Error analysis of surface-distribution and non-deformation of fluorescent beads for the IC-GN2 DVC algorithm

Abstract Digital volume correlation (DVC) method is extensively used for the internal displacement measurement. In biomechanical experiments, fluorescent beads are used, instead of traditional speckles (or microstructure of materials), as the information feature of the volume image for DVC algorithm. The traditional experimental method and DVC algorithm, together, provide an effective measurement method for the cell deformation. Nevertheless, the aforesaid method has three limitations, viz., (1) low accuracy for complex displacement and poor efficiency for traditional second-order forward additive Gauss-Newton (FA-GN2) algorithm, (2) shape function mismatch induced by the non-deformation of fluorescent beads, and (3) the extreme phototoxicity caused by the long scanning time. To tackle these issues, we introduce the inverse compositional Gauss-Newton DVC algorithm with the second-order shape function (IC-GN2 DVC algorithm) to achieve higher accuracy and establish the four speckle volume image models to analyze the influence of the distribution and non-deformation of fluorescent beads on the results of calculation of DVC method. Henceforth, we propose an experimental method, considering that fluorescent beads are only distributed on the surface of the gel substrate (cells are also placed on the surface of gel substrate) enabling short scanning time (termed speckle-surface-distributed experimental method). The results from the analysis by numerical simulations show that the proposed IC-GN2 DVC algorithm has a very high accuracy (local error