Dear CASToR users,

I am Zhao Xin. I am interested about the way about calculating the time resolution(CTR) when using GATE simulation data. As we know, in GATE we set Singles time resolution by command：

/gate/digitizer/Singles/insert timeResolution

/gate/digitizer/Singles/timeResolution/setTimeResolution 200 ps

Is it corrected that we obtain the CTR by simply 200ps * sqrt(2) → 200ps * 1.414 = 282.84ps? If 282.84ps is used as CTR value and applied in CASToR TOF recon, is the reconstructed image correct according to the settings in GATE simulation (200ps singles time resolution)?

Hi Xin,

From my experience, it is correct. The system CTR should be the root sum square of two single time resolutions from the paired scintillator crystals, which is

sqrt(200^2+200^2)

and that can be simplified to 200*sqrt(2). I am not 100% sure it is correct because I didn’t see any description of this in any paper. I learned it by asking a good professor I met before, and I am using it for my reconstruction too.

Hope this helps!

Best,

Xinjie

With a typical PET configuration/geometry and a singleTimingResolution of 200 ps, this estimation is plenty good enough!

The rest is not relevant for the question: I just want to provide more details on why the “With A and B”.

In typical configuration and timing resolution, the difference in position of interaction for coincident event has a negligible effect on the timing. If my memory serves right, the expected error in timing induced purely by DOI for 3x3x20 mm LYSO is round 30 ps (Don’t cite me on this! XD), which is almost nothing compared to 200 ps. However, it start to become significant with better Single Time Resolution (STR), as is highlighted in this paper [1] (Disclaimer: I am one of the author).

Furthermore, the example provided previously neglect another factor: the variation in STR induced by the position of interaction in the detector. This can happen, for example, in fancy-fast photodetectors that can exploit the Cerenkov of the BGO (see [2])! In [3], the authors provide a analysis of the impact of the resulting multi-kernel TOF. Note: If memory serves right, the bias/error induced by difference in DOI is not taken into account in this paper but it might be negligible with their STR-s.

To conclude:

In GATE, the basic approach of timing, i.e. if you do not simulate the optical photons, assumes that annihilation photon detection time in a detector is invariant to the position of interaction, whether it is in the variation or bias it induces compared to the position of the annihilation. However, both are negligible, as far as I can tell, in most cases!

So, CTR \approx sqrt(2) * STR, almost always (for now!)

[1] ShieldSquare Captcha

[2] ShieldSquare Captcha

[3] TOF-PET Image Reconstruction With Multiple Timing Kernels Applied on Cherenkov Radiation in BGO | IEEE Journals & Magazine | IEEE Xplore

Hi Xinjie, thanks a lot for your help. In future work, I will set CTR as STR*sqrt(2). Hope we can have more experience exchanges. Have a good day.

Thank you for such a detailed explanation！ I learned so much from your answer. From now on I will set the CTR value with great confidence. I wish we can discuss interesting TOF reon of PET in the future.