Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. Anatomical atlases are important tools for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g., machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers.

The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications.

The atlas was constructed based on 3D magnetic resonance images (MRI) of 107 human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. T1w+T2w MRI images were used to segment the main structures of the head while angiography MRI was used to segment the main artery. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equation in the main arteries and their vascular territories.

Please cite this article in your work

Moura, Fernando S, Beraldo, Roberto G, Ferreira, Leonardo A, & Siltanen, Samuli. (2021). Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications. Physiological Measurement, 42(10). 105015. https://doi.org/10.1088/1361-6579/ac3218

@article{Moura_2021,
	author = {Fernando S Moura and Roberto G Beraldo and Leonardo A Ferreira and Samuli Siltanen},
	title = {Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications},
	journal = {Physiological Measurement},
	doi = {10.1088/1361-6579/ac3218},
	url = {https://doi.org/10.1088/1361-6579/ac3218},
	year = 2021,
	month = {oct},
	publisher = {{IOP} Publishing},
	volume = {42},
	number = {10},
	pages = {105015}
}

If you use the source code, please also cite

Moura, Fernando S, Beraldo, Roberto G, Ferreira, Leonardo A, & Siltanen, Samuli. (2021). openSAHE: Open Source Statistical Anatomical Atlas of the Human head for Electrophysiology Applications (source code) (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.5567086

@software{moura_fernando_s_2021_5567086,
  author       = {Moura, Fernando S and Beraldo, Roberto G and Ferreira, Leonardo A and Siltanen, Samuli},
  title        = {{openSAHE: Open Source Statistical Anatomical Atlas of the Human head for Electrophysiology Applications (source code)}},
  month        = oct,
  year         = 2021,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.5567086},
  url          = {https://doi.org/10.5281/zenodo.5567086}
}

If you use the precomputed atlases, please also cite

Moura, Fernando S, Beraldo, Roberto G, Ferreira, Leonardo A, & Siltanen, Samuli. (2021). openSAHE: Open Source Statistical Anatomical Atlas of the Human head for Electrophysiology Applications (precomputed atlases) (1.0) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.5559624

@dataset{moura_fernando_s_2021_5559624,
  author       = {Moura, Fernando S and Beraldo, Roberto G and Ferreira, Leonardo A and Siltanen, Samuli},
  title        = {{openSAHE: Open Source Statistical Anatomical Atlas  of the Human head for Electrophysiology Applications (precomputed atlases)}},
  month        = oct,
  year         = 2021,
  publisher    = {Zenodo},
  version      = {1.0},
  doi          = {10.5281/zenodo.5559624},
  url          = {https://doi.org/10.5281/zenodo.5559624}
}

Precomputed atlases used in the publication (see above) can be found at

Source code version used for the publication (see above) can be found at

This toolbox was developed in a linux machine. No tests were performed in other OSs.

The toolbox requires the following software

• Julia
• OpenBF
• Intel Python 3.8+ via conda or miniconda
• SingularityCE
• neurodocker image created with singularityCE (see instructions below)

Instructions for miniconda. Anaconda users can follow the same instructions

1. Miniconda install. Download install script

2. run the installer

sudo bash Miniconda3-latest-Linux-x86_64.sh

3. Initialize conda to add its initialization to your .bashrc

/opt/miniconda3/bin/conda init

4. Add Intel' python channel. (other option is to edit .condarc created in your home folder. see below)

conda config --add channels intel

5. (optional but recommended =) ) Avoid activating conda's (base) in all terminals. Open (or create) a file ~/.condarc and paste the following:

channels:        <-- channels to be considered priority channels are on top.
 - intel
 - conda-forge
 - defaults
auto_activate_base: false   <-- disable (base) auto load

6. Create a new python environment for the atlas

conda create -n atlasIntelPython_3 pyqt pyyaml matplotlib nipype nibabel meshio lxml pycairo psutil nptyping tornado simpleitk scikit-image pandas jill

7. If matplotlib shows the following error:

Bad key "text.kerning_factor" on line 4 in /home/samyak/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test_patch.mplstyle. You probably need to get an updated matplotlibrc file from https://github.com/matplotlib/matplotlib/blob/v3.1.3/matplotlibrc.template or from the matplotlib source distribution

Do the following steps ( source ) :

 1- Go to ~/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/
 2- open _classic_test_patch.mplstyle and comment out the line of text.kerning_factor:6

(Tested in Kubuntu 20.04)

1. install Jill using pip3.

pip3 install jill -U

This comand will add a few binaries inside ~/. local/bin/

2. Install julia

~/.local/bin/jill install

3. Install openBF. Run julia and type the following

julia> ]
pkg> add https://github.com/INSIGNEO/openBF

4. (optional) if you want to update openBF:

julia> ]
pkg> update openBF

5. (optional) if you want to test it

julia> ]
pkg> test openBF

6. Open the console and find julia's executable using which command

$which julia
path/to/juliaExe/julia

7. Open forwardProblem/tools.py and add the path to the executable to the juliaExe variable

juliaExe = 'path/to/juliaExe/julia'

8. Look for the folder where the package was installed. In linux machine it is located at

~/.julia/packages/openBF/XXXXX/

9. Open forwardProblem/tools.py and add this path to the openBFDir variable

openBFDir = '~/.julia/packages/openBF/XXXXX/'

As of today (Oct/2021) singularity does not have binaries for Kubuntu. The following instructions compiles singularity in your machine (kubuntu 20.04, Oct/2021). You can skip these steps if you can install singularity using other methods. installed versions: singularity-ce-3.8.3, go v. 1.17

1. dependencies

   sudo apt-get update && sudo apt-get install -y build-essential uuid-dev libgpgme-dev squashfs-tools libseccomp-dev wget pkg-config git cryptsetup-bin
   

2. install go

export VERSION=1.17 OS=linux ARCH=amd64
wget https://dl.google.com/go/go$VERSION.$OS-$ARCH.tar.gz
sudo tar -C /usr/local -xzvf go$VERSION.$OS-$ARCH.tar.gz
rm go$VERSION.$OS-$ARCH.tar.gz

3. setup GO

echo 'export GOPATH=${HOME}/go' >> ~/.bashrc
echo 'export PATH=/usr/local/go/bin:${PATH}:${GOPATH}/bin' >> ~/.bashrc
source ~/.bashrc

4. download singularity

export VERSION=3.8.3
wget https://github.com/sylabs/singularity/releases/download/v${VERSION}/singularity-ce-${VERSION}.tar.gz
tar -xzf singularity-ce-${VERSION}.tar.gz
cd singularity-ce-{$VERSION}

5. make and install

./mconfig --prefix=/opt/singularity
make -C ./builddir

6. create link

sudo ln -s /opt/singularity/bin/singularity /usr/local/bin/singularity

7. testing

singularity version
singularity exec library:https://alpine cat /etc/alpine-release

Use the config file in src/singularityImages/confSingularity_nipype_ANTS_SPM12_PYTHON.txt.

cd path/to/atlas/singularityImages
sudo singularity build nipype_ANTS_SPM12_SingularityImg_test.simg confSingularity_nipype_ANTS_SPM12_PYTHON.txt

This command will take time to prepare the image... have a cup of coffe =).

Contents of the image

• Base: Ubuntu 20.04
• MATLAB Runtime R2019b Update 3 glnxa64
• SPM12 version r7771 (method binaries)
• Python3.6
• Nipype

The project has 3 main python functions

./anatomicalAtlas/staticComponent/src/main_staticAtlas.py
./anatomicalAtlas/dynamicComponent/src/main_dynamicAtlas.py
./forwardProblem/EITmodel.py

The two first files creat the static and dynamic components of the atlas. The last is used to solve Electrical impedance tomography forward problem with the atlas.

This component is generated by calling

python3 main_staticAtlas.py

The user can edit 3 variables inside main_staticAtlas.py to specify the type of atlas

rFactList = [ 2 ]  # list with resampling factors. use integer values
propList = [ 'resistivity' ] # electrical property list. Valid values: 'resistivity', 'conductivity' , 'relPermittivity'
freqHzList = [ 1000 ]  # list of frequencies in Hz

• rFact controls the resampling factor used for the atlas. USE INTEGER VALUES
  • rFact=1: no resampling (highest resolution 1x1x1 mm voxels)
  • rFact=2: 2x downlampling. resamples, reducing by a factor of 2
  • ...
  • rFact=n: nx downlampling. resamples, reducing by a factor of n
• prop: electrical property to be considered. Valid values: 'resistivity', 'conductivity' , 'relPermittivity'
• freqHz: frequency in hertz.

If the user set more than one element per list, one atlas will be generated for each combination. (Imagine there are 3 nested for loops)

Input T1 and T2 MRI images files must be placed inside ./anatomicalAtlas/staticComponent/inputData folder. Intermediate files will be created inside ./anatomicalAtlas/staticComponent/outputData and the files of the atlas will be craeted inside ./anatomicalAtlas/staticComponent/atlas. These folders can be configured in . /anatomicalAtlas/staticComponent/src/utils.py

The output files inside the ./anatomicalAtlas/staticComponent/atlas folder are:

File name prefix The resulting files of the atlas have the prefix Atlas_[propType]_freq_XXX_RFact_YYY, where

• [propType] is the property set on propList input list
• XXX is the frequency set on freqHzList input list
• YYY is the resampling factor set on rFactList input list

1. HEAD GEOMETRY: Files related to the geometry of the entire head:

   • [PREFIX]_Mask.nii Binary image in NIfTI format with the mask of the entire head, that is, if the voxel lies within the head volume, then the voxels receives a True value. These voxels are refered as valid pixels
   • [PREFIX]_Mask.npy The same [PREFIX]_Mask.nii but in numpy format.
   • [PREFIX]_Mask_indices.csv CSV file with the indices of the valid voxels. Each line is in the form i,j,k where the voxel is located at mask[i,j,k]
   • [PREFIX]_Mask_coords.csv CSV file with the coords of the valid voxels. Each line is in the form x,y,z where the i-th line is associated with the voxel with indices at the same i-th line in [PREFIX]_Mask_indices.csv

• [PREFIX]_validPixels.npy vector with the indices of the valid pixels. The elements of this vectors are computed by collapsing the 3D mask image into one dimension using numpy.ndarray.flatten('C') (‘C’ stands for flattening in row-major (C-style) order.), followed by searching the elements with True value.

• [PREFIX]_vascularTerritories.nii Image in NIfTI format with the segments that define the vascular territories.

  Territory	region value	Territory	region value
  Left Anterior Cerebral Artery	1	Right Anterior Cerebral Artery	2
  Left Middle Cerebral Artery	3	Right Middle Cerebral Artery	4
  Left Posterior Cerebral Artery	5	Right Posterior Cerebral Artery	6
  Left Superior Cerebellar Artery	7	Right Superior Cerebellar Artery	8
  Stem	9
  Left External Carotid Artery	10	Right External Carotid Artery	11

• [PREFIX]_vascularTerritories.npy Equal to [PREFIX]_vascularTerritories.nii, but in numpy array and only for valid pixels.

2. BRAIN GEOMETRY: Files related to the geometry of the entire brain volume, defined as Gray matter + White Matter + CSF:

   • [PREFIX]_BRAIN_Mask.nii Equal to [PREFIX]_Mask.nii, but for GM+WM+CSF volume only.
   • [PREFIX]_BRAIN_Mask.npy Equal to [PREFIX]_Mask.npy, but for GM+WM+CSF volume only.
   • [PREFIX]_BRAIN_Mask_indices.csv Equal to [PREFIX]_Mask_indices.npy, but for GM+WM+CSF volume only.
   • [PREFIX]_BRAIN_Mask_coords.csv Equal to [PREFIX]_Mask_coords.npy, but for GM+WM+CSF volume only.

3. SCALP GEOMETRY: Files related to the geometry of the scalp volume.

   • [PREFIX]_BRAIN_Mask.nii Equal to [PREFIX]_Mask.nii, but for scalp volume only.
   • [PREFIX]_BRAIN_Mask.npy Equal to [PREFIX]_Mask.npy, but for scalp volume only.
   • [PREFIX]_BRAIN_Mask_indices.csv Equal to [PREFIX]_Mask_indices.npy, but for scalp volume only.
   • [PREFIX]_BRAIN_Mask_coords.csv Equal to [PREFIX]_Mask_coords.npy, but for scalp volume only.

4. ATLAS STATISTICS: Files related to the statistics of the atlas

   • [PREFIX]_Avg.nii Average image of the atlas in NIfTI format. The values are in international System of Units (SI)

   • [PREFIX]_Avg.npy Numpy array with the average. The values are in international System of Units (SI). Only valid pixels are stored. See valid pixels below.

   • [PREFIX]_CovK.npy Covariance matrix factor matrix K in numpy .npy array fromat. The values are in international System of Units (SI). Only valid pixels are stored. See valid pixels below.

     

This component is generated by calling

python3 main_dynamicAtlas.py

The user can edit 1 variable inside this file to specify the type of atlas

rFactList = [ 4 ]  # list with resampling factors. use integer values

• rFact controls the resampling factor used for the atlas. USE INTEGER VALUES

  • rFact=1: no resampling (highest resolution 1x1x1 mm voxels)
  • rFact=2: 2x downlampling. resamples, reducing by a factor of 2
  • ...
  • rFact=n: nx downlampling. resamples, reducing by a factor of n

  Obs: the user does not specify frequency and property type here because the dynamic atlas is computed in a different way. The type and frequency is specified in another moment.

Input Angiographic MRI images files must be placed inside ./anatomicalAtlas/dynamicComponent/inputData folder. Intermediate files will be created inside ./anatomicalAtlas/dynamicComponent/outputData and the files of the atlas will be craeted inside ./anatomicalAtlas/dynamicComponent/atlas. These folders can be configured in . /anatomicalAtlas/dynamicComponent/src/utils.py

The resulting files of the atlas have the prefix Atlas_normalized_Rfactor_YYY, where

• YYY is the resampling factor set on rFactList input list

The output files inside the ./anatomicalAtlas/dynamicComponent/atlas folder are:

1. HEAD GEOMETRY: Files related to the geometry of the entire head:

   • [PREFIX]_Mask.nii Same of the static component.
   • [PREFIX]_Mask.npy Same of the static component.
   • [PREFIX]_Mask_indices.csv Same of the static component.
   • [PREFIX]_Mask_coords_aligned.csv Same of the static component.

• [PREFIX]_validPixels.npy Same of the static component.

2. BLOOD GEOMETRY: Files related to the geometry of the arterial tree:

   • [PREFIX]_BLOOD_Mask.nii Equal to [PREFIX]_Mask.nii, but for arterial tree volume only.
   • [PREFIX]_BLOOD_Mask.npy Equal to [PREFIX]_Mask.npy, but for arterial tree volume only.
   • [PREFIX]_BLOOD_Mask_indices.csv Equal to [PREFIX]_Mask_indices.npy, but for arterial tree volume only.
   • [PREFIX]_BLOOD_Mask_coords.csv Equal to [PREFIX]_Mask_coords.npy, but for arterial tree volume only.

One example of usage is provided in the forwardProblem folder. It can be called by:

python3 EITmodel.py -i path/to/configurationFile.conf

where some configuration files are provided in the ./forwardProblem/inputFiles directory. In this same directory there is a zip file with the FEM meshes that must be uncompressed.

The configuration file specifies the solver. Description of the fields are presented in the file.

• The segment of the configuration file associated with the atlas is EITmodel>AnatomicalAtlas
• Frequency of the atlas is configure in the section EITmodel>current>frequency_Hz
• Segment associated with blood flow simulation is EITmodel>AnatomicalAtlas>openBF
• Segment associated with Visser model is EITmodel>AnatomicalAtlas>visserModel
• Segment associated with the forward problem is EITmodel>forwardProblem
• Segment associated with the FEM mesh is EITmodel>FEMmodel