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Gangming Luo
07-13-1999, 12:43 AM
Dear Biomch-l subscribers,

Last week I posted a message about FEA biphasic model for soft
tissues. I have received a lot of feedback. Thank to all people for
their encouraging and helpful replies. The following is a summary of
responses starting with my original question.

>>>> Original Message: >>>>
I am trying to use biphasical model to simulate soft issues, e.g.
muscle, fat..., mechanical behavior. At this time, I am using MARC 7.2
(MARC Analysis Research Corporation). In the FEA package, there is a
soil model that allows a fully solid-fluid coupled approach with
following features and limits.

(1) The fluid behavior is modeled using Darcy's law and the fluid is
assumed to be slightly compressible.
(2) The solid behavior is defined by
(a) linear elasticity: the Young's moduli and the Poisson ratio;
(b) non-linear elasticity: hypoelastic model.
(In MARC 'User Information' book, it states the solid grains are assumed

to be incompressible. It seems conflicting with the solid behavior as
defined above, because if Poisson ratio < 0.5, solid is compressible. I
prefer a FEA package that allows to use hyperelastic model for solid,
i.e. use a user defined strain energy function.)

Here are my questions:

(1) Is the above MARC FEA soil model appropriate for biphasic model to
simulate soft tissues?
(2) Are there other commercial FEA packages that have a biphasic model
to simulate soft tissues?

Any comments are welcome. Thank you in advance.

>>>>Summary of Responses >>>>

>>>>
> In MARC 'User Information' book, it states the solid
> grains are assumed to be incompressible. It seems
> conflicting with the solid behavior as defined above,
> because if Poisson ratio < 0.5, solid is compressible.

I believe that in this formulation, the individual solid
constitutents are incompressible, but the poisson's ratio
refers to the poisson's ratio of the drained solid
continuum. These two conditions do not conflict.

> (1) Is the above MARC FEA soil model appropriate for
> biphasic model to simulate soft tissues?
Commercial FEA software with soil elements has been shown to
adequately model "biphasic" tissues. See papers by
Prendergast, P.J. in 1996 (Proc.Instn.Mech.Eng.) and Wu, J.Z.
in 1998 (J.Biomech.)

>(2) Are there other commercial FEA packages that have a
>biphasic model to simulate soft tissues?

ABAQUS and DIANA come to mind. ABAQUS has quite a nice
selection of elements, with the ability to model
poroelastic objects in 3D, and also to model contact
between two poroelastic objects.


regards
Stephen

Stephen Ferguson
AO ASIF Research Institute
Davos, Switzerland

>>>>
Hello Gangming,

you might get a lot of replies with this answer, but ABAQUS is a good
choice to model poroelastic materials. It uses a similar model as
MARC, but it is more flexible in the sense of user material definitions.
If you look in the literature under Articular Cartilage, you will find
a lot of work has been done to qualify ABAQUS as a solver for cartilage
problems.

I myself used it for my MS thesis to examine osteoporosis in the rabbit
knee with very good results.

Give it a try if you can and let me know what you came up with.

Cheers, Michael

Michael Nilsson
Senior Research Engineer
Cleveland Clinic Foundation
Biomedical Engineering Department


>>>>
For details of using the program FiDAP, see:

SL Butler, SS Kohles, RJ Thielke, CT Chen, R Vanderby Jr. "Interstitial
Fluid Flow in tendons or Ligaments: A Porous Medium Finite Element
Simulation," Medical & Biological Engineering & Computing,
35(6):742-746, 1997.

Good luck,
Sean S. Kohles, PhD
Assistant Professor of Biomedical and
Mechanical Engineering
Dept. of Biomedical Engineering
Worcester Polytechnic Institute
100 Institute Road
Worcester, MA 01609-2280 USA

Ph1: 508-831-5384 (Office 414 Salisbury Labs)
Ph2: 508-831-5097 (Lab 306B SL)
Ph3: 508-831-5424 (Lab 124 Higgins Labs)
FAX: 508-831-5541
email: kohles@wpi.edu
http://www.wpi.edu/~kohles

>>>>
Gangming,

I use COSMOS/M for modelling bone tissue using my own constitutive
model. The package allows you to write your own fortran subroutines
for linking

with the solver module to define the stress and stress/strain matrices
given the current strain vector during the analysis (non-linear or say
pseudo-linear: ie. very few iterations to converge). A fellow student
here has used this approach to model bone as a biphasic material.

regards,

Dean

Dean Inglis, B. Eng., PhD candidate
Department of Civil Engineering \ Email: dean@numog.eng.mcmaster.ca
BSB B101A \ Voice: (905) 525-9140 x23167
McMaster University \ Fax: (905) 524-2121
Hamilton, Ontario, Canada L8S 4M1 \

>>>>
Dr Luo,

I am not familiar with MARC - but I use ABAQUS to do biphasic modelling
of articular cartilage.

In abaqus, a mixture theory is used - a typical example being a mixture
of a porous solid like sand and a fluid, like water. There can be two
types of fluid - a highly compressible and and an almost incompressible
type - there are also provisions of dealing with absorption/trapping of
some of the fluid by the solid particles.

The behaviour of the mixture is described by an effective stress
principle, where total stress at a point is the sum of the solid and
fluid stresses. The effective stress of the solid phase has regular
terms that can be derived from principles of elasticity, for example,
and an interaction term with fluid pressure components. You might be
able to implement a user defined strain energy function - but I have
never tried it.

For fluid flow Forchheimers's Law is used, which accounts for changes in
permeability as a function of fluid flow velocity - and reduces to
Darcy's law as fluid velocity reduces.

Equilibrium is expressed from virtual work principles.
A continuity equation is also enforced.
The material properties input into the model are really partially
structural, because the equations consider the interaction between the
two phases. Thus, it is possible to have both phases as intrinsically
incompressible and still have the mixture behave as a compressible
substance. This also means that the solid phase could have a high
modulus, but the mixture could behave as something with a much lower
modulus.

The biphasic theory proposed by Mow et al, 1980, uses similar
constitutive equations. They have a tutorial web page where they
derive all their equations.... I don't remember the exact URL - but
if you go to the Columbia University website - You can look for it
as a link from Dr Mow's page.

Wu et al. J Biomech 31( 1998)165-169..... showed that the two theories
(biphasic and the one used by ABAQUS) predict similar results if the
fluid phase is inviscid.

Mostly, I have seen ABAQUS being used to model cartilage, because that
is what I was looking for - but I am sure, it could be and probably has
been used for other soft tissues as well. I have seen ABAQUS being used
to model whole joints - but the ones I have seen, cartilage and
ligaments
are often used as elastic components.

I have tried to test the ABAQUS output in a variety of ways - and so far
I am satisfied with my test results. The model shows characteristic
properties of creep and stress relaxation. There is a transfer of stress

from fluid to solid when a load is applied and held... with the fluid
taking all the stress in the beginning, then a stress transfer, then
equilibrium reached at which point all the stress is taken by the solid
and fluid pressures are zero . For cyclic loading,for the right
frequencies,

you can see a significant time lag between the applied force and the
fluid pressures .

Hope this helps
Nilay

Nilay Mukherjee, Ph. D.

Cartilage and Connective Tissue Research Lab
Room 3-31, Medical Sciences Building
Mayo Clinic
Rochester, MN 55905

Ph : (507) 280-7826 (h)
(507) 284-3484 (w)
Fax: (507) 284-5075 (w)

>>>>
Gangming,

We have been using MARC 7.2 successfully to model cartilage
behavior, using both the linear elastic approach, and the non-linear
hypoelastic model, as well as a transverse isotropy implemented with the

hypoelastic subroutine. When I say "successfully", I mean that we have
been able to validate our results against others' numerical and
analytical solutions for some standard problems of creep or stress
relaxation. (Prendergast et al, Proc Inst Mech Eng [H],1996 and
Wu et al, J. Biomechanics 1998, for example) Whether it truly captures
the cartilage behavior accurately is for another debate. I will
caution
you that in order to achieve this validation, we needed to obtain a
subroutine from MARC which was not part of the standard code (This was
after contacting Prendergast who had the same experience). It's
possible
that this is now included with whatever version of the code you have,
but
it was not for us. Thus - before considering any complicated problems
with
your code, I would take the time to do some validation tests.
Obviously,
this is always a good idea, but I would say it is particularly important
here... If you test it out and believe that you do need the subroutine,
I'd suggest you contact MARC yourself, so we can perhaps convince them
that enough people are interested so they will modify the code. If you
have trouble obtaining it, let me know, and I can provide a contact.
I don't see any reason that you couldn't implement a
hyperelastic model with a subroutine in MARC. The structure of the
program
allows quite a bit of access to the needed variables.
Another option that others have used is ABAQUS. I don't know if
it
has a hyperelastic model, but it does have at least a linear elastic
poroelastic model.

Best of luck with your analyses.

Amy

Amy L. Lerner
Asst. Professor
Mechanical and Biomedical Engineering
215 Hopeman Building
University of Rochester
Box Number 270132
Rochester, NY 14627-0132

Phone: 716-275-7847
Fax: 716-256-2509
e-mail: amlerner@me.rochester.edu

>>>>
Dear Gangming,
Your e-mail was particularly of a great interest to me. Since I have
been working on the FEA biphasic modeling for the past ten years, I feel
that I can answer some of your questions.

1) The Poisson's ratio of the solid component is defined in an apparent
geometric aspect, not a material aspect. In other words, the solid
material is incompressible. However, in the case of porous material,
the whole structure can be compressible even if the material
constituting
the structure is incompressible. One example is a porous sponge. Even
if
we make this porous sponge with an incompressible rubber, the porous
rubbery sponge is compressible since we can collapse the pores within
the porous sponge.

2) There are several other commercial FE packages which can handle the
biphasic modeling. Both ANSYS and ABAQUS have the capability. I have
developed my own FE formulation of the biphasic modeling back in 1989.
The FE biphasic model was not commercially available at that time.
You can easily incorporate the strain energy function into other
program.

3) If you need further information, please check the following articles:

R.L. Spilker and J-K. Suh, (1990) Formulation and evaluation of a finite

element model for the biphasic model of hydrated soft tissues, Computers

and Structures, 35:425-439.

J-K. Suh, R.L. Spilker, and M.H. Holmes, (1991) A penalty finite element

analysis for nonlinear mechanics of biphasic hydrated soft tissue under
large deformation, Int. J. Numerical Method in Engineering,
32:1411-1439.

Good luck,

J-K. Francis Suh, Ph.D.
Associate Professor
Dept. of Biomedical Engineering
Tulane University

>>>>
To Arik, to Gangming Luo,

First , if MARC says the solid is incompressible, it means a block of
pure solid, without pores is incompressible. When Poisson's ratio is <
0.5,
it means that the POROUS solid with no pressurised water in it is
compressible, i.e. its pores change volume during deformation.
MARC is fine for biphasic soft tissue analysis although the hypoelastic
behaviour might in many cases be better to replace by hyperelastic
behaviour. Alternative packages are ABACUS and DIANA. I think at least
one of them offers porohyperelasticity , maybe even
poroviscohyperelasticity.

Jacques Huyghe, Eindhoven University of Technology.

Jacques M. Huyghe
Dr.ir.
Eindhoven University of Technology

P.O. Box 513
Eindhoven
5645JN
The Netherlands
Work: +31-40-2473137
Fax: +31-40-2461418
Conference Software Address
Default Directory Server

>>>> End of Summary >>>>

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