mrphy.beffective

B-effective related functions

mrphy.beffective.beff2ab(beff: Tensor, *, E1: Tensor = tensor(0.), E2: Tensor = tensor(0.), γ: Tensor = tensor(4257.6000, dtype=torch.float64), dt: Tensor = tensor(4.0000e-06, dtype=torch.float64)) → Tuple[Tensor, Tensor]

Compute Hargreave’s 𝐴/𝐵, mat/vec, from B-effectives

See: doi:10.1002/mrm.1170.

Usage:

A, B = beff2ab(beff, *, E1, E2, γ, dt)

Inputs:

  • beff: (N,*Nd,nT,xyz), B-effective.

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:

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

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

mrphy.beffective.beff2uφ(beff: Tensor, γ2πdt: Tensor, *, dim=-1) → Tuple[Tensor, Tensor]

Compute rotation axes and angles from B-effectives

Usage:

U, Φ = beff2uϕ(beff, γ2πdt, *, dim)

Inputs:

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

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

Optionals:

  • dim: int. Indicate the xyz-dim, allow beff.shape != (N, *Nd, xyz)

Outputs:

  • U: (N, *Nd, xyz), rotation axis

  • Φ: (N, *Nd), rotation angle

mrphy.beffective.rfgr2beff(rf: Tensor, gr: Tensor, loc: Tensor, *, Δf: Tensor | None = None, b1Map: Tensor | None = None, γ: Tensor = tensor(4257.6000, dtype=torch.float64)) → Tensor

Compute B-effectives from rf and gradients

Usage:

beff = rfgr2beff(rf, gr, loc, *, Δf, b1Map, γ)

Inputs:

  • rf: (N,xy,nT,(nCoils)), “Gauss”, xy for separating real and imag part.

  • gr: (N,xyz,nT), “Gauss/cm”.

  • loc: (N,*Nd,xyz), “cm”, locations.

Optionals:

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

  • b1Map: (N, *Nd, xy (, nCoils), a.u., transmit sensitivity.

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

Outputs:

  • beff: (N,*Nd,nT,xyz), “Gauss”