LorentzianSimulator

class torchsim.simulators.LorentzianSimulator(*args, **kwargs)

Bases: Simulator

A Z-spectrum as equilibrium minus one Lorentzian line per pool.

Each pool saturates the water signal along a Lorentzian line centred on its own offset [1], and the lines add:

M0 (1 - sum_i A_i (W_i / 2)^2 / ((W_i / 2)^2 + (offset - shift_i)^2))

Pool i, counted from one, exposes pool{i}_amplitude, pool{i}_width (the full width at half maximum) and pool{i}_shift.

Parameters:

• pools (int) – How many Lorentzian lines.

• **values – Properties or sequence arguments to fix, as for any simulator.

References

[1]

Zaiss, M., Schmitt, B., Bachert, P., “Quantitative separation of CEST effect from magnetization transfer and spillover effects by Lorentzian-line-fit analysis of z-spectra”, Journal of Magnetic Resonance 211.2 (2011), pp. 149-155. https://doi.org/10.1016/j.jmr.2011.05.001

Examples

import torch
from torchsim.simulators import LorentzianSimulator

sequence = LorentzianSimulator(2, offsets=torch.linspace(-5.0, 5.0, 41))
signal = sequence.simulate(
    pool1_amplitude=0.9, pool1_width=1.5, pool1_shift=0.0,
    pool2_amplitude=0.1, pool2_width=2.0, pool2_shift=3.5,
)
print(signal.shape)

torch.Size([41])

Methods

bind	This simulator with more fixed on it, values or settings alike.
describe	Return the description this protocol plays.
evaluate	Evaluate the closed form, no state machine and no description.
from_description	Return a simulator over a stream someone else assembled.
from_pulseq	Return a simulator over one repetition of a Pulseq sequence.
jacobian	Return the signal and its derivative with respect to diff.
layout	Return the operators of one repetition, in the order they play.
played	Return the protocol as it will be laid out.
repetition_s	Return how long one repetition lasts, given what the layout played.
simulate	Return the recorded signal.

evaluate(properties, **sequence)

Evaluate the closed form, no state machine and no description.