Simulating the Interfrequency Delay

[srveale]

The simulation now runs through the saturation pulse, allows the system to relax for some time defined by adjustable sequence parameters with a hard flip here and there, and uses the resulting magnetization state as the initial state for the next saturation frequency.

Here I simulated alternating frequencies to try and replicate the double-peak phenomenon we've observed in phantoms. There is only one simulated species to the left of the water peak; the peak on the right is an artifact of residual saturation from the previous frequency. It dissappears if the inter-frequency time is long enough, about 5000 - 70000 ms (in excellent agreement with phantom studies... almost too excellent).

Also note the shoulders on either side of the spectrum as the system approaches a steady state.

(Forgot to say that the legend gives the interfreq delay for each spectrum)

Some parameters: B0 = 7.0 T (easy upgrade!) B1 = 1.0e-6 saturation pulse duration = 500 ms there is one 20 degree flip in the sequence

M0a = 1000.0 M0b = M0ax1e-3x10 (so 10mM, used a high concentration for easily cest effect) T1a = 2.0 # seconds T2a = 0.6 T1b = 1.0 T2b = 0.2 kb = 40. ka = M0b/M0a*kb #Transfer rate of pool a to pool b, s^-1. We want a-->b = b-->a accFactor = 1 (more on this later)

[DrSAR]

Stunning. This is something worth to brag about this PM.

[firasm]

Agreed - beautiful results and almost suspicious at how accurately the simulations predict experimental behaviour. See issue #22 for the exact same effect in phantoms.

[srveale]

This is a higher resolution version. You can now notice that there are small-scale oscillations in the spectrum, which also disappear with long interfreq delay.

[DrSAR]

What;s the explanation for the small-scale oscillation?

[firasm]

Well, when @srveale first showed me those oscillations in the plot with linear saturation offsets, I thought it may be due to leftover saturation magnetization when doing two saturations sequentially... If the offsets are done in an alternating fashion, it results in the mirror peak - if they're done linearly then those small oscillations arise.

I asked him to create the same plot with alternating frequency offsets and that's the plot above, which tosses cold water on my theory that linear saturation frequency offsets cause the bumps.

@srveale can you put up the original plot you showed me as well? With the linear saturation frequency offsets?

[srveale]

The sequential version:

[DrSAR]

Can you plot the phantom peak (the one that shouldn't be there) intensity vs interfrequency delay. I would hope there is some relationship to T1 of the water. This should give us the needed handle on how to choose the interfrequency delay. Also, in a different thread @firasm claims that the issue is reproduced in simulations but not yet understood physically. I'd argue that approach to steady-state eq'm explains it.

[srveale]

Just updating this issue with the latest version of the sim. It agrees with the experience we've had where the mirror peak, established to be a result of alternating frequency offsets, disappears with inter-frequency delay of 6-7 seconds. This is apart from the unreasonable T1 of 4.0 s that I just threw in there.

[firasm]

Cool, that's interesting to see. It never actually goes to 0 eh ? that's what we saw in #22 as well, even at 10s, it didn't fully disappear.

P.S. I don't actually think that 4s is that unreasonable of a T1. Our tumour T1s are between 2s and 3s so @srveale could you add a 3s one as well for reference ?

Other than that, this issue seems to be resolved and addressed. @DrSAR can we close this one and #22 ?

[srveale]

In the sim they do go to zero, I just shifted the scale down to see what was happening. The graph is updated with T1 = 3.0 s and I reset the axes to be sure.

[firasm]

Okay, much better. I'll close this issue then.