mrphy.slowsims

Simulation codes with implicit Jacobian operations.

mrphy.slowsims.blochsim(M: Tensor, Beff: Tensor, *, T1: Tensor | None = None, T2: Tensor | None = None, γ: Tensor = tensor(4257.6000, dtype=torch.float64), dt: Tensor = tensor(4.0000e-06, dtype=torch.float64)) → Tensor

Bloch simulator with implicit Jacobian operations.

Usage:

Mo = blochsim(Mi, Beff, *, T1, T2, γ, dt) Mo = blochsim(Mi, Beff, *, T1=None, T2=None, γ, dt)

Inputs:

  • M: (N, *Nd, xyz), Magnetic spins, assumed equilibrium [[[0 0 1]]].

  • Beff: (N, *Nd, nT, xyz), “Gauss”, B-effective, magnetic field.

OPTIONALS:

  • T1: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “Sec”, T1 relaxation.

  • T2: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “Sec”, T2 relaxation.

  • γ: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “Hz/Gauss”, gyro ratio.

  • dt: () ⊻ (N ⊻ 1,), “Sec”, dwell time.

Outputs:

  • M: (N, *Nd, xyz), Magetic spins after simulation.

Note

spin history during simulations is not provided.

mrphy.slowsims.blochsim_1step(M: Tensor, M1: Tensor, b: Tensor, E1: Tensor, E1_1: Tensor, E2: Tensor, γ2πdt: Tensor) → Tuple[Tensor, Tensor]

Single step bloch simulation

Usage:

M = blochsim_1step(M, M1, b, E1, E1_1, E2, γ2πdt)

Inputs:

  • M: (N, *Nd, xyz), Magnetic spins, assumed equilibrium [[[0 0 1]]].

  • M1: (N, *Nd, xyz), pre-allocated variable for uϕrot output.

  • b: (N, *Nd, xyz), “Gauss”, B-effective, magnetic field applied.

  • E1: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), a.u., T1 reciprocal exponential.

  • E1_1: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), a.u., T1 reciprocal exponential subtracted by 1.

  • E2: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), a.u., T2 reciprocal exponential.

  • γ2πdt: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “rad/Gauss”, gyro ratio in radiance mutiplied by dt.

Outputs:

  • M: (N, *Nd, xyz), Magetic spins after simulation.

mrphy.slowsims.blochsim_ab(M: Tensor, A: Tensor, B: Tensor) → Tensor

Bloch simulation via Hargreave’s mat/vec representation

Usage:

M = blochsim_ab(M, A, B)

Inputs:

  • M: (N, *Nd, xyz), Magnetic spins, assumed equilibrium magnitude [0 0 1]

  • A: (N, *Nd, xyz, 3), A[:,iM,:,:] is the iM-th 𝐴.

  • B: (N, *Nd, xyz), B[:,iM,:] is the iM-th 𝐵.

Outputs:

  • M: (N, *Nd, xyz), Result magnetic spins

mrphy.slowsims.freeprec(M: Tensor, dur: Tensor, *, T1: Tensor | None = None, T2: Tensor | None = None, Δf: Tensor | None = None) → Tensor

Isochromats free precession with given relaxation and off-resonance

Usage:

M = freeprec(M, dur, *, T1, T2, Δf)

Inputs:

  • M: (N, *Nd, xyz), Magnetic spins, assumed equilibrium magnitude [0 0 1]

  • dur: () ⊻ (N ⊻ 1,), “Sec”, duration of free-precession.

OPTIONALS:

  • T1: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “Sec”, T1 relaxation.

  • T2: () ⊻ (N ⊻ 1, *Nd ⊻ 1,), “Sec”, T2 relaxation.

  • Δf: (N ⊻ 1, *Nd ⊻ 1,), “Hz”, off-resonance.

Outputs:

  • M: (N, *Nd, xyz), Result magnetic spins