RE: [EXT] Re: Computing the linear elastic strain energy

[Lesage,Anne Cecile J]

Dear Konstantinos

 

The problem with patient specific surgery modeling is that we ignore a lot of the surgery scenario

One way to model it with FEM is to precompute an atlas of organ deformation with a variety of surgery scenario parameter (here direction of gravity, loss of brain buoyancy by csf drainage, shrinkage due to drug,

swelling due to edema, tumor resection, etc …) That is about 1000 simulations

 

Then the idea is to match intraoperative data, the surgeons measure a ground truth displacement on a few brain surface points

The idea is to minimize function equation 7 in attached pdf:

the first term is the least square between the ground truth displacement and the simulated one see equation

the second term use the elastic strain energy on fem points pondered by the distance to the ground truth measurement points

Finally we want to get the optimal alpha pondering vector to match the surgery measurement

 

Ideally I would like my python script to output after poroelastic simulation converge

The simulated displacements on the few measurement points (15)

The pondered energy term

So that I can assemble the function to minimize for the whole atlas

 

Thank you

Regards

Anne-Cecile

 

 

From: Konstantinos Poulios <logari81@googlemail.com>
Sent: Tuesday, January 25, 2022 2:40 AM
To: Lesage,Anne Cecile J <AJLesage@mdanderson.org>
Cc: getfem-users@nongnu.org
Subject: [EXT] Re: Computing the linear elastic strain energy

 

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Dear Anne-Cecile

 

The elastic strain energy density (is a scalar) at each node is easy to calculate. However, I have to ask you what you need this quantity for. Your reference suggests calculating this quantity on nodes which is probably not the best solution. If you calculate the strain energy density at a node between different elements, you get different results depending on which element you are evaluating the common node from. Then some averaging is required to get a value somewhere between all neighboring elements. Normally we evaluate strain energy densities at integration points. If you tell us what you need this result for I can maybe help with a better solution.

 

Best regards

K.

 

On Mon, Jan 24, 2022 at 9:09 PM Lesage,Anne Cecile J <AJLesage@mdanderson.org> wrote:

Dear all

 

I need to output tat the end of my poroelastic simulation the linear elastic strain energy matrix at each node of my mesh

See attached formula

What is an optimal way to compute it from the displacement u?

Epsilon i = 0.5 (grad u + grad ut) right?

And S here is the stress-strain law for isotropic materials?

 

Thank you

Anne-Cecile

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Optimize_disp_precomputed atlas.pdf
Description: Optimize_disp_precomputed atlas.pdf