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util.jl
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util.jl
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# Handful of useful, but misc. functions that helped along the way.
using StatsBase, Statistics, LinearAlgebra, Distributions
function getLTGprct(u::Vector{Float64},p)
# Converts mM --> % liver fat on volumetric basis.
# Future extension: error check that vd_cyt and vd_er are correct with p-vector.
rho_tg = 0.9*1000.0 # [g/L], includes /cm^3 --> /L conversion
mw_tg = 772
vd_cyt = p[16] # [L]
vd_er = p[17] # [L]
hepat_vol = 0.95*0.7089 # [L], estimate of non-LTG hepatocyte volume, see Pluto notebook: derived_parameters.jl
ltg_mass = (u[2]*vd_cyt+u[4]*vd_er)*mw_tg/1000.0 # [g-TG], includes mg-->g conversion
ltg_vol = ltg_mass/rho_tg # [L-TG]
ltg_prct = 100*ltg_vol/(ltg_vol + hepat_vol) # [%]
return ltg_prct
end
function getLTGprct(u::Matrix{Float64},p)
# Converts mM --> % liver fat on volumetric basis.
# Future extension: error check that vd_cyt and vd_er are correct with p-vector.
rho_tg = 0.9*1000.0 # [g/L], includes /cm^3 --> /L conversion
mw_tg = 772
vd_cyt = p[16] # [L]
vd_er = p[17] # [L]
hepat_vol = vd_cyt + vd_er # [L]
ltg_mass = (u[2,:] .* vd_cyt .+ u[4,:] .* vd_er) .* mw_tg/1000.0 # [g-TG], includes mg-->g conversion
ltg_vol = ltg_mass ./ rho_tg # [L-TG]
ltg_prct = 100 .* ltg_vol ./ (ltg_vol .+ hepat_vol) # [%]
return ltg_prct
end
function joint_tg_dist(frac_fast_tg)
# Creates a MvLogNormal distribution from the data below based on the mean and covariance of the data.
# Data from captured from:
# Anna Kotronen, Jukka Westerbacka, Robert Bergholm, Kirsi H. Pietiläinen, Hannele Yki-Järvinen,
# Liver Fat in the Metabolic Syndrome,
# The Journal of Clinical Endocrinology & Metabolism,
# Volume 92, Issue 9, 1 September 2007, Pages 3490–3497,
# https://doi.org/10.1210/jc.2007-0482
x = [1.98E-01 6.78E-01
4.93E-01 4.12E-01
3.93E-01 6.47E-01
3.86E-01 7.71E-01
4.84E-01 5.30E-01
4.92E-01 5.78E-01
5.00E-01 6.24E-01
5.00E-01 6.98E-01
4.91E-01 7.91E-01
4.91E-01 8.64E-01
4.82E-01 9.43E-01
4.90E-01 1.02E+00
4.73E-01 1.15E+00
4.89E-01 1.27E+00
4.80E-01 1.72E+00
8.46E-01 1.81E+00
8.64E-01 1.10E+00
9.64E-01 3.47E-01
1.01E+00 4.69E-01
1.01E+00 5.25E-01
9.94E-01 6.17E-01
1.23E+00 2.06E+00
1.49E+00 2.33E+00
4.29E+00 1.00E+01
6.70E+00 9.92E+00
3.89E+00 3.72E+00
1.93E+00 2.19E+00
2.45E+00 2.22E+00
3.07E+00 2.25E+00
2.91E+00 2.40E+00
3.01E+00 2.90E+00
2.00E+00 1.91E+00
1.90E+00 1.77E+00
1.93E+00 1.55E+00
1.66E+00 1.52E+00
1.42E+00 1.54E+00
1.47E+00 1.25E+00
1.57E+00 1.26E+00
1.45E+00 9.71E-01
1.45E+00 8.78E-01
1.50E+00 7.75E-01
1.48E+00 6.92E-01
1.48E+00 6.18E-01
1.48E+00 5.39E-01
2.01E+00 5.06E-01
1.94E+00 6.11E-01
1.94E+00 7.10E-01
1.94E+00 7.85E-01
1.97E+00 8.79E-01
1.94E+00 9.96E-01
1.90E+00 1.09E+00
1.94E+00 1.22E+00
1.90E+00 1.38E+00
2.42E+00 1.65E+00
2.42E+00 1.02E+00
2.92E+00 1.69E+00
2.97E+00 1.47E+00
9.93E-01 7.27E-01
9.93E-01 8.13E-01
9.75E-01 8.99E-01
9.92E-01 9.57E-01
9.73E-01 1.21E+00
9.73E-01 1.29E+00
9.89E-01 1.47E+00
1.01E+00 1.58E+00
9.88E-01 1.75E+00
9.55E-01 1.86E+00
2.87E+00 1.30E+00
2.87E+00 1.22E+00
2.93E+00 1.09E+00
2.83E+00 1.06E+00
2.98E+00 9.37E-01
2.88E+00 8.48E-01
2.93E+00 7.48E-01
3.36E+00 7.12E-01
3.86E+00 7.68E-01
4.43E+00 7.49E-01
5.00E+00 7.04E-01
5.93E+00 6.62E-01
5.83E+00 7.69E-01
5.93E+00 8.19E-01
5.08E+00 9.04E-01
4.50E+00 8.71E-01
3.92E+00 9.99E-01
3.66E+00 9.15E-01
3.30E+00 9.61E-01
3.41E+00 1.09E+00
3.97E+00 1.87E+00
4.63E+00 2.20E+00
4.87E+00 2.56E+00
4.87E+00 2.69E+00
5.79E+00 2.66E+00
5.79E+00 2.18E+00
6.32E+00 1.92E+00
5.70E+00 1.97E+00
5.90E+00 1.80E+00
5.80E+00 1.65E+00
4.81E+00 1.46E+00
4.34E+00 1.38E+00
4.50E+00 1.09E+00
5.43E+00 1.12E+00
5.34E+00 1.08E+00
5.91E+00 1.22E+00
5.92E+00 9.76E-01
6.91E+00 9.17E-01
6.80E+00 8.29E-01
8.82E+00 5.09E-01
9.28E+00 6.71E-01
1.06E+01 7.90E-01
9.59E+00 8.73E-01
1.03E+01 1.02E+00
1.12E+01 1.09E+00
1.35E+01 9.54E-01
1.84E+01 8.43E-01
2.47E+01 7.26E-01
2.23E+01 4.51E-01
1.64E+01 5.39E+00
3.88E+01 6.69E+00
3.33E+01 4.59E+00
2.21E+01 3.89E+00
1.62E+01 4.14E+00
1.46E+01 3.39E+00
1.37E+01 2.54E+00
2.10E+01 2.71E+00
3.34E+01 2.45E+00
4.32E+01 2.30E+00
3.71E+01 1.50E+00
3.85E+01 1.02E+00
2.73E+01 8.76E-01
2.51E+01 1.04E+00
2.64E+01 1.10E+00
2.11E+01 1.03E+00
1.84E+01 1.10E+00
1.97E+01 1.11E+00
2.22E+01 1.20E+00
2.11E+01 1.37E+00
1.93E+01 1.31E+00
1.52E+01 1.15E+00
1.42E+01 1.29E+00
1.37E+01 1.41E+00
1.60E+01 1.41E+00
1.80E+01 1.48E+00
2.26E+01 1.68E+00
2.72E+01 1.98E+00
2.91E+01 2.08E+00
3.24E+01 1.56E+00
3.52E+01 1.77E+00
2.82E+01 1.68E+00
2.77E+01 1.54E+00
2.59E+01 1.43E+00
2.68E+01 1.36E+00
2.25E+01 1.91E+00
2.21E+01 2.05E+00
2.00E+01 1.90E+00
1.74E+01 1.77E+00
8.06E+00 1.19E+00
8.48E+00 1.30E+00
9.57E+00 1.16E+00
1.06E+01 1.27E+00
1.16E+01 1.30E+00
9.40E+00 1.29E+00
1.08E+01 1.48E+00
7.38E+00 1.53E+00
6.22E+00 1.48E+00
7.25E+00 1.76E+00
7.37E+00 2.05E+00
8.17E+00 2.23E+00
7.24E+00 2.56E+00
9.55E+00 1.78E+00
1.06E+01 1.92E+00
1.15E+01 1.81E+00
1.26E+01 1.79E+00
1.23E+01 1.95E+00
1.24E+01 1.58E+00
1.35E+01 1.52E+00
3.47E+00 1.24E+00] # Liver Fat [%], TG [mM]
x[:,2] = x[:,2]./frac_fast_tg
xl = log.(x)
mu = vec(mean(xl,dims=1))
cov = StatsBase.cov(xl)
d_joint = MvLogNormal(mu,cov) # Multivariate log-normal distribution
return d_joint
end
function errorellipse(d::Distribution)
# Returns a 2D error ellipse at the 95% prediction interval
# Future exensions:
# Expansion to 3D+ (projections)
# Assumes distribution is MvLogNormal
nvar = 100000 # number of points to estimate ellipse using
nplot = nvar # number of points for plotting
r = log.(rand(d,nvar)) # draw variates
rcov = StatsBase.cov(r')
reigval = LinearAlgebra.eigvals(rcov)
reigvec = LinearAlgebra.eigvecs(rcov)
reigval_max = findmax(reigval)[1]
reigvec_max = reigvec[:,findmax(reigval)[2]]
reigval_min = findmin(reigval)[1]
reigvec_min = reigvec[:,findmin(reigval)[2]]
rangle = atan(reigvec_max[2],reigvec_max[1])
if (rangle < 0)
rangle = rangle + 2*pi
end
rmean = mean(r,dims=2)
chisquare_val = 2.4477
theta_grid = LinRange(0,2*pi,nplot)
phi = rangle
X0 = rmean[1]
Y0 = rmean[2]
a = chisquare_val*sqrt(reigval_max)
b = chisquare_val*sqrt(reigval_min)
R = [cos(phi) sin(phi);
-sin(phi) cos(phi)]
ellipsexy = Matrix{Float64}(undef,nplot,2)
ellipsexy[:,1] = a*cos.(theta_grid)
ellipsexy[:,2] = b*sin.(theta_grid)
ellipsexy = ellipsexy * R
ellipsexy[:,1] = ellipsexy[:,1] .+ X0
ellipsexy[:,2] = ellipsexy[:,2] .+ Y0
return ellipsexy
end
function LogNormFromUT(MeanX::Float64,LV::Float64,HV::Float64)
# Univariate LogNormal from untransformed values
sigma = log(HV/LV)/3.2897072539029435
#VarX = StdX^2
mu = log(MeanX) - sigma^2/2#log(MeanX^2/sqrt(VarX + MeanX^2))
#sigma = sqrt(log(VarX/MeanX^2+1))
return LogNormal(mu,sigma)
end