Laplacian on Cortical Mesh

[xelgzh]

Hi Stuart,

I wanted to use your code to solve the Helmholtz equation on a cortical mesh. I've downloaded your BrainNetworkModels but haven't figured out how to implement the simulation. Specifically, I would like to know

1/ How to load and display the default cortex the Cortex_reg13.mat (I don't really need the connectivity data)

2/ How to run the scripts related to the Laplacian such that I can solve the Helmholtz equation on this surface.

Thanks!

[stuart-knock]

Hey,

I'm not checking gitHub or my mail that regularly at the moment. In case
you
haven't already figured this stuff out by yourself, I've added a few
pointers
for what's available below. While the Matlab code and TVB include elements
that will be useful for you, the problem you want to solve is not what this
code was written for, so won't provide a complete solution -- more details
below.

For Matlab, the first thing to note is that I haven't properly checked the
surface stuff recently (since publishing on GitHub), the surface stuff is
built around matlab's TriRep object which isn't supported by Octave (I don't
currently have access to matlab). That being said, last time I checked it
worked...

All the Matlab functions have basic usage instructions in the header, as
well
as comments throughout the code. For displaying the mesh surface, in the
PlottingTools directory:

SurfaceMesh() -- visualises the whole surface
PlotLocalSurface() -- visualise a small piece of the mesh surface.

and for basic surface information there is a function in the Surfaces
directory:

GetSurfaceSummaryInfo() -- which extract info such as number of vertices,
edge-lengths, etc...

For the discrete approximation of the Laplace-Beltrami operator (2nd order
spatial derivative operator), you want the function called MeshLaplacian()
in the Surfaces directory. The biggest short coming with the Matlab version
is that I never implemented a geodesic distance algorithm (I moved over to
Python when I reached this point). This function just uses mesh distance,
which isn't too bad a first approximation when using a fairly well
regularise
mesh, however I wouldn't consider it publication quality -- that is, for
what
you're doing it would be important to use geodesic rather than mesh
distance.
TVB includes a geodesic distance algorithm which is accessible via methods
on
the surface objects. As the surface in the Matlab and in TVB is the same, a
short cut would be to use TVB/Python to get geodesic distances and then
calculate the approximation of the Laplace-Beltrami operator using the
Matlab
code.

As far as actual algorithms for solving the Helmholtz equation on the
surface,
there isn't anything implemented for this purely spatial type of problem.
All
of the simulation code is about dynamic evolution on the surface (ie,
temporal
integration), and quite specifically about the inclusion of delays in
this...

For TVB/python, take a look at the "Getting To Know Your Mesh Surface"
tutorial:

https://github.com/the-virtual-brain/scientific_library/wiki/Tutorials

Unless someone has finalised it since I last looked, it is only partially
written but it should get you started looking at the mesh and it's
properties,
which can be accessed via a method on the surface object.
The surface visualisations make use of Mayavi, via the functions such as
plot_surface() found in tvb/simulator/plot/tools.py

While I have done a basic port of the Matlab MeshLaplacian() function to
python, so far it's not publicly available anywhere as it hasn't been
properly
tested... I do plan to get around to this, though it may be a while before
I do.

Best,
Stuart.

On 26 November 2013 13:31, xcavier notifications@github.com wrote:

Hi Stuart,

I wanted to use your code to solve the Helmholtz equation on a cortical
mesh. I've downloaded your BrainNetworkModels but haven't figured out how
to implement the simulation. Specifically, I would like to know

1/ How to load and display the default cortex the Cortex_reg13.mat (I
don't really need the connectivity data)

2/ How to run the scripts related to the Laplacian such that I can solve
the Helmholtz equation on this surface.

Thanks!

—
Reply to this email directly or view it on GitHubhttps://github.com//issues/1
.

[xelgzh]

Thanks for the reply. I've been playing around with the code and surface and it seems things are still working! Though there was an issue with the anisotropic cpp files in compile_mex. I am however wondering if its possible to split the default cortex into two; more specifically is it possible to work the two hemispheres separately?