Clinical interventions can change the mechanical environment of the tissues targeted for therapy. In order to design better procedures, it is important to understand cellular responses to altered mechanical stress. Rigid fixation is one example of a constraint imposed on living tissues as a result of implanted devices. This results in disturbed stress and strain fields, with potentially strong gradients. Herein, we numerically solve the governing nonlinear ordinary differential equation for the stress distribution in a finitely deformed anisotropic circular membrane with a concentric fixation by applying a zero-displacement condition at the inner circumference. Results show that rigid fixations yield distributions of stress and strain that are markedly different from tissue defects with traction-free boundaries. Moreover, the material anisotropy plays a significant role in the manner the stress redistributes regardless of the size of fixation. The present study will contribute to the design of experiments to determine cellular reactions involved in the failure of interventional treatments.

1.
Dewey
,
C. F.
, Jr.
,
Bussolari
,
S. R.
,
Gimbrone
,
M. A.
, Jr.
, and
Davies
,
P. F.
, 1981, “
The Dynamic Response of Vascular Endothelial Cells to Fluid Shear Stress
,”
ASME J. Biomech. Eng.
0148-0731,
103
, pp.
177
185
.
2.
Nerem
,
R. M.
,
Levesque
,
M. J.
, and
Cornhill
,
J. F.
, 1981, “
Vascular Endothelial Morphology as an Indicator of the Pattern of Blood Flow
,”
ASME J. Biomech. Eng.
0148-0731,
103
, pp.
172
176
.
3.
Buck
,
R. C.
, 1983, “
Behaviour of Vascular Smooth Muscle Cells during Repeated Stretching of the Substratum in Vitro
,”
Atherosclerosis
0021-9150,
46
, pp.
217
223
.
4.
Kessler
,
D.
,
Dethlefsen
,
S.
,
Haase
,
I.
,
Plomann
,
M.
,
Hirche
,
F.
,
Krieg
,
T.
, and
Eckes
,
B.
, 2001, “
Fibroblasts in Mechanically Stressed Collagen Lattices Assume a “Synthetic” Phenotype
,”
J. Biol. Chem.
0021-9258,
276
, pp.
36575
36585
.
5.
Wang
,
J. H.
,
Yang
,
G.
,
Li
,
Z.
, and
Shen
,
W.
, 2004, “
Fibroblast Responses to Cyclic Mechanical Stretching Depend on Cell Orientation to the Stretching Direction
,”
J. Biomech.
0021-9290,
37
, pp.
573
576
.
6.
Voytik-Harbin
,
S. L.
,
Roeder
,
B. A.
,
Sturgis
,
J. E.
,
Kokini
,
K.
, and
Robinson
,
J. P.
, 2003, “
Simultaneous Mechanical Loading and Confocal Reflection Microscopy for Three-Dimensional Microbiomechanical Analysis of Biomaterials and Tissue Constructs
,”
Microsc. Microanal.
1431-9276,
9
, pp.
74
85
.
7.
DePaola
,
N.
,
Gimbrone
,
M. A.
Jr.
,
Davies
,
P. F.
, and
Dewey
,
C. F.
Jr.
, 1992, “
Vascular Endothelium Responds to Fluid Shear Stress Gradients
,”
Arterioscler., Thromb., Vasc. Biol.
1079-5642,
12
, pp.
1254
1257
.
8.
Nagel
,
T.
,
Resnick
,
N.
,
Dewey
,
C. F.
, Jr.
, and
Gimbrone
,
M. A.
, Jr.
, 1999, “
Vascular Endothelial Cells Respond to Spatial Gradients in Fluid Shear Stress by Enhanced Activation of Transcription Factors
,”
Arterioscler., Thromb., Vasc. Biol.
1079-5642,
19
, pp.
1825
1834
.
9.
Truskey
,
G. A.
,
Barber
,
K. M.
,
Robey
,
T. C.
,
Olivier
,
L. A.
, and
Combs
,
M. P.
, 1995, “
Characterization of a Sudden Expansion Flow Chamber to Study the Response of Endothelium to Flow Recirculation
,”
ASME J. Biomech. Eng.
0148-0731,
117
, pp.
203
210
.
10.
Tardy
,
Y.
,
Resnick
,
N.
,
Nagel
,
T.
,
Gimbrone
,
M. A.
Jr.
, and
Dewey
,
C. F.
Jr.
, 1997, “
Shear Stress Gradients Remodel Endothelial Monolayers in Vitro via a Cell Proliferation-Migration-Loss Cycle
,”
Arterioscler., Thromb., Vasc. Biol.
1079-5642,
17
, pp.
3102
3106
.
11.
Wong
,
J. Y.
,
Velasco
,
A.
,
Rajagopalan
,
P.
, and
Pham
,
Q.
, 2003, “
Directed Movement of Vascular Smooth Muscle Cells on Gradient-Compliant Hydrogels
,”
Langmuir
0743-7463,
19
, pp.
1908
1913
.
12.
Lo
,
C. M.
,
Wang
,
H. B.
,
Dembo
,
M.
, and
Wang
,
Y. L.
, 2000, “
Cell Movement Is Guided by the Rigidity of the Substrate
,”
Biophys. J.
0006-3495,
79
, pp.
144
152
.
13.
David
,
G.
, and
Humphrey
,
J. D.
, 2004, “
Redistribution of Stress Due to a Circular Hole in a Nonlinear Anisotropic Membrane
,”
J. Biomech.
0021-9290,
37
, pp.
1197
1203
.
14.
Fung
,
Y. C.
, 1990,
Biomechanics: Motion, Flow, Stress, and Growth
,
Springer
, New York.
15.
Fung
,
Y. C.
, 1993,
Biomechanics: Mechanical Properties of Living Tissues
, 2nd ed.,
Springer
, New York.
16.
Humphrey
,
J. D.
, 2002,
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
Springer
, New York.
17.
Moore
,
J. E.
, Jr.
, and
Berry
,
J. L.
, 2002, “
Fluid and Solid Mechanical Implications of Vascular Stenting
,”
Ann. Biomed. Eng.
0090-6964,
30
, pp.
498
508
.
18.
Wilson
,
E.
,
Mai
,
Q.
,
Sudhir
,
K.
,
Weiss
,
R. H.
, and
Ives
,
H. E.
, 1993, “
Mechanical Strain Induces Growth of Vascular Smooth Muscle Cells via Autocrine Action of PDGF
,”
J. Cell Biol.
0021-9525,
123
, pp.
741
747
.
19.
Vande Geest
,
J. P.
,
Di Martino
,
E. S.
, and
Vorp
,
D. A.
, 2004, “
An Analysis of the Complete Strain Field within Flexercell™ Membranes
,”
J. Biomech.
0021-9290,
37
, pp.
1923
1928
.
You do not currently have access to this content.