Abstract
Atomic force microscopy (AFM) is one of many new technologies available to study the mechanical properties and mechanobiological responses of living cells. Despite the widespread usage of this technology, there has been little attempt to develop new theoretical frameworks to interpret the associated data. Rather, most analyses rely on the classical Hertz solution for the indentation of an elastic half-space within the context of linearized elasticity. In contrast, we propose a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the three primary structural constituents of the cytoskeleton. Moreover, we extend a prior solution for a small indentation superimposed on a finite equibiaxial extension by incorporating in this mixture model for the special case of an initially random distribution of constituents (actin, intermediate filaments, and microtubules). We submit that this theoretical framework will allow an improved interpretation of indentation force–depth data from a sub-class of atomic force microscopy tests and will serve as an important analytical check for future finite element models. The latter will be necessary to exploit further the capabilities of both atomic force microscopy and nonlinear mixture theories for cell behavior.
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Notes
Explicit derivations were carried out for a Mooney–Rivlin material whereby the classical result was confirmed (see Eq. 8 in Humphrey et al. 1991).
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Acknowledgements
This work was supported, in part, by a Special Opportunity Award from the Whitaker Foundation, a grant from the NIH (R01 HL-64372) through its Bioengineering Research Partnerships Program, and NIH grants R01 HL-58690 and HL-62863.
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Na, S., Sun, Z., Meininger, G.A. et al. On atomic force microscopy and the constitutive behavior of living cells. Biomech Model Mechanobiol 3, 75–84 (2004). https://doi.org/10.1007/s10237-004-0051-x
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DOI: https://doi.org/10.1007/s10237-004-0051-x