I've used an inverse langevin equation (using Pade Approximation) to get the initial modulus and locking stretch for samples of skin and muscle tissue I tested with a mechanical tester. Here is the paper that describes the Pade Approximation. http://link.springer.com/article/10.1007%2FBF00366640

I've used an inverse langevin equation (using Pade Approximation) to get the initial modulus and locking stretch for samples of skin and muscle tissue I tested with a mechanical tester. Here is the paper that describes the Pade Approximation. http://link.springer.com/article/10.1007%2FBF00366640

If use Neo-Hookean based model you only needs one parameter testing. However, Mooney-Rivilin based model you need to have two parameters testing.

It depends on your model. If it is a linear model, you may use a least-squares (or your preferred fitting routine) to fit the data into a line. If your model is nonlinear, the simplest approach is to use a piecewise-linear fit, which is identical to a linear fit except that you will break the strain range into sub-intervals and repeat the process for each of them.

Be very careful about mixing data from multiple subjects. If you have a constant bias in any of them, you could end up with an "averaged" data set that is not physical! (Does not represent human anatomy).

Dear researcher;

This is very interesting and very broad questions, however I can share with you some of my thoughts that I used in Abaqus.

My expertise with animal & human tissues; they are pretty close to viscoelastic materials! Therefore, the time domain is very essential when you define their material properties to include to your model. As you may know, viscoelastic materials such as human tissues possess the time domain parameter because of the viscous behavior. Therefore, you need to conduct or ask for either creep or relaxation test. The creep test, is to apply a constant load and measure the deflection as a function of time. Whereas the relaxation test, is to apply a constant deflection and measure the relaxation stress as a function of time. Either one of these test is okay to use to see the affect of time domain on your pressure/stress. If you don't include the creep or the relaxation test, then you simulation will not be as accurate since you didn't include the time domain. All of this are available in Abaqus material calibration technique. You can provide the deflection as a function of time or the stress as a function of time, of course you can use the biaxial and uniaxial data that you have already to include in your model. Now, be sure that the test you provide in simulation has to be close to the actual model. I meant to say, if material in reality is subjected to compression loading, then your testing calibration data have to be in compression mode. If it is subjected to a mix of compression/tension and shear, then you need to carry all of the these above testing. Also, as colleagues said above you can use either one of the proposed polynomial that is very close to your testing data. This is also available in Abaqus and ANSYS. I hope this is a boost for you to start your simulation.

Hi all,

indeed as mentioned by Mohamed, if you consider your tissue as viscoelastic, the time domain to consider is referred as long or short time memory. Creep and relaxation aspects are related to long memory effects while there exists also a short time memory effect which is related to strain rate dependency. I did some works on this during my PhD and if interested you could have a look at the related papers (full text could be found in pdf at):

http://infoscience.epfl.ch/record/88204/files/J%20Biomechanics98.pdf?version=1

http://infoscience.epfl.ch/record/88209/files/EJM2000.pdf?version=1

http://infoscience.epfl.ch/record/88204/files/J%20Biomechanics98.pdf?version=1

Hi all,

Thank you very much for all of your inputs. That's really helpful.

James: Pade Approximation is new for me, will have a look on it. Thanks for wonderful suggestion

Isaac and Eihab: My model is more on non linear model. Piecewise linear-fit would be among the options I have so far, but really concern when dealing with more data (try to avoid average)

Mohamed: My testing data is on tensile and probably need to apply the creep test with a constant load to measure the deflection (including after yield deflection) as a function of time for my simulation. This still need to be considered what is the best approach to work on after yield deflection to maybe maximum limit.

Dominique: Thanks for your great input for the short time memory effect on strain rate. I think this would be useful for my short time material respond.

Sorry guys, but its harder than the posts I have seen above (which are all very good, btw). The key things for soft tissues are:

1) having access to multi-loading state mechanical data, such as planar biaxial and flexure.

2) having access to mutiple protocol data for each loading regime.

3) having a very good optimizer/parameter estimation code. We have been using mathematica coupled with C-code routines. Its taken my student about 1 year to do this but the results are quite good with up to a 15 parameter model.

Hi Michael,

Thanks for the sharing. Appreciate that.

Btw, for the item number 3), how many specimens approximately were required by your student to get 15 parameters? It should be a good references that I can refer with.

The fundamental problem is that tissues are not materials, they are structures. Unlike materials (e.g amorphous materials, polycrystalline metals and ceramics, quasi-crystalline polymers), structure and properties and structure vary in extreme ways over short distances in different directions.

To be sure, people have measured and reported "material" mechanical properties (e.g stiffness) for tissues, using specimens of different kinds of specimens or using methods (e.g. dynamic indentation at mm and nm scales) that do not require creation and use of specimens of fixed dimensions. Any of the mechanical data obtained can be useful, but they are NOT material mechanical properties.

Also as Alzoubi said, tissues must in any case be recognized as being viscoelastic. Therefore, the dimension of time must be included in any method of measuring and reporting tissue mechanical properties. Alzoubi correctly mentions creep and stress relaxation tests as a means for this.

A highly useful alternative is cyclic dynamic mechanical testing. In this case properties can be measured at a series of frequencies and amplitudes (at best, ones appropriate to expected dynamic loading patterns in vivo).

Stiffness of materials or structures is of course THE fundamental design and functional parameter. Using cyclic dynamic mechanical testing one can determine the storage and loss modulus and the phase angle which relates them--for a tissue specimen tested in a given direction in a given mode (e.g. tension, compression). One can use the change in these parameters with frequency as modeling and design data.

I specifically recommend dynamic cyclic indentation as a fine method for obtaining fundamental tissue stiffness dara. Specimen preparation is minimized and it is even possible to map stiffness as a function of anatomical location and direction. Indentation can be used on excised specimens and is also finding use in vivo on living tissues. Let me know if you would like pertinent references.

Jennifer,

I have not read the above posts in great detail, but you should be aware that there are no real ASTM standards for soft tissues. the approach you take depends very much on the particulars of your tissue and your specific problem. It is true that tissues are structures (isn't everything, ultimately?) , but a continuum material approach can be quite useful if you are not concerned with micro-mechanical mechanisms. Indentation can be useful but not for large strain application, for example. Tissues are also not hydrogels - very different animals.

@ Jennifer Wagner -

I agree, consistency and relative comparisons are the core strategies. They have worked fine for me too.

Thank you all for your continuous support in providing answers to my question.

Consistency and relative comparisons are very good basic tools, but one also needs to consider the question to be asked. For example, I often get questions like "what is Young's modulus for skin?" The problems with this question should be obvious to everyone reading this post, but think about it in terms of consistency and relative comparisons - both could be done but the answer - defining a Young's modulus for a non-LEHI material, is still wrong.

This is a huge field. Attached was our attempt to do this in normal and desmin knockout muscle fibers. I hope it helps.

You need to have a material model at the beginning, it is true.

The complexity of the model depends on what you are trying to model.

If you are interested in highly transient behavior, than possibly viscoelasticity, remodeling and/or damage accumulation terms should exist. For only elasticity-style behavior, you need to have only stress-strain relation terms (which should include some anisotropy possibly)

Try to obtain working algorithms with virtual data first: Choose a model, input loads, calculate stresses & strains (FE works good here), then feed your outcomes back into your parameter estimation algorithm and check whether you find the same parameters (you should!).

Experiments should represent what you are looking for. Try eliminating material-inherent noise data (for example, viscoelastic response by pre-conditioning to get an almost steady-state response with well-defined repeatable dissipation for an elastic curve-fitting). Also try having layouts where you can apply stress&strain fields that dominate one parameter or a subset of parameters so that you can have a virtual "seperation of variables".

Normalizing data based on number of available data points should reduce risk of one experiment dominating all the results during residual calculations. Independent evaluation of each specimen's data and statistics based on material parameters (finding mean, etc..) do not yield the same (proper) results if the equation system is highly non-linear. Unit consistency and balancing the order-of-magnitudes will greatly help finding the correct "average path".

I hope this helps.

In fact, this is not an easy task. It is very difficult to propose a model for this purpose. It depends on several factors, such as age, type of tissue, strain rate, orientation of the specimen, among others. Those tests in which there is no contact with specimen, may be advisable. This is the case of interferometry.

In other words, once that the physical conditions have been established, the analysis may be complemented with a numerical approach. At the end, unfortunately, some assumption, which leads to simplifications, have to be taken.

Tfere are some synthesis values to simulate elasticity of single biological tissue.

A milestone in this field is Fung, Y.C. who published different books on this matter.

YC Fung is indeed the (grand)father of tissue mechanics.

He did is work in the '50s and '60s and trained some of the subequent stars, such as Savio L.Y. Woo (who is still active in his '70s).

Actually, Woo did not train with YC, he and YC were colleagues @ UCSD.

YC did train many people, such as my advisor, CJ Chuong.

@ Michael S. Sacks

Sort of colleagues. Woo is ca. 72 and Fung is 94.

Woo's first job after his PhD was with Fung at UCSD in 1970.

At that time Woo would have been ca. 27 and Fung 51. Ask Savio, but I expect he saw Fung as a mentor. I would have.

See:

http://en.wikipedia.org/wiki/Yuan-Cheng_Fung

http://www.linkedin.com/pub/savio-l-y-woo/35/b6a/374

Dear Friends, I said Fung is a milestone! I think all the work that follows his studies is significant.

YCF influenced many, many people and that is perhaps his greatest legacy.

As for Dr. Woo, I was referring to people he trained as students, not those he collaborated with. I am sure Dr. Woo and the rest of us feel as if we were YCF's students as well.

We tend to look for low-variability and physiologically relevant "shape" features in the material curve (stress-strain, stress-time, etc), and choose a well fitting constitutive model whose parameters capture these features.

It's even better when the parameters match up with physical (mechanical) features of the tissue (e.g. tangential stiffness/modulus at physiologically relevant material curve points (e.g. resting tension, peak tension, failure tension).

This kind of behavior depends on humidity, so we must be carefull to it.

Large strain and strong anisotropy are abserved. Visco elasticity and viscoplasticity also.

This kind of material are some times preconditioning before test. But this phase changes the initial behavior with a kind of initial plasticity.

To acces to the mechanical response, a oligocyclic test with some cycles, relaxation and recovary phases can be quite well adapted to begin a separation between : viscoelasticity, viscoplasticity, plastic strain, non linear visco-elasticity, and all this in an anisotropic context.

It it quite difficult to maintain the material in the testing machine (it is a kind of terry towelling full of grease. Thus a camera with a strain correlation can be quite well adapted to compute true strain (if sliding happened during test).

I would suggest first analyzing the type of curves you have.  Are there distinct regions present in all samples?  Are there theories and studies into the meaning of different strain regions?  What models do others in the field use?  Once you've answered these questions, you know a lot more about what direction you should go, because you need a method that reveals something about the material and is reliable enough to trust.

BTW - preconditioning is not a form of plasticity - it can be completely recovered in time.