Limit of Detection P-32 in Urin

[Andreas]

Hello,
can you help with the correct formular to determine P-32 detection limit by direct measurement in Urin via LSC by double measurment. First measurment after sampelpreparation, second measurment after 14 days.
The problem is the K-40 in Urin.
We have in the P-32/ K-40 Window a LSC background of 12 CPM. With 2.5 ml Urin wie have 30 CPM ( LSC-background and K-40 ). Is it possible to achieve the required Detectionlimit of 16 Bq/L?

Eff. P-32 in the Window 98 %.
k1-alpa= 1,645

Can you help? May be also the formular for error determination with Bayesstatistic?
Thanks a lot

[Sven]

My first quick shot:

The specific model of evaluation:


Uncertainty:


Decision threshold:


Detection limit:


With:
n1 = Number of gross counts (first measurement)
t1 = Duration of first measurement
n2 = Number of gross counts (Second measurement)
t2 = Duration of second measurement
epsilon = Counting efficiency
eta = Chemical yield
V = Original sample volume
Vtot = Volume of the total fraction containing phosphorus after chemical separation (if necessary)
Va = Volume of aliquot used for LSC (if necessary)
fa = Aliquot correction factor (if necessary)
tw = Waiting time between first and second measurement
lamda = Decay constant for P-32
kw = Decay correctionf actor, due to waiting time between first and second measurement
A = Activity concentration
A* = Decision threshold
alpha* = Detection limit

Decay correction factor:


Aliquot correction factor:


This is only a first guess. No responsibility is accepted for the accuracy of this information.
I hope it helps, nevertheless.

Sven

[Sven]

You may possibly want to include other correction factors.
In order to give a more general formula, I bring all individual correction factors together in one calibration factor:

The respective type B uncertainties are brought together in:


Now, all required expressions appear much clearer.

Mathematical model of the evaluation:


Standard uncertainty:


Decision threshold:


Detection limit:


Please note that the equation for the detection limit is still an implicit one.

[Sven]

If you prefer using count rates, you may change the formulae accordingly (but mind the units!).

Mathematical model of the evaluation:


Standard uncertainty:


Decision threshold:


Detection limit:

[Sven]

In order to estimate the detection limit, I am working on assumptions based on your numerical example.

Sample volume:


Aliquot correction factor:


Chemical yield:


Counting efficiency:


Waiting time between first and second measurement:




Calibration factor:


I deliberately neglect any type B uncertainties for now:


Background count rate:


In order to achieve the demanded detection limit, I simply assume sufficiently long measurement durations:


Quantiles of the standardized normal distribution:


Decision threshold:


Detection limit:


Please note:
The results are not corrected for the decay of P-32 during the measurement duration of 8 h.
The results are also not corrected for the decay of P-32 between sampling and first measurement.
Significant type B uncertainties would raise the detection limit.

[Andreas]

Hello Sven,
thanks a lot for your very detailed and competent reply. I am not so familiar with the statistik and I need a little time to understand the formulars and to formulate correct questions. And I still have some in the moment.
May be its possible for you meanwhile to calculate the Limit of detection when I measure the P-32 and K-40 in 2 Windows. The Formular is:
CPS(roi1)=A(p32)*eta(p32,roi1)+A(K40)*eta(K40,roi1)
CPS(roi2)=A(p32)*eta(p32,roi2)+A(K40)*eta(K40,roi2)
Solving this gives:
A(p32)= [ (CPM(roi1)*eta(K40,roi2))-(cpm(roi2)*eta(K40,roi1)) ] / [ (eta(p32,roi1*eta(K40,roi2)) - (eta(p32,roi2)*eta(K40,roi1) ]

eta=counting eff. in the window
A= activity
O.K. Volume is 2,5 ml ( 3ml or more is sometimes to much for the cocktail )


Lets assume eta(K40,roi1)=70% , eta(K40,roi2)=30% , eta(p32,roi1)=30% eta(p32,roi2)=60%

Very best regards and thank you very much in advance
Andreas

[Sven]

May be its possible for you meanwhile to calculate the Limit of detection when I measure the P-32 and K-40 in 2 Windows.

得寸进尺 *scnr*
I will see what I can do.

3ml or more is sometimes to much for the cocktail

What cocktails have you tried (e.g. Ultima Gold XR, Ultima Gold AB, Hionic-Fluor)?
Is salt content the only problem or does the sample need to be acid or alkaline?

Lets assume eta(K40,roi1)=70% , eta(K40,roi2)=30% , eta(p32,roi1)=30% eta(p32,roi2)=60%

When using narrow energy windows, any variability of sample composition would cause significant uncertainties about efficiency values. Do you use a quench calibration for the efficiencies?

[Andreas]

What cocktails have you tried (e.g. Ultima Gold XR, Ultima Gold AB, Hionic-Fluor)?

Normally for Urin direct measurement the HiIonic Fluor. High salt capacity and on the label stands extremly fast chemoluminiscence decay.

Is salt content the only problem or does the sample need to be acid or alkaline?

We dont stabilize the Urin with acid or alkaline. So the salt and may be some other bad smelling ingredience make the problems.

When using narrow energy windows, any variability of sample composition would cause significant uncertainties about efficiency values. Do you use a quench calibration for the efficiencies?

Yes! We determine the K-40 and P-32 eff in the 2 windows against the quenchlevel.

[Sven]

Yes! We determine the K-40 and P-32 eff in the 2 windows against the quenchlevel.

How do you treat background in both windows?
Do you assume constant background count rates or do you use quench calibrations for background count rates?
Or do you simply assume that all background is coming from K-40?

Can you give typical background count rates for the estimation of detection limits?

[Andreas]

How do you treat background in both windows?
Do you assume constant background count rates or do you use quench calibrations for background count rates?
Or do you simply assume that all background is coming from K-40?

Yes we are quenching the counter background because the Beckman LSC ( Urincounter) can subtract quenched background automatically. And so we are using this feature....
I will send you the values as soon as possible!

[Sven]

Lets assume eta(K40,roi1)=70% , eta(K40,roi2)=30% , eta(p32,roi1)=30% eta(p32,roi2)=60%

If I assume a relative uncertainty of 1 % for each efficiency factor and a counting time of one hour, the estimated detection limit would be about 23 Bq/l just due to K-40 (ignoring any detector background).

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