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

[Johannes]

Dear Eben,

please observe that an isotropic conductivity does NOT correspond to a
tensor with the same value for every entry as you assume (COND = repmat(
cond, [1,6] )), but to a diagonal tensor (xx=yy=zz=COND, all other entries
zero), i.e., something like COND = [repmat( cond, [1,3]
),zeros(length(cond),3)] should be correct.

Best,
    Johannes

Am Mo., 8. Juli 2019 um 04:31 Uhr schrieb eben Andronicus <
ebenandronicus at gmail.com>:

> 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
>
>
>
>
> _______________________________________________
> fieldtrip mailing list
> https://mailman.science.ru.nl/mailman/listinfo/fieldtrip
> https://doi.org/10.1371/journal.pcbi.1002202
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.science.ru.nl/pipermail/fieldtrip/attachments/20190708/7101b476/attachment-0002.html>
-------------- next part --------------
_______________________________________________
fieldtrip mailing list
https://mailman.science.ru.nl/mailman/listinfo/fieldtrip
https://doi.org/10.1371/journal.pcbi.1002202