### A Pluto.jl notebook ###
# v0.20.5

#> [frontmatter]
#> image = "https://upload.wikimedia.org/wikipedia/commons/a/a0/Textformatting.svg"
#> title = "Low-Field CMRA Optimization"
#> tags = ["CMRA", "Low Field", "Optimization"]
#> date = "2024-04-16"
#> description = "Optimizing sequence to improve SNR and fat supression."
#> 
#>     [[frontmatter.author]]
#>     name = "Carlos Castillo Passi"
#>     url = "https://avatars.githubusercontent.com/u/5957134?s=400&u=fe62a2a899ced18e8b882cebde6b1eefe6a1222c&v=4"

using Markdown
using InteractiveUtils

# ╔═╡ 7deadd58-b202-4508-b4c7-686f742cb713
begin
	begin
		using Pkg
		begin
		  println("OS $(Base.Sys.MACHINE)")    # OS
		  println("Julia $VERSION")            # Julia version
		  # Koma sub-packages
		  for (_, pkg) in filter(((_, pkg),) -> occursin("KomaMRI", pkg.name), Pkg.dependencies())
		    println("$(pkg.name) $(pkg.version)")
		  end
		end
	end
end

# ╔═╡ 0b7a405e-bbb5-11ee-05ca-4b1c8567398d
using KomaMRICore, KomaMRIPlots, PlutoPlotly # Essentials

# ╔═╡ 70dbc2bd-8b93-471d-8340-04d98a008ca6
using Suppressor, PlutoUI, ProgressLogging # Extras

# ╔═╡ a99c0c47-1b70-4362-a2f6-a7e3259606fa
md"""# Low-Field CMRA Optimization

This notebook reproduces the simulation experiments performed in our manuscript:

> **"Highly Efficient iNAV-based 3D Whole-Heart CMRA at 0.55T"**
>
> **Carlos Castillo-Passi**, Karl P. Kunze, Michael G. Crabb, Camila Muñoz, Anastasia Fotaki, Radhouene Neji, Pablo Irarrazaval, Claudia Prieto, and René M. Botnar
>
> (2024)

Submitted to Magnetic Resonance in Medicine (MRM).
"""

# ╔═╡ 1bb3e49b-1a19-4343-ac09-fbaf1cae4ba3
TableOfContents()

# ╔═╡ fc58640b-c44c-4c25-a4fd-5a0e17d7becd
md"# 1. Simulation setup"

# ╔═╡ dbf16676-64f2-4d9b-bf1b-8de06b048602
md"## 1.1. Loading required packages"

# ╔═╡ f49655cc-460e-4981-92ea-dfd6147308bf
md"Bloch simulations were performed using **KomaMRI.jl** to optimize the proposed whole-heart CMRA parameters."

# ╔═╡ 77153e5c-71bd-42e3-bae9-e4811ffa7a3d
md"""## 1.2. Scanner

We start by defining the hardware characteristics. The `sys.B0` will be used to calculate the off-resonance of fat."""

# ╔═╡ 9e397426-b60b-4b98-be8b-f7f128621c44
begin
	sys = Scanner()
	sys.B0 = 0.55
	sys.Gmax = 40.0e-3
	sys.Smax = 25.0
	sys
end

# ╔═╡ 92194fcb-582a-49ce-aad7-20b0145d40d3
md"## 1.3. Sequence"

# ╔═╡ ae72ffc5-7f8e-4907-a99e-8ad7cb8fddab
md"""
The CMRA sequence (`CMRA_iNAV_bSSFP_cardiac`) consists of:
"""

# ╔═╡ cb659118-9f22-43c3-801d-49241dee4df6
begin
	# General sequence parameters
	Trf = 500e-6  			# 500 [ms]
	B1 = 1 / (360*γ*Trf)    # B1 amplitude [uT]
	Tadc = 1e-6 			# 1us

	# Prepulses
	Tfatsat = 26.624e-3     # 26.6 [ms]
	T2prep_duration = 50e-3 # 50 [ms]

	# Acquisition
	RR = 1.0 				# 1 [s]
	dummy_heart_beats = 3 	# Steady-state
	TR = 5.3e-3             # 5.3 [ms] RF Low SAR
	TE = TR / 2 			# bSSFP condition
	iNAV_lines = 6          # FatSat-Acq delay: iNAV_lines * TR
	iNAV_flip_angle = 3.2   # 3.2 [deg]
	im_segments = 20        # Acquisitino window: im_segments * TR

	# To be optimized
	im_flip_angle = 110    # 110 [deg]
	FatSat_flip_angle = 180 # 180 [deg]

	seq_params = (;
		dummy_heart_beats,
		iNAV_lines,
		im_segments,
		iNAV_flip_angle,
		im_flip_angle,
		T2prep_duration,
		FatSat_flip_angle,
		RR
	)

	seq_params
end

# ╔═╡ a15d6b64-f8ee-4ee4-812c-d49cf5ea784d
md"""
## 1.4. Phantom
Each tissue was represented with 200 isochromats distributed along the $z$-axis to simulate gradient spoiling effects. The isochromats for each tissue were inside a 1D voxel of size $1.5\,\mathrm{mm}$. The values for $T_1$ and $T_2$ for blood, myocardial muscle, and fat at 0.55T were obtained from the work of Campbell-Washburn, et al. Fat spins were simulated using a chemical shift of $-3.4\,\mathrm{ppm}$, simulating regular fat with $T_1=183\,\mathrm{ms}$, and fast-recovering fat with $T_1=130\,\mathrm{ms}$.
"""

# ╔═╡ f0a81c9f-5616-4663-948f-a4084e1719af
begin
    fat_ppm = -3.4e-6 			# -3.4ppm fat-water frequency shift
    Niso = 200        			# 200 isochromats in spoiler direction
    Δx_voxel = 1.5e-3 			# 1.5 [mm]
    fat_freq = γ*sys.B0*fat_ppm # -80 [Hz]
    dx = Array(range(-Δx_voxel/2, Δx_voxel/2, Niso))
	md"- Phantom parameters (show/hide code)"
end

# ╔═╡ 6b870443-7be5-4287-b957-ca5c14eda89c
begin
	function FatSat(α, Δf; sample=false)
	    # FatSat design
		# cutoff_freq = sqrt(log(2) / 2) / a where B1(t) = exp(-(π t / a)^2)
		cutoff = fat_freq / π 			      # cutoff [Hz] => ≈1/10 RF power to water
		a = sqrt(log(2) / 2) / cutoff         # a [s]
		τ = range(-Tfatsat/2, Tfatsat/2, 64) # time [s]
		gauss_pulse = exp.(-(π * τ / a) .^ 2) # B1(t) [T]
		# FatSat prepulse
	    seq = Sequence()
	    seq += Grad(-8e-3, 3000e-6, 500e-6) #Spoiler1
	    seq += RF(gauss_pulse, Tfatsat, Δf)
	    α_ref = get_flip_angles(seq)[2]
	    seq *= (α/α_ref+0im)
	    if sample
	        seq += ADC(1, 1e-6)
	    end
	    seq += Grad(8e-3, 3000e-6, 500e-6) #Spoiler2
	    if sample
	        seq += ADC(1, 1e-6)
	    end
	    return seq
	end

	function T2prep(TE; sample=false)
	    seq = Sequence()
	    seq += RF(90 * B1, Trf)
	    seq += sample ? ADC(20, TE/2 - 1.5Trf) : Delay(TE/2 - 1.5Trf)
	    seq += RF(180im * B1 / 2, Trf*2)
	    seq += sample ? ADC(20, TE/2 - 1.5Trf) : Delay(TE/2 - 1.5Trf)
	    seq += RF(-90 * B1, Trf)
	    seq += Grad(8e-3, 6000e-6, 600e-6)
	    if sample
	        seq += ADC(1, 1e-6)
	    end
	    return seq
	end

	function bSSFP(iNAV_lines, im_segments, iNAV_flip_angle, im_flip_angle; sample=false)
	    k = 0
	    seq = Sequence()
	    for i = 0 : iNAV_lines + im_segments - 1
	        if iNAV_lines != 0
	            m = (im_flip_angle - iNAV_flip_angle) / iNAV_lines
	            α = min( m * i + iNAV_flip_angle, im_flip_angle ) * (-1)^k
	        else
	            α = im_flip_angle * (-1)^k
	        end
	        seq += RF(α * B1, Trf)
	        if i < iNAV_lines && !sample
	            seq += Delay(TR - Trf)
	        else
	            seq += Delay(TE - Trf/2 - Tadc/2)
	            seq += ADC(1, Tadc)
	            seq += Delay(TR - TE - Tadc/2 - Trf/2)
	        end
	        k += 1
	    end
	    return seq
	end

	md"- Sequence building blocks: `T2prep`, `FatSat`, `bSSFP` (show/hide code)"
end

# ╔═╡ 7890f81e-cb15-48d2-a80c-9d73f9516056
begin
	function CMRA(
				dummy_heart_beats,
				iNAV_lines,
				im_segments,
				iNAV_flip_angle,
				im_flip_angle,
				T2prep_duration=50e-3,
				FatSat_flip_angle=180,
				RR=1.0;
				sample_recovery=zeros(Bool, dummy_heart_beats+1)
				)
		# Seq init
	    seq = Sequence()
	    for hb = 1 : dummy_heart_beats + 1
			sample = sample_recovery[hb] # Sampling recovery curve for hb
			# Generating seq blocks
	        t2p = T2prep(T2prep_duration; sample)
	        fatsat = FatSat(FatSat_flip_angle, fat_freq; sample)
	        bssfp = bSSFP(iNAV_lines, im_segments, iNAV_flip_angle, im_flip_angle; sample)
	        # Concatenating seq blocks
	        seq += t2p
	        seq += fatsat
	        seq += bssfp
			# RR interval consideration
			RRdelay = RR  - dur(bssfp) - dur(t2p) - dur(fatsat)
	        seq += sample ? ADC(80, RRdelay) : Delay(RRdelay)
	    end
	    return seq
	end

	md"""- `CMRA` (show/hide code)

	```julia
	# Seq init
	seq = Sequence()
	for hb = 1 : dummy_heart_beats + 1
		# Generating seq blocks
		t2p = T2prep(T2prep_duration)
		fatsat = FatSat(FatSat_flip_angle, fat_freq)
		bssfp = bSSFP(iNAV_lines, im_segments, iNAV_flip_angle, im_flip_angle)
		# Concatenating seq blocks
		seq += t2p
		seq += fatsat
		seq += bssfp
		# RR interval consideration
		RRdelay = RR  - dur(bssfp) - dur(t2p) - dur(fatsat)
		seq += Delay(RRdelay)
	end
	```"""
end

# ╔═╡ f57a2b6c-eb4c-45bd-8058-4a60b038925d
begin
	function cardiac_phantom(off; off_fat=fat_freq)
	    myocard = Phantom(x=dx, ρ=0.6*ones(Niso), T1=701e-3*ones(Niso),
	                               T2=58e-3*ones(Niso),    Δw=2π*off*ones(Niso))
	    blood =   Phantom(x=dx, ρ=0.7*ones(Niso), T1=1122e-3*ones(Niso),
	                               T2=263e-3*ones(Niso),   Δw=2π*off*ones(Niso))
	    fat1 =    Phantom(x=dx, ρ=1.0*ones(Niso), T1=183e-3*ones(Niso),
	                               T2=93e-3*ones(Niso),    Δw=2π*(off_fat + off)*ones(Niso))
	    fat2 =    Phantom(x=dx, ρ=1.0*ones(Niso), T1=130e-3*ones(Niso),
	                               T2=93e-3*ones(Niso),    Δw=2π*(off_fat + off)*ones(Niso))
	    obj = myocard + blood + fat1 + fat2
	    return obj
	end
	md"- Cardiac phantom (show/hide code)"
end

# ╔═╡ f21e9e59-25c3-4f06-8de4-792cb305eb01
md"""# 2. Simulation

Two simulation experiments were performed to optimize the sequence parameters, (1) to optimize the imaging flip angle, and (2) to optimize the FatSat flip angle.

"""

# ╔═╡ eceb326a-cab6-465e-8e5c-e835881bd3b0
md"""
## 2.0. Magnetization dynamics
"""

# ╔═╡ d54d6807-444f-4e0e-8fd6-84457974115a
md"Here we show the magnetization dynamics of the myocardium, blood, and fat signals at 0.55T."

# ╔═╡ d05dcba7-2f42-47bf-a172-6123d0113b3f
sim_params = Dict{String,Any}(
	"return_type"=>"mat",
	"sim_method"=>BlochDict(save_Mz=true),
	"Δt_rf"=>Trf,
	"gpu"=>false,
	"Nthreads"=>1
)

# ╔═╡ 37f7fd7f-5cb1-48b5-b877-b2bc23a1e7dd
begin
    seq = CMRA(seq_params...; sample_recovery=ones(Bool, dummy_heart_beats+1))
	obj = cardiac_phantom(0)
    magnetization = @suppress simulate(obj, seq, sys; sim_params)
	nothing # hide output
end

# ╔═╡ 0b6c1f72-b040-483c-969b-88bfe09b32c3
plot_seq(seq; show_adc=true, range=[2900, 3325], slider=true)

# ╔═╡ 1a62ae71-58db-49ea-ae6a-9aea66145963
begin
	phantom_T1 = plot(
		scatter(
			x=obj.x * 1e3,
			y=obj.T1 * 1e3,
			mode="markers",
			marker=attr(;
				color=obj.T1 * 1e3,
				colorscale=[
					[0.0, "black"],
					[183.0/maximum(obj.T1 .* 1e3), "green"],
					[701.0/maximum(obj.T1 .* 1e3), "blue"],
					[1122.0/maximum(obj.T1 .* 1e3), "red"],
				],
				cmin=0.0,
				cmax=1122.0,
				colorbar=attr(;ticksuffix="ms", title="T1"),
				showscale=false
			),
			showlegend=false
		)
	)
	relayout!(
		phantom_T1,
		yaxis_title="T1 [ms]",
		xaxis_title="x [mm]",
		xaxis_tickmode="array",
		xaxis_tickvals=[-1.5/2, 0.0, 1.5/2],
		yaxis_tickmode="array",
		yaxis_tickvals=unique(obj.T1 * 1e3),
		xaxis_range=[-1.5, 1.5],
		yaxis_range=[0.0, 1200.0],
		title="T1 map of 1D Phantom"
	)
	phantom_T2 = plot(
		scatter(
			x=obj.x * 1e3,
			y=obj.T2 * 1e3,
			mode="markers",
			marker=attr(;
				color=obj.T2 * 1e3,
				colorscale=[
					[0.0, "black"],
					[58.0/maximum(obj.T2 .* 1e3), "blue"],
					[93.0/maximum(obj.T2 .* 1e3), "green"],
					[263.0/maximum(obj.T2 .* 1e3), "red"],
				],
				cmin=0.0,
				cmax=263.0,
				colorbar=attr(;ticksuffix="ms", title="T2"),
				showscale=false
			),
			showlegend=false
		)
	)
	relayout!(
		phantom_T2,
		yaxis_title="T2 [ms]",
		xaxis_title="x [mm]",
		xaxis_tickmode="array",
		xaxis_tickvals=[-1.5/2, 0.0, 1.5/2],
		yaxis_tickmode="array",
		yaxis_tickvals=unique(obj.T2 * 1e3),
		xaxis_range=[-1.5, 1.5],
		yaxis_range=[0.0, 300.0],
		title="T2 map of 1D Phantom"
	)
	[phantom_T1 phantom_T2]
end

# ╔═╡ d9715bc1-49cd-4df8-8dbf-c06de42ad550
begin
    # Prep plots
    labs = ["Myocardium", "Blood", "Fat"]
	cols = ["blue", "red", "green"]
    spin_group = [(1:Niso)', (Niso+1:2Niso)', (2Niso+1:3Niso)']
    t = KomaMRICore.get_adc_sampling_times(seq)
    Mxy(i) = abs.(sum(magnetization[:,spin_group[i],1,1][:,1,:],dims=2)[:]/length(spin_group[i]))
    Mz(i) = real.(sum(magnetization[:,spin_group[i],2,1][:,1,:],dims=2)[:]/length(spin_group[i]))

    # Plot
    p0 = make_subplots(
		rows=2,
		cols=1,
		subplot_titles=["Mxy" "Mz" "Sequence"],
		shared_xaxes=true,
		vertical_spacing=0.1
	)
    for i=eachindex(spin_group)
        p1 = scatter(
			x=t, y=Mxy(i),
			name=labs[i],
			legendgroup=labs[i],
			marker_color=cols[i]
		)
        p2 = scatter(
			x=t,
			y=Mz(i),
			name=labs[i],
			legendgroup=labs[i],
			showlegend=false,
			marker_color=cols[i]
		)
        add_trace!(p0, p1, row=1, col=1)
        add_trace!(p0, p2, row=2, col=1)
    end
	relayout!(p0,
		yaxis_range=[0, 0.4],
		xaxis_range=[RR*dummy_heart_beats, RR*dummy_heart_beats+.250]
	)
    p0
end

# ╔═╡ 8dd704a4-bf50-4ddc-a832-d074bd52ad01
md"Three heartbeats were considered to achieve steady-state and the fourth heartbeat was used to measure the magnetization results in the next sections."

# ╔═╡ 39f44025-2974-4c4c-b0c2-e21399bbdb1f
md"""
## 2.1. Flip angle optimization

For the first simulation experiment, SNR was maximized by varying the imaging flip angle (between 20 and 180 deg). To optimize SNR independently of heart rate, multiple heart rates (between 55 and 85 bpm) were simulated and the mean and standard deviation of the obtained blood signal were calculated.
"""

# ╔═╡ 7b9ae381-d0fc-4d1d-b1ee-ad31a6445ff6
begin
    FAs = 20:10:180 		# flip angle [deg]
	RRs = 60 ./ (55:10:85)  # RR [s]
    mag1 = zeros(ComplexF64, im_segments, Niso*4, length(FAs), length(RRs))
    @progress for (m, RR) = enumerate(RRs), (n, im_flip_angle) = enumerate(FAs)
		seq_params1 = merge(seq_params, (; im_flip_angle, RR))
		sim_params1 = merge(sim_params, Dict("sim_method"=>BlochDict()))
		seq1        = CMRA(seq_params1...)
		obj1        = cardiac_phantom(0)
		magaux = @suppress simulate(obj1, seq1, sys; sim_params=sim_params1)
		mag1[:, :, n, m] .= magaux[end-im_segments+1:end, :] # Last heartbeat
    end
end

# ╔═╡ d0377f9a-680d-4501-90ca-9ea3ab681db4
md"""## 2.2. FatSat flip angle optimization

For the second simulation experiment, the fat signal was minimized by varying the FatSat flip angle (between 20 and 250 deg) using six iNAV readouts (identified experimentally to result in good fat suppression). To be robust to $B_0$ inhomogeneities, multiple simulations with tissue frequency shifts (between $-1$ and $1\,\mathrm{ppm}$, twice of what was reported by Restivo et al.) were performed, and the mean and standard deviation of the obtained fat signal were calculated."""

# ╔═╡ d750cd5a-3c90-41ea-9942-5723a21da60a
begin
    FFAs = 20:20:250 						 # flip angle [deg]
	Δfs = (-1:0.2:1) .* (γ * sys.B0 * 1e-6)  # off-resonance Δf [s]
    mag2 = zeros(ComplexF64, im_segments, Niso*4, length(FFAs), length(Δfs))
    @progress for (m, Δf) = enumerate(Δfs), (n, FatSat_flip_angle) = enumerate(FFAs)
		seq_params2 = merge(seq_params, (; FatSat_flip_angle))
		sim_params2 = merge(sim_params, Dict("sim_method"=>BlochDict()))
		seq2        = CMRA(seq_params2...)
		obj2        = cardiac_phantom(Δf)
		magaux = @suppress simulate(obj2, seq2, sys; sim_params=sim_params2)
		mag2[:, :, n, m] .= magaux[end-im_segments+1:end, :] # Last heartbeat
    end
end

# ╔═╡ 8dc11175-ebc8-407a-ab0b-6d543f849a72
begin
	# Labels
	labels = ["Myocardium", "Blood", "Fat (T₁=183 ms)", "Fat (T₁=130 ms)"]
	colors = ["blue", "red", "green", "purple"]
	spins = [(1:Niso)', ((Niso + 1):(2Niso))', ((2Niso + 1):(3Niso))', ((3Niso + 1):(4Niso))']
	mean(x, dim) = sum(x; dims=dim) / size(x, dim)
	std(x, dim; mu=mean(x, dim)) = sqrt.(sum(abs.(x .- mu) .^ 2; dims=dim) / (size(x, dim) - 1))
	md"Aux functions (show/hide code)"
end

# ╔═╡ f73082ff-a6d3-41f8-8796-4114fa89d2bb
begin
	# Reducing tissues's signal
	signal_myoc = reshape(
	    mean(abs.(mean(mag1[:, spins[1], :, :], 3)), 1), length(FAs), length(RRs)
	)
	signal_bloo = reshape(
	    mean(abs.(mean(mag1[:, spins[2], :, :], 3)), 1), length(FAs), length(RRs)
	)
	diff_bloo_myoc = abs.(signal_bloo .- signal_myoc)
	# Mean
	mean_myoc = mean(signal_myoc, 2)
	mean_bloo = mean(signal_bloo, 2)
	mean_diff = mean(diff_bloo_myoc,2)
	# Std
	std_myoc  = std(signal_myoc, 2)
	std_bloo  = std(signal_bloo, 2)
	std_diff = std(diff_bloo_myoc,2)
	# Plotting results
	# Mean
	s1 = scatter(;
	    x=FAs,
	    y=mean_myoc[:],
	    name=labels[1],
	    legendgroup=labels[1],
	    line=attr(; color=colors[1]),
	)
	s2 = scatter(;
	    x=FAs,
	    y=mean_bloo[:],
	    name=labels[2],
	    legendgroup=labels[2],
	    line=attr(; color=colors[2]),
	)
	s3 = scatter(;
		x=FAs,
		y=mean_diff[:],
		name="|Blood-Myoc|",
		legendgroup="|Blood-Myoc|",
		line=attr(color=colors[4])
	)
	# Std
	s4 = scatter(;
	    x=[FAs; reverse(FAs)],
	    y=[(mean_myoc .- std_myoc)[:]; reverse((mean_myoc .+ std_myoc)[:])],
	    name=labels[1],
	    legendgroup=labels[1],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(0,0,255,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none"
	)
	s5 = scatter(;
	    x=[FAs; reverse(FAs)],
	    y=[(mean_bloo .- std_bloo)[:]; reverse((mean_bloo .+ std_bloo)[:])],
	    name=labels[2],
	    legendgroup=labels[2],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(255,0,0,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none"
	)
	s6 = scatter(;
		x=[FAs; reverse(FAs)],
		y=[(mean_diff .- std_diff)[:]; reverse((mean_diff .+ std_diff)[:])],
		name="|Blood-Myoc|",legendgroup="|Blood-Myoc|",
		showlegend=false,
		fill="toself",
		fillcolor="rgba(255,0,255,0.2)",
		line=attr(color="rgba(0,0,0,0)"),
		hoverinfo="none"
	)
	# Plots
	fig = plot([s1, s2, s3, s4, s5, s6])
	relayout!(
	    fig;
	    yaxis=attr(; title="Signal [a.u.]", tickmode="array"),
	    xaxis=attr(;
	        title="Flip angle [deg]",
	        tickmode="array",
	        tickvals=[FAs[1], 85, 110, 130, FAs[end]],
	        constrain="domain",
	    ),
	    font=attr(; family="CMU Serif", size=16, scaleanchor="x", scaleratio=1),
	    yaxis_range=[0, 0.3],
		xaxis_range=[FAs[1], FAs[end]],
	    width=600,
	    height=400,
	    hovermode="x unified",
	)
	fig
end

# ╔═╡ 44a31057-7b34-4c80-a273-6621c0773dc7
begin
	## Calculating results
	signal_myoc2 = reshape(
	    mean(abs.(mean(mag2[:, spins[1], :, :], 3)), 1), length(FFAs), length(Δfs)
	)
	signal_bloo2 = reshape(
	    mean(abs.(mean(mag2[:, spins[2], :, :], 3)), 1), length(FFAs), length(Δfs)
	)
	signal_fat2 = reshape(
	    mean(abs.(mean(mag2[:, spins[3], :, :], 3)), 1), length(FFAs), length(Δfs)
	)
	signal_fat22 = reshape(
	    mean(abs.(mean(mag2[:, spins[4], :, :], 3)), 1), length(FFAs), length(Δfs)
	)
	mean_myoc2 = mean(signal_myoc2, 2)
	mean_bloo2 = mean(signal_bloo2, 2)
	mean_fat2  = mean(signal_fat2, 2)
	mean_fat22 = mean(signal_fat22, 2)
	std_myoc2  = std(signal_myoc2, 2)
	std_bloo2  = std(signal_bloo2, 2)
	std_fat2   = std(signal_fat2, 2)
	std_fat22  = std(signal_fat22, 2)
	# Plotting results
	# Mean
	s12 = scatter(;
	    x=FFAs,
	    y=mean_myoc2[:],
	    name=labels[1],
	    legendgroup=labels[1],
	    line=attr(; color=colors[1]),
	)
	s22 = scatter(;
	    x=FFAs,
	    y=mean_bloo2[:],
	    name=labels[2],
	    legendgroup=labels[2],
	    line=attr(; color=colors[2]),
	)
	s32 = scatter(;
	    x=FFAs,
	    y=mean_fat2[:],
	    name=labels[3],
	    legendgroup=labels[3],
	    line=attr(; color=colors[3]),
	)
	s52 = scatter(;
	    x=FFAs,
	    y=mean_fat22[:],
	    name=labels[4],
	    legendgroup=labels[4],
	    line=attr(; color=colors[3], dash="dash"),
	)
	# Std
	s42 = scatter(;
	    x=[FFAs; reverse(FFAs)],
	    y=[(mean_myoc2 .- std_myoc2)[:]; reverse((mean_myoc2 .+ std_myoc2)[:])],
	    name=labels[1],
	    legendgroup=labels[1],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(0,0,255,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none",
	)
	s62 = scatter(;
	    x=[FFAs; reverse(FFAs)],
	    y=[(mean_bloo2 .- std_bloo2)[:]; reverse((mean_bloo2 .+ std_bloo2)[:])],
	    name=labels[2],
	    legendgroup=labels[2],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(255,0,0,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none",
	)
	s72 = scatter(;
	    x=[FFAs; reverse(FFAs)],
	    y=[(mean_fat2 .- std_fat2)[:]; reverse((mean_fat2 .+ std_fat2)[:])],
	    name=labels[3],
	    legendgroup=labels[3],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(0,255,0,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none",
	)
	s82 = scatter(;
	    x=[FFAs; reverse(FFAs)],
	    y=[(mean_fat22 .- std_fat22)[:]; reverse((mean_fat22 .+ std_fat22)[:])],
	    name=labels[4],
	    legendgroup=labels[4],
	    showlegend=false,
	    fill="toself",
	    fillcolor="rgba(0,255,0,0.2)",
	    line=attr(; color="rgba(0,0,0,0)"),
		hoverinfo="none",
	)
	# Plots
	fig2 = plot([s12, s22, s32, s42, s52, s62, s72, s82])
	relayout!(
	    fig2;
	    yaxis=attr(; title="Signal [a.u.]", tickmode="array"),
	    xaxis=attr(;
	        title="FatSat flip angle [deg]",
	        tickmode="array",
	        tickvals=[FFAs[1], 130, 150, 180, FFAs[end]],
	        constrain="domain",
	    ),
	    font=attr(; family="CMU Serif", size=16, scaleanchor="x", scaleratio=1),
	    yaxis_range=[0, 0.4],
		xaxis_range=[FFAs[1], FFAs[end]],
	    width=600,
	    height=400,
	    hovermode="x unified",
	)
	fig2
end

# ╔═╡ 3d7e7d20-a77a-48b3-ad2e-6b621227be16
md"""# References
 - **Castillo-Passi C**, Coronado R, Varela-Mattatall G, Alberola-López C, Botnar R, Irarrazaval P. KomaMRI.jl: An open-source framework for general MRI simulations with GPU acceleration. Magnetic Resonance in Medicine. 2023;90(1):329-342. [doi:10.1002/mrm.29635](doi:10.1002/mrm.29635)
 - **Campbell-Washburn AE**, Ramasawmy R, Restivo MC, et al. Opportunities in Interventional and Diagnostic Imaging by Using High-Performance Low-Field-Strength MRI. Radiology. 2019;293(2):384-393. [doi:10.1148/radiol.2019190452](doi:10.1148/radiol.2019190452)
- **Restivo MC**, Ramasawmy R, Bandettini WP, Herzka DA, Campbell-Washburn AE. Efficient spiral in-out and EPI balanced steady-state free precession cine imaging using a high-performance 0.55T MRI. Magnetic Resonance in Medicine. 2020;84(5):2364-2375. [doi:10.1002/mrm.28278](doi:10.1002/mrm.28278)
"""

# ╔═╡ abea2c43-d83e-4438-8cd3-4be06b8174b3
md"""# Reproducibility

This [Pluto notebook](https://plutojl.org/) is reproducible by default, as it has an embedded `Project.toml` and `Manifest.toml`, that store the exact package versions used to create the notebook."""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
KomaMRICore = "4baa4f4d-2ae9-40db-8331-a7d1080e3f4e"
KomaMRIPlots = "76db0263-63f3-4d26-bb9a-5dba378db904"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
PlutoPlotly = "8e989ff0-3d88-8e9f-f020-2b208a939ff0"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
ProgressLogging = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"

[compat]
KomaMRICore = "~0.9.1"
KomaMRIPlots = "~0.9.2"
PlutoPlotly = "~0.5.0"
PlutoUI = "~0.7.58"
ProgressLogging = "~0.1.4"
Suppressor = "~0.2.8"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.11.3"
manifest_format = "2.0"
project_hash = "26563a43ea8c1b9491611f48849d7fd35205423e"

[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.5.0"
weakdeps = ["ChainRulesCore", "Test"]

    [deps.AbstractFFTs.extensions]
    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
    AbstractFFTsTestExt = "Test"

[[deps.AbstractNFFTs]]
deps = ["LinearAlgebra", "Printf"]
git-tree-sha1 = "292e21e99dedb8621c15f185b8fdb4260bb3c429"
uuid = "7f219486-4aa7-41d6-80a7-e08ef20ceed7"
version = "0.8.2"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.2"

[[deps.Accessors]]
deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "MacroTools"]
git-tree-sha1 = "3b86719127f50670efe356bc11073d84b4ed7a5d"
uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
version = "0.1.42"

    [deps.Accessors.extensions]
    AxisKeysExt = "AxisKeys"
    IntervalSetsExt = "IntervalSets"
    LinearAlgebraExt = "LinearAlgebra"
    StaticArraysExt = "StaticArrays"
    StructArraysExt = "StructArrays"
    TestExt = "Test"
    UnitfulExt = "Unitful"

    [deps.Accessors.weakdeps]
    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "f7817e2e585aa6d924fd714df1e2a84be7896c60"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "4.3.0"
weakdeps = ["SparseArrays", "StaticArrays"]

    [deps.Adapt.extensions]
    AdaptSparseArraysExt = "SparseArrays"
    AdaptStaticArraysExt = "StaticArrays"

[[deps.ArgCheck]]
git-tree-sha1 = "f9e9a66c9b7be1ad7372bbd9b062d9230c30c5ce"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.5.0"

[[deps.ArgTools]]
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version = "1.1.2"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.11.0"

[[deps.AssetRegistry]]
deps = ["Distributed", "JSON", "Pidfile", "SHA", "Test"]
git-tree-sha1 = "b25e88db7944f98789130d7b503276bc34bc098e"
uuid = "bf4720bc-e11a-5d0c-854e-bdca1663c893"
version = "0.1.0"

[[deps.Atomix]]
deps = ["UnsafeAtomics"]
git-tree-sha1 = "b5bb4dc6248fde467be2a863eb8452993e74d402"
uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
version = "1.1.1"

    [deps.Atomix.extensions]
    AtomixCUDAExt = "CUDA"
    AtomixMetalExt = "Metal"
    AtomixOpenCLExt = "OpenCL"
    AtomixoneAPIExt = "oneAPI"

    [deps.Atomix.weakdeps]
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
    OpenCL = "08131aa3-fb12-5dee-8b74-c09406e224a2"
    oneAPI = "8f75cd03-7ff8-4ecb-9b8f-daf728133b1b"

[[deps.AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.1.0"

[[deps.BangBang]]
deps = ["Accessors", "ConstructionBase", "InitialValues", "LinearAlgebra"]
git-tree-sha1 = "26f41e1df02c330c4fa1e98d4aa2168fdafc9b1f"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.4.4"

    [deps.BangBang.extensions]
    BangBangChainRulesCoreExt = "ChainRulesCore"
    BangBangDataFramesExt = "DataFrames"
    BangBangStaticArraysExt = "StaticArrays"
    BangBangStructArraysExt = "StructArrays"
    BangBangTablesExt = "Tables"
    BangBangTypedTablesExt = "TypedTables"

    [deps.BangBang.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
    TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
version = "1.11.0"

[[deps.BaseDirs]]
git-tree-sha1 = "cb25e4b105cc927052c2314f8291854ea59bf70a"
uuid = "18cc8868-cbac-4acf-b575-c8ff214dc66f"
version = "1.2.4"

[[deps.Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[deps.BitFlags]]
git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.9"

[[deps.Blink]]
deps = ["Base64", "Distributed", "HTTP", "JSExpr", "JSON", "Lazy", "Logging", "MacroTools", "Mustache", "Mux", "Pkg", "Reexport", "Sockets", "WebIO"]
git-tree-sha1 = "bc93511973d1f949d45b0ea17878e6cb0ad484a1"
uuid = "ad839575-38b3-5650-b840-f874b8c74a25"
version = "0.12.9"

[[deps.BufferedStreams]]
git-tree-sha1 = "6863c5b7fc997eadcabdbaf6c5f201dc30032643"
uuid = "e1450e63-4bb3-523b-b2a4-4ffa8c0fd77d"
version = "1.2.2"

[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra"]
git-tree-sha1 = "1713c74e00545bfe14605d2a2be1712de8fbcb58"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.25.1"
weakdeps = ["SparseArrays"]

    [deps.ChainRulesCore.extensions]
    ChainRulesCoreSparseArraysExt = "SparseArrays"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "962834c22b66e32aa10f7611c08c8ca4e20749a9"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.8"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "403f2d8e209681fcbd9468a8514efff3ea08452e"
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version = "3.29.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d"
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version = "0.11.5"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

    [deps.ColorVectorSpace.weakdeps]
    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.11"

[[deps.Compat]]
deps = ["TOML", "UUIDs"]
git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215"
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version = "4.16.0"
weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"

[[deps.CompositionsBase]]
git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
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version = "0.1.2"
weakdeps = ["InverseFunctions"]

    [deps.CompositionsBase.extensions]
    CompositionsBaseInverseFunctionsExt = "InverseFunctions"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "d9d26935a0bcffc87d2613ce14c527c99fc543fd"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
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[[deps.ConstructionBase]]
git-tree-sha1 = "76219f1ed5771adbb096743bff43fb5fdd4c1157"
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    [deps.ConstructionBase.extensions]
    ConstructionBaseIntervalSetsExt = "IntervalSets"
    ConstructionBaseLinearAlgebraExt = "LinearAlgebra"
    ConstructionBaseStaticArraysExt = "StaticArrays"

    [deps.ConstructionBase.weakdeps]
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
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[[deps.DataValueInterfaces]]
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[[deps.Dates]]
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[[deps.DelimitedFiles]]
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[[deps.Distributed]]
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[[deps.DocStringExtensions]]
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[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
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[[deps.ExceptionUnwrapping]]
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[[deps.FFTW]]
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version = "1.8.1"

[[deps.FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6d6219a004b8cf1e0b4dbe27a2860b8e04eba0be"
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deps = ["Statistics"]
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[[deps.FunctionalCollections]]
deps = ["Test"]
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[[deps.Functors]]
deps = ["Compat", "ConstructionBase", "LinearAlgebra", "Random"]
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[[deps.Future]]
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version = "1.11.0"

[[deps.HDF5]]
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    PlotlyKaleidoExt = "PlotlyKaleido"
    UnitfulExt = "Unitful"

    [deps.PlutoPlotly.weakdeps]
    PlotlyKaleido = "f2990250-8cf9-495f-b13a-cce12b45703c"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "d3de2694b52a01ce61a036f18ea9c0f61c4a9230"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.62"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.3"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
version = "1.11.0"

[[deps.ProgressLogging]]
deps = ["Logging", "SHA", "UUIDs"]
git-tree-sha1 = "80d919dee55b9c50e8d9e2da5eeafff3fe58b539"
uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
version = "0.1.4"

[[deps.ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "13c5103482a8ed1536a54c08d0e742ae3dca2d42"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.10.4"

[[deps.QMRIColors]]
deps = ["Colors", "DelimitedFiles"]
git-tree-sha1 = "77d0d5f446d544beaa568b837fade390d9d38721"
uuid = "2bec176e-9e8c-4764-a62f-295118d1ec05"
version = "1.0.1"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
version = "1.11.0"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
version = "1.11.0"

[[deps.Ratios]]
deps = ["Requires"]
git-tree-sha1 = "1342a47bf3260ee108163042310d26f2be5ec90b"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.5"
weakdeps = ["FixedPointNumbers"]

    [deps.Ratios.extensions]
    RatiosFixedPointNumbersExt = "FixedPointNumbers"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.Referenceables]]
deps = ["Adapt"]
git-tree-sha1 = "02d31ad62838181c1a3a5fd23a1ce5914a643601"
uuid = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"
version = "0.1.3"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "62389eeff14780bfe55195b7204c0d8738436d64"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.1"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
version = "1.11.0"

[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
git-tree-sha1 = "c5391c6ace3bc430ca630251d02ea9687169ca68"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "1.1.2"

[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
version = "1.11.0"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.2.0"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
version = "1.11.0"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.11.0"

[[deps.SplittablesBase]]
deps = ["Setfield", "Test"]
git-tree-sha1 = "e08a62abc517eb79667d0a29dc08a3b589516bb5"
uuid = "171d559e-b47b-412a-8079-5efa626c420e"
version = "0.1.15"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
git-tree-sha1 = "0feb6b9031bd5c51f9072393eb5ab3efd31bf9e4"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.9.13"
weakdeps = ["ChainRulesCore", "Statistics"]

    [deps.StaticArrays.extensions]
    StaticArraysChainRulesCoreExt = "ChainRulesCore"
    StaticArraysStatisticsExt = "Statistics"

[[deps.StaticArraysCore]]
git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.3"

[[deps.Statistics]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.11.1"
weakdeps = ["SparseArrays"]

    [deps.Statistics.extensions]
    SparseArraysExt = ["SparseArrays"]

[[deps.StyledStrings]]
uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
version = "1.11.0"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.7.0+0"

[[deps.Suppressor]]
deps = ["Logging"]
git-tree-sha1 = "6dbb5b635c5437c68c28c2ac9e39b87138f37c0a"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.8"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "OrderedCollections", "TableTraits"]
git-tree-sha1 = "598cd7c1f68d1e205689b1c2fe65a9f85846f297"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.12.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
version = "1.11.0"

[[deps.ThreadsX]]
deps = ["Accessors", "ArgCheck", "BangBang", "ConstructionBase", "InitialValues", "MicroCollections", "Referenceables", "SplittablesBase", "Transducers"]
git-tree-sha1 = "70bd8244f4834d46c3d68bd09e7792d8f571ef04"
uuid = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"
version = "0.1.12"

[[deps.TranscodingStreams]]
git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.11.3"

[[deps.Transducers]]
deps = ["Accessors", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "ConstructionBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "SplittablesBase", "Tables"]
git-tree-sha1 = "7deeab4ff96b85c5f72c824cae53a1398da3d1cb"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.84"

    [deps.Transducers.extensions]
    TransducersAdaptExt = "Adapt"
    TransducersBlockArraysExt = "BlockArrays"
    TransducersDataFramesExt = "DataFrames"
    TransducersLazyArraysExt = "LazyArrays"
    TransducersOnlineStatsBaseExt = "OnlineStatsBase"
    TransducersReferenceablesExt = "Referenceables"

    [deps.Transducers.weakdeps]
    Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
    BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
    OnlineStatsBase = "925886fa-5bf2-5e8e-b522-a9147a512338"
    Referenceables = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"

[[deps.Tricks]]
git-tree-sha1 = "6cae795a5a9313bbb4f60683f7263318fc7d1505"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.10"

[[deps.URIs]]
git-tree-sha1 = "cbbebadbcc76c5ca1cc4b4f3b0614b3e603b5000"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.2"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
version = "1.11.0"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
version = "1.11.0"

[[deps.UnsafeAtomics]]
git-tree-sha1 = "b13c4edda90890e5b04ba24e20a310fbe6f249ff"
uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
version = "0.3.0"

    [deps.UnsafeAtomics.extensions]
    UnsafeAtomicsLLVM = ["LLVM"]

    [deps.UnsafeAtomics.weakdeps]
    LLVM = "929cbde3-209d-540e-8aea-75f648917ca0"

[[deps.WebIO]]
deps = ["AssetRegistry", "Base64", "Distributed", "FunctionalCollections", "JSON", "Logging", "Observables", "Pkg", "Random", "Requires", "Sockets", "UUIDs", "WebSockets", "Widgets"]
git-tree-sha1 = "0eef0765186f7452e52236fa42ca8c9b3c11c6e3"
uuid = "0f1e0344-ec1d-5b48-a673-e5cf874b6c29"
version = "0.8.21"

[[deps.WebSockets]]
deps = ["Base64", "Dates", "HTTP", "Logging", "Sockets"]
git-tree-sha1 = "4162e95e05e79922e44b9952ccbc262832e4ad07"
uuid = "104b5d7c-a370-577a-8038-80a2059c5097"
version = "1.6.0"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "e9aeb174f95385de31e70bd15fa066a505ea82b9"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.7"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "1.0.0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.libaec_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "f5733a5a9047722470b95a81e1b172383971105c"
uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0"
version = "1.1.3+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.0.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"
"""

# ╔═╡ Cell order:
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