A field theory is presented for the study of swelling in soft tissue structures that are modeled as poroelastic materials. As a first approximation, soft tissues are assumed to be linear isotropic materials undergoing infinitesimal strains. Material properties are identified that are necessary for the solution of initial boundary value problems where swelling and convection are significant. A finite element model is developed that includes the solid displacements, the relative fiuid displacements, and a representative concentration as the primary unknowns. A numerical example is presented based on a triphasic model. The finite model simulates a typical experimental protocol for soft tissue testing and demonstrates the interaction and coupling associated with relative fluid motion and swelling in a deforming poroelastic material. The theory and finite element model provide a starting point for nonlinear porohyperelastic transport-swelling analyses of soft tissue structures that include finite strains in anisotropic materials.

Issue Section:
Technical Papers
Topics:
Finite element analysis, Soft tissues, Finite element model, Anisotropy, Approximation, Boundary-value problems, Convection, Field theories (Physics), Fluids, Materials properties, Testing
1.
Biot
M. A.
,
1962
, “
Mechanics of Deformation and Acoustic Propagation in Porous Media
,”
J. Applied Physics
, Vol.
33
, pp.
1482
–
1498
.
2.
Biot
M. A.
,
1972
, “
Theory of Finite Deformations of Porous Solids
,”
Indiana Math. J.
, Vol.
21
, pp.
597
–
620
.
3.
Eisenberg
S. R.
, and
Grodzinsky
A. J.
,
1987
, “
The Kinetics of Chemically Induced Nonequilibrium Swelling of Articular Cartilage and Corneal Stroma
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
109
, pp.
79
–
89
.
4.
Fung, Y. C, 1990, Biomechanics, Motion, Flow, Stress, and Growth, Chapter 8, Springer-Verlag, New York, pp. 300–305.
5.
Grodzinsky, A. J., 1990, “Mechanical and Electrical Properties and Their Relevance to Physiological Processes,” Methods in Cartilage Research, Chapter 11, Sec. 65, Academic Press, New York, pp. 275–287.
6.
Grodzinsky
A. J.
,
Roth
V.
,
Myers
E.
,
Grossman
W. D.
, and
Mow
V. C.
,
1981
, “
The Significance of Electromechanical and Osmotic Forces in the Non-Equilibrium Swelling Behavior of Articular Cartilage in Tension
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
103
, pp.
221
–
231
.
7.
Lai, W. M., Hou, J. S., and Mow, V. C., 1990, “A Triphasic Theory for the Swelling Properties of Hydrated Charged Soft Biological Tissues,” Biomechanics of Diarthrodial Joints, Vol. I (V. C. Mow, A. Ratclifffe, and S. L-Y, Woo, eds,), Springer-Verlag, New York, pp. 283–312.
8.
Lai
W. M.
,
Hou
J. S.
, and
Mow
V. C.
,
1991
, “
A Triphasic Theory for the Swelling and Deformation Behavior of Articular Cartilage
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
113
, pp.
245
–
258
.
9.
Lanir
Y.
,
1987
, “
Biorheology and Fluid Flux in Swelling Tissues. I. Biocomponent Theory for Small Deformations, Including Concentration Effects
,”
Biorheology
, Vol.
24
, pp.
173
–
187
.
10.
Liable
J. P.
,
Pflaster
D.
,
Simon
B. R.
,
Krag
M. H.
,
Pope
M. H.
,
Haugh
L. D.
, and
Yuan
Y.
,
1991
, “
Recent Advances in Poroelastic Finite Element Modeling
,”
Advances in Bioengineering
, BED-Vol.
20
, ASME, New York, pp.
41
–
44
.
11.
Mow
V. C.
,
Kuei
S. C.
,
Lai
W. M.
, and
Armstrong
C. G.
,
1980
, “
Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
102
, pp.
73
–
84
.
12.
Myers
E. R.
,
Lai
W. M.
, and
Mow
V. C.
,
1984
, “
A Continuum Theory and an Experiment for the Ion-Induced Swelling Behavior of Articular Cartilage
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
106
, pp.
151
–
158
.
13.
Simon
B. R.
,
1992
, “
Multiphase Poroelastic Finite Element Models for Soft Tissue Structures
,”
Applied Mech. Rev.
, Vol.
45
, pp.
191
–
219
.
14.
Simon, B. R., and Gaballa, M. A., 1988, “Poroelastic Finite Element Models for the Spinal Motion Segment Including Ionic Swelling,” Computational Methods in Bioengineering, (R. L. Spilker and B. R. Simon, eds.), BED-Vol. 9, ASME, New York, pp. 93–100.
15.
Simon
B. R.
,
Wu
J. S. S.
,
Cariton
M. W.
,
Evans
J. H.
, and
Kazarian
L. E.
,
1985
a, “
Structural Models for Human Spinal Motion Segments Based on a Poroelastic View of the Intervertebral Disk
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
107
, pp.
327
–
335
.
16.
Simon
B. R.
,
Wu
J. S. S.
,
Carlton
M. W.
,
Kazarian
L. E.
,
France
E. P.
,
Evans
J. H.
, and
Zienkiewicz
O. C.
,
1985
b, “
Poroelastic Dynamic Structural Models of Rhesus Spinal Motion Segments
,”
Spine
, Vol.
10
, pp.
494
–
507
.
17.
Simon
B. R.
,
Wu
J. S. S.
,
Zienkiewicz
O. C.
, and
Paul
D. K.
,
1986
, “
Evaluation of u-w and u-π Finite Element Methods for the Dynamic Response of Saturated Porous Media Using One-Dimensional Models
,”
Int. J. Num. and Anal. Methods in Geomech.
, Vol.
10
, pp.
461
–
482
.
18.
Urban
J. P. G.
, and
Maroudas
A.
,
1981
, “
Swelling of the Intervertebral Disc In Vitro
,”
Connective Tissue Res.
, Vol.
9
, pp.
1
–
10
.
19.
Urban
J. P. G.
,
Maroudas
A.
,
Bayliss
M. T.
, and
Dillon
J.
,
1979
, “
Swelling Pressures of Proteoglycans at the Concentrations Found in Cartilagenous Tissues
,”
Biorheoiogy
, Vol.
16
, pp.
447
–
464
.
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