Is relaxation applied during tipping?

[nathanjbeaumont]

Hello,
I am simulating a sequence with KomaMRI as well as with EPG via Matlab and I am trying to get the signal output to be identical between the two. With EPG a tip is applied instantly, and then you apply relaxation for a given period of time before instantly applying the next tip. So the EPG code runs in a loop like this:

P = zeros(3,N);
for i=1:100
    P = epg_rf(P, FAs(n), 0);		% RF excitation
    s(n) = P(1,1);  			% Signal is F0 state.
    P = epg_relax(P, T1, T2, TRs(n));
    for q = 1:4
        P = epg_grad(P, 1);  % 8pi spoiler
    end
end

Of course in reality the RF pulse tip takes time, and during this time T1 and T2 relaxation still occur. Does KomaMRI apply relaxation during tips? If KomaMRI does apply relaxation during tips my TR in Pulseq should be the length of the green line below:

[cncastillo]

Hi! Yes, KomaMRI does apply relaxation effects during excitation. The signals will not be identical, as the EPG model has some assumptions that are not necessarily satisfied in the more realistic case. For the solution to be similar I would try to add isochromats in the gradient spoiling direction. Assuming it is the z-direction:

voxel_size = 8e-3  # 8 mm, <-- Play with this
Niso = 100         # <-- Play with this
T1 = 1000e-3       # 1000 ms <-- Modify
T2 = 80e-3         # 80 ms <-- Modify

obj = Phantom(
	x=zeros(Niso), 
	z=collect(range(-voxel_size/2, voxel_size/2, Niso)), 
	T1=T1.*ones(Niso),
	T2=T2.*ones(Niso)
)

plot_phantom_map(obj, :z) # The color is their position in z

The TR is generally calculated between the RF "iso-center", so in the case of this sinc-shaped RF pulse it would be better to put instantaneous pulses in the blue "x"s in the bottom of your plot. This is the center of the RF in this case, or Trf/2.

If you want to see the more realistic effects in the slice profile, you can use

sys = Scanner()
# Replace with your RF, probably seq[1:2]
seq = PulseDesigner.RF_sinc(0.5e-6, 10e-3, sys; G=[0, 0, 2e-3]) # Long-RF pulse, FA=19 deg
sim_params = KomaMRICore.default_sim_params()
sim_params["return_type"] = "state"
M = simulate(obj, seq, sys; sim_params)

using Plots
plot(obj.z, real.(M.xy), label="Mx")
plot!(obj.z, imag.(M.xy), label="My")

You can see that even if the gradient refocusing pulse is half of the area of the slice-selective gradient, there is still a remaining phase. This is because the "isco-center" depends on the flip angle. So for a larger flip angle of FA = 76 deg:

julia> seq = PulseDesigner.RF_sinc(2e-6, 10e-3, sys; G=[0, 0, 2e-3])

So it is complicated. The calculation of the iso-center is generally ignored, and put at the middle of the RF pulse for simple pulses, but for more complicated ones like hyperbolic-Secant Adabatic pulses the correct position is the end of the pulse, so it depends. Putting it at the center is a good approximation for sinc pulses with low flip angles.

[nathanjbeaumont]

Here is with two sinc pulses of 10 deg, 13ms delay between them

[cncastillo]

Some oscillations are to be expected, as each RF in the EPG representation adds a new higher frequency state. So this is not necessarily wrong I believe.

[nathanjbeaumont]

Actually RF rotations in EPG don't add higher order states, they just mix the states of a given order. See this video at 9:55. I confirmed that with the EPG library I'm using this is the case.

Maybe this isn't an issue with Koma simulation, it's just a limitation of sinc pulses?

[cncastillo]

Oh sorry I will try to make myself clearer. You are correct that the RFs only mix the states at order k, but an RF after a gradient (shift of states) does indeed generate higher order oscillations. This is the case for unbalanced gradients, which for us would happen for the first and second RF if the gradient refocusing is not correct.

[cncastillo]

Thanks for the EPG repo btw, it would be interesting to recreate some of those examples.

I believe that the simulation is correct, but sometimes it's hard to understand why :) (even for me). If you want, we can have a Zoom meeting or something if that would be helpful for you. Let me know in the Julia Slack if that is the case!