Abstract

A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.

Issue Section:
Technical Papers
Keywords:
finite element analysis, cellular biophysics, biomechanics, physiological models, muscle
Topics:
Biological tissues, Deformation, Finite element analysis, Muscle, Stress

References

1.
Guilak
,
F.
, and
Mow
,
V. C.
,
2000
, “
The Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions in Articular Cartilage
,”
J. Biomech.
,
33
, No.
12
, pp.
1663
–
1673
.
2.
Wu
,
J. Z.
, and
Herzog
,
W.
,
2000
, “
Finite Element Simulation of Location and Time-Dependent Mechanical Behavior of Chondrocytes in Unconfined Compression Tests
,”
Ann. Biomed. Eng.
,
28
, pp.
318
–
330
.
3.
Jain
,
M. K.
,
Chernomorsky
,
A.
,
Silver
,
F.
, et al.,
1988
, “
Material Properties of Living Soft Tissue Composites
,”
J. Biom. Mater. Res.: Applied Biomaterials
,
22
, No.
A3
, pp.
311
–
326
.
4.
Huang
,
D.
,
Chang
,
T. R.
,
Aggarwal
,
A.
, et al.,
1993
, “
Mechanisms and Dynamics of Mechanical Strenghtening in Ligament-Equivalent Fibroblast-Populated Collagen Matrices
,”
Ann. Biomed. Eng.
,
21
, pp.
289
–
305
.
5.
Knapp
,
D. M.
,
Tower
,
T. T.
,
Tranquillo
,
R. T.
, et al.,
1999
, “
Estimation of Cell Traction and Migration in an Isometric Cell Traction Assay
,”
AIChE J.
,
45
, No.
12
, pp.
2628
–
2640
.
6.
Wu
,
J. Z.
,
Herzog
,
W.
, and
Epstein
,
M.
,
1999
, “
Modelling of Location and Time-Dependent Deformation of Chondrocytes During Cartilage Loading
,”
J. Biomech.
,
32
, No.
6
, pp.
563
–
572
.
7.
Eshelby, J. D., 1956, “The Continuum Theory of Lattice Defects,” F. Setz, and D. Turnbull, eds., in Progress in Solid State Physics, New York, Academic Press, 3, pp. 79.
8.
Christensen, R. M., 1991, Mechanics of Composite Materials, S. I. Wiley Interscience.
9.
Barocas
,
V. H.
, and
Tranquillo
,
R. T.
,
1997
, “
A Finite Element Solution for the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Effect of Contact Guidance on Isometric Cell Traction Measurement
,”
J. Biomech. Eng.
,
119
, No.
3
, pp.
261
–
268
.
10.
Barocas
,
V. H.
, and
Tranquillo
,
R. T.
,
1997
, “
An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment, and Cell Contact Guidance
,”
J. Biomech. Eng.
,
119
, No.
2
, pp.
137
–
145
.
11.
Zahalak
,
G. I.
,
Wagenseil
,
J. E.
,
Wakatsuki
,
T.
, et al.,
2000
, “
A Cell-Based Constitutive Relation for Bio-Artificial Tissues
,”
Biophys. J.
,
79
, No.
5
, pp.
2369
–
2381
.
12.
Smit
,
R. J. M.
,
Brekelmans
,
W. A. M.
, and
Meijer
,
H. E. H.
,
1998
, “
Prediction of the Mechanical Behavior of Nonlinear Heterogeneous Systems by Multi-Level Finite Element Modeling
,”
Comp. Methods Appl. Mech. Eng.
155
, No.
1-2
, pp.
181
–
192
.
13.
Kouznetsova
,
V.
,
Brekelmans
,
W. A. M.
, and
Baaijens
,
F. P. T.
,
2001
, “
Approach to Micro-Macro Modeling of Heterogeneous Materials
,”
Computational Mechanics
,
27
, No.
1
, pp.
37
–
48
.
14.
Nagtegaal
,
J. C.
,
1982
, “
On the Implementation of Inelastic Constiturive Equations With Special Reference to Large Deformation Problems
,”
Comp. Methods Appl. Mech. Eng.
33
, pp.
469
–
484
.
15.
Saad
,
Y.
, and
Schultz
,
M. H.
,
1986
, “
GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
7
, pp.
856
–
869
.
16.
Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
17.
Vandenburgh
,
H. H.
,
Del Tatto
,
M.
Shansky
,
J.
, et al.,
1996
, “
Tissue-Engineered Skeletal Muscle Organoids for Reversible Gene Therapy
,”
Hum. Gene Ther.
,
7
, No.
17
, pp.
2195
–
2200
.
18.
Bouten
,
C. V.
,
Knight
,
M. M.
,
Lee
,
D. A.
, et al.,
2001
, “
Compressive Deformation and Damage of Muscle Cell Subpopulations in a Model System
,”
Ann. Biomed. Eng.
,
29
, No.
2
, pp.
153
–
163
.
19.
Wakatsuki
,
T.
,
Kolodney
,
M. S.
,
Zahalak
,
G. I.
, et al.,
2000
, “
Cell Mechanics Studied by a Reconstituted Model Tissue
,”
Biophys. J.
,
79
, No.
5
, pp.
2353
–
2368
.
20.
Umazume
,
Y.
, and
Kasuga
,
N.
,
1984
, “
Radial Stiffness of Frog Skinned Muscle Fibres in Relaxed and Rigor Conditions
,”
Biophys. J.
,
45
, pp.
783
–
388
.
21.
Knapp
,
D. M.
,
Barocas
,
V. H.
,
Moon
,
A. G.
, et al.,
1997
, “
Rheology of Reconstituted Type I Collagen Gel in Confined Compression
,”
J. Rheology
,
41
, No.
5
, pp.
971
–
993
.
22.
Harris
,
A. K.
,
Stopak
,
D.
, and
Wild
,
P.
,
1981
, “
Fibroblast Traction As a Mechanism for Collagen Morphogenesis
,”
Nature (London)
,
290
, No.
5803
, pp.
249
–
251
.
Copyright © 2002
 by American Society of Mechanical Engineers
You do not currently have access to this content.