EFMouse: 1x1 montage
EFMouse is a Matlab tool for electric field modelling in the mouse brain.
This notebook reproduces results for the 1x1 montage in:
Sanchez-Romero R., Akyuz, S., & Krekelberg, B. (2024). EFMouse: a Matlab toolbox to model electric fields in the mouse brain. bioRxiv. https://doi.org/10.1101/2024.07.25.605227
The notebook is also an introductory tutorial to simulate other montages.
(Developed by Ruben Sanchez-Romero and Bart Krekelberg,
Rutgers-Newark, Center for Molecular and Behavioral Neuroscience,
for support open an issue in https://github.com/klabhub/EFMouse/issues)
Introduction
EFMouse combines several elements from previous work:
- Anatomical data from the Digimouse project.
- A refined finite element mesh of the Digimouse by Alekseichuk et al., (2019), Neuroimage.
- Matlab code and inspiration from the ROAST toolbox.
- The getDP finite element method (FEM) solver (v 3.2.0).
- The Allen mouse brain atlas.
Key new functionality includes:
- Positioning electrodes in arbitrary locations on the mouse body.
- Modeling craniotomies in the mouse skull.
- Analyzing the electric field in user-defined regions of interest
- Analyzing the electric field in brain regions defined in the Allen mouse atlas.
- A measure of relative focality of the electric field.
- A measure of direction homogeneity of the electric field.
For details see Sanchez-Romero et al., (2024) and EFMouse.m Matlab code.
Typical workflow
The typical workflow to generate a model consists of several stages
- stage 0 : Initialize.
- stage 1: Define elecrodes and (optionally) a craniotomy.
- stage 2: Impose boundary conditions.
- stage 3: Export files for the FEM solver getDP.
- stage 4: Run the FEM solver.
- stage 5: Map the results to the Allen mouse atlas.
Stage 0: Initialize
We start by setting up the basic parameters of the EFMouse object:
o = EFMouse; % Create a default empty object of the class EFMouse
o.dir = '/Users/rubensanchez/desktop/EFMouse/1x1Montage'; % Results and the object (1x1.mat) will be saved here.
o.ID = '1x1'; % A name/tag for this simulation.
o.log = true; % Create a log file.
Note: The log file is created but doesn't update when running a simulation from a notebook (like here). It will properly update when running EFMouse directly from the Matlab command line.
initialize() creates the folder to store the results. With overwrite=true, anything in this folder will be deleted.
o.initialize(overwrite=true);
The initialized EFMouse object contains the default mouse mesh (without stimulation electrodes). Let's visualize it.
The mesh is pretty dense, so it will look like a black blob. The olfactory bulbs are visible on the top. In a regular figure window, you can use the Matlab figure tools to rotate or zoom. (You can also adapt the plotMesh() function in EFMouse.m to modifiy the figure directly.)
Stage 1: Create electrodes and a craniotomy
Now we define a 1x1 stimulation montage: 1 electrode on the anterior and 1 return electrode on the posterior targeting visual areas.
o.eTag = ["Anterior" "Posterior"];
% currents need to sum to 0. (In milliamps (mA) units.)
% center coordinate of the electrode position (in mesh space)
o.eCenter = [-3.56,29.5,5.45;
% radius of the electrodes (in mesh space units) (1 mesh unit ~ 1 mm)
o.eRadius = [0.71,0.67]
o = EF Mouse Model (label: 1x1) in directory /Users/rubensanchez/desktop/EFMouse/1x1Montage (stage=0).
Add a craniotomy:
% center coordinate of the craniotomy position (in mesh space)
o.cCenter = [-3.4236,27.1067,5]';
% radius of the creaniotomy (in mesh space units) (1 mesh unit ~ 1 mm)
To add these to the model, we run the pipeline to stage 1. With show=true, this also opens a figure for inspection of the mesh:
o.run(targetStage=1,show=true)
Compute stage 1 - computeMesh
EF Mouse Model (label: 1x1) in directory /Users/rubensanchez/desktop/EFMouse/1x1Montage (stage=0).
-Creating craniotomy-
Craniotomy: touching tissue:
gray: num elements = 6884
csf: num elements = 6083
bone: num elements = 8247
skin: num elements = 1551
Craniotomy only removes skin and bone.
-Creating 2 electrodes-
Electrode: Anterior: touching tissue:
skin: num elements = 39
Creating electrode Anterior in max touched tissue: skin.
Electrode: Posterior: touching tissue:
skin: num elements = 46
Creating electrode Posterior in max touched tissue: skin.
Stage 1 complete - 57.9925 seconds
This mesh now shows the electrodes in red and blue (return), for the craniotomy, skin removal is shown in green and skull removal shown in yellow.
Stage 2: Find the electrode boundaries and add to the mesh
In this stage, EFMouse searches for the edges of the electrodes as this is where the current flows into the model. The boundary conditions of the Laplace equation are set here.
o.run(targetStage=2)
Compute stage 2 - computeBoundary
Electrode Area
______________
Anterior 0.78309
Posterior 0.67532
Stage 2 complete - 64.5896 seconds
Stage 3: export the mesh and model
Up until this stage, all changes were internal to the Matlab object (saved in 1x1.mat), now we export files that the FEM solver getDP can read. The .msh file contains information on the mesh (all the nodes, elements, labels and boundaries), and the .pro file tells getDP which partial differential equations (PDE) model it needs to solve in this mesh.
o.run(targetStage=3)
Compute stage 3 - export data
----Starting saveMesh...29-Jan-2025 20:37:03
----saveMesh elapsed time: 32.8988 seconds
----Starting savePro...29-Jan-2025 20:37:36
----savePro elapsed time: 0.0752 seconds
Stage 3 complete - 54.5425 seconds
For troubleshooting, have a look at the .pro file in the project folder; it contains all the model specifications, including conductivity (in siemens per meter S/m) for the different tissues/elements.
type(file(o,"PRO"))
/*
.pro file created by EFMouse on 29-Jan-2025 20:37:36
ID: 1x1
Dir: /Users/rubensanchez/desktop/EFMouse/1x1Montage
*/
Group {
gray = Region[1];
csf = Region[2];
bone = Region[3];
skin = Region[4];
eye = Region[5];
craniotomy = Region[6];
skinremoved = Region[7];
Anterior = Region[8];
Posterior = Region[9];
boundaryAnterior = Region[10];
boundaryPosterior = Region[11];
DomainC = Region[{gray,csf,bone,skin,eye,craniotomy,skinremoved,Anterior,Posterior}];
AllDomain = Region[{gray,csf,bone,skin,eye,craniotomy,skinremoved,Anterior,Posterior,boundaryAnterior,boundaryPosterior}];
}
Function {
sigma[gray] = 0.275;
sigma[csf] = 1.654;
sigma[bone] = 0.01;
sigma[skin] = 0.465;
sigma[eye] = 0.5;
sigma[craniotomy] = 1.654;
sigma[skinremoved] = 2.5e-14;
sigma[Anterior] = 5.9e+07;
sigma[Posterior] = 5.9e+07;
du_dn1[] = 255.398816;
du_dn2[] = -296.157649;
}
Jacobian {
{ Name Vol ;
Case {
{ Region All ; Jacobian Vol ; }
}
}
{ Name Sur ;
Case {
{ Region All ; Jacobian Sur ; }
}
}
}
Integration {
{ Name GradGrad ;
Case { {Type Gauss ;
Case { { GeoElement Triangle ; NumberOfPoints 3 ; }
{ GeoElement Quadrangle ; NumberOfPoints 4 ; }
{ GeoElement Tetrahedron ; NumberOfPoints 4 ; }
{ GeoElement Hexahedron ; NumberOfPoints 6 ; }
{ GeoElement Prism ; NumberOfPoints 9 ; } }
}
}
}
}
FunctionSpace {
{ Name Hgrad_v_Ele; Type Form0;
BasisFunction {
// v = v s , for all nodes
// n n
{ Name sn; NameOfCoef vn; Function BF_Node;
Support AllDomain; Entity NodesOf[ All ]; }
}
}
}
Formulation {
{ Name Electrostatics_v; Type FemEquation;
Quantity {
{ Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
}
Equation {
Galerkin { [ sigma[] * Dof{d v} , {d v} ]; In DomainC;
Jacobian Vol; Integration GradGrad; }
Galerkin{ [ -du_dn1[], {v} ]; In boundaryAnterior ; Jacobian Sur; Integration GradGrad;}
Galerkin{ [ -du_dn2[], {v} ]; In boundaryPosterior ; Jacobian Sur; Integration GradGrad;}
}
}
}
Resolution {
{ Name EleSta_v;
System {
{ Name Sys_Ele; NameOfFormulation Electrostatics_v; }
}
Operation {
Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
}
}
}
PostProcessing {
{ Name EleSta_v; NameOfFormulation Electrostatics_v;
Quantity {
{ Name v;
Value {
Local { [ {v} ]; In AllDomain; Jacobian Vol; }
}
}
{ Name e;
Value {
Local { [ -{d v} ]; In AllDomain; Jacobian Vol; }
}
}
}
}
}
PostOperation {
{ Name Map; NameOfPostProcessing EleSta_v;
Operation {
Print [ v, OnElementsOf DomainC, File "/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_v.pos", Format NodeTable ];
Print [ e, OnElementsOf DomainC, Smoothing, File "/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_e.pos", Format NodeTable ];
}
}
}
This file can be opened in the getDP gui to run it manually, but stage 4 runs it for you.
Stage 4: run getDP
It will take getDP between 15 and 30 minutes to compute the solutions of the Laplace equation (on 2024 Mac or Windows hardware). The results are saved in _e.pos and _v.pos files (in getDP format). In the object the results are saved as .field and .voltage.
o.run(targetStage=4,show=false);
Compute stage 4 - computeField
Info : Running '/Users/rubensanchez/Desktop/roast/EFmouse_class/EFMouse/lib/getdp-3.2.0/bin/getdpMac /Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1.pro -solve EleSta_v -msh /Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1.msh -pos Map' [GetDP 3.2.0, 1 node, max. 1 thread]
Info : Started (Wed Jan 29 20:48:20 2025, Wall = 0.056675s, CPU = 0.050258s, Mem = 5.33594Mb)
Info : Initializing Gmsh
[1m[31mError : Unknown number option 'General.NativeFileChooser'[0m
Info : Loading problem definition '/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1.pro'
Info : Selected Resolution 'EleSta_v'
Info : Loading Geometric data '/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1.msh'
Info : System 'Sys_Ele' : Real
[34mP r e - P r o c e s s i n g . . .[0m
Info : Treatment Formulation 'Electrostatics_v'
0% : Pre-processing
10% : Pre-processing
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Info : System 1/1: 1027341 Dofs
Info : (Wall = 41.8548s, CPU = 34.0105s, Mem = 683.652Mb)
[34mE n d P r e - P r o c e s s i n g[0m
[34mP r o c e s s i n g . . .[0m
Info : Generate[Sys_Ele]
0% : Processing (Generate)
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Info : Solve[Sys_Ele]
Info : N: 1027341 - preonly lu mumps
Info : SaveSolution[Sys_Ele]
Info : (Wall = 1701.34s, CPU = 2046.29s, Mem = 7523.01Mb)
[34mE n d P r o c e s s i n g[0m
[34mP o s t - P r o c e s s i n g . . .[0m
Info : NameOfSystem not set in PostProcessing: selected 'Sys_Ele'
Info : Selected PostProcessing 'EleSta_v'
Info : Selected Mesh '/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1.msh'
Info : PostOperation 1/2
> '/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_v.pos'
0% : Post-processing (Compute)
10% : Post-processing (Compute)
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Info : PostOperation 2/2
> '/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_e.pos'
0% : Post-processing (Generate)
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90% : Post-processing (Generate)
0% : Post-processing (Compute)
Info : Smoothing (phase 1)
Info : Smoothing (phase 2)
Info : (Wall = 1985.36s, CPU = 2243.16s, Mem = 7523.01Mb)
[34mE n d P o s t - P r o c e s s i n g[0m
Info : Stopped (Wed Jan 29 21:21:26 2025, Wall = 1986.86s, CPU = 2243.59s, Mem = 7523.01Mb)
Stage 4 complete - 2057.4535 seconds
Use the plotEf() function to visualize the electric field in the X direction, and then the electric field magnitude.
plotEf(o,type='eX',percentile=98, tissue='gray');
----Starting plotEf...29-Jan-2025 22:31:45
----plotEf elapsed time: 5.4188 seconds
plotEf(o,type='eMag',percentile=98,tissue='gray')
----Starting plotEf...29-Jan-2025 22:31:50
----plotEf elapsed time: 2.4874 seconds
Tissue Based Analysis
In general, we focus on the brain, but if necessary, we can compute electric field estimates for the rest of the mouse body for a full characterization of the anatomical effects of the electrical stimulation protocol. See Sanchez-Romero et al., (2024) for a full description of the electric field metrics.
analyzeTissue(o)
----Starting analyzeTissue...29-Jan-2025 22:32:05
Electric field summary statistics for gray tissue
mean median std min max
_______ ________ ______ _______ ______
eX 0.79299 0.67688 1.6794 -11.718 26.464
eY -1.6743 -1.3555 2.2744 -31.965 19.517
eZ -0.7507 -0.39775 2.1183 -40.614 12.768
eMag 2.8329 1.9901 2.907 0.16347 46.878
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.7158, for ef_norm_mean: (0.311 -0.591 -0.258)
Electric field summary statistics for csf tissue
mean median std min max
_______ ________ ______ _______ ______
eX 1.0715 0.63196 8.8472 -146.11 156.66
eY -3.5474 -1.4987 6.7035 -116.41 23.956
eZ -2.1805 -0.43898 15.95 -320.87 220.04
eMag 8.656 3.5688 17.922 0.16347 375.57
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.5590, for ef_norm_mean: (0.233 -0.437 -0.260)
Electric field summary statistics for bone tissue
mean median std min max
________ ___________ ______ __________ ______
eX 0.38235 -8.4878e-05 7.4283 -246.54 228.78
eY -1.7159 -0.00010046 6.5135 -291.83 53.14
eZ -0.81987 0.00018048 13.909 -469.68 363.73
eMag 4.5893 0.32701 16.546 3.8421e-07 549.63
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.2119, for ef_norm_mean: (-0.119 -0.099 0.144)
Electric field summary statistics for skin tissue
mean median std min max
________ ___________ ______ __________ ______
eX 0.070676 -0.00014692 3.4757 -164.39 204.77
eY -0.35876 -1.6779e-05 3.5846 -291.83 135.88
eZ -0.11102 0.00051892 5.7609 -351.37 268.62
eMag 1.1142 0.027176 7.5513 1.8066e-07 393.33
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.3722, for ef_norm_mean: (-0.237 -0.076 0.277)
Electric field summary statistics for eye tissue
mean median std min max
_______ ________ ________ ________ ________
eX 0.32421 0.31987 0.098822 0.11803 0.70714
eY 0.18109 -0.32307 0.63697 -0.53708 1.4884
eZ -1.065 -0.42903 0.78516 -2.723 -0.24954
eMag 1.3183 0.73095 0.7522 0.51214 3.0326
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.8006, for ef_norm_mean: (0.345 -0.142 -0.708)
Electric field summary statistics for craniotomy tissue
mean median std min max
________ _______ ______ _______ ______
eX 2.1583 2.4491 15.216 -90.646 106.97
eY -20.948 -16.524 21.146 -243.81 21.396
eZ 0.036908 0.37678 27.394 -185.12 235.45
eMag 27.737 18.292 33.214 5.6737 330.1
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.8593, for ef_norm_mean: (0.107 -0.851 0.057)
Electric field summary statistics for skinremoved tissue
mean median std min max
_______ _______ ______ _______ ______
eX -1.1064 0.85367 33.668 -110.51 118.73
eY -50.387 -40.131 36 -227 -10.55
eZ 9.5068 5.1237 62.022 -211.26 246.39
eMag 75.225 59.257 56.943 14.853 330.1
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.7491, for ef_norm_mean: (-0.006 -0.737 0.132)
ROI Analysis
Now that we have the field estimates for each node in the mesh, we can do an ROI based analysis. For instance, a box ROI.
For the relative focality the reference area is the rest of the gray tissue.
roi.dim = [[-4.0087 -2.56];[26.4022 27.64];[3 4]]';% Define the limits of the box ROI (x,y,z)(in mesh space units) (1 mesh unit ~ 1 mm)
summary = analyzeRoi(o,roi,plot=true,foc_percentile_max=99.9,foc_threshold=75); % Define values for relative focality metric.
----Starting analyzeRoi...29-Jan-2025 22:32:39
Electric field summary statistics for a box roi in gray
mean median std min max
_________ _______ ______ _______ _______
eX 2.5123 2.5692 1.1623 -1.4944 5.4232
eY -8.5358 -7.9802 3.063 -16.525 -2.7663
eZ -0.062983 0.44015 2.6286 -9.1839 4.856
eMag 9.4239 8.6681 2.8276 5.3249 18.619
[Relative focality ranges from 0 to 1]
Relative focality = 0.9880, with 161805 reference nodes (cutoff: eMag > 75.00% of the target area max (99.90th percentile))
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.9392, for ef_norm_mean: (0.296 -0.891 0.023)
% Rotate and zoom to view the (purple) box ROI underneath the craniotomy
For comparison, define an homologous box ROI but in the right hemisphere
roi_control.shape = 'box';
roi_control.dim = [[2.56 4.0087];[26.4022 27.64];[3 4]]';% Define the limits of the box ROI (in mesh space units)
summary = analyzeRoi(o,roi_control,plot=true,foc_percentile_max=99.9,foc_threshold=75);
----Starting analyzeRoi...29-Jan-2025 22:32:47
Electric field summary statistics for a box roi in gray
mean median std min max
________ ________ _______ ________ _______
eX 0.20141 0.27985 0.29016 -0.64429 0.7175
eY -1.6552 -1.6222 0.27954 -2.4277 -1.0444
eZ -0.15023 -0.15194 0.11007 -0.4589 0.17793
eMag 1.7029 1.6824 0.27753 1.1081 2.4321
[Relative focality ranges from 0 to 1]
Relative focality = 0.4278, with 161865 reference nodes (cutoff: eMag > 75.00% of the target area max (99.90th percentile))
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.9823, for ef_norm_mean: (0.111 -0.971 -0.095)
% Rotate and zoom to view the (purple) box ROI underneath the craniotomy
Stage 5: Volumetric Analysis
The mesh coordinates are not particularly intuitive, and you may want to estimate electric fields in specific brain areas (as defined in an atlas). EFMouse does this in reference to the Allen Mouse Brain Atlas.
To use this, we first have to map the mesh-based results to the Allen Atlas. This is Stage 5 of the pipeline. This stage first exports the mesh-based results to a volume (using linear interpolation) and then uses the FLIRT tool in FSL to transform this volume to the coordinates of the Allen Atlas. Note that the alignment between the Digimouse mesh and the Allen Atlas is not perfect because they are based on different imaging modalities (and different mouse strains). (See Sanchez-Romero et al., (2014), for more details.)
This will fail if FSL is not installed.
o.run(targetStage=5,startStage=5)
Compute stage 5 - computeVoxelSpace
----Starting computeVoxelSpace...29-Jan-2025 22:35:54
----Exporting to NIFTI volumes
---/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_efm.nii.gz created
---/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_efX.nii.gz created
---/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_efY.nii.gz created
---/Users/rubensanchez/desktop/EFMouse/1x1Montage/1x1_efZ.nii.gz created
----computeVoxelSpace elapsed time: 41.8426 seconds
Atlas Based Analysis
Once stage 5 has completed we can query electric fields based on a region that is defined in the Allen Atlas. For instance: 'Visual areas' for the left hemisphere.
For the relative focality the reference area is the rest of the Allen atlas "Isocortex".
T = analyzeAtlas(o,"Visual areas",hemisphere="left",foc_threshold=75,foc_percentile_max=99.9,foc_reference='Isocortex');
----Starting analyzeAtlas...29-Jan-2025 22:37:34
Area: Visual areas (1.0% of brain) , hemisphere left
mean median std min max
_______ _______ ______ _________ ______
eX 4.7816 3.8599 4.6812 -5.4848 23.523
eY -10.723 -10.354 5.2165 -28.129 3.3482
eZ -3.4174 -2.1581 5.6399 -31.189 10.11
eMag 13.909 12.969 6.1341 0.0061045 36.793
[Relative focality ranges from 0 to 1]
Relative focality = 0.9988, with 92410 reference voxels (cutoff: eMag > 75.00% of the target area max (99.90th percentile))
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.8764, for ef_norm_mean: (0.342 -0.787 -0.176)
----analyzeAtlas elapsed time: 3.2990 seconds
For comparison, we can query results for the right hemisphere, which is contra-lateral from the targeted area.
T = analyzeAtlas(o,"Visual areas",hemisphere="right",foc_threshold=75,foc_percentile_max=99.9,foc_reference='Isocortex');
----Starting analyzeAtlas...29-Jan-2025 22:37:37
Area: Visual areas (1.0% of brain) , hemisphere right
mean median std min max
__________ _________ _______ _________ _______
eX 0.51646 0.37269 0.48088 -0.60438 2.2759
eY -1.9512 -2.1449 0.83912 -3.5042 0
eZ -0.0027768 -0.063365 0.27453 -0.76167 0.81006
eMag 2.0683 2.2373 0.89994 0.0022396 3.5414
[Relative focality ranges from 0 to 1]
Relative focality = 0.5179, with 92457 reference voxels (cutoff: eMag > 75.00% of the target area max (99.90th percentile))
[Homogeneity ranges from 0 to 1]
Homogeneity = 0.9763, for ef_norm_mean: (0.241 -0.946 -0.002)
----analyzeAtlas elapsed time: 2.8087 seconds
Tips and Tricks
- The run function can be called with any targetStage from 0 to 5. Stages that have already been completed will not be run again, and all stages that need to be completed to reach the targetStage will be completed in turn.
- IMPORTANT: To continue working with a model from a previous Matlab session, you create an EFMouse object with the dir and ID input arguments to specify the folder with the (previously saved) results and the ID of the montage. For instance, to open the simulation from the tutorial and also know the stage:
o = EFMouse(dir='/Users/rubensanchez/desktop/EFMouse/1x1Montage',ID='1x1')