Research Papers

Analysis and Interpretation of Stress Fiber Organization in Cells Subject to Cyclic Stretch

[+] Author and Article Information
Zhensong Wei, Anthony G. Evans

Mechanical Engineering Department and Materials Department, University of California, Santa Barbara, CA 93106

Vikram S. Deshpande

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

Robert M. McMeeking

Mechanical Engineering Department and Materials Department, University of California, Santa Barbara, CA 93106rmcm@engr.ucsb.edu

The polymerization level η(ϕ) oscillates during each loading cycle. However, for all the simulations presented in this study, these oscillations are small and hence the plots of the temporal variation of polymerization level employ a mean value η over each cycle.

J Biomech Eng 130(3), 031009 (Apr 28, 2008) (9 pages) doi:10.1115/1.2907745 History: Received March 09, 2007; Revised July 30, 2007; Published April 28, 2008

Numerical simulations that incorporate a biochemomechanical model for the contractility of the cytoskeleton have been used to rationalize the following observations. Uniaxial cyclic stretching of cells causes stress fibers to align perpendicular to the stretch direction, with degree of alignment dependent on the stretch strain magnitude, as well as the frequency and the transverse contraction of the substrate. Conversely, equibiaxial cyclic stretching induces a uniform distribution of stress fiber orientations. Demonstrations that the model successfully predicts the alignments experimentally found are followed by a parameter study to investigate the influence of a range of key variables including the stretch magnitude, the intrinsic rate sensitivity of the stress fibers, the straining frequency, and the transverse contraction of the substrate. The primary predictions are as follows. The rate sensitivity has a strong influence on alignment, equivalent to that attained by a few percent of additional stretch. The fiber alignment increases with increasing cycling frequency. Transverse contraction of the substrate causes the stress fibers to organize into two symmetrical orientations with respect to the primary stretch direction.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Fibers , Stress
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Figure 1

The effects of stretch magnitude on stress fiber orientation in cells subject to uniaxial strain cycling. Representative micrographs with cells stained for actin are shown as well as circular histograms at 15deg intervals. The results have been obtained for bovine aortic endothelial cells (BAECs) either kept as an unstretched control or subjected to cyclic stretch (amplitudes of 1%–10%) for 6h at 1Hz. The directions of stretch are indicated by double-headed arrows. The p values indicate the significance (via the Rayleigh test) to which the distributions differ from randomness, with 1 indicating the latter. Mean orientation angles and 99% confidence intervals are shown in light gray, where p<0.01. Both the micrographs and the histograms are reproduced from Ref. 3, copyright by The National Academy of Sciences of the United States of America, all rights reserved.

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Figure 2

Schematics of the experimental setup employed in the cyclic stretching of cells and the corresponding two-dimensional cyclic stretching problem. The coordinate system employed in the calculation is also sketched.

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Figure 3

The temporal variations of (a) the cyclic stretch magnitude with a period of T and (b) the corresponding activation signal initiating the formation of stress fibers.

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Figure 4

The evolution of the polymerization level of stress fibers η at selected angles, plotted from the initial to the steady state in cells subject to uniaxial cyclic stretch (at 1Hz) with maximum magnitudes: (a) εmax=3% and (b) εmax=10%. Also shown are the circular histograms at 10deg intervals of stress fiber orientation at the steady state. The 10deg interval was chosen due to some of our results that are not effectively represented with a 15deg interval and we prefer to use the same interval throughout the paper for reporting the simulations. The stretch direction is shown using double-headed arrows above each histogram.

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Figure 5

The evolution of (a) polymerization level of stress fibers and (b) associated equibiaxial tensile stresses for equibiaxial cyclic stretching (at 1Hz) with εmax=3% and εmax=10%. (c) Circular histogram illustrating the stress fiber organization at steady state.

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Figure 6

The temporal dependence of the alignment r for the uniaxial stretching of the cells considered in Fig. 4

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Figure 11

The effect of the transverse contraction of the substrate on stress fiber alignment, expressed in terms of the steady-state mean alignment rss as a function of stretch magnitude for selected νs. Also shown are the circular histograms of stress fiber organization.

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Figure 12

Comparisons of the analytical and numerical predictions of the steady-state polymerization level η(ϕ) of stress fibers for cyclic stretching at 1Hz. (a) Case I: uniaxial stretch (ε¯22=0) and (b) Case II: with transverse contraction of the substrate.

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Figure 7

The evolution of the tensile stresses associated with the uniaxial stretching of cells considered in Fig. 4. The stress σ11 is in the stretching direction, while σ22 is perpendicular to the stretching direction.

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Figure 8

The effect of stress fiber rate sensitivity k¯v on alignment, expressed in terms of rss, as a function of stretch magnitude. Also shown are the circular histograms of stress fiber organization for selected cases, with the stretch direction indicated as double-headed arrows.

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Figure 9

The effect of cycle frequency f on stress fiber alignment. Also shown are the circular histograms of stress fiber organization for selected cases.

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Figure 10

The evolution of the polymerization level of stress fibers at selected orientations for uniaxial cyclic stretching of the cell at 1Hz with εmax=3%. The cell is subject to uniaxial cyclic stretch in one direction for 20,000cycles, followed by another 20,000cycles after a 90deg change in stretch direction. Circular histograms are included after the first 20,000cycles, 0.5h after the change in the stretch direction and after 20,000cycles in the new direction.




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