[FieldTrip] FEM (SimBio) stiffness matrix for isotropic and pseudo-anisotropic white matter

[eben Andronicus]

Hi there,

Following instructions posted earlier by Carsten Wolters,  Johannes
Vorwerk, Marios Antonakakis and others on this list, I have managed to get
my way to the calc_stiff_matrix_val function call. Verifying on my way
sanity of every step and results.

For the sake of curiosity, I have tried to input the regular conductivity
values (num_nodes × 1) and the tensor conductivity values for "xx yy zz xy
yz zx“ (num_nodes × 6) as suggested by Johannes, but I have cheated a bit,
and I have used the same conductivity value for every direction (COND =
repmat( cond, [1,6] ).

Now, I haven't expected to get the very same results (identical) for the
two inputs, but two very similar matrices would be a sane thing to expect
(disregarding noise related to floating point rounding and multiplication
by some scaling factor, as I haven't normalized the COND magnitude and only
"repmatted" it). The resulting stiffness matrices are highly correlated but
not as high as I have expected (the correlation is about 0.9434. However, I
have expected something closer to 0.9999).

Can anybody explain what is happening here or point me to math/papers that
can provide any insight?

Below is the code snippet. Thank you in advance for any help or
suggestions...


[diinsy,cols,sysmat] = calc_stiff_matrix_val(node,elem,cond,mele);
npnt = double(npnt);
diinsy = double(diinsy);
cols = double(cols);
rows = sb_sparse_to_mat(diinsy);
stiff = sparse(rows,cols,sysmat,npnt,npnt,length(sysmat));

COND = repmat( cond, [1,6] );
[diinsy,cols,sysmat] = calc_stiff_matrix_val(node,elem,COND,mele);
npnt = double(npnt);
diinsy = double(diinsy);
cols = double(cols);
rows = sb_sparse_to_mat(diinsy);
STIFF = sparse(rows,cols,sysmat,npnt,npnt,length(sysmat));

<the values are returned to the variables below>

spar_04 = sphe_simbio_vol_headmodel_04_final.stiff(1:20000,1:20000);
spar_05 = sphe_simbio_vol_headmodel_05_isotr.STIFF(1:20000,1:20000);

full_04 = full(spar_04);
full_05 = full(spar_05);

coeff = corrcoef(full_04(:),full_05(:));
coeff


Best
Eben
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https://doi.org/10.1371/journal.pcbi.1002202