Discrepancy Between Yield Peak and Cumulative Activity Peak for 11C, 15O, and 10C in FLUKA Simulation

I am working with FLUKA simulations involving the yield and activity distributions of 11C, 15O, and 10C isotopes. I have calculated the yield distribution at 0 seconds and the cumulative activity distribution from 0-5 seconds(add together), both in terms of their 1D spatial profiles. However, I noticed that the peak of the cumulative activity appears before the peak of the yield distribution.

This discrepancy suggests that the activity distribution does not directly correlate with the yield distribution at every depth, which raises questions about the underlying processes. I would like to understand why the activity peak is occurring at a shallower depth compared to the yield peak, considering that the activity should be a function of both the yield and the decay process.

I would appreciate any insights or suggestions on how to resolve this issue or if there are specific parameters in FLUKA that could help address this.

Hello @sy2119104, welcome to the FLUKA forum!

Could you either share your Flair and/or FLUKA input file, or explain how you defined the scorings from which you are showing the results in the plot. Based on this I can check in a bit more detail if this is where the discrepancy comes from.

Best regards,

Andreas

Hi Andreas,

Thank you for your response. Below, I provide a summary of my FLUKA input setup and the scoring I used, which may help clarify the issue:

I am simulating the production of 11C, 15O, and 10C isotopes in a CT phantom material. The input file includes the following key components:

Finally, I used python to plot the pictures:

I hope this helps clarify the setup. If you need more specific details from the input file or additional parameters, I can share them as well.

Looking forward to your insights!

Best regards,
Hu

Hello @sy2119104,

Thanks for providing this additional input. It seems to me that you are comparing two different things in the way you defined them here:

  • On one hand you have the yield obtained through a RES-NUCLEi scoring, this will have as output the total amount of residual nuclei produced when fully de-excited to ground or isomeric state per cubic centimeter per primary, i.e. no time dependence whatsoever.
  • On the other hand you have the activity which will have as output the activity at the requested DCYTIMES, which is given as Bq (so decays/s) per cubic centimeter per primary. These you sum up in the first five seconds only, however C-11 for example has a half life of around 20 minutes … .

The specific decay process indeed enters in the game here as you correctly mentioned. In your plot you see as well that for example C-11 has the highest contribution to the yield but much lower to the activity. Please also check carefully the RES-NUCLEi documentation and notes to make sure the physics settings are correct for this problem. To ensure you are comparing the same quantity perhaps may I suggest you only look at this post on activation and the use of the usrrnc.f routine which could provide you with additional information you need? For more information I’m also happy to recommend you to further check the course material of the FLUKA topical course on radiation protection.

Best regards, hope it helps,

Andreas

Thank you for your reply and insights.

I understand your point, and I appreciate the clarification on the difference between yield and activity. However, although these are two distinct physical quantities, they are directly related. I believe it is still expected that the location with the highest amount of a particular nuclide should also have the highest activity, as more nuclide production would lead to more decays.

Or, could it be that the RES-NUCLEi scoring reports the nuclide yield at “static” positions, whereas decay does not occur at these static locations? Some nuclides may decay along their path to these static locations, which might explain why the activity peak appears before the yield peak in my results, especially within the first 5 seconds.

Below is a figure showing four plots that represent the dose, yield, and activity profiles for the same target, irradiated with two different energies (0.21 GeV on the left and 0.25 GeV on the right).

Key Observations

  1. Top Row (Dose & Yield Profiles):
  • These plots show the dose (red line), nuclide yield (blue line), and contributions from individual isotopes (e.g., C-11, O-15, and C-10).
  • The blue line represents the total yield of residual nuclei.
  • It can be observed that the peak of the yield is located near the Bragg peak of the dose, with a slight spatial shift.
  1. Bottom Row (Dose & Activity Profiles):
  • These plots compare the dose (red line) with the activity (blue line) and the contributions of individual isotopes to the activity.
  • The blue line here represents the total activity at specific decay times.
  • Notably, for the same energy, the maximum value of the activity (bottom blue line) is located slightly earlier than the maximum value of the nuclide yield (top blue line).

Summary

This figure highlights the relationship between nuclide yield and activity distribution. The activity (bottom row) peaks at a shallower depth compared to the nuclide yield (top row). This may be attributed to decay occurring during the transport of nuclides, as well as differences in decay rates and the half-lives of the isotopes produced.

I would appreciate any further advice on how to account for these effects or refine my model.

Thank you again for your help!

Dear @sy2119104 , many thanks for your further explanations. Addressing your statements here:

I believe it is still expected that the location with the highest amount of a particular nuclide should also have the highest activity, as more nuclide production would lead to more decays.

This is fully correct. To clarify how it works in FLUKA: the activity is calculated based on the residual nuclei produced (which you can obtain through RES-NUCLEi scoring) but just applying the decay law for that particular isotope (which takes also into account its possible production through the decay of other isotopes).

Or, could it be that the RES-NUCLEi scoring reports the nuclide yield at “static” positions, whereas decay does not occur at these static locations? Some nuclides may decay along their path to these static locations, which might explain why the activity peak appears before the yield peak in my results, especially within the first 5 seconds.

This is incorrect since, as mentioned above, the activity is calculated directly from the residual nuclei which are scored at their final position, i.e. when they came to rest.

It can be observed that the peak of the yield is located near the Bragg peak of the dose, with a slight spatial shift.

This also makes sense, since the prompt dose is mostly due to the primary 12C ions. The different radioisotopes you look at are produced all along the primary 12C ions path and a perfect agreement between the dose (due to 12C) and the yield (resulting from all residual nuclei coming to rest) does not happen.

Notably, for the same energy, the maximum value of the activity (bottom blue line) is located slightly earlier than the maximum value of the nuclide yield (top blue line).

Not really, since here you are comparing activity vs dose, not yield. It is also not so easy to see when comparing the top and bottom rows if there is a clear difference between yield and activity. We would suggest to score the yield and activity curves corresponding to a single isotope (e.g. 11C). When doing this check on our side, the yield and activity curves are identical apart from a normalization factor, so they peak at exactly the same depth.

This may be attributed to decay occurring during the transport of nuclides, as well as differences in decay rates and the half-lives of the isotopes produced.

So no decay during transport happens but the different decay rates are correctly applied as in fact you can see very well from your plots: e.g., the yield for 10C is the lowest but in fact the resulting activity is the highest.

Hopefully this helps!

Andreas & Francesco

Thank you very much for your patient and detailed response. I have now understood the concepts clearly and successfully plotted the results. As expected, the normalized yield and normalized activity for a single nuclide are consistent with each other. However, when summing over all nuclides, there are differences between the total yield and total activity due to the differences in the peak positions and half-lives of various nuclides.

Finally, I have one more question:
For the simulation results, does the relationship between the yield (RES-NUCLEi scoring) and the activity at time zero (DCYSCORE:Coolingt:0) follow the equation:
Here is the revised formula with annotations:


Such as 22BIN = λ(C-11) * 41BIN * 10^6:

Thank you again for your kind assistance!

Best regards,

Hello @sy2119104 ,

The relationship you describe is not completely accurate. The quantity N which you incorrectly say is the total number of primary particles in the simulation is rather the particle intensity you defined in the IRRPROFile card, this value is used to calculate the activity. To then also be entirely correct, when you score the activity due to one isotope, say 11C, it could be that these are not due to the promptly generated 11C but result from the decay of another isotope. In this particular case it is probably negligible but for more complex problems should be kept in mind.

Best regards,

Andreas

Thank you very much for your detailed explanation.

To further deepen my understanding, could you kindly recommend any references, documentation, or example implementations that focus on methodologies and best practices for comprehensively analyzing positron distributions and the spatial distribution of their annihilation sites?

I would greatly appreciate any advice or recommendations you can offer.

Best regards,

Hello @sy2119104, I’m sorry but providing literature references or documentation is not within the scope of the FLUKA forum. If you would like to know more about implementations within the scope of FLUKA Monte Carlo simulations I suggest you use the search bar on this forum for related forum questions, or you could start a new forum question based on your own attempt at an implementation of the problem which you try to address.

Have a nice day,

Andreas

1 Like