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conductivity.py
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from math import erf
import dolfin as d
import numpy as np
import parameters as params
import meshes
import os
import sys
sig_ele = 1e+07
sig_air = 1e-14
sig_zero = 0.00
sig_csf = 1.5 # See M.Rullmann, NeuroImage 44 (2009) Table 1
sig_brain = 0.33
sig_wm = 0.142
sig_wm_long = 0.65 # See C.H.Wolters, NeuroImage 30 (2006) Table 1
sig_wm_trans = 0.065
def scale_gm_wm(fa, s_gm, s_wm):
# (x) -1. --> 1. :: (fa) 0.3 --> 0.5
# (y) -1. --> 1. :: (scale) s_gm --> s_wm
s_diff = s_gm - s_wm
k = (np.sqrt(np.pi) * 10) / 2.
scaled_val = (s_diff * ((-1 * erf(k * (fa - 0.4)) + 1) / 2.))
return s_wm + scaled_val
def tensor_components(mesh):
''' c00 c01 c02
c11 c12
c22 '''
c00 = d.MeshFunction("double", mesh, 3)
c01 = d.MeshFunction("double", mesh, 3)
c02 = d.MeshFunction("double", mesh, 3)
c11 = d.MeshFunction("double", mesh, 3)
c12 = d.MeshFunction("double", mesh, 3)
c22 = d.MeshFunction("double", mesh, 3)
return c00, c01, c02, c11, c12, c22
def compute_conductivity(conductivity, save=False):
print('Computing sigma tensor for case :', conductivity)
mesh = meshes.load_just_mesh()
cells_all = d.cells(mesh)
idx_out, idx_grnd, idx_csf, np_fa = params.load_barycenters_ids()
points_to_sample = params.load_barycenters()
idx_all = np.arange(len(points_to_sample))
if conductivity == 'anisotropic':
np_v1, np_v2, np_v3 = params.load_eigen_vectors()
longi_sigma = []
trans_sigma = []
for jj in idx_all:
longi_sigma.append(scale_gm_wm(np_fa[jj], sig_brain, sig_wm_long))
trans_sigma.append(scale_gm_wm(np_fa[jj], sig_brain, sig_wm_trans))
print 'Did the scaling, now assigning vals'
c00, c01, c02, c11, c12, c22 = tensor_components(mesh)
for jj in idx_all:
cell = cells_all.next()
if jj in idx_grnd: # Electrode
c00[cell] = sig_ele
c11[cell] = sig_ele
c22[cell] = sig_ele
c01[cell] = sig_zero
c02[cell] = sig_zero
c12[cell] = sig_zero
elif jj in idx_out: # Pt outside brain volume
c00[cell] = sig_air
c01[cell] = sig_zero
c02[cell] = sig_zero
c11[cell] = sig_air
c12[cell] = sig_zero
c22[cell] = sig_air
elif jj in idx_csf:
c00[cell] = sig_csf
c01[cell] = sig_zero
c02[cell] = sig_zero
c11[cell] = sig_csf
c12[cell] = sig_zero
c22[cell] = sig_csf
else:
sig_wm_matrix = np.zeros((3, 3))
np.fill_diagonal(sig_wm_matrix,
(longi_sigma[jj],
trans_sigma[jj],
trans_sigma[jj]))
S = np.matrix((np_v1[jj], np_v2[jj], np_v3[jj]))
# This is correct. S is eigen vectors are row vectors
sigma_mat = np.around(S.T * sig_wm_matrix * S, decimals=4)
c00[cell] = sigma_mat[0, 0]
c11[cell] = sigma_mat[1, 1]
c22[cell] = sigma_mat[2, 2]
c01[cell] = sigma_mat[0, 1]
c02[cell] = sigma_mat[0, 2]
c12[cell] = sigma_mat[1, 2]
if save:
c00_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d0.xml.gz"))
c01_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d1.xml.gz"))
c02_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d2.xml.gz"))
c11_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d3.xml.gz"))
c12_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d4.xml.gz"))
c22_file = d.File(os.path.join(params.anis_path,
"sigma_anis_d5.xml.gz"))
c00_file << c00
c01_file << c01
c02_file << c02
c11_file << c11
c12_file << c12
c22_file << c22
elif conductivity == 'inhomogeneous':
c = d.MeshFunction("double", mesh, 3)
fa_scaled_sigma = []
for jj in idx_all:
fa_scaled_sigma.append(scale_gm_wm(np_fa[jj], sig_brain, sig_wm))
print 'Did the scaling, now assigning vals'
for jj in idx_all:
cell = cells_all.next()
if jj in idx_grnd:
c[cell] = sig_ele
elif jj in idx_out:
c[cell] = sig_air
elif jj in idx_csf:
c[cell] = sig_csf
else:
c[cell] = fa_scaled_sigma[jj]
if save:
c00_file = d.File(os.path.join(params.inhom_path,
"sigma_inhom.xml.gz"))
c00_file << c
elif conductivity == 'homogeneous':
c = d.MeshFunction("double", mesh, 3)
for jj in idx_all:
cell = cells_all.next()
if jj in idx_grnd:
c[cell] = sig_ele
elif jj in idx_out:
c[cell] = sig_air
elif jj in idx_csf:
c[cell] = sig_csf
else:
c[cell] = sig_brain
if save:
c00_file = d.File(os.path.join(params.hom_path,
"sigma_hom.xml.gz"))
c00_file << c
if __name__ == '__main__':
if sys.argv[-1] == 'redo_all':
print('Preproduction phase')
print('Previous files will be overwritten')
compute_conductivity('anisotropic', save=True)
compute_conductivity('inhomogeneous', save=True)
compute_conductivity('homogeneous', save=True)
else:
print('What else is there to do?')
pass