BlochSimulators.EPGStatesType
EPGStates = Union{MMatrix{3}, SizedMatrix{3}}

In the EPG model, the configuration state matrix Ω will be updated inplace. On CPU, we use StaticArrays.MMatrix. The MMatrix will not escape _simulate! and therefore should not result in allocations. On GPU, we use shared memory (CUDA.CuStaticSharedArray). The shared memory is allocated for all threads within a block simultaneously. We then take a @view and wrap it in a SizedArray. Without the SizedArray, the type would be long and unreadable. By wrapping, we can then simply dispatch on a SizedArray instead.

BlochSimulators.AbstractTissueParametersType
AbstractTissueParameters{N,T} <: FieldVector{N,T}

Abstract type for structs that hold different combinations of tissue parameters.

Possible fields

  • T₁::T: T₁ relaxation parameters of a voxel
  • T₂::T: T₂ relaxation parameters of a voxel
  • B₁::T: Scaling factor for effective B₁ excitation field within a voxel
  • B₀::T: Off-resonance with respect to main magnetic field within a voxel
  • ρˣ::T: Real part of proton density within a voxel
  • ρʸ::T: Imaginary part of proton density within a voxel
  • x::T: Position of voxel along the x direction
  • y::T: Position of voxel along the y direction
  • z::T: Position of voxel along the z direction

The structs are subtypes of FieldVector, which is a StaticVector with named fields (see the documentation of StaticArrays.jl). There are three reasons for letting the structs be subtypes of FieldVector:

  1. FieldVectors/StaticVectors have sizes that are known at compile time. This is beneficial for performance reasons
  2. The named fields improve readability of the code (e.g. p.B₁ vs p[3])
  3. Linear algebra operations can be performed on instances of the structs. This allows, for example, subtraction (without having to manually define methods) and that is useful for comparing parameter maps.
BlochSimulators.AbstractTrajectoryType
AbstractTrajectory

The abstract type of which all gradient trajectories will be a subtype. The subtypes should contain fields that can describe the full trajectory during a sequence.

BlochSimulators.AdiabaticInversionType
AdiabaticInversion{T<:Real, V<:AbstractVector} <: IsochromatSimulator{T}

This struct is used to simulate an adiabatic inversion pulse. This struct itself could be used as field in other sequence structs.

Fields

  • γΔtA::V: # Time-dependent amplitude modulation.
  • Δω::V # Time-dependent frequency modulation
  • Δt::T: Time discretization step, assumed constant
BlochSimulators.BlochSimulatorType
BlochSimulator{T}

The abstract type of which all sequence simulators will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type. By convention, a BlochSimulator will be used to simulate magnetization at echo times only without taking into account spatial encoding gradients (i.e. readout or phase encoding gradients). To simulate the magnetization at other readout times, including phase from spatial encoding gradients, an AbstractTrajectory will be needed as well.

To make a simulator for a particular pulse sequence:

  1. Make a struct that's a subtype of either IsochromatSimulator or EPGSimulator. The struct will hold parameters that are necessary for performing the simulations.

  2. Add a method to simulate_magnetization! that implements the pulse sequence. For both performance and GPU compatibility, make sure that simulate_magnetization! does not do any heap allocations. Examples for pSSFP and FISP sequences are found in src/sequences.

  3. Add methods to output_eltype and output_size that are used to allocate an output array within the simulate function.

  4. [Optional] Add a method to show for nicer printing of the sequence in the REPL

  5. [Optional] Add a method to getindex to easily reduce the length of the sequence

  6. [Optional] Add a constructor for the struct that takes in data from Matlab or something else and assembles the struct

IMPORTANT

The simulate_magnetization! functions (which dispatch on the provided sequence) are assumed to be type-stable and non-allocating Should be possible to achieve when using functions from operators/epg.jlandoperators/isochromat.jl` and a properly parametrized sequence struct.

BlochSimulators.CartesianTrajectoryType
CartesianTrajectory{T,I,U,V} <: SpokesTrajectory

Struct that is used to implement a typical Cartesian gradient trajectory. The trajectory is described in a compact fashion by only storing the starting position in k-space (k_start_readout) for each readout as well as the step in k-space per readout point Δk_adc.

Note that CartesianTrajectory and RadialTrajectory are essentially the same in when using when using this compact description. A SpokesTrajectory struct is therefore defined as a supertype of both and methods are defined for SpokesTrajectory instead to avoid code repetition.

The type parameters are intentionally left vague. The J, for example, may be an integer for sequences where each readout has the same number of samples, but for sequences with different numbers of samples per readout it may be a vector of integers.

Fields

  • nreadouts::I: The total number of readouts for this trajectory
  • nsamplesperreadout::I: The total number of samples per readout
  • Δt::T: Time between sample points
  • k_start_readout::U: Starting position in k-space for each readout
  • Δk_adc::U: k-space step Δkₓ per sample point (same for all readouts)
  • py::V: Phase encoding index for each readout
BlochSimulators.EPGSimulatorType
EPGSimulator{T,Ns} <: BlochSimulator{T}

Abstract type of which all sequence simulators that are based on the EPG model will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type. The parameter Ns corresponds to the maximum order of configuration states that are tracked in the simulations.

BlochSimulators.FISP2DType
FISP2D{T, Ns, U<:AbstractVector, V<:AbstractMatrix} <: EPGSimulator{T,Ns}

This struct is used to simulate gradient-spoiled sequence with varying flip angle scheme and adiabatic inversion prepulse using the EPG model. The TR and TE are fixed throughout the sequence. Instantenous RF excitations are assumed. Slice profile correction is done using the partitioned EPG model, where for each flip angle a vector of RF scaling factors are determined prior to the simulation (using, for example, the small tip-angle approximation or Shinnar LeRoux forward model).

Within each TR, a single time steps is used to simulate the RF excitation. Then, in one time step we go from the end of the RF excitation to the echo time (applying T₁ and T₂ decay, T₁ regrowth and B₀ rotation), and again in one time step from the echo time to the start of the next RF excitation.

Fields

  • RF_train::U Vector with flip angle for each TR with abs.(RFtrain) the RF flip angles in degrees and angle.(RFtrain) should be the RF phases in degrees.
  • sliceprofiles::V # Matrix with RF scaling factors (a.u.) to simulate slice profile effects. Each column represents the (flip angle dependent) scaling factors for one position along the slice direction.
  • TR::T: Repetition time in seconds, assumed constant during the sequence
  • TE::T: Echo time in seconds, assumed constant during the sequence
  • max_state::Val{Ns}: Maximum number of states to keep track of in EPG simulation
  • TI::T: Inversion delay after the inversion prepulse in seconds
BlochSimulators.Generic2DType
Generic2D{T,V,M,S} where {T<:AbstractFloat, V<:AbstractVector, M<:AbstractMatrix, S} <: IsochromatSimulator{T}

Simulate a generic 2D sequence defined by arrays containing RF and gradient waveforms. Contains a loop over z locations to take into account slice profile effects. The Δt vector stores the time intervals for the waveforms.

Fields

  • RF::V{Complex{T}}: Vector with (complex) RF values during each time interval
  • GR::M{T}: Matrix with GRx, GRy and GRz values during each time interval
  • sample::S: Vector with Bool's to indicate the sample points
  • Δt::V{T}: Vector with time intervals
  • z::V{T}: Vector with different positions along the slice direction
BlochSimulators.Generic3DType
Generic3D{T,V<:AbstractVector{Complex{T}},W<:AbstractVector{T},M<:AbstractMatrix{T},S} <: IsochromatSimulator{T}

Simulate a generic sequence defined by arrays containing RF and gradient waveforms. Unlike the Generic2D sequence, it is assumed that the excitation is homogenous over the voxel and therefore no summation over a slice direction is applied. The Δt vector stores the time intervals for the waveforms.

Fields

  • RF::V{Complex{T}}: Vector with (complex) RF values during each time interval
  • GR::M{T}: Matrix with GRx, GRy and GRz values during each time interval
  • sample::S: Vector with Bool's to indicate the sample points
  • Δt::V{T}: Vector with time intervals
BlochSimulators.IsochromatType
struct Isochromat{T<:Real} <: FieldVector{3,T}
    x::T
    y::T
    z::T
end

Holds the x,y,z components of a spin isochromat in a FieldVector, which is a StaticVector (from the package StaticArrays) with custom fieldnames.

BlochSimulators.IsochromatSimulatorType
IsochromatSimulator{T} <: BlochSimulator{T}

Abstract type of which all sequence simulators that are based on the isochromat model will be a subtype. The parameter T should be a number type (e.g. Float64, Float32) and the tissueparameters that are used as input to the simulator should have the same number type.

BlochSimulators.RadialTrajectoryType
RadialTrajectory{T,I,U,V} <: SpokesTrajectory

Struct that is used to implement a typical radial gradient trajectory. The trajectory can is described in a compact fashion by only storing the starting position in k-space (k_start_readout) for each readout as well as the step in k-space per readout point Δk_adc.

Note that CartesianTrajectory and RadialTrajectory are essentially the same in when using when using this compact description. A SpokesTrajectory struct is therefore defined as a supertype of both and methods are defined for SpokesTrajectory instead to avoid code repetition.

The type parameters are intentionally left vague. The J, for example, may be an integer for sequences where each readout has the same number of samples, but for sequences with different numbers of samples per readout it may be a vector of integers.

Fields

  • nreadouts::I: The total number of readouts for this trajectory
  • nsamplesperreadout::I: The total number of samples per readout
  • Δt::T: Time between sample points
  • k_start_readout::U: Starting position in k-space for each readout
  • Δk_adc::U: k-space step Δk between each readout
  • φ::V: Radial angle for each readout
BlochSimulators.SpokesTrajectoryType
SpokesTrajectory <: AbstractTrajectory

Typical Cartesian and radial trajectories have a lot in common: a readout can be described by a starting point in k-space and a Δk per sample point. To avoid code repetition, both type of trajectories are made a subtype of SpokesTrajectory such that some methods that would be the same for both trajectories otherwise are written for SpokesTrajectory instead.

BlochSimulators.pSSFP2DType
pSSFP2D{T<:AbstractFloat,N,M,U<:AbstractVector{Complex{T}},V<:Number} <: IsochromatSimulator{T}

This struct is used to simulate a inversion-recovery, gradient-balanced transient-state sequence with varying flip angle scheme based on the isochromat model. The TR and TE are fixed throughout the sequence. The TR and TE are fixed throughout the sequence. Slice profile correction is done by discretizing the RF excitation waveform in time and using multiple Isochromats with different positions along the slice direction (z) per voxel. The sequence also uses an 'α/2' prepulse after the inversion.

Within each TR, multiple time steps are used to simulate the RF excitation. Then, in one time step we go from the end of the RF excitation to the echo time (applying slice refocussing gradient, T₂ decay and B₀ rotation), and again in one time step from the echo time to the start of the next RF excitation.

Fields

  • RF_train::U Vector with flip angle for each TR with abs.(RFtrain) the RF flip angles in degrees and angle.(RFtrain) should be the RF phases in degrees.
  • TR::T: Repetition time in seconds, assumed constant during the sequence
  • γΔtRF::SVector{N}{V}: Time-discretized RF waveform, normalized to flip angle of 1 degree
  • Δt::NamedTuple{(:ex, :inv, :pr),NTuple{3,T}}: Time interval for each sample of excitation pulse (ex), inversion delay (inv) and time between RF and TE (pr)
  • γΔtGRz::NamedTuple{(:ex, :inv, :pr),NTuple{3,T}}: Slice select gradients for ex, inv and pr
  • z::SVector{M}{T} # Vector with different positions along the slice direction.
BlochSimulators.pSSFP3DType
pSSFP3D{T<:AbstractFloat,N,U<:AbstractVector{Complex{T}},V<:Number} <: IsochromatSimulator{T}

This struct is used to simulate an inversion-recovery, gradient-balanced, transient-state sequence with varying flip angle scheme based on the isochromat model. The TR and TE are fixed throughout the sequence. The RF excitation waveform can be discretized in time but no slice profile mechanism is provided. The sequence also uses an 'α/2' prepulse after the inversion.

Within each TR, multiple time steps are used to simulate the RF excitation. Then, in one time step we go from the end of the RF excitation to the echo time (applying slice refocussing gradient, T₂ decay and B₀ rotation), and again in one time step from the echo time to the start of the next RF excitation.

Fields

  • RF_train::U Vector with flip angle for each TR with abs.(RFtrain) the RF flip angles in degrees and angle.(RFtrain) should be the RF phases in degrees.
  • TR::T: Repetition time in seconds, assumed constant during the sequence
  • γΔtRF::SVector{N}{V}: Time-discretized RF waveform, normalized to flip angle of 1 degree
  • Δt::NamedTuple{(:ex, :inv, :pr),NTuple{3,T}}: Time interval for each sample of excitation pulse (ex), inversion delay (inv) and time between RF and TE (pr)
BlochSimulators.F̄₋Method
F̄₋(Ω)

View into the second row of the configuration state matrix Ω, corresponding to the F̄₋ states.

BlochSimulators.F₊Method
F₊(Ω)

View into the first row of the configuration state matrix Ω, corresponding to the F₊ states.

BlochSimulators.ZMethod
Z(Ω)

View into the third row of the configuration state matrix Ω, corresponding to the Z states.

BlochSimulators._allocate_outputMethod
_allocate_output(resource, sequence::BlochSimulator, parameters)

Allocate an array to store the output of the Bloch simulations (per voxel, echo times only) to be performed with the sequence. For each BlochSimulator, methods should have been added to output_eltype and output_dimensions for this function to work properly.

BlochSimulators._allocate_signal_outputMethod
_allocate_signal_output(resource, trajectory::AbstractTrajectory, coil_sensitivities)

Allocate an array to store the output of the signal simulation (all readout points, integrated over all voxels).

BlochSimulators._get_readout_and_sample_idxMethod
_get_readout_and_sample_idx(trajectory, t)

Given time index t, compute the associated readout and sample indices (r,s). For trajectories where each readout has the same length, this is equivalent to r,s = fld1(t,ns), mod1(t,ns) with ns being the (constant) number of samples per readout.

BlochSimulators.add_gradient_delay!Method
add_gradient_delay!(tr::RadialTrajectory, S)

Apply gradient delay to radial trajectory in in-place fashion. The delay is described by the 2x2 matrix S and is assumed to influence the start of the readout only, not the readout direction.

BlochSimulators.decay!Method
decay!(Ω::EPGStates, E₁, E₂)

T₂ decay for F-components, T₁ decay for Z-component of each state.

BlochSimulators.decayMethod
decay(m::Isochromat{T}, E₁, E₂) where T

Apply T₂ decay to transverse component and T₁ decay to longitudinal component of Isochromat.

BlochSimulators.dephasing!Method
dephasing!(Ω::EPGStates)

Shift states around due to dephasing gradient: The F₊ go up one, the F̄₋ go down one and Z do not change

BlochSimulators.excite!Method
excite!(Ω::EPGStates, RF::Complex, p::AbstractTissueParameters)

Mixing of states due to RF pulse. Magnitude of RF is the flip angle in degrees. Phase of RF is the phase of the pulse. If RF is real, the computations simplify a little bit.

BlochSimulators.excite!Method
excite!(Ω::EPGStates, RF::T, p::AbstractTissueParameters) where T<:Union{Real, Quantity{<:Real}}

If RF is real, the calculations simplify (and probably Ω is real too, reducing memory (access) requirements).

BlochSimulators.f32Method
f32(x)

Change precision of x to Float32. It uses Functors.fmap to recursively traverse the fields of the struct x. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

It may be necessary to add new adapt rules (by adding new methods to adapt_storage) if new structs with complicated nested fields are introduced.

BlochSimulators.f64Method
f64(x)

Change precision of x to Float64. It uses Functors.fmap to recursively traverse the fields of the struct x. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

It may be necessary to add new adapt rules (by adding new methods to adapt_storage) if new structs with complicated nested fields are introduced.

BlochSimulators.gpuMethod
gpu(x)

Move x to CUDA device. It uses Functors.fmap to recursively traverse the fields of the struct x, converting <:AbstractArrays to CuArrays, and ignoring isbitsarrays. For custom structs (e.g. <:BlochSimulator or <:AbstractTrajectory), it is required that typeof(x) be made a Functors.@functor (e.g. @functor FISP).

BlochSimulators.initial_conditions!Method
initial_conditions!(Ω::EPGStates)

Set all components of all states to 0, except the Z-component of the 0th state which is set to 1.

BlochSimulators.initialize_statesMethod
initialize_states(::AbstractResource, sequence::EPGSimulator{T,Ns}) where {T,Ns}

Initialize an MMatrix of EPG states on CPU to be used throughout the simulation.

BlochSimulators.initialize_statesMethod
initialize_states(::CUDALibs, sequence::EPGSimulator{T,Ns}) where {T,Ns}

Initialize an array of EPG states on a CUDA GPU to be used throughout the simulation.

BlochSimulators.initialize_statesMethod
initialize_states(::AbstractResource, ::IsochromatSimulator{T}) where T

Initialize a spin isochromat to be used throughout a simulation of the sequence.

This may seem redundant but to is necessary to share the same programming interface with EPGSimulators.

BlochSimulators.invert!Method
invert!(Ω::EPGStates, p::AbstractTissueParameters)

Invert Z-component of states of all orders. Assumes fully spoiled transverse magnetization.

BlochSimulators.invert!Method
invert!(Ω::EPGStates)

Invert with B₁ insenstive (i.e. adiabatic) inversion pulse

BlochSimulators.invertMethod
invert(m::Isochromat{T}, p::AbstractTissueParameters) where T

Invert Isochromat with B₁ insenstive (i.e. adiabatic) inversion pulse

BlochSimulators.invertMethod
invert(m::Isochromat{T}, p::AbstractTissueParameters) where T

Invert z-component of Isochromat (assuming spoiled transverse magnetization so xy-component zero).

BlochSimulators.kspace_coordinatesMethod
kspace_coordinates(tr::CartesianTrajectory)

Return matrix (nrsamplesperreadout, nrreadouts) with kspace coordinates for the trajectory. Needed for nuFFT reconstructions.

BlochSimulators.kspace_coordinatesMethod
kspace_coordinates(tr::RadialTrajectory)

Return matrix (nrsamplesperreadout, nrreadouts) with kspace coordinates for the trajectory. Needed for nuFFT reconstructions.

BlochSimulators.magnetization_to_signalMethod
magnetization_to_signal(resource, magnetizationtization, parameters, trajectory, coil_sensitivities)

Given the magnetization in all voxels (typically at echo times only), allocate memory for the signal output on CPU, then loop over all time points t and use the (generic) magnetization_to_signal! implementation to compute the signal for that time point.

This loop order is not necessarily optimal (and performance may be) across all trajectories and computational resources. If a better implementation is available, add new methods to this function for those specific combinations of resources and trajectories.

BlochSimulators.nreadoutsMethod
nreadouts(::AbstractTrajectory)

For each ::AbstractTrajectory, a method should be added to this function that specifies how many readouts the trajectory consists of.

BlochSimulators.nsamplesMethod
nsamples(trajectory::AbstractTrajectory)

Determines the total number of samples acquired with the trajectory. Requires nreadouts and nsamplesperreadout to be implemented.

BlochSimulators.nsamplesperreadoutMethod
nsamplesperreadout(::AbstractTrajectory, readout_idx)

For each ::AbstractTrajectory, a method should be added to this function that specifies how many samples in total are acquired during the trajectory.

BlochSimulators.output_dimensionsMethod
output_dimensions(::BlochSimulator)

For each <:BlochSimulator, a method should be added to this function that specifies the output size of the simulation for a single ::AbstractTissueParameters.

BlochSimulators.output_eltypeMethod
output_eltype(::BlochSimulator)

For each <:BlochSimulator, a method should be added to this function that specifies the output type of the simulation. For MR signal simulation, this is typically a complex number representing the transverse magnetization. For other types of simulations, one may want to retrieve the x,y and z components of an isochromat as output (implemented as a FieldVector perhaps) or state configuration matrices Ω.

BlochSimulators.phase_encoding!Method
phase_encoding!(magnetization, trajectory::AbstractTrajectory, parameters)

For each ::AbstractTrajectory, a method should be added to this function if it does any kind of phase encoding (so far Cartesian only).

BlochSimulators.regrowthMethod
regrowth(m::Isochromat{T}, E₁) where T

Apply T₁ regrowth to longitudinal component of Isochromat.

BlochSimulators.rotate!Method
rotate!(Ω::EPGStates, eⁱᶿ::T) where T

Rotate F₊ and F̄₋ states under the influence of eⁱᶿ = exp(i * ΔB₀ * Δt)

BlochSimulators.rotateMethod
rotate(m::Isochromat, γΔtGRz, z, Δt, p::AbstractTissueParameters)

Rotation of Isochromat without RF (so around z-axis only) due to gradients and B0 (i.e. refocussing slice select gradient).

BlochSimulators.rotateMethod
rotate(m::Isochromat{T}, γΔtRF::Complex, γΔtGR::Tuple, (x,y,z), Δt, p::AbstractTissueParameters, Δω = zero(T)) where T

RF, gradient and/or ΔB₀ induced rotation of Isochromat computed using Rodrigues rotation formula (https://en.wikipedia.org/wiki/Rodrigues%27rotationformula).

BlochSimulators.sample_transverse!Method
sample!(output, index::Union{Integer,CartesianIndex}, m::Isochromat)

Sample transverse magnetization from Isochromat. The "+=" is needed for 2D sequences where slice profile is taken into account.

BlochSimulators.sample_transverse!Method
sample_transverse!(output, index::Union{Integer,CartesianIndex}, Ω::EPGStates)

Sample the measurable transverse magnetization, that is, the F₊ component of the 0th state. The += is needed for 2D sequences where slice profile is taken into account.

BlochSimulators.sample_xyz!Method
sample_xyz!(output, index::Union{Integer,CartesianIndex}, m::Isochromat)

Sample m.x, m.y and m.z components from Isochromat. The "+=" is needed for 2D sequences where slice profile is taken into account.

BlochSimulators.sample_Ω!Method
sample_Ω!(output, index::Union{Integer,CartesianIndex}, Ω::EPGStates)

Sample the entire configuration state matrix Ω. The += is needed for 2D sequences where slice profile is taken into account.

BlochSimulators.sampling_maskMethod
sampling_mask(tr::CartesianTrajectory)

For undersampled Cartesian trajectories, the gradient trajectory can also be described by a sampling mask.

BlochSimulators.simulate_magnetization!Method
simulate_magnetization!(magnetization, sequence::BlochSimulator, state, p::AbstractTissueParameters) end

For each <:BlochSimulator, a method should be added to this function that implements the actual pulse sequence using information contained in the sequence struct together with the operators from src/operators/{isochromat,epg}.jl. For performance reasons as well as GPU compatibility it is important that the implementation is type-stable and non-allocating.

Arguments

  • magnetization: Pre-allocated array with size(magnetization) = output_dimensions(sequence) and eltype(magnetization) = output_eltype(sequence) to store the output of the simulation.
  • sequence: Sequence struct containing fields that are used to implement the actual pulse sequence.
  • state: Either an Isochromat or EPGStates, depending on which model is used.
  • p: Custom struct (<:AbstractTissueParameters) containing input parameters to the simulation (e.g. T₁T₂)
BlochSimulators.simulate_magnetizationMethod
simulate_magnetization(resource, sequence, parameters)

Simulate the magnetization at echo times (without any spatial encoding gradients applied) for all combinations of tissue parameters contained in parameters.

This function can also be used to generate dictionaries for MR Fingerprinting purposes.

Arguments

  • resource::AbstractResource: Either CPU1(), CPUThreads(), CPUProcesses() or CUDALibs()
  • sequence::BlochSimulator: Custom sequence struct
  • parameters::AbstractVector{<:AbstractTissueParameters}: Vector with different combinations of tissue parameters

Returns

  • output::AbstractArray: Array of size (output_dimensions(sequence), length(parameters)) containing the magnetization at echo times for all combinations of input tissue parameters.
BlochSimulators.simulate_magnetizationMethod
simulate_magnetization(::CPU1, sequence, parameters)

Perform simulations on a single CPU by looping over all entries of parameters and performing Bloch simulations for each combination of tissue parameters.

BlochSimulators.simulate_magnetizationMethod
simulate_magnetization(::CPUThreads, sequence, parameters)

Perform simulations by looping over all entries of parameters in a multi-threaded fashion. See the Julia documentation for more details on how to launch Julia with multiple threads of execution.

BlochSimulators.simulate_magnetizationMethod
simulate_magnetization(::CUDALibs, sequence, parameters::CuArray)

Perform simulations on NVIDIA GPU hardware by making use of the CUDA.jl package. Each thread perform Bloch simulations for a single entry of the parameters array.

BlochSimulators.simulate_signalMethod
simulate_signal(resource, sequence, parameters, trajectory, coil_sensitivities)

Simulate the MR signal at timepoint t from coil i as: sᵢ(t) = ∑ⱼ cᵢⱼρⱼmⱼ(t), where cᵢⱼis the coil sensitivity of coil i at position of voxel j, ρⱼ is the proton density of voxel j and mⱼ(t) the (normalized) transverse magnetization in voxel j obtained through Bloch simulations.

Arguments

  • resource::AbstractResource: Either CPU1(), CPUThreads(), CPUProcesses() or CUDALibs()
  • sequence::BlochSimulator: Custom sequence struct
  • parameters::AbstractVector{<:AbstractTissueParameters}: Vector with tissue parameters for each voxel
  • trajectory::AbstractTrajectory: Custom trajectory struct
  • coil_sensitivities::AbstractVector{<:SVector{ncoils}}: Vector with ncoils coil sensitivities for each voxel

Returns

  • signal::Vector{<:SVector{ncoils}}: Simulated MR signal for the sequence and trajectory.

At each timepoint, the signal for each of the ncoils is stored.

BlochSimulators.spoil!Method
spoil!(Ω::EPGStates)

Perfectly spoil the transverse components of all states.

BlochSimulators.to_sample_pointMethod
to_sample_point(m, trajectory, readout_idx, sample_idx, parameters)

For each ::AbstractTrajectory, a method should be added to this function that, given the magnetization m at the readout with index readout_idx, it computes the magnetization at the readout point with index sample_idx (by applying spatial encoding gradients, T₂ decay, B₀ rotation, etc...) based on the trajectory and parameters.

Arguments

  • m: Magnetization at the echo with index readout_idx.
  • trajectory: Trajectory struct containing fields that are used to compute the magnetization at other readout times, including the effects of spatial encoding gradients.
  • readout_idx: Index that corresponds to the current readout.
  • sample_idx: Index for the desired sample during this readout.
  • parameters: Tissue parameters of current voxel, including spatial coordinates.

Output:

  • mₛ: Magnetization at sample with index sample_idx
BlochSimulators.Ω_eltypeMethod
Ω_eltype(sequence::EPGSimulator{T,Ns}) where {T,Ns} = Complex{T}

By default, configuration states are complex. For some sequences, they will only ever be real (no RF phase, no complex slice profile correction) and for these sequences a method needs to be added to this function.