theory_simulation.jl

### A Pluto.jl notebook ###
# v0.20.4

using Markdown
using InteractiveUtils

# ╔═╡ b971e995-0d79-436c-a205-63e1193661ad
begin
	using PyCall
	using LsqFit
	using FFTW
	using LinearAlgebra
	using ProgressMeter
	using StatsBase
	using NaNStatistics
	using Plots
	include("./B0navigator.jl")
	md"Julia imports completed! 🚀"
end

# ╔═╡ 22b98076-c364-11ef-3eff-09be90dac5ee
md"""
# B0 navigator in simplified two-species model
"""

# ╔═╡ 4e62cac8-ca38-40f4-9894-10d72841c6b7
md"""
## Imports
"""

# ╔═╡ ae65c7e1-b691-42fb-8337-3bbbcf769f95
try
    pyimport("hmrGC")
	md"""
	✅ Python package `hmrGC` is installed. 
	"""
catch e
	md"""
	❌ Python package `hmrGC` is not installed. 
	
	- **Suggestion:** Ensure `hmrGC` is installed in the Python environment used by PyCall 
	- **Error details:** $(e)
	"""
end

# ╔═╡ fa7ea41e-155f-4032-afbc-4eb86e278856
md"""
## General phantom preparation
"""

# ╔═╡ 2c8964e2-35b2-40cb-b8a8-58b88f4aaf14
md"""
Define phantom parameters:
"""

# ╔═╡ 2a5640f9-30c7-4a65-8646-6ce45185f0b0
begin
	fov = 232
	rad_rho1 = 50
	rad_rho2 = 70
	fm_rho1 = 30
	fm_rho2 = 70
	t1_rho1 = 850*1e-3
	t1_rho2 = 380*1e-3
	ti_s = [0.01021 , 0.307167, 0.604124, 0.901081, 1.198038, 1.494995, 1.791952]
	te_s = [1.07669997215271, 2.144199848175049, 3.211699962615967, 4.279199600219727]*1e-3
	# Fat model:
	fatModel = Dict{String, Any}()
	fatModel["freqs_ppm"] = [-3.8 , -3.4 , -3.1 , -2.68, -2.46, -1.95, 
		-0.5 ,  0.49,  0.59]
	fatModel["relAmps"] = [0.08991009, 0.58341658, 0.05994006, 0.08491508, 
		0.05994006, 0.01498501, 0.03996004, 0.00999001, 0.05694306]
	centerFreq_Hz = 1.2775709f8
end;

# ╔═╡ 7b61566d-7de7-408e-8fce-01a4e5a71003
begin
	arr = zeros(fov, fov)
	# Create meshgrid-like arrays for x and y
	x = repeat(-fov/2:fov/2-1, 1, fov)
	y = repeat((-fov/2:fov/2-1)', fov, 1)
	# Create masks
	rho1_mask = x.^2 + y.^2 .< (rad_rho1)^2
	rho2_mask = x.^2 + y.^2 .< (rad_rho2)^2

	fm_Hz = zeros((fov, fov))
	fm_Hz[rho2_mask] .= fm_rho2
	fm_Hz[rho1_mask] .= fm_rho1
end;

# ╔═╡ 91f280bd-69d0-4199-8ec7-070e4f5c7539
md"""
Simulated field-map:
"""

# ╔═╡ db0501d7-611b-4062-99a4-5fa2cfaf2803
heatmap(fm_Hz, cmap=:magma, colorbar_title="(Hz)")

# ╔═╡ ea29ddca-8069-43f4-9bc2-3467271ac3b4
md"""
## Case 1: $\varrho_1$, $\varrho_2$ water
"""

# ╔═╡ bd1dd89c-e62c-4bd3-94f2-e603f50dbdac
begin
	t1_s = zeros((fov, fov))
	t1_s[rho2_mask] .= t1_rho2
	t1_s[rho1_mask] .= t1_rho1

	mask = (t1_s .> 0)
end;

# ╔═╡ 84e2128b-51fc-4981-823f-898ed05ec21b
md"""
Simulated T1 map:
"""

# ╔═╡ 594be2f3-510c-48dc-af64-20de72629005
heatmap(t1_s*1e3, cmap=:plasma, colorbar_title="(ms)")

# ╔═╡ e7452c0f-68e9-4276-9583-8952d243f9cf
md"""
Compute water signal based on inversion recovery signal model:
"""

# ╔═╡ 9be771dd-39f6-47f4-b6b5-cbfca7d1fc97
begin
	water = zeros((fov, fov, length(ti_s)))
	for (i, ti) in enumerate(ti_s)
		water[mask,i] = (1 .- 2 .* exp.(- ti ./ t1_s[mask]))
	end
end;

# ╔═╡ 08a4a9d9-c768-4288-9d5b-c6a27685ec4f
begin
	p_size=500
	p = plot(layout=(1, length(ti_s)), size=(p_size*length(ti_s), p_size))  # Adjust size as needed
	for i in 1:length(ti_s)
    	heatmap!(abs.(water[:, :, i]), cmap=:grays, aspect_ratio=:equal, clim=(0, maximum(water)), colorbar=false, axis=nothing, subplot=i)
	end
	p
end

# ╔═╡ 2d6203dc-76d6-4323-9c50-3978202c75f6
md"""
Compute echo signal for each TI based on multi-echo gradient echo signal model:
"""

# ╔═╡ 5d851331-9f51-418d-8fa9-dfa0d260d31b
begin
	signal = zeros(ComplexF32, fov, fov, length(ti_s), length(te_s))
	for i in 1:length(ti_s)
		for (j, te) in enumerate(te_s)
			signal[mask,i,j] = water[mask,i] .* exp.(2im*pi*fm_Hz[mask]*te)
		end
	end
end;

# ╔═╡ 6c945ac6-36b2-4d2f-aa9e-76272344822a
md"""
Set parameters for B0 navigator:"""

# ╔═╡ 05bc8f2d-2a6f-4fba-8049-f34aedc0d3c8
begin
	params = Dict{Symbol,Any}()
	params[:TE_s] = te_s
	params[:centerFreq_Hz] = centerFreq_Hz
	params[:fieldStrength_T] = 3
	params[:range_fm_ppm] = 2*[-1,1]
	params[:sampling_stepsize_fm] = 0.25 # determines the accuracy
end;

# ╔═╡ 671cfc4c-b0ad-4fa8-9de3-ef16b478bafc
md"""
Extract k-space center (equivalent to integration of the complex signal in x/y-plane):
"""

# ╔═╡ 61f20280-a5a8-43af-a21a-c7170343f9ab
begin
	numSpokes = 131
	data = repeat(permutedims(sum(signal, dims=(1,2))[1,:,:,:], [3,1,2]), 1, numSpokes, 1)
	"Size of input data: " * string(size(data))
end

# ╔═╡ 3892b797-4925-4885-85ee-ce13c318da91
md"""
Estimate B0 navigator using graph-cut algorithm:
"""

# ╔═╡ 57bfe9c5-93aa-4ef2-bfe2-1f31c353d2ad
b0nav = deltaB0EstimationLL(data, params);

# ╔═╡ 54e13b4a-76dd-4991-b6cc-668f4b35ef8a
md"""
Compute linear approximation as comparison (small field-map induced phase terms): """

# ╔═╡ ff336ad4-a405-410e-81d0-b87535fdd319
begin
	rho1 = sum((water[rho1_mask,:]), dims=1)
	rho2 = sum((water[rho2_mask .& .!rho1_mask,:]), dims=1)
	rho_linear_approx = rho1+rho2
	b0nav_linear_approx = (rho1*fm_rho1 + rho2*fm_rho2) ./ (rho1+rho2)
end

# ╔═╡ 445e4468-25e7-4db7-9af8-db5501876b3b
begin
	default()
	plot(b0nav[:deltaB0_raw_b0][1:3*length(ti_s),1,1,1],
		label = "Estimated", xlabel = "Shots", ylabel = "Field-map (Hz)",
		lw = 3, grid = :off, legend = :outerbottom,  guidefont = font(16),
		size = (500, 350), tickfont = font(12)
	)
	plot!(repeat(b0nav_linear_approx',3), label = "Linear approximation", lw = 3, linestyle = :dash)
	hline!([fm_rho1], color = :black, linestyle = :dash, linewidth = 2, label=false)
	hline!([fm_rho2], color = :black, linestyle = :dash, linewidth = 2, label=false)
end

# ╔═╡ 4bb576a2-3da4-462a-bc4f-ee333fc72930
begin
	default()
	plot(abs.(b0nav[:deltaB0_raw_water][1:3*length(ti_s),1,1,1])/maximum(abs.(b0nav[:deltaB0_raw_water])), 
		label = "Estimated", xlabel = "Shots", ylabel = "Magnitude (a.u.)",
		lw = 3, grid = :off, legend = :outerbottom, guidefont = font(16),
		size = (500, 350), tickfont = font(12)
	)
	plot!(repeat((abs.(rho_linear_approx)/maximum(abs.(rho_linear_approx)))',3), label = "Linear approximation", lw = 3, linestyle = :dash)
end

# ╔═╡ ca0027c8-1dba-4cd1-9cf1-f2f4c74d1074
md"""
Estimated $f_{B,nav}$ for the different TIs in Hz:
"""

# ╔═╡ 6c2d4b72-a2c3-44d2-a1e2-3f6c063cba2d
round.(b0nav[:deltaB0_raw_b0][1:length(ti_s),1,1,1],digits=1)

# ╔═╡ 3f9d91c3-d141-4e75-949a-fdab231d3f89
md"""
## Case 2: $\varrho_1$ water, $\varrho_2$ fat
"""

# ╔═╡ c154d5ed-963b-4c7c-9377-dcfa69248054
begin
	t1_water_s = zeros((fov, fov))
	t1_fat_s = zeros((fov, fov))
	t1_water_s[rho1_mask] .= t1_rho1
	t1_fat_s[rho2_mask] .= t1_rho2
	t1_fat_s[rho1_mask] .= 0

	mask_water = (t1_water_s .> 0)
	mask_fat = (t1_fat_s .> 0)
end;

# ╔═╡ d88b8fa4-943e-4674-9fee-56e7c8c227cb
md"""
Compute water and fat signals based on inversion recovery signal model:
"""

# ╔═╡ 6b58b45c-031e-42b7-999e-2cf1c59208c7
begin
	water2 = zeros((fov, fov, length(ti_s)))
	fat2 = zeros((fov, fov, length(ti_s)))
	for (i, ti) in enumerate(ti_s)
		water2[mask_water,i] = (1 .- 2 .* exp.(- ti ./ t1_water_s[mask_water]))
		fat2[mask_fat,i] = (1 .- 2 .* exp.(- ti ./ t1_fat_s[mask_fat]))
	end
end;

# ╔═╡ 27787949-3638-433a-9e06-0eb4c8c4a53c
begin
	p2_size=500
	p2 = plot(layout=(1, length(ti_s)), size=(p2_size*length(ti_s), p2_size))  # Adjust size as needed
	for i in 1:length(ti_s)
    	heatmap!(abs.(water2[:, :, i]), cmap=:grays, aspect_ratio=:equal, clim=(0, maximum(water2)), colorbar=false, axis=nothing, subplot=i)
	end
	p2
end

# ╔═╡ 39de9c9a-1d6a-4bb9-a8b0-ffa409926074
md"""
Compute echo signal for each TI based on multi-echo gradient echo signal model:
"""

# ╔═╡ 4a70b743-f586-4fe5-a3ad-38ab97deaed8
begin
	signal2 = zeros(ComplexF32, fov, fov, length(ti_s), length(te_s))
	for (j, te) in enumerate(te_s)
		fatphasor = 0.0
		for (shift, amp) in zip(fatModel["freqs_ppm"], fatModel["relAmps"])
			fatphasor += amp * exp.(2im*pi*shift*centerFreq_Hz*1e-6*te)
		end
		for i in 1:length(ti_s)
			signal2[:,:,i,j] = (water2[:,:,i] + fat2[:,:,i] .* fatphasor) .* exp.(2im*pi*fm_Hz*te)
		end
	end
end;

# ╔═╡ aae3dce0-e3a9-4fbc-b53c-9e3053c16d16
md"""
Extract k-space center (equivalent to integration of the complex signal in x/y-plane):
"""

# ╔═╡ ec7bfd9b-c4b6-478f-89ca-678416475d86
begin
	data2 = repeat(permutedims(sum(signal2, dims=(1,2))[1,:,:,:], [3,1,2]), 1, numSpokes, 1)
	"Size of input data: " * string(size(data2))
end

# ╔═╡ f007d94d-991d-4a2a-942a-b07198016428
md"""
Estimate B0 navigator using graph-cut algorithm (first: water-only model, second: water-fat model):
"""

# ╔═╡ 833cb5b5-88af-4741-a3c6-47506dbc27f2
b0nav2_waterOnly = deltaB0EstimationLL(data2, params);

# ╔═╡ dec43d33-6967-48bf-a978-24bb97b8e152
begin
	params2 = deepcopy(params)
	params2[:fatModel] = fatModel
	b0nav2_waterFat = deltaB0EstimationLL(data2, params2)
end;

# ╔═╡ 75933d33-c803-4fd1-a9fc-80d96e2405cb
begin
	default()
	defaults = get_color_palette(:auto, plot_color(:white))
	plot(b0nav2_waterFat[:deltaB0_raw_b0][1:3*length(ti_s),1,1,1],
		label = "Estimated, water-fat model", xlabel = "Shots", 
		ylabel = "Field-map (Hz)", lw = 3, grid = :off, legend = :outerbottom,  
		guidefont = font(16), size = (500, 350), tickfont = font(12)
	)
	plot!(b0nav2_waterOnly[:deltaB0_raw_b0][1:3*length(ti_s),1,1,1],
		label = "Water-only model", color=defaults[3], linestyle = :dash, 
		xlabel = "Shots", ylabel = "Field-map (Hz)", lw = 3, grid = :off, 
		legend = :outerbottom,  guidefont = font(16), size = (500, 350), 
		tickfont = font(12)
	)
	hline!([fm_rho1], color = :black, linestyle = :dash, linewidth = 2, label=false)
	hline!([fm_rho2], color = :black, linestyle = :dash, linewidth = 2, label=false)
end

# ╔═╡ d6b4e8f7-6f1e-456f-bf2d-87598a20402c
begin
	default()
	plot(abs.(b0nav2_waterFat[:deltaB0_raw_water][1:3*length(ti_s),1,1,1])/maximum(abs.(b0nav2_waterFat[:deltaB0_raw_water])), 
		label = "Estimated water, water-fat model", xlabel = "Shots", ylabel = "Magnitude (a.u.)",
		lw = 3, grid = :off, legend = :outerbottom, guidefont = font(16),
		size = (500, 350), tickfont = font(12)
	)
	plot!(abs.(b0nav2_waterFat[:deltaB0_raw_fat][1:3*length(ti_s),1,1,1])/maximum(abs.(b0nav2_waterFat[:deltaB0_raw_fat])), 
		label = "Estimated fat, water-fat model", xlabel = "Shots", ylabel = "Magnitude (a.u.)",
		lw = 3, grid = :off, legend = :outerbottom, guidefont = font(16),
		size = (500, 350), tickfont = font(12), color=defaults[4]
	)
	plot!(abs.(b0nav2_waterOnly[:deltaB0_raw_water][1:3*length(ti_s),1,1,1])/maximum(abs.(b0nav2_waterOnly[:deltaB0_raw_water])), 
		label = "Water-only model", xlabel = "Shots", ylabel = "Magnitude (a.u.)", color=defaults[3], linestyle = :dash, lw = 3, grid = :off, 
		legend = :outerbottom, guidefont = font(16), size = (500, 350), 
		tickfont = font(12)
	)
end

# ╔═╡ e4d8e9f0-3fee-4234-b20e-1522df82fa8b
md"""
Estimated $f_{B,nav}$ for the different TIs in Hz:
"""

# ╔═╡ ec5479ad-b403-4e84-adeb-379c815c1ab8
round.(b0nav2_waterFat[:deltaB0_raw_b0][1:length(ti_s),1,1,1],digits=1)

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version = "1.6.44+1"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+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 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

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

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "63406453ed9b33a0df95d570816d5366c92b7809"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+2"
"""

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