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J Appl Physiol (June 21, 2002). doi:10.1152/japplphysiol.00255.2002
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Articles in PresS, published online ahead of print June 21, 2002
J Appl Physiol, 10.1152/jap.00255.2002
Submitted on March 27, 2002
Accepted on June 17, 2002

A FINITE ELEMENT MODEL OF CELL DEFORMATION DURING MAGNETIC BEAD TWISTING

Srboljub M Mijailovich1*, Milos Kojic2, Miroslav Zivkovic3, Ben Fabry1, and Jeffrey J Fredberg1

1 Environmental Health, Harvard School of Public Health, Boston, Massachusetts, USA
2 Environmental Health, Harvard School of Public Health, Boston, Massachusetts, USA; Mechanical Engineering, University of Kragujevac, Kragujevac, Srbija, Yugoslavia
3 Mechanical Engineering, University of Kragujevac, Kragujevac, Srbija, Yugoslavia

* To whom correspondence should be addressed. E-mail: smijailo{at}hsph.harvard.edu.

Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15°, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast with the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.




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