initialize_mt_sat

torchsim.epg.initialize_mt_sat(duration, b1rms, df=0.0, slice_prof=1.0, B1=1.0)

Calculate RF energy deposition.

This is the energy deposited by and RF pulse on a bound pool, i.e., a spin pool without transverse magnetization (e.g., T2 almost 0.0).

Parameters:

• duration (float) – Pulse duration in [s].

• b1rms (float) – Pulse root-mean-squared B1 in [T] for each transmit channel. Expected shape is (nchannels,).

• df (float) – Frequency offset of the pulse in [Hz].

• slice_prof (float | torch.Tensor, optional) – Flip angle profile along slice. The default is 1.0.

• B1 (float, optional) – Flip angle scaling factor. The default is 1.0.

Returns:

WT – Energy yielded by the RF pulse.

Return type:

torch.Tensor

Notes

When flip angle is constant throughout acquisition, user should use the output exp_WT. When flip angle changes (e.g., MR Fingerprinting), user should provide the b1rms for a normalized pulse (i.e., when fa=1.0 [rad]). Then, user rescale the output WT by the square of current flip angle, and use this to re-calculate exp_WT. This can be achieved using the provided scale_mt_sat function.

Examples

import torch
from torchsim.epg import initialize_mt_sat, mt_sat_op

Constant flip angle case. We will use a pulse duration of 1ms and define B1rms so that the b1rms * tau is 32.7 uT**2 * ms.

duration = 1e-3 # 1ms pulse duration
b1rms = 1e-6 * (32.7**0.5) / 1e-3 # B1 rms in [T]
df = 0.0 # assume on-resonance pulse

In this case, we can directly use the exp(WT) output.

WT = initialize_mt_sat(torch.as_tensor(duration), torch.as_tensor(b1rms), df, slice_prof=1.0, B1=1.0)
S = mt_sat_op(WT)

Variable flip angle case. We will use a pulse duration of 1ms and define B1rms so that the b1rms * tau is 54.3 uT**2 * ms when fa = 1 rad.

duration = 1e-3 # 1ms pulse duration
b1rms = 1e-6 * (54.3**0.5) / 1e-3 # B1 rms in [T]
df = 0.0 # assume on-resonance pulse

In this case, we use the exponential argument only:

WT = initialize_mt_sat(torch.as_tensor(duration), torch.as_tensor(b1rms), df)

Then, for each RF pulse of in the train, we rescale WT and recompute the exponential. Here, we do it explicitly:

fa = torch.linspace(5, 60.0, 1000)
fa = torch.deg2rad(fa)
for n in range(fa.shape[0]):
    # update saturation operator
    S = mt_sat_op(WT, fa[n], slice_prof=1.0, B1=1.0)

    # apply saturation here
    ...