Evaluation of biological cell properties using dynamic indentation measurement

Viscoelastic mechanical properties of biological cells are commonly measured using atomic force microscope (AFM) dynamic indentation with spherical tips. A semiempirical analysis based on numerical simulation is built to determine the cell mechanical properties. It is shown that the existing analysis cannot reflect the accurate values of cell elastic/dynamic modulus due to the effects of substrate, indenter tip size, and cell size. Among these factors, substrate not only increases the true contact radius but also interferes the indentation stress field, which can cause the overestimation of cell moduli. Typically, the substrate effect is much stronger than the other two influences in cell indentation; and, thus, the cell modulii are usually overestimated. It is estimated that the moduli can be overestimated by as high as over 200% using the existing analysis. In order to obtain the accurate properties of cells, correction factors that account for these effects are required in the existing analysis.

Figure 1

(Color online) The schematic of cell indentation and simplified disklike shape.

Figure 2

(Color online) The standard linear solid model of viscoelastic material.

Figure 3

(Color online) The relationship between normalized contact radius, $a/R$, and normalized indentation displacement, $\delta /h$.

Figure 4

(Color online) The fitting parameter $k$ in Eq. (2).

Figure 5

(Color online) The schematics of cell indentation with and without substrate.

Figure 6

(Color online) The relationship between the normalized indentation force and the normalized indentation displacement.

Figure 7

(Color online) The correction factors to compensate for the effect from the Hertz contact radius on the cell elastic modulus, $f_{c1}$ and $f_{c2}$.

Figure 8

(Color online) The relationship of the overall indentation correction factor $f_{tot1}$ and normalized indentation depth, $\delta /h$.

Figure 9

(Color online) The comparison between the overall correction factors, $f_{tot1}$ and $f_{tot2}$ of the elastic modulus.

Figure 10

(Color online) The fitting parameters $b$ and $c$ in Eq. (24).