t have to bother with the reverse chemical reaction, as it’s on the
order of the lifespan of the RBCs.  But I need to find another reference on
this to make sure.
——

The Abstract for ref 5 above is:

Application of a biokinetic model for prediction and assessment of glycated
haemoglobins in diabetic patients.

Mortensen HB, Volund A.

Department of Pediatrics, Glostrup Hospital, University of Copenhagen,
Denmark.

An improved biokinetic model describing the haemoglobin A1c ketoamine
fraction (HbA1c), and the haemoglobin A1d aldimine fraction (HbA1d), as a
function of preceding blood glucose levels has been studied. The model
requires knowledge of the chemical reaction rate constants and the life
span of the erythrocytes. Calculated HbA1c corresponding to constant blood
glucose levels was about 6% lower than previously found using a simplified
method of calculation. The predicted variations in the glycated
haemoglobins in response to simulated variations in the glucose
concentration were, however, similar to the improved and the simplified
model calculations. Thus, HbA1d reached a new steady state level within 24
h and HbA1c within 4 weeks after sudden change in glucose concentration.
When the blood glucose concentration was simulated by sine waves with
periods from 2 to 60 days it was observed that the HbA1d varied in parallel
with the glucose concentration with a time delay of about 2 h, whereas the
HbA1c was almost constant with periods less than 7 days. Haemoglobin A1c
predicted from observed blood glucose levels in diabetic patients followed
over several weeks varied in parallel with measured HbA1c. However, the
measured values were systematically higher than the calculated. This could
be due to an underestimation of the daily mean blood glucose levels used
for calculation of HbA1c or to inaccurate estimates of the reaction rate
constants. Based on the model it could be demonstrated that the HbA1c
fraction corresponds to an exponentially weighted average of daily mean
blood glucose levels over the preceding 4 weeks.(ABSTRACT TRUNCATED AT 250
WORDS)
——

This points out that fast variations in BG less than a 7 day cycle (3.5 max,
3.5 min sinewave) have no effect on the HbA1c.  This means that prandial
spikes in BG have little impact on HbA1c provided they are short-lived
(less than 3.5 days long).  This is because the forward reaction has a
half-life of 4 days to form the near irreversible HbA1c.  But the model
they use has some error since it under estimates HbA1c relative to all the
people tested.  My hypothesis is this model uses a reverse reaction that is
too fast.  It has a forward reaction, with the 7 day cycle observation,
that is similar to the reference I gave above.  So this rules out the
forward reaction as the problem in the model.  It could also be that the
model has a red blood cell lifespan that is too short.  This would
contribute to a lower HbA1c than measured with the DM subjects.

In any case, this model has some error and this is probably why it never
became important to the professionals.  That is to say, it never became
popular in ADA academic circles.  This also suggests we should not draw
many conclusions from this model, as in the 4 week exponential weighting on
BG recommended by this model.  (For example, I would argue that the 7 day
cycle suggests we can under-weight this data unless it lasts for more than
4 days [half the cycle].)

My model for HbA1c ignores the reverse reaction of HbA1c.  This reverse
reaction is indirectly handled in the curve fit that is specific to my
metabolism.  Based on the reference #2 you cited, where each subject had a
relatively constant HbA1c, (i.e., individual HbA1c did not vary much), this
is a safe assumption, where minor changes in HbA1c seems to be the norm (at
least for me).

Finally, we need to be careful that the simple weighting of BG, recommended
by all the researchers to date, is not just an artifact of the data set
they are using.  That is to say, if the math model has no or a poor
physiological basis, then we will draw wrong conclusions about how much BG
data we need.

So I disagree
…

read more »

> Except for one thing, The level of A1C and it’s "lifetime" is not
> determined by the rate of decay of RBC. So RBC lifetime forms
> an upper bound. What is more relevant is the rate of A1C production
> and the rate of A1C decay. Check the references in the FAQ
> in particular reference 2. A1C is an exponentially weighted one month
> average.

Apparently there are more concerns about the A1c:

"There is compelling evidence that patients with the same mean blood
glucose can have greatly different HbA1c values"

"… the greatest source of concern with HbA1c measurement has become
the inherent limitations of the test itself. All the targets mentioned
previously are an incentive to try and ensure that the risk of diabetes
complications is minimised. However, these targets are based on data for
an average patient found in the DCCT and UKPDS studies. This raises two
potential issues. The first is how applicable the targets from these
studies are to all the patients who participated, and the second is how
applicable the findings from these studies are to patients from parts of
the world outside the USA and the UK where they were performed. The
first concern stems from the fact that there is compelling evidence that
patients with the same mean blood glucose can have greatly different
HbA1c values, as demonstrated by the DCCT study itself, which showed
that patients with a mean plasma glucose of 10 mmol/litre could have an
HbA1c value anywhere between 6% and 11%.14 Some of this variability is
undoubtedly caused by limitations in the study, such as the use of a
single seven point day plasma glucose profile (converted from laboratory
measured whole blood measurements) to compare with the subsequent HbA1c
value, but this is partially offset by the power of averaging 18 such
comparisons in the 1439 participants throughout the study period. The
findings also corroborate those from biological variation studies, which
suggest that although "within individual" changes in glycated
haemoglobin are small, differences between non-diabetic individuals can
be as much as 2% HbA1c.15 The inference from these data is that by
slavishly aiming for the same HbA1c in all patients, for some the target
is probably unrealistically low (with a high risk of hypoglycaemia if it
is attempted to be reached), whereas for others it can be achieved with
apparent ease, thereby leaving the patient and clinician falsely
reassured." Source: HbA1c measurement –
http://jcp.bmjjournals.com/cgi/content/full/57/4/344

Frank

<j-dumas@.no.SPAM!mindspring.com> wrote:
>Last year someone else asked the same question.  I have an HbA1c model that
>mimicks the death rate (turnover) of red blood cells based on the fact that
>the average lifespan of RBCs is 120 days.  This means that a daily cohort
>of RBCs still have 50% left at 120 days!  So my model weights daily cohorts
>of RBCs with a normal (Gaussian) curve with a guess at the death rate
>standard deviation of 10 days.  This basically says: "What is the
>probability that a daily cohort of RBCs is still circulating in the body,"
>is the weighting used on the daily BG data.  This RBC cohort weighted
>average is summed and this value is curve fit to my HbA1c data.

Except for one thing, The level of A1C and it’s "lifetime" is not
determined by the rate of decay of RBC. So RBC lifetime forms
an upper bound. What is more relevant is the rate of A1C production
and the rate of A1C decay. Check the references in the FAQ
in particular reference 2. A1C is an exponentially weighted one month
average.

- Hide quoted text — Show quoted text -

On Mon, 02 Aug 2004 16:27:10 GMT, Jim Dumas <j-dumas@.no.SPAM!mindspring.com> wrote:
> JC wrote:

> > Can you point me at a reference for the RBC die off rate?

> Hi JC,

> I’m using a very old math textbook reference that says the average lifespan
> of red blood cells is 90 days from old radioactive tracer studies.  But the
> math model presented is useful.  So I went searching NLM PubMed and found
> one interesting reference that I’ll try to look up at a nearby university:

> 3. Deiss A. Destruction of erythrocytes. In: Richard Lee G,Foerster J,Lukens
> J, et al., eds. Wintrobe’s Clinical Hematology. Baltimore, MD: Williams &
> Wilkins; 1999:267-299.

> I need to nail down the standard deviation guess of 10 days in my model.  
> Maybe this will be in this textbook.

> An interesting article I ran across was the shorter RBC lifespan in DMs
> caused by white blood cell phagocytosis of RBCs, (macrophages destroy the
> old RBCs).  Another one was older normals have shorter RBC lifespans from
> this same phagocytosis destruction of RBCs that increases with age.  See:

> http://www.bloodjournal.org/cgi/content/full/100/4/1511

> for the article on type 2 RBCs with a shorter lifespan.  But this is still a
> controversial topic.

I wish these guys wrote in English and not in medico-jargon.

- Hide quoted text — Show quoted text -

> Next, I save 160 days of BG data "just in case" the standard deviation of
> the RBC death rate is more than 10 days.  The delay of 40 days is my choice
> based on the old math reference that used 50 days before RBC destruction
> began.  So in my model, 120-40=80 days for the Normal curve mean used in
> the RBC lifespan roll-off (days>40) of a statistical weighting function.

> Next, I only use the home A1cNow kit in my HbA1c data, since this can be
> worked back to the DCCT lab reference BioRad HPLC instrument.  You must be
> extremely careful with your HbA1c data, as the labs tend to change
> instruments at will, (to save money), and you only see a reference range
> glitch as an indicator that you’ve been screwed.  That is, your new data
> has a new range for normals and you have no conversion equation that
> permits you to compare your old data with this new lab instrument assay.  
> So I pick the $23 A1cNow kit, do it myself and don’t worry about the lab
> politics.  In any case, be extremely careful with mixing HbA1c data from
> different instruments as they all have biases in the assay that will skew
> your data.

> Finally, all this is done on a small HP48 calculator dedicated to DM
> modeling primarily for insulin dosing.  So I don’t use a spreadsheet.

> HTH,

Hi Jim,

Our meters probably have a 10% accuracy.   The Accu-Chek Active strips I use say they are 4% but I
have no data on the Glucotrend meter accuracy.   This means that there is little point in bringing
factors into the calculations that have less than 10% bearing on the result unless the meter
accuracy can be improved.

For our purposes a simple model will suffice.   I gather from what you have written and the
referenced article on http://www.bloodjournal.org that the RBCs stay alive up to 50 days and then start
dying off so that by 90 days they are all gone.

What is not evident is whether the die off is linear or not.   Maybe it doesn’t matter for our
purposes and use of a linear die off rate is sufficient.  For a linear die off the decline is 2.5%
per day.

Is that how you have programmed your HP48?

Cheers . . . JC

Hi JC,

I’ve seen HbA1c reference ranges of normal <= 5.0% to <= 6.5%, depending on
the instrument used.  So in theory, your lab could be using the reference
of <= 5.0% as normal, then change instruments overnight to a new normal of
<= 6.5%.  This represents a change of (6.5-5)/5=0.3 or 30% change in your
data set.  Not good.  This just blew your data set and you should start
collecting new HbA1c data.  This is why I’m staying with the Metrika
A1cNow.  I’ve seen labs change HbA1c assay methods on a yearly basis and
this destroys historical data.

The same is true for BG meters.  I keep all BG data used in the HbA1c model
from a "reference" AccuChek Complete with Comfort Curve strips.  I never
polute this data with BG assays from another meter methodology.  I use the
Elite but never in the morning or at bedtime when I require my nocturnal BG
data for this HbA1c model.  To tighten up the tolerances further, I also
have a reference strip lot that I check new strip lots against.  This
minimizes the possible errors in the measurements.

> For our purposes a simple model will suffice.   I gather from what you
> have written and the referenced article on http://www.bloodjournal.org that the
> RBCs stay alive up to 50 days and then start dying off so that by 90 days
> they are all gone.

I believe that for my metabolism, the average lifespan of 120 days is
correct.  This means that some live longer and some live shorter lives with
50% of the 120 day old RBC cohort dead (or alive, glass half full).  The
abrupt 90 day RBC death estimate by squarewave is incorrect for my
metabolism per the data that I’ve collected.  I believe this 90 day model
is in error because it does not represent the true physiology of the RBC
life cycle, where each daily group of RBCs will experience a different
average BG.

> What is not evident is whether the die off is linear or not.   Maybe it
> doesn’t matter for our
> purposes and use of a linear die off rate is sufficient.  For a linear die
> off the decline is 2.5% per day.

> Is that how you have programmed your HP48?

The fall-off is an asymmetrical backward S:

1.00++++++
0.75++++++++++++++++++++++
0.50+++++++++++++++++++++++
0.25++++++++++++++++++++++++
0.00++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++>>>oo
———40——-…—-120————days

This is from the Normal curve where the probability that the RBC cohort is
still in circulation is 1 for days 1-40.  This backward S gets linear when
the standard deviation increases and gets squarewave-like (step drop off at
120 days) when the standard deviation is zero.  The pivot point is the mean
of 120 days.  So this statistical model covers all bases depending on the
standard deviation of the RBC lifespan.

But again note that this weighting is for the average BG that each daily
cohort experiences.  The sum of the weighted cohort average BG represents
the hematocrit (all RBCs in circulation) with both young and old RBCs in
the mixture.

So your linear model suggests a large standard deviation in your RBC
lifespan.  I think that is in error.  When I find a good reference for the
RBC lifespan standard deviation, we’ll know for sure.

Technically speaking, we should use the time averaged BG.  But I don’t have
the time to bother.  Note that the nocturnal BG is the time average two
point nocturnal BG.  So the nocturnal two point average is a time average.  
This make the averaging process simple but error prone.  But for me, I’m in
tight BG control during the day and loose BG control at night while
sleeping.  So this nocturnal BG is the worst data of the day for me.  This
is why it predicts HbA1c so well, IMO.

HTH,
—
Jim Dumas
T1 4/86, background retinopathy, rarely hypoglycemic: <1/mo.
lispro+R+U+NPH daily, moderate exercise, typically <6% HbA1c

> An interesting article I ran across was the shorter RBC lifespan in DMs
> caused by white blood cell phagocytosis of RBCs, (macrophages destroy the
> old RBCs).  Another one was older normals have shorter RBC lifespans from
> this same phagocytosis destruction of RBCs that increases with age.  See:

It looks like there have been other correspondences on this topic.

This was a correspondence dated Blood, 15 August 2002, Vol. 100, No. 4,
pp. 1511-1511
Acidic and neutral sialidase in the erythrocytes of patients with Type 2
diabetes: influence on erythrocyte lifespan
> http://www.bloodjournal.org/cgi/content/full/100/4/1511

> for the article on type 2 RBCs with a shorter lifespan.  But this is still a
> controversial topic.

Blood, 1 February 2002, Vol. 99, No. 3, pp. 1064-1070
Acidic and neutral sialidase in the erythrocyte membrane of type 2
diabetic patients
http://www.bloodjournal.org/cgi/content/full/99/3/1064

Blood, 1 March 2003, Vol. 101, No. 5, pp. 2071-2071
Acidic and neutral sialidase in the erythrocytes of patients with type 2
diabetes: an answer to comments by Richard et al
http://www.bloodjournal.org/cgi/content/full/101/5/2071

I have not read all of these exchanges. What do you make of it?

Frank

- Hide quoted text — Show quoted text -

On Sun, 01 Aug 2004 14:46:10 GMT, Jim Dumas <j-dumas@.no.SPAM!mindspring.com> wrote:
> JC wrote:

> > I use an excel spreadsheet to record my BG readings.    Over time I have
> > added some other features to calculate the
> > 1.  Average readings for each waking hour,
> > 2.  Average readings for each day, and
> > 3.  A guesstimate of the HbA1C reading by taking a 90 day average of the
> > daily averages.

> > It struck me during a rest period between sessions at the gym that the
> > HbA1C reading may not be a simple average of the daily averages but may be
> > a weighted average with current BG readings contributing more than
> > readings taken up to 13 weeks ago.

> > I tried googling for info on this but came up with nothing that helped.

> > We could do the calculation in 2 ways if there is a linear drop off in the
> > amount that each daily BG reading contributes to the final figure.

> > 1.  The readings for the current day could count 100% towards the
> > calculated figure and each preceding day contributing n x 1.1% less where
> > n is the number of days prior to the current day. That would involve 90
> > parts to the formula.

> > 2.  A simpler method would count the weekly average readings for the
> > current week 100% towards the calculated figure with those in each
> > previous week contributing n x 7.7% less where n is 1 for the
> > previous week, 2 for 2 weeks ago etc etc out to 12 weeks.  The simpler
> > method would still need 13 parts to the formula.

> > If the drop off is non linear does anyone have the formula?

> Hi JC,

> Last year someone else asked the same question.  I have an HbA1c model that
> mimicks the death rate (turnover) of red blood cells based on the fact that
> the average lifespan of RBCs is 120 days.  This means that a daily cohort
> of RBCs still have 50% left at 120 days!  So my model weights daily cohorts
> of RBCs with a normal (Gaussian) curve with a guess at the death rate
> standard deviation of 10 days.  This basically says: "What is the
> probability that a daily cohort of RBCs is still circulating in the body,"
> is the weighting used on the daily BG data.  This RBC cohort weighted
> average is summed and this value is curve fit to my HbA1c data.

> Next I use a nocturnal average BG instead of a fasting BG.  This is the
> bedtime and fasting BG divided by 2.  I always measure these two no matter
> how busy I get.  This NBG seems more accurate in a side by side comparison
> I currently doing.

> Finally, I transform this NBG data to an average that each daily cohort of
> RBCs would see before taking the weighted average sum.  So today’s BG data
> is unchanged, yesterday’s is (tNBG+yNBG)/2…for 160 days of data.  I also
> use a 40 day delay before RBCs begin to be removed from the bloodstream by
> the spleen.  (So if you do not have a spleen then your RBCs will live much
> longer than normal and all bets are off.)

> You should also know that we DMs have seasonal variations in HbA1c.  This
> averages 0.5% per a Swedish article in Diabetes Care about 1997.  The low
> point was in July and the high point was in January.  I currently have a
> seasonal variation of 0.3%, so my summer HbA1c is 5.7% and my winter HbA1c
> is 6% currently.  I curve fit summer data and winter data separately.

> I have no other references for you since this math is my handy work.  But
> any good math model should simulate red blood cell turnover.  So simple 90
> day averages are too gross an estimate for the lifespan of the RBC.

> I’m still collecting HbA1c data so subject to change.  HTH,

Jim,

I’m impressed with the scale of your calculations.   I’m going to have to sit down and think through
your advice to see how I can encode this into my spreadsheet.

I gather that you have the normal display screen with all of the readings taken during the day and
then off screen to the right you have 160 cells calculating the weighted figures which you then sum
to a cell in the display screen.

Can you point me at a reference for the RBC die off rate?

JC
Replace .invalid in the Reply-to address with .au to email me.