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An implementation of the Bloch-McConnell equations for simulating MR spin dynamics.

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BlochSim.jl

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This Julia package provides functionality for simulating arbitrary MRI pulse sequences. It includes support for (traditional) single-compartment Bloch simulations (using Spin objects) as well as multi-compartment Bloch-McConnell simulations (using SpinMC objects).

Getting started

This package is registered in the General registry, so you can install it at the REPL with ] add BlochSim.

The main functionality is provided by the functions freeprecess, excite, and spoil (and their mutating variants freeprecess!, excite!, and spoil!). These functions can be used to simulate a wide variety of MRI sequences. In addition, this package provides implementations for a multi-echo spin echo (MESE) scan (MESEBlochSim) and a spoiled gradient-recalled echo (SPGR) scan (SPGRBlochSim).

Examples

See the examples given in the documentation strings for how to use the provided functions. To access the documentation for, e.g., freeprecess, simply type ?freeprecess at the Julia REPL after loading the package.

For examples of how to simulate full MRI sequences, see src/mese.jl and src/spgr.jl in this repo, and STFR.jl.

Below are some concrete examples of how to use this package.

julia> using BlochSim

julia> spin = Spin(1, 1000, 100, 3.75)
Spin{Float64}:
 M = Magnetization(0.0, 0.0, 1.0)
 M0 = 1.0
 T1 = 1000.0 ms
 T2 = 100.0 ms
 Δf = 3.75 Hz
 pos = Position(0.0, 0.0, 0.0) cm

julia> excite!(spin, InstantaneousRF/2)) # 90° excitation

julia> spin.M # Mz is not quite 0 due to numerical roundoff
Magnetization vector with eltype Float64:
 Mx = 1.0
 My = 0.0
 Mz = 6.123233995736766e-17

julia> freeprecess!(spin, 100) # Free-precess for 100 ms

julia> spin.M
Magnetization vector with eltype Float64:
 Mx = -0.2601300475114444
 My = -0.2601300475114445
 Mz = 0.09516258196404054

julia> spgr! = SPGRBlochSim(5, 2.5, deg2rad(20)) # Create an object to simulate an SPGR scan
Spoiled Gradient-Recalled Echo (SPGR) Bloch Simulation:
 TR = 5.0 ms
 TE = 2.5 ms
 rf (excitation pulse) = Instantaneous RF pulse with eltype Float64:
 α = 0.3490658503988659 rad
 θ = 0.0 rad
 spoiling = IdealSpoiling()
 steady-state

julia> spgr!(spin) # Simulate a steady-state SPGR scan applied to the given spin

julia> spin.M # Steady-state magnetization
Magnetization vector with eltype Float64:
 Mx = 0.025553542433162182
 My = -0.0015069712547712193
 Mz = 0.07442699373678281

julia> spinmc = SpinMC(1, (0.2, 0.8), (400, 1000), (20, 80), (15, 0), (100, 25))
SpinMC{Float64,2}:
 M = MagnetizationMC((0.0, 0.0, 0.2), (0.0, 0.0, 0.8))
 M0 = 1.0
 frac = (0.2, 0.8)
 T1 = (400.0, 1000.0) ms
 T2 = (20.0, 80.0) ms
 Δf = (15.0, 0.0) Hz
 r = ((0.0, 0.01), (0.04, 0.0)) 1/ms
 pos = Position(0.0, 0.0, 0.0) cm

julia> spgr!(spinmc) # The same SPGR scan can be used on multi-compartment spins

julia> spinmc.M # Steady-state magnetization
2-compartment Magnetization vector with eltype Float64:
 Compartment 1:
  Mx = -0.09359002635156467
  My = 0.02433674787041617
  Mz = -0.36973998540693054
 Compartment 2:
  Mx = 0.1541252837882581
  My = 0.00031515000730316224
  Mz = 0.5077167235922019

julia> signal(spin) # Grab the observed signal from the spin
0.025553542433162182 - 0.0015069712547712193im

julia> signal(spinmc)
0.060535257436693427 + 0.02465189787771933im

Related package(s)

Acknowledgement

This package was developed based on Brian Hargreaves' Bloch simulation tutorial. All tests for this package of the form testX0x (like testA5b or testF3d) are based on the corresponding section in the tutorial (see test/matlab.jl).

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An implementation of the Bloch-McConnell equations for simulating MR spin dynamics.

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