AW: [ RadSafe ] Cumulated Activity and Dosimetry Question (UNCLASSIFIED)

Rainer.Facius at Rainer.Facius at
Fri Jul 18 09:58:04 CDT 2008


from what you describe and I understand, I think you un-necessarily complicate the issue. 

>From a dosimetric point of view all I am interested in is the energy deposited in a system in a given time interval. For that purpose I multiply the total number of decays in that time interval with the energy per decay. 

If you plot activity (ordinate: decays-in-a-given-system per unit time) against time (abscissa) then the integral of this function gives you the total number of decays in the system between two moments in time, i.e., that what you need. 

The number of decays per unit time is proportional to the number of radioactive atoms present at this moment. The number of radioactive atoms present decreases by (a) the decay itself with a decay constant C-phys and (b) biological metabolism. In a more or less crude approximation biological removal is modelled as an exponential process with a decay constant C-biol. This approximation leads to an exponential decay with the decay constant:

C-total = C-phys + C-biol.

To summarize: The total number of decays is what I need to know. I get them by integration of the activity curve over time. You may call this total number of decays "cumulated activity" though I would dissuade from doing so.

HTH, Rainer 

Dr. Rainer Facius
German Aerospace Center
Institute of Aerospace Medicine
Linder Hoehe
51147 Koeln
Voice: +49 2203 601 3147 or 3150
FAX:   +49 2203 61970

-----Ursprüngliche Nachricht-----
Von: radsafe-bounces at [mailto:radsafe-bounces at] Im Auftrag von Falo, Gerald A Dr USACHPPM
Gesendet: Freitag, 18. Juli 2008 15:49
An: radsafe at
Betreff: [ RadSafe ] Cumulated Activity and Dosimetry Question (UNCLASSIFIED)

Classification:  UNCLASSIFIED
Caveats: NONE


I was reading Mike Stabin's new book "Fundamentals of Nuclear Medicine Dosimetry," and it got me thinking about cumulated activity.  The thinking then got me confused, which is more common than I'd like it to be.

The cumulated activity is defined at the time integral of the activity in a particular organ or tissue (compartment).  In this integral the effective (biological + physical) removal rate constant is used.  This cumulated activity is often called the number of nuclear transitions, decays, or distintegrations.  This is where I get confused.  By using the effective removal rate constant in the integrand, the result is the total number of atoms removed by biological and physical process, not just radiological decay.  I thought that only those atoms "removed" by decay would contribute to dose.

For dosimetry, it seems that what is needed is the total number of decays that occur in the compartment of interest, not the total removed.
So, it seems that the cumulated activity as defined above should be multiplied by the fraction of the atoms removed that decay, which is the ratio of the physical removal rate constant (the decay constant) to the effective (total) removal rate constant.

Is there an underlying assumption that the physical half-life for the radionuclides used will always be much shorter than the biological half-life so that the effective removal rate equals the decay constant?

What am I missing here?  I'd appreciate someone pointing out where I've gone astray.

BTW, I've enjoyed Mike Stabin's book very much so far, and what I've skimmed ahead to looks excellent.


The statements and opinions expressed herein are my responsibility; no one else (certainly not my employer) is responsible, but I still reserve the right to make mistakes.
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Gerald A. Falo, Ph.D., CHP
U.S. Army Center for Health Promotion and Preventive Medicine - Health Physics Program jerry.falo at
DSN: 584-4852
Classification:  UNCLASSIFIED
Caveats: NONE

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