Here we explore the different methods of refining the mesh that are available to the user, and describe use cases for each. For simplicity we will be using a single layer mesh.
Starting with an initial unrefined head mesh using Params_0.txt. All refinements are disabled by the setting the relevant flags to 0. The parameter cell_coarse_size_mm determines the baseline element size. The electrode file must be included even if the electrodes are not refined, as it required for the output mesh files.
facet_angle_deg = 30.000
facet_distance_mm = 2.000
cell_radius_edge_ratio = 3.000
cell_coarse_size_mm = 5.000We have disabled optimisations for speed, but it is recommended to run the MESHER again with them turned on when you have found the settings you are happy with to smooth the transitions between element sizes.
electrode_refinement = 0
depth_refinement = 0
planar_refinement = 0
cuboid_refinement = 0
sphere_refinement = 0Which can then be called with the following:
../../bin/mesher -i input.inr -e Elecs.txt -p Params_0.txt -o 0_InitialProduces the following 25k element mesh with uniform element size:
Typically a higher mesh density is required at the electrodes due to the higher field gradients and increased sensitivity. This is achieved by increasing the sizing field value in a sphere around each electrode centre. The centres are specified in the Elecs.txt file, and the following options must be set in the parameter file:
electrode_refinement = 1
electrode_radius_mm = 5.000
cell_size_electrodes_mm = 2.000The MESHER can then be called, and the and the denser regions are clearly visible in the output mesh.
../../bin/mesher -i input.inr -e Elecs.txt -p Params_1.txt -o 1_Elecs
Prior to refinement, the electrode coordinates specified in Elecs.txt are scaled by the VX VY VZ parameters specified in the .inr file to obtain the final positions in mm. Therefore, either the electrode positions must be determined either in the .inr coordinate space, like the unit cube or brain examples, or they should be scaled prior to saving to the text file, as in the neonatal head mesh example. NOTE The output Mesh is in m, so electrode positions determined from this mesh should be converted to mm and scaled by 1/VX etc.
As the sensitivity decreases with distance from the electrodes, less elements are required towards the centre of the volume. Therefore, as outlined a methods paper it is possible to specify a linear decrease from the surface to the centre. This is particularly useful in applications like the brain or thorax where the electrodes are limited to the outside surface, and are a significant distance from the centre of the mesh.
The following parameters create a linear gradient from 5mm element size in the centre of the mesh to 2mm at the boundary.
depth_refinement = 1
elements_with_fine_sizing_field_percentage = 100.000
cell_fine_size_mm = 2.000
cell_coarse_size_mm = 5.000../../bin/mesher -i input.inr -e Elecs.txt -p Params_2.txt -o 2_Depth
The gradient is clearly visible inside the mesh and the resulting sizing field can also be plotted using figures\Sizing_fields.m, to better visualise the effects the different parameters. The gradient can also be overwritten at the centre to a fixed value of cell_coarse_size_mm if a less gradual gradient is required. Setting elements_with_fine_sizing_field_percentage = 50.000 creates a sphere of fixed element size at the centre.
A separate sphere anywhere in the mesh, separate from the electrodes, can be defined through the following parameters:
sphere_refinement = 1
sphere_radius = 20.000
sphere_centre_x = 60.00
sphere_centre_y = 50.00
sphere_centre_z = 60.00
sphere_cell_size = 2.000All inputs are specified in mm, and are in the coordinates of the final mesh i.e. not scaled by vx,vy,vz. Defining the element size within a volume like this is useful either to 1) increase the mesh density around internal electrodes like this study, or 2) to explicitly decrease mesh density in the centre similar to depth refinement.
../../bin/mesher -i input.inr -e Elecs.txt -p Params_3.txt -o 3_Sphere
A cuboid of constant element size can also be defined in the same manner as the sphere. All inputs are in mm with respect to the final mesh (not scaled by vx,vy,vz). "Extent" is the distance along one axis from the centre to the edge, so the cube in this case has WxLxH of 60x20x20.
cuboid_refinement = 1
cuboid_x_extent = 30.000
cuboid_y_extent = 10.000
cuboid_z_extent = 10.000
cuboid_centre_x = 60.00
cuboid_centre_y = 50.200
cuboid_centre_z = 60.900
cuboid_cell_size = 2../../bin/mesher -i input.inr -e Elecs.txt -p Params_4.txt -o 4_Cuboid
Note, it is not recommended to use planar and depth refinement at the same time.
Planar refinement creates a gradient along a single dimension specified by planar_direction_xyz. This is useful in similar applications to the depth refinement, except the electrodes are only on a single surface of the mesh, such as the rat brain. The sizing field decreases from cell_fine_size_mm at the plane specified by height to cell_coarse_size_mm at a distance xdim away from this plane. It is possible to specify a region that is fixed to cell_fine_size_mm through the elements_with_fine_sizing_field_percentage parameter, after which the gradient starts. For example the parameters below creates a gradient from 2 to 5 mm along the z axis, with 10% of the distance fixed at 2mm.
planar_refinement = 1
cell_coarse_size_mm = 5.000
cell_fine_size_mm = 2.000
elements_with_fine_sizing_field_percentage = 10.000
height = 0.000
planar_direction_xyz = 3.000 // Dimension x = 1, y = 2, z = 3../../bin/mesher -i input.inr -e Elecs.txt -p Params_5.txt -o 5_PlanarThe gradient is clear within the mesh, and using figures/Sizing_fields.m the sizing field itself can be visualised:
The plane is specified at height = 0, with 10 % of the mesh height fixed at cell_fine_size_mm before increasing linearly towards cell_coarse_size_mm. The gradient is symmetric about the plane specified by height so this value must be chosen carefully to avoid undesirable results. For example to create a gradient in the opposite directions, the height should be specified at the top of the mesh:
