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mass-spring model for soft tissue deformation

hello

I am new to mechanical modeling of tissue. So, please forgive me if I say something obviously wrong.

what I want to do is to compute an "internal pressure" distribution for soft-tissue under compression, specifically, breast under mammography compression. I wrote a simple mass-spring program to comptue the deformation of a breast by supplying Hooke coefficients for each spring. With one step compression, the program comptue the steady-state node positions by solving the force-equilibrium equation at each node with an Euler's method.

now, from the steady-state, how can I extract such an "internal pressure"? I can compute the summation of all force amplitudes at each node, or the total force amplitudes devided by spring number connected to this node (i.e. averaged force per spring). But I can not do vector summation, because they are all zeros for internal nodes. How would the (averaged) total force amplitudes correlate to the internal pressure?

a friend suggested me to compute a stress for each spring, and display the distribution of these stresses (z-axis component). But I found this is spring-connection-topology dependent, the plot looks funny and does not make sense.

I am wondering if anyone can give me some suggestions to compute this distribution .

thanks

Qianqian

Reply to
FangQ
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If someone else is paying for your time or if you're more interested in answers than inventing and exploring methods, use a proven 3D stress program.

If you're interested in inventing and exploring models and methods, then apply this first hack to your spring network:

  1. Strike a plane intersection across your model.
  2. Compute locations where your springs intersect the plane.
  3. To associate an area with each spring (and as a hack to resolve your "spring-connection-topology dependence", construct a Voronoi diagram on the section plane using the spring intersections, assigning an area to each polygon.
  4. Based on spring force and polygon area, compute normal and shear stress on the plane at the spring intersections.

An examination of the results will guide your remodeling. If "the plot looks funny and does not make sense," then add more springs or move springs around. You have to look carefully at the materials properties to decide the relative importance of shear and membrane tension. Be gentle if you run tests.

Hope this helps, Fred Klingener

Reply to
Fred Klingener

FangQ wrote: [snip]

Ok, it's unlikely that this will be valid. Soft tissue does not behave that way. A large part of the behaviour of tissue will involve changes in blood vessels, and this will not be according to Hooke's law. The tissue will tend to deform by letting fluid flow in/out. And this will have a big time dependancy. To get anywhere near getting this correct, you'd need to have quite a bit of experimental data.

Also, to solve the category of problem you are trying to set up, you need something better than a bunch of springs. Even neglecting the time dep. parts. Tissue has complicated 3-D behaviour. You will need to get such things as how the tissue resists shearing. To get at such stuff you are going to have to do some continuum mechanics. You will need to study stress/strain relations. And again, to get it even close to right you will need some experimental data.

Consider: tissue isn't like a fluid. If you push on it here, the tissue deflects to some extent, but it isn't simple compression. There is some resistance based on the tissue not wanting to be out of place, one part with another. There is also resistance to compression.

For example: You have got a topology dependence. That indicates that you have got some problems with how you've set things up. You probably are not solving the stress/strain relationship for the material correctly. This is a complicated matter if you want to take into account such things as tissue resisting sideways squashing.

You could start with _Schaum's Outline of Continuum Mechanics_ which you can get at

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for about $11. But IIRC, that is so introductory as to be unlikely to be enough. You will probably want some more advanced text after that, and possibly some numerical methods texts.

If you are serious about this effort, you should be doing this with the help of a professor. It really isn't hobby level stuff. I'd say this is about right for an honours project effort, say finishing a BSc in some science or engineering. Socks

Reply to
Puppet_Sock

A quick search of 'model soft tissue deformation breat' returned 5 results on PubMed:

1: Liu Y, Sun LZ, Wang G. Related Articles, Links Abstract Tomography-based 3-D anisotropic elastography using boundary measurements. IEEE Trans Med Imaging. 2005 Oct;24(10):1323-33. PMID: 16229418 [PubMed - indexed for MEDLINE] 2: Samani A, Plewes D. Related Articles, Links Abstract A method to measure the hyperelastic parameters of ex vivo breast tissue samples. Phys Med Biol. 2004 Sep 21;49(18):4395-405. PMID: 15509073 [PubMed - indexed for MEDLINE] 3: Dehghani H, Doyley MM, Pogue BW, Jiang S, Geng J, Paulsen KD. Related Articles, Links Abstract Breast deformation modelling for image reconstruction in near infrared optical tomography. Phys Med Biol. 2004 Apr 7;49(7):1131-45. PMID: 15128194 [PubMed - indexed for MEDLINE] 4: Han L, Noble JA, Burcher M. Related Articles, Links Abstract A novel ultrasound indentation system for measuring biomechanical properties of in vivo soft tissue. Ultrasound Med Biol. 2003 Jun;29(6):813-23. PMID: 12837497 [PubMed - indexed for MEDLINE] 5: Ruiter NV, Muller TO, Stotzka R, Kaiser WA. Related Articles, Links Abstract Elastic registration of x-ray mammograms and three-dimensional magnetic resonance imaging data. J Digit Imaging. 2001 Jun;14(2 Suppl 1):52-5. PMID: 11442120 [PubMed - indexed for MEDLINE]

Additionally, there's entire Journals that cover this topic: J. Biomechanics, for example. I recommend seeing what's out there before spending a lot of time coding.

Reply to
Andy Resnick

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