Fig. 3.

In-plane prestretch has an important effect on out-of-plane indentation stiffness. The schematic drawing shows a potential arterial wall sample isolated for AFM testing. This planar sample could similarly represent an adherent cell after spreading on a surface. Panel a shows the effect of equibiaxial stretching (${\lambda }_{\mathrm{\theta }}={\lambda }_z\equiv \lambda >\hspace{0.17em}1$) on mean (integrate through the thickness) in-plane Cauchy stress for an assumed isotropic behavior. Panel b shows the relationship between indentation force ($f$) and indentation depth ($\delta$) for values of in-plane stretch $\lambda$ increasing from 1.0 to 1.8 in steps of 0.1. The slope of these lines, effectively the transverse structural stiffness $\alpha$, is plotted as a function of in-plane equibiaxial stretch $\lambda$ in panel c. Closed dots (panels a and c) indicate approximate values of the in vivo in-plane stretch (${\lambda }_{\mathrm{\theta }}={\lambda }_z=1.70$); open dots indicate the absence of in-plane stretch (${\lambda }_{\mathrm{\theta }}={\lambda }_z=1.00$), consistent with many reports in the literature. The thick line in panel b similarly corresponds to ${\lambda }_{\theta }={\lambda }_z=1.70$. Note the marked effect of in-plane stretching on the out-of-plane (transverse) stiffness as measured, for example, in atomic force microscopy.