mrpro.operators.models.MOLLI

class mrpro.operators.models.MOLLI(ti: float | Tensor)

Bases: SignalModel[Tensor, Tensor, Tensor]

Signal model for Modified Look-Locker inversion recovery (MOLLI).

This model describes \(M_z(t) = a(1 - c)e^{(-t / T1^*)}\) with \(T1^* = T1 / (c - 1)\).

This is a small modification from the original MOLLI signal model [MESS2004]: \(M_z(t) = a - be^{(-t / T1^*)}\) with \(T1^* = T1 / (b/a - 1)\).

[MESS2004]

Messroghli DR, Radjenovic A, Kozerke S, Higgins DM, Sivananthan MU, Ridgway JP (2004) Modified look-locker inversion recovery (MOLLI) for high-resolution T 1 mapping of the heart. MRM, 52(1). https://doi.org/10.1002/mrm.20110

__init__(ti: float | Tensor)

Initialize MOLLI signal model for T1 mapping.

Parameters:

ti – inversion times with shape (time, …)

forward(a: Tensor, c: Tensor, t1: Tensor) → tuple[Tensor]

Apply MOLLI signal model.

Parameters:

• a – parameter a in MOLLI signal model with shape (… other, coils, z, y, x)

• c – parameter c = b/a in MOLLI signal model with shape (… other, coils, z, y, x)

• t1 – longitudinal relaxation time T1 with shape (… other, coils, z, y, x)

Return type:

signal with shape (time … other, coils, z, y, x)