KomaMRIBase

sys = Scanner(B0, B1, Gmax, Smax, ADC_Δt, seq_Δt, GR_Δt, RF_Δt,
    RF_ring_down_T, RF_dead_time_T, ADC_dead_time_T)

The Scanner struct. It contains hardware limitations of the MRI resonator. It is an input for the simulation.

Arguments

• B0: (::Real, =1.5, [T]) main magnetic field strength
• B1: (::Real, =10e-6, [T]) maximum RF amplitude
• Gmax: (::Real, =60e-3, [T/m]) maximum gradient amplitude
• Smax: (::Real, =500, [mT/m/ms]) gradient's maximum slew-rate
• ADC_Δt: (::Real, =2e-6, [s]) ADC raster time
• seq_Δt: (::Real, =1e-5, [s]) sequence-block raster time
• GR_Δt: (::Real, =1e-5, [s]) gradient raster time
• RF_Δt: (::Real, =1e-6, [s]) RF raster time
• RF_ring_down_T: (::Real, =20e-6, [s]) RF ring down time
• RF_dead_time_T: (::Real, =100e-6, [s]) RF dead time
• ADC_dead_time_T: (::Real, =10e-6, [s]) ADC dead time

Returns

• sys: (::Scanner) Scanner struct

Examples

julia> sys = Scanner()

julia> sys.B0

obj = Phantom(name, x, y, z, ρ, T1, T2, T2s, Δw, Dλ1, Dλ2, Dθ, motion)

The Phantom struct. Most of its field names are vectors, with each element associated with a property value representing a spin. This struct serves as an input for the simulation.

Arguments

• name: (::String) phantom name
• x: (::AbstractVector{T<:Real}, [m]) spin x-position vector
• y: (::AbstractVector{T<:Real}, [m]) spin y-position vector
• z: (::AbstractVector{T<:Real}, [m]) spin z-position vector
• ρ: (::AbstractVector{T<:Real}) spin proton density vector
• T1: (::AbstractVector{T<:Real}, [s]) spin T1 parameter vector
• T2: (::AbstractVector{T<:Real}, [s]) spin T2 parameter vector
• T2s: (::AbstractVector{T<:Real}, [s]) spin T2s parameter vector
• Δw: (::AbstractVector{T<:Real}, [rad/s]) spin off-resonance parameter vector
• Dλ1: (::AbstractVector{T<:Real}) spin Dλ1 (diffusion) parameter vector
• Dλ2: (::AbstractVector{T<:Real}) spin Dλ2 (diffusion) parameter vector
• Dθ: (::AbstractVector{T<:Real}) spin Dθ (diffusion) parameter vector
• motion: (::MotionModel{T<:Real}) motion model

Returns

• obj: (::Phantom) Phantom struct

Examples

julia> obj = Phantom(x=[0.0])

julia> obj.ρ

phantom = brain_phantom2D(;axis="axial", ss=4)

Creates a two-dimensional brain Phantom struct. Default ss=4 sample spacing is 2 mm. Original file (ss=1) sample spacing is .5 mm.

References

• B. Aubert-Broche, D.L. Collins, A.C. Evans: "A new improved version of the realistic digital brain phantom" NeuroImage, in review - 2006
• B. Aubert-Broche, M. Griffin, G.B. Pike, A.C. Evans and D.L. Collins: "20 new digital brain phantoms for creation of validation image data bases" IEEE TMI, in review - 2006
• https://brainweb.bic.mni.mcgill.ca/brainweb

Keywords

• axis: (::String, ="axial", opts=["axial", "coronal", "sagittal"]) orientation of the phantom
• ss: (::Integer or ::Vector{Integer}, =4) subsampling parameter for all axes if scaler, per axis if 2 element vector [ssx, ssy]
• us: (::Integer or ::Vector{Integer}, =1) upsampling parameter for all axes if scaler, per axis if 2 element vector [usx, usy], if used ss is set to ss=1

Returns

• obj: (::Phantom) Phantom struct

Examples

julia> obj = brain_phantom2D(; axis="sagittal", ss=1)

julia> obj = brain_phantom2D(; axis="axial", us=[1, 2])

julia> plot_phantom_map(obj, :ρ)

obj = brain_phantom3D(; ss=4, us=1)

Creates a three-dimentional brain Phantom struct. Default ss=4 sample spacing is 2 mm. Original file (ss=1) sample spacing is .5 mm.

References

• B. Aubert-Broche, D.L. Collins, A.C. Evans: "A new improved version of the realistic digital brain phantom" NeuroImage, in review - 2006
• B. Aubert-Broche, M. Griffin, G.B. Pike, A.C. Evans and D.L. Collins: "20 new digital brain phantoms for creation of validation image data bases" IEEE TMI, in review - 2006
• https://brainweb.bic.mni.mcgill.ca/brainweb

Keywords

• ss: (::Integer or ::Vector{Integer}, =4) subsampling parameter for all axes if scaler, per axis if 3 element vector [ssx, ssy, ssz]
• us: (::Integer or ::Vector{Integer}, =1) upsampling parameter for all axes if scaler, per axis if 3 element vector [usx, usy, usz]
• start_end: (::Vector{Integer}, =[160,200]) z index range of presampled phantom, 180 is center

Returns

• obj: (::Phantom) 3D Phantom struct

Examples

julia> obj = brain_phantom3D(; ss=5)

julia> obj = brain_phantom3D(; us=[2, 2, 1])

julia> plot_phantom_map(obj, :ρ)

obj = pelvis_phantom2D(; ss=4, us=1)

Creates a two-dimensional pelvis Phantom struct. Default ss=4 sample spacing is 2 mm. Original file (ss=1) sample spacing is .5 mm.

Keywords

• ss: (::Integer or ::Vector{Integer}, =4) subsampling parameter for all axes if scaler, per axis if 2 element vector [ssx, ssy]
• us: (::Integer or ::Vector{Integer}, =1) upsampling parameter for all axes if scaler, per axis if 2 element vector [usx, usy]

Returns

• obj: (::Phantom) Phantom struct

Examples

julia> obj = pelvis_phantom2D(; ss=2])

julia> obj = pelvis_phantom2D(; us=[1, 2])

julia> pelvis_phantom2D(obj, :ρ)

obj = heart_phantom(...)

Heart-like LV 2D phantom. The variable circumferential_strain and radial_strain are for streching (if positive) or contraction (if negative). rotation_angle is for rotation.

Arguments

• circumferential_strain: (::Real, =-0.3) contraction parameter
• radial_strain: (::Real, =-0.3) contraction parameter
• rotation_angle: (::Real, =1) rotation parameter

Returns

• phantom: (::Phantom) Heart-like LV phantom struct

x, y, z = get_spin_coords(motion, x, y, z, t)

Calculates the position of each spin at a set of arbitrary time instants, i.e. the time steps of the simulation. For each dimension (x, y, z), the output matrix has $N_{ ext{spins}}$ rows and length(t) columns.

Arguments

• motion: (::MotionModel) phantom motion
• x: (::AbstractVector{T<:Real}, [m]) spin x-position vector
• y: (::AbstractVector{T<:Real}, [m]) spin y-position vector
• z: (::AbstractVector{T<:Real}, [m]) spin z-position vector
• t: (::AbstractArray{T<:Real}) horizontal array of time instants

Returns

• x, y, z: (::Tuple{AbstractArray, AbstractArray, AbstractArray}) spin positions over time

motion = SimpleMotion(types)

SimpleMotion model. It allows for the definition of motion by means of simple parameters. The SimpleMotion struct is composed by only one field, called types, which is a tuple of simple motion types. This tuple will contain as many elements as simple motions we want to combine.

Arguments

• types: (::Tuple{Vararg{<:SimpleMotionType{T}}}) tuple of simple motion types

Returns

• motion: (::SimpleMotion) SimpleMotion struct

Examples

julia> motion = SimpleMotion(
            Translation(dx=0.01, dy=0.02, dz=0.0, t_start=0.0, t_end=0.5),
            Rotation(pitch=15.0, roll=0.0, yaw=20.0, t_start=0.1, t_end=0.5),
            HeartBeat(circumferential_strain=-0.3, radial_strain=-0.2, longitudinal_strain=0.0, t_start=0.2, t_end=0.5)
        )

translation = Translation(dx, dy, dz, t_start, t_end)

Translation motion struct. It produces a linear translation of the phantom. Its fields are the final displacements in the three axes (dx, dy, dz) and the start and end times of the translation.

Arguments

• dx: (::Real, [m]) translation in x
• dy: (::Real, [m]) translation in y
• dz: (::Real, [m]) translation in z
• t_start: (::Real, [s]) initial time
• t_end: (::Real, [s]) final time

Returns

• translation: (::Translation) Translation struct

Examples

julia> tr = Translation(dx=0.01, dy=0.02, dz=0.03, t_start=0.0, t_end=0.5)

rotation = Rotation(pitch, roll, yaw, t_start, t_end)

Rotation motion struct. It produces a rotation of the phantom in the three axes: x (pitch), y (roll), and z (yaw). We follow the RAS (Right-Anterior-Superior) orientation, and the rotations are applied following the right-hand rule (counter-clockwise):

The applied rotation matrix is obtained as follows:

\[\begin{equation} \begin{aligned} R &= R_z(\alpha) R_y(\beta) R_x(\gamma) \\ &= \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ -\sin \beta & 0 & \cos \beta \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos \gamma & -\sin \gamma \\ 0 & \sin \gamma & \cos \gamma \end{bmatrix} \\ &= \begin{bmatrix} \cos \alpha \cos \beta & \cos \alpha \sin \beta \sin \gamma - \sin \alpha \cos \gamma & \cos \alpha \sin \beta \cos \gamma + \sin \alpha \sin \gamma \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta \sin \gamma + \cos \alpha \cos \gamma & \sin \alpha \sin \beta \cos \gamma - \cos \alpha \sin \gamma \\ -\sin \beta & \cos \beta \sin \gamma & \cos \beta \cos \gamma \end{bmatrix} \end{aligned} \end{equation}\]

Arguments

• pitch: (::Real, [º]) rotation in x
• roll: (::Real, [º]) rotation in y
• yaw: (::Real, [º]) rotation in z
• t_start: (::Real, [s]) initial time
• t_end: (::Real, [s]) final time

Returns

• rotation: (::Rotation) Rotation struct

Examples

julia> rt = Rotation(pitch=15.0, roll=0.0, yaw=20.0, t_start=0.1, t_end=0.5)

heartbeat = HeartBeat(circumferential_strain, radial_strain, longitudinal_strain, t_start, t_end)

HeartBeat struct. It produces a heartbeat-like motion, characterised by three types of strain: Circumferential, Radial and Longitudinal

Arguments

• circumferential_strain: (::Real) contraction parameter
• radial_strain: (::Real) contraction parameter
• longitudinal_strain: (::Real) contraction parameter
• t_start: (::Real, [s]) initial time
• t_end: (::Real, [s]) final time

Returns

• heartbeat: (::HeartBeat) HeartBeat struct

Examples

julia> hb = HeartBeat(circumferential_strain=-0.3, radial_strain=-0.2, longitudinal_strain=0.0, t_start=0.2, t_end=0.5)

periodic_translation = PeriodicTranslation(dx, dy, dz, period, asymmetry)

PeriodicTranslation motion struct. It produces a periodic translation of the phantom in the three directions x, y and z. The amplitude of the oscillation will be defined by dx, dy and dz

Arguments

• dx: (::Real, [m]) translation in x
• dy: (::Real, [m]) translation in y
• dz: (::Real, [m]) translation in z
• period: (::Real, [s]) period
• asymmetry: (::Real) asymmetry factor, between 0 and 1

Returns

• periodic_translation: (::PeriodicTranslation) PeriodicTranslation struct

periodic_rotation = PeriodicRotation(pitch, roll, yaw, period, asymmetry)

PeriodicRotation motion struct. It produces a rotation of the phantom in the three axes: x (pitch), y (roll), and z (yaw)

Arguments

• pitch: (::Real, [º]) rotation in x
• roll: (::Real, [º]) rotation in y
• yaw: (::Real, [º]) rotation in z
• period: (::Real, [s]) period
• asymmetry: (::Real) asymmetry factor, between 0 and 1

Returns

• periodic_rotation: (::PeriodicRotation) PeriodicRotation struct

periodic_heartbeat = PeriodicHeartBeat(circumferential_strain, radial_strain, longitudinal_strain, period, asymmetry)

HeartBeat struct. It produces a heartbeat-like motion, characterised by three types of strain: Circumferential, Radial and Longitudinal

Arguments

• circumferential_strain: (::Real) contraction parameter
• radial_strain: (::Real) contraction parameter
• longitudinal_strain: (::Real) contraction parameter
• period: (::Real, [s]) period
• asymmetry: (::Real) asymmetry factor, between 0 and 1

Returns

• periodic_heartbeat: (::PeriodicHeartBeat) PeriodicHeartBeat struct

motion = ArbitraryMotion(t_start, t_end, dx, dy, dz)

ArbitraryMotion model. For this motion model, it is necessary to define motion for each spin independently, in x (dx), y (dy) and z (dz). dx, dy and dz are three matrixes, of ($N_{spins}$ x $N_{discrete\,times}$) each. This means that each row corresponds to a spin trajectory over a set of discrete time instants. The motion duration is determined by t_start and t_end. The discrete time instants are evenly spaced, ($dt = rac{t_{end} - t_{start}}{N_{discrete\,times}}$).

This motion model is useful for defining arbitrarly complex motion, specially for importing the spin trajectories from another source, like XCAT or a CFD.

Arguments

• t_start: (::T, [s])
• t_end: (::T, [s])
• dx: (::Array{T,2}, [m]) matrix for displacements in x
• dy: (::Array{T,2}, [m]) matrix for displacements in y
• dz: (::Array{T,2}, [m]) matrix for displacements in z

Returns

• motion: (::ArbitraryMotion) ArbitraryMotion struct

Examples

julia> motion = ArbitraryMotion(
            0.0,
            1.0, 
            0.01.*rand(1000, 10), 
            0.01.*rand(1000, 10), 
            0.01.*rand(1000, 10)
        )

seq = Sequence()
seq = Sequence(GR)
seq = Sequence(GR, RF)
seq = Sequence(GR, RF, ADC)
seq = Sequence(GR, RF, ADC, DUR)
seq = Sequence(GR::Array{Grad,1})
seq = Sequence(GR::Array{Grad,1}, RF::Array{RF,1})
seq = Sequence(GR::Array{Grad,1}, RF::Array{RF,1}, A::ADC, DUR, DEF)

The Sequence struct. It contains events of an MRI sequence. Most field names (except for the DEF field) consist of matrices or vectors, where each column index represents a sequence block. This struct serves as an input for the simulation.

Arguments

• GR: (::Matrix{Grad}) gradient matrix. Rows for x-y-z amplitudes and columns are for blocks
• RF: (::Matrix{RF}) RF matrix. The 1 row is for the coil and columns are for blocks
• ADC: (::Array{ADC,1}) ADC block vector
• DUR: (::Vector, [s]) duration block vector
• DEF: (::Dict{String, Any}) dictionary with relevant information of the sequence. Possible keys could be ["AdcRasterTime", "GradientRasterTime", "Name", "Nz", "Num_Blocks", "Nx", "Ny", "PulseqVersion", "BlockDurationRaster", "FileName", "RadiofrequencyRasterTime"]

Returns

• seq: (::Sequence) Sequence struct

y = dur(x::Grad)
y = dur(x::Vector{Grad})
y = dur(x::Matrix{Grad})

Duration time in [s] of Grad struct or Grad Array.

Arguments

• x: (::Grad or ::Vector{Grad} or ::Matrix{Grad}) Grad struct or Grad Array

Returns

• y: (::Float64, [s]) duration of the Grad struct or Grad Array

y = dur(x::RF)
y = dur(x::Vector{RF})
y = dur(x::Matrix{RF})

Duration time in [s] of RF struct or RF Array.

Arguments

• x: (::RF or ::Vector{RF} or ::Matrix{RF}) RF struct or RF array

Returns

• y: (::Float64, [s]) duration of the RF struct or RF array

T = dur(x::Sequence)

The total duration of the sequence in [s].

Arguments

• x: (::Sequence) Sequence struct

Returns

• T: (::Real, [s]) total duration of the sequence

T0 = get_block_start_times(seq::Sequence)

Returns a vector containing the start times of blocks in a sequence. The initial time is always zero, and the final time corresponds to the duration of the sequence.

Arguments

• seq: (::Sequence) Sequence struct

Returns

• T0: (::Vector, [s]) start times of the blocks in a sequence

y = get_flip_angles(x::Sequence)

Returns all the flip angles of the RF pulses in the sequence x.

Arguments

• x: (::Sequence) Sequence struct

Returns

• y: (::Vector{Float64}, [deg]) flip angles

gr = Grad(A, T)
gr = Grad(A, T, rise)
gr = Grad(A, T, rise, delay)
gr = Grad(A, T, rise, fall, delay)
gr = Grad(A, T, rise, fall, delay, first, last)

The Grad struct represents a gradient of a sequence event.

Arguments

• A: (::Real or ::Vector, [T/m]) amplitude of the gradient
• T: (::Real or ::Vector, [s]) duration of the flat-top
• rise: (::Real, [s]) duration of the rise
• fall: (::Real, [s]) duration of the fall
• delay: (::Real, [s]) duration of the delay

Returns

• gr: (::Grad) gradient struct

Examples

julia> gr = Grad(1, 1, 0.1, 0.1, 0.2)

julia> seq = Sequence([gr]); plot_seq(seq)

gr = Grad(f::Function, T::Real, N::Integer; delay::Real)

Generates an arbitrary gradient waveform defined by the function f in the interval t ∈ [0,T]. The time separation between two consecutive samples is given by T/(N-1).

Arguments

• f: (::Function) function that describes the gradient waveform
• T: (::Real, [s]) duration of the gradient waveform
• N: (::Integer, =300) number of samples of the gradient waveform

Keywords

• delay: (::Real, =0, [s]) delay time of the waveform

Returns

• gr: (::Grad) gradient struct

Examples

julia> gx = Grad(t -> sin(π*t / 0.8), 0.8)

julia> seq = Sequence([gx]); plot_seq(seq)

rf = RF(A, T)
rf = RF(A, T, Δf)
rf = RF(A, T, Δf, delay)

The RF struct represents a Radio Frequency excitation of a sequence event.

Arguments

• A: (::Complex, [T]) RF complex amplitud modulation (AM), $B_1(t) = |B_1(t)| e^{i\phi(t)} = B_{1}(t) + iB_{1,y}(t)$
• T: (::Real, [s]) RF duration
• Δf: (::Real or ::Vector, [Hz]) RF frequency difference with respect to the Larmor frequency. This can be a number but also a vector to represent frequency modulated signals (FM).
• delay: (::Real, [s]) RF delay time

Returns

• rf: (::RF) the RF struct

Examples

julia> rf = RF(1, 1, 0, 0.2)

julia> seq = Sequence(); seq += rf; plot_seq(seq)

rf = RF_fun(f::Function, T::Real, N::Int64)

Generate an RF sequence with amplitudes sampled from a function waveform.

Arguments

• f: (::Function, [T]) function for the RF amplitud waveform
• T: (::Real, [s]) duration of the RF pulse
• N: (::Int64) number of samples of the RF pulse

Returns

• rf:(::RF) RF struct with amplitud defined by the function f

α = get_flip_angle(x::RF)

Calculates the flip angle α [deg] of an RF struct. α = γ ∫ B1(τ) dτ

Arguments

• x: (::RF) RF struct

Returns

• α: (::Int64, [deg]) flip angle RF struct x

adc = ADC(N, T)
adc = ADC(N, T, delay)
adc = ADC(N, T, delay, Δf, ϕ)

The ADC struct represents the Analog to Digital Converter (ADC) of a sequence event.

Arguments

• N: (::Int64) number of acquired samples
• T: (::Float64, [s]) duration to acquire the samples
• delay: (::Float64, [s]) delay time to start the acquisition
• Δf: (::Float64, [Hz]) delta frequency. It is meant to compensate RF pulse phases
• ϕ: (::Float64, [rad]) phase. It is meant to compensate RF pulse phases

Returns

• adc: (::ADC) ADC struct

Examples

julia> adc = ADC(16, 1, 0.1)

julia> seq = Sequence(); seq += adc; plot_seq(seq)

times = get_adc_sampling_times(seq)

Returns an array of times when the samples of the sequence seq are acquired.

Arguments

• seq: (::Sequence) sequence struct

Returns

• times: (::Vector{Float64}, [s]) time array when samples are acquired

comp = get_adc_phase_compensation(seq)

Returns an array of phase compensation factors, $\exp(-\mathrm{i}\varphi)$, which are used to compensate the acquired signal $S$ by applying the operation $S_{\mathrm{comp}} = S \exp(-\mathrm{i}\varphi)$ after the simulation. This compensation is necessary because the signal typically exhibits a phase offset of $\varphi$ following RF excitation with a phase of $\varphi$. Such pulses are commonly employed in sequences involving RF spoiling.

Arguments

• seq: (::Sequence) sequence struct

Returns

• comp: (::Vector{Complex}, [rad]) array of phase compensations for every acquired sample

delay = Delay(T)

The Delay struct is meant to add a delay to a sequence by using a sum operator.

Arguments

• T: (::Real, [s]) time delay value

Returns

• delay: (::Delay) delay struct

Examples

julia> delay = Delay(0.5)

julia> s = Sequence([Grad(1, 1, 0.1)])

julia> seq = delay + s; plot_seq(seq)

Rx = rotx(θ::Real)

Rotates vector counter-clockwise with respect to the x-axis.

Arguments

• θ: (::Real, [rad]) rotation angle

Returns

• Rx: (::Matrix{Int64}) rotation matrix

Ry = roty(θ::Real)

Rotates vector counter-clockwise with respect to the y-axis.

Arguments

• θ: (::Real, [rad]) rotation angle

Returns

• Ry: (::Matrix{Int64}) rotation matrix

Rz = rotz(θ::Real)

Rotates vector counter-clockwise with respect to the z-axis.

Arguments

• θ: (::Real, [rad]) rotation angle

Returns

• Rz: (::Matrix{Int64}) rotation matrix

Mk, Mk_adc = get_Mk(seq::Sequence, k; Δt=1, skip_rf=zeros(Bool, sum(is_RF_on.(seq))))

Computes the $k$th-order moment of the Sequence seq given by the formula $\int_0^T t^k G(t) dt$.

Arguments

• seq: (::Sequence) Sequence struct
• k: (::Integer) order of the moment to be computed
• Δt: (::Real, =1, [s]) nominal delta time separation between two time samples for ADC acquisition and Gradients
• skip_rf: (::Vector{Bool}, =zeros(Bool, sum(is_RF_on.(seq)))) boolean vector which indicates whether to skip the computation for resetting the integral for excitation or refocusing RF type

Returns

• Mk: (3-column ::Matrix{Real}) $k$th-order moment
• Mk_adc: (3-column ::Matrix{Real}) $k$th-order moment sampled at ADC times

Computes the k-space trajectory of the Sequence seq. Refer to get_Mk and get_M0

Computes the zero-order moment of the Sequence seq. Refer to get_Mk and get_kspace

Computes the 1st-order moment of the Sequence seq. Refer to get_Mk

Computes the 2nd-order moment of the Sequence seq. Refer to get_Mk

y = is_RF_on(x::Sequence)
y = is_RF_on(x::Sequence, t::Vector{Float64})

Tells if the sequence seq has elements with RF active, or active during time t.

Arguments

• x: (::Sequence) Sequence struct
• t: (::Vector{Float64}, [s]) time to check

Returns

• y: (::Bool) boolean that tells whether or not the RF in the sequence is active

y = is_GR_on(x::Sequence)

Tells if the sequence seq has elements with GR active.

Arguments

• x: (::Sequence) Sequence struct

Returns

• y: (::Bool) boolean that tells whether or not the GR in the sequence is active

y = is_Gx_on(x::Sequence)

Tells if the sequence seq has elements with GR active in x direction.

Arguments

• x: (::Sequence) Sequence struct

Returns

• y: (::Bool) boolean that tells whether or not the GRx in the sequence is active

y = is_Gy_on(x::Sequence)

Tells if the sequence seq has elements with GR active in y direction.

Arguments

• x: (::Sequence) Sequence struct

Returns

• y: (::Bool) boolean that tells whether or not the GRy in the sequence is active

y = is_Gz_on(x::Sequence)

Tells if the sequence seq has elements with GR active in z direction.

Arguments

• x: (::Sequence) Sequence struct

Returns

• y: (::Bool) boolean that tells whether or not the GRz in the sequence is active

y = is_ADC_on(x::Sequence)
y = is_ADC_on(x::Sequence, t::Union{Array{Float64,1}, Array{Float64,2}})

Tells if the sequence seq has elements with ADC active, or active during time t.

Arguments

• x: (::Sequence) sequence struct
• t: (::Union{Array{Float64,1}, Array{Float64,2}}, [s]) time to check

Returns

• y: (::Bool) boolean that tells whether or not the ADC in the sequence is active

seqd = DiscreteSequence(Gx, Gy, Gz, B1, Δf, ADC, t, Δt)

A sampled version of a Sequence struct, containing vectors for event amplitudes at specified times. DiscreteSequence is the struct used for simulation.

Arguments

• Gx: (::AbstractVector{T<:Real}, [T/m]) x-gradient vector
• Gy: (::AbstractVector{T<:Real}, [T/m]) y-gradient vector
• Gz: (::AbstractVector{T<:Real}, [T/m]) z-gradient vector
• B1: (::AbstractVector{Complex{T<:Real}}, [T]) RF amplitude vector
• Δf: (::AbstractVector{T<:Real}, [Hz]) RF carrier frequency displacement vector
• ADC: (::AbstractVector{Bool}) ADC sample vector
• t: (::AbstractVector{T<:Real}, [s]) time vector
• Δt: (::AbstractVector{T<:Real}, [s]) delta time vector

Returns

• seqd: (::DiscreteSequence) DiscreteSequence struct

seqd = discretize(seq::Sequence; sampling_params=default_sampling_params())

This function returns a sampled Sequence struct with RF and gradient time refinements based on simulation parameters.

Arguments

• seq: (::Sequence) sequence

Keywords

• sampling_params: (::Dict{String, Any}, =default_sampling_params()) sampling parameter dictionary

Returns

• seqd: (::DiscreteSequence) DiscreteSequence struct

samples = get_samples(seq::Sequence; off_val=0, max_rf_samples=Inf)

Returns the samples of the events in seq.

Arguments

• seq: (::Sequence) Sequence struct

Keywords

• off_val: (::Number, =0) offset value for amplitude. Typically used to hide points in plots by setting it to Inf
• max_rf_samples: (::Integer, =Inf) maximum number of samples for the RF struct

Returns

• samples: (::NamedTuple) contains samples for gx, gy, gz, rf, and adc events. Each event, represented by e::NamedTuple, includes time samples (e.t) and amplitude samples (e.A)

t = times(gr::Grad)
t = times(rf::RF)
t = times(adc::ADC)

Get time samples of MRI sequence event.

Arguments

• gr: (::Grad) Gradient struct
• rf: (::RF) RF struct
• adc: (::ADC) ADC struct

Returns

• t: (::Vector{Number}) vector with time samples

limits = times(obj.motion)

A = ampls(g::Grad)
A = ampls(r::RF)
A = ampls(d::ADC)

Get amplitude samples of MRI sequence event.

Arguments

• gr: (::Grad) Gradient struct
• rf: (::RF) RF struct
• adc: (::ADC) ADC struct

Returns

• A: (::Vector{Number}) vector with amplitude samples

f = freqs(r::RF)

Get frequency samples of MRI sequence event.

Arguments

• rf: (::RF) RF struct

Returns

• f: (::Vector{Number}) vector with frequency samples

y = trapz(Δt, x)

Trapezoidal integration for every spin of a phantom.

Arguments

• Δt: (1 x NΔt ::Matrix{Float64}, [s]) delta time 1-row array
• x: (Ns x (NΔt+1) ::Matrix{Float64}, [T]) magnitude of the field Gx * x + Gy * y + Gz * z

Returns

• y: (Ns x 1 ::Matrix{Float64}, [T*s]) vector where every element is the integral of (Gx * x + Gy * y + Gz * z) * Δt for every spin of a phantom

y = cumtrapz(Δt, x)

Trapezoidal cumulative integration over time for every spin of a phantom.

Arguments

• Δt: (1 x NΔt ::Matrix{Float64}, [s]) delta time 1-row array
• x: (Ns x (NΔt+1) ::Matrix{Float64}, [T]) magnitude of the field Gx * x + Gy * y + Gz * z

Returns

• y: (Ns x NΔt ::Matrix{Float64}, [T*s]) matrix where every column is the cumulative integration over time of (Gx * x + Gy * y + Gz * z) * Δt for every spin of a phantom

cumtrapz

A more efficient GPU implementation of the cumtrapz method defined in TrapezoidalIntegration.jl. Uses a kernel to compute cumsum along the second dimension.

Arguments

• Δt: (1 x NΔt ::Matrix{Float64}, [s]) delta time 1-row array
• x: (Ns x (NΔt+1) ::Matrix{Float64}, [T]) magnitude of the field Gx * x + Gy * y + Gz * z

Returns

• y: (Ns x NΔt ::Matrix{Float64}, [T*s]) matrix where every column is the cumulative integration over time of (Gx * x + Gy * y + Gz * z) * Δt for every spin of a phantom

array_of_ranges = kfoldperm(N, k; breaks=[])

Divides a list of indices from 1 to N into k groups.

Arguments

• N: (::Integer) number of elements to be ordered
• k: (::Integer) number of groups to divide the N elements.

Keywords

• breaks: (::Vector{<:Integer}, =[]) array of indices where predefined breakpoints are placed.

Returns

• array_of_ranges: (::Vector{UnitRange{<:Integer}}) array containing ranges of different groups. The target is k groups, but this could increase by adding elements to the breaks input array

PulseDesigner

A module to define different pulse sequences.

seq = RF_hard(B1, T, sys; G=[0, 0, 0], Δf=0)

Returns a sequence with a RF excitation pulse.

Arguments

• B1: (::Number, [T]) RF pulse amplitude
• T: (::Real, [s]) RF pulse duration
• sys: (::Scanner) Scanner struct

Keywords

• G: (::Vector{Real}, =[0, 0, 0], [T/m]) gradient amplitudes for x, y, z
• Δf: (::Real, =0, [Hz]) RF pulse carrier frequency displacement

Returns

• seq: (::Sequence) Sequence struct with a RF pulse

Examples

julia> sys = Scanner(); durRF = π / 2 / (2π * γ * sys.B1);

julia> seq = PulseDesigner.RF_hard(sys.B1, durRF, sys);

julia> plot_seq(seq)

seq = RF_sinc(B1, T, sys; G=[0, 0, 0], Δf=0, a=0.46, TBP=4)

Returns a sequence with a RF sinc waveform.

References

• Matt A. Bernstein, Kevin F. King, Xiaohong Joe Zhou, Chapter 2 - Radiofrequency Pulse

Shapes, Handbook of MRI Pulse Sequences, 2004, Pages 35-66, https://doi.org/10.1016/B978-012092861-3/50006-6.

Arguments

• B1: (::Number, [T]) RF sinc amplitude
• T: (::Real, [s]) RF sinc duration
• sys: (::Scanner) Scanner struct

Keywords

• G: (::Vector{Real}, =[0, 0, 0], [T/m]) gradient amplitudes for x, y, z
• Δf: (::Real, =0, [Hz]) RF pulse carrier frequency displacement
• a: (::Real, =0.46) height appodization window parameter
• TBP: (::Real, =4) width appodization window parameter

Returns

• seq: (::Sequence) Sequence struct with a RF pulse

Examples

julia> sys = Scanner(); durRF = π / 2 / (2π * γ * sys.B1);

julia> seq = PulseDesigner.RF_sinc(sys.B1, durRF, sys);

julia> plot_seq(seq)

seq = EPI(FOV::Real, N::Integer, sys::Scanner)

Returns a sequence with EPI gradients.

Arguments

• FOV: (::Real, [m]) field of view
• N: (::Integer) number of pixels in the x and y axis
• sys: (::Scanner) Scanner struct

Returns

• seq: (::Sequence) Sequence struct with EPI gradients

Examples

julia> sys, FOV, N = Scanner(), 23e-2, 101

julia> seq = PulseDesigner.EPI(FOV, N, sys)

julia> plot_seq(seq)

julia> plot_kspace(seq)

seq = radial_base(FOV::Real, Nr::Integer, sys::Scanner)

Returns a sequence with radial gradients for a single trajectory.

Arguments

• FOV: (::Real, [m]) field of view
• N: (::Integer) number of pixels along the diameter
• sys: (::Scanner) Scanner struct

Returns

• seq: (::Sequence) Sequence struct of a single radial trajectory

Examples

julia> sys, FOV, N = Scanner(), 23e-2, 101

julia> seq = PulseDesigner.radial_base(FOV, N, sys)

julia> plot_seq(seq)

julia> plot_kspace(seq)

spiral = spiral_base(FOV, N, sys; S0=sys.Smax*2/3, Nint=8, λ=Nint/FOV, BW=60e3)

Definition of a spiral base sequence.

References

• Glover, G.H. (1999), Simple analytic spiral K-space algorithm. Magn. Reson. Med.,

42: 412-415. https://doi.org/10.1002/(SICI)1522-2594(199908)42:2<412::AID-MRM25>3.0.CO;2-U

Arguments

• FOV: (::Real, [m]) field of view
• N: (::Integer) number of pixels along the radious
• sys: (::Scanner) Scanner struct

Keywords

• S0: (::Vector{Real}, =sys.Smax*2/3, [T/m/s]) slew rate reference
• Nint: (::Integer, =8) number of interleaves
• λ: (::Real, =Nint/FOV, [1/m]) kspace spiral parameter
• BW: (::Real, =60e3, [Hz]) adquisition parameter

Returns

• spiral: (::Function) function that returns a Sequence struct when evaluated

Examples

julia> sys, FOV, N = Scanner(), 23e-2, 101

julia> spiral = PulseDesigner.spiral_base(FOV, N, sys)

julia> seq = spiral(0)

julia> plot_seq(seq)

seq = EPI_example(; sys=Scanner())

Returns a sequence suitable for acquiring the 2D brain example in the provided examples.

Keywords

• sys: (::Scanner) Scanner struct

Returns

• seq: (::Sequence) EPI example Sequence struct

Examples

julia> seq = PulseDesigner.EPI_example();

julia> plot_seq(seq)