Cell Mechanics Modeling and Identification by Atomic Force Microscopy

Exponential convergence bounds in least squares estimation: Identification of viscoelastic properties in atomic force microscopy

“…In general, λ increases with increasing β , but at some point, around β = 10 4 , a starts to rapidly increase. On the other hand, λ does not change with p 0 , but a reaches its minimum at p 0 =m 2 /(α 0 T 0 ) ≈ 3 × 10 19 . Thus, β = 10 4 , p 0 = 3 × 10 19 are appropriate choices for this problem.…”

“…In the viscoelastic identification in AFM [19], the parameter vector is instead piecewise constant at regular intervals T . Convergence properties of the parameter estimates in this case, as well as insights for determining the interval, is desired and established in the following.…”

“…The primary motivation for developing the theory in the previous sections was for use in identification of viscoelastic sample properties in AFM operating in DIVE mode, as detailed in [17], [19]. The sample properties are modeled as laterally spaced spring-damper elements to be identified, as seen in Fig.…”

“…This approach can be operated in two distinct dynamic modes, both of which employ an oscillating cantilever. In dynamic indentation viscoelastic (DIVE) mode, the sample is periodically indented at discrete points across the sample [19]; while in scanning viscoelastic (SVE) mode, the cantilever is kept at a constant mean depth into the sample while scanning in a raster pattern [20].…”

“…The topic of time-varying parameters has been the focus of several studies [23], [24], [25], [26]. In DIVE mode identification using AFM [19], the viscoelastic properties of the sample are considered spatially inhomogeneous but constant in time. Accordingly, during each tap the parameters are constant, but for subsequent taps they can attain different constant values.…”