How to understand radiation dose and dose-area-product?

Question

I am learning about radiation protection measures and am confused about the idea behind certain measures and practices, and I hope somebody can help me.

Dose definition and Gy The absorbed dose is measured in Gy, which is defined as J/kg, or the energy that is transferred from the radiation to 1kg of mass. This is a function of the number of photons and their energy, and could be measured by an ionisation chamber by counting how many ions are being created by the radiation passing through. By using appropriate factors one can pass to equivalent and effective dose, ending up with Sieverts, which still is J/kg, but never is the actual mass of the radiated body-part ever taken into account in these calculations.

As an example: a radiation chamber of 10 cm^2 measures a radiation pulse to contain 1mGy. With this radiation I radiate a human subject (whole body), giving an effective dose of 1mSv. Why is the mass of the subject never taken into account? Why even bother with the Gy, and not just say: this xray pulse contained x Photons with y total energy?

Dose area product (DAP) and its use

I just cannot wrap my head around the whole idea of dose area product, and nothing I read about it helped clarify the idea. Everybody keeps mentioning that the dose varies inversely with the square of the distance and that therefore the DAP is independent of the distance to the source. But why does dose vary inversely with 1/r^2 - it is proportional to the number of photons created, so it should stay the same. The number of photons hitting a certain area does of course decrease, but that would be a fluence with units of e.g. J/m^2. I just fail to understand what the practical purpose of this calculation is.

As an example: I have a x-ray tube creating x-rays, passing trough a collimator, a DAP meter (a square slightly larger than the size of an uncollimated beam exiting the source), a subject and hitting an image intensifier. After taking an image, the DAP meter reads 1.0 Gy m^2 (unrealistic, but I just put a number here). My image intensifier has an area of 0.1 m^2, so what do I do now to get the dose I incurred onto the patient? Divide by the area of the intensifier or by the area of the DAP ionisation chamber? Why not just measure the total dose that came out of the machine, and realise that the overall dose arriving at the intensifier must be the same?

Also, if I take a larger DAP-meter to measure the same beam, wouldnt I just get a higher DAP measurement, even though the beam stayed exactly the same? Or does this DAP idea only work if DAP-meter exactly covers the geometry of the beam?

I feel like I am struggling with a fundamental misunderstanding here somewhere, and hope somebody can give me pointer.

Answer 1

So, I will just answer my own question in case it is useful for anyone else.

First, the dose is defined as the Energy deposited in a certain mass, usually given differentially as $ dE / dm. $ This (differentially) small mass element has a certain size $ dm = \rho \cdot dl^3 $ and thus the dose decreases with distance from the source, because the mass element remains the same size and less photons hit the same area. In that respect, differential dose is very similar to radiation exposure, fluence, or intensity.

Second, as dose decreases with $ 1 / r^2 $, it follows that the DAP is indeed constant as a function of distance $r$.

Third, a DAP meter actually does not measure dose, which is a point quantity, but the average dose over its whole volume/mass. By measuring the ionisation events it measures the energy deposited (and it is known how much air the DAP meter contains), but it cannot measure the actual beam area, it only knows its own area. So the DAP measured is actually (average dose over the full volume of the DAP meter, multiplied by the DAP meter area). Fourth, to get the average dose at a certain location (e.g. the image intensifer) from the measured DAP, you divide it by the irradiated area / image intensifer area.

Fifth, the tissue weighting factors (e.g. https://en.wikipedia.org/wiki/Effective_dose_(radiation)) are given for whole body exposure, so e.g. if all bone was irradiated. As in medical imaging we typically only image part of a bone, using the value given in this table is a very conservative overestimation.

Lastly, radiation protection seems to be a topic as deep as an ocean and all of the above are simplifications. Calculating the biological (stochastic risk) of radiation field with a certain size, energy, and distribution hitting a certain geometry of masses with different compositions gets complex very fast. I have learned to be careful around the often deceivingly simple looking formulas.