Tao Zhu

A high-efficiency digital image correlation method based on a fast recursive scheme

Due to computational complexity of correlation searching, the digital image correlation (DIC) method is often extremely time consuming in image processing and optical measurement, which has limited its further applications to a great extent. This paper develops a fast recursive scheme to mathematically reduce the computational burden of the traditional DIC technique and therefore improve its efficiency in deformation calculation. A global sum-table approach is proposed to simplify the computations of all double sums arising in the zero-normalized cross-correlation coefficient (ZNCC). A fast recursive algorithm is established to accelerate the calculation of the cross-correlation term in the ZNCC. Both theoretical analysis and actual displacement acquisition are carried out to validate the performance of the new DIC algorithm, which indicates that the fast recursive scheme can improve computational efficiency of integer-pixel correlation searching by about 10 to 50 times in comparison with the classic DIC algorithm, on the condition of keeping the measurement accuracy.

Determination of cellular tractions on elastic substrate based on an integral Boussinesq solution.

Cell-substrate interaction is implicated in many physiological processes. Dynamical monitoring of cellular tractions on substrate is critical in investigating a variety of cell functions such as contraction, migration, and invasion. On account of the inherent ill-posed property as an inverse problem, cellular traction recovery is essentially sensitive to substrate displacement noise and thus likely produces unstable results. Therefore, some additional constraints must be applied to obtain a reliable traction estimate. By integrating the classical Boussinesq solution over a small rectangular area element, we obtain a new analytical solution to express the relation between tangential tractions and induced substrate displacements, and then form an alternative discrete Greens function matrix to set up a new framework of cellular force reconstruction. Deformation images of flexible substrate actuated by a single cardiac myocyte are processed by digital image correlation technique and the displacement data are sampled with a regular mesh to obtain cellular tractions by the proposed solution. Numerical simulations indicate that the 2-norm condition number of the improved coefficient matrix typically does not exceed the order of 100 for actual computation of traction recovery, and that the traction reconstruction is less sensitive to the shift or subdivision of the data sampling grid. The noise amplification arising from ill-posed inverse problem can be restrained and the stability of inverse solution is improved so that regularization operations become less relevant to the present force reconstruction with economical sampling density. The traction recovery for a single cardiac myocyte, which is in good agreement with that obtained by the Fourier transform traction cytometry, demonstrates the feasibility of the proposed method. We have developed a simple and efficient method to recover cellular traction field from substrate deformation. Unlike previous force reconstructions that numerically employ some regularization schemes, the present approach stabilizes the traction recovery by analytically improving the Greens function such that the intricate regularizations can be avoided under proper conditions. The method has potential application to a real-time traction force microscopy in combination with a high-efficiency displacement acquisition technique.

Cellular traction force recovery: An optimal filtering approach in two-dimensional Fourier space

Quantitative estimation of cellular traction has significant physiological and clinical implications. As an inverse problem, traction force recovery is essentially susceptible to noise in the measured displacement data. For traditional procedure of Fourier transform traction cytometry (FTTC), noise amplification is accompanied in the force reconstruction and small tractions cannot be recovered from the displacement field with low signal-noise ratio (SNR). To improve the FTTC process, we develop an optimal filtering scheme to suppress the noise in the force reconstruction procedure. In the framework of the Wiener filtering theory, four filtering parameters are introduced in two-dimensional Fourier space and their analytical expressions are derived in terms of the minimum-mean-squared-error (MMSE) optimization criterion. The optimal filtering approach is validated with simulations and experimental data associated with the adhesion of single cardiac myocyte to elastic substrate. The results indicate that the proposed method can highly enhance SNR of the recovered forces to reveal tiny tractions in cell-substrate interaction.

STUDY ON MECHANICAL INTERACTIONS BETWEEN SINGLE CARDIAC MYOCYTE AND ELASTIC SUBSTRATE

Quantitative investigation on mechanical characteristics of cardiac myocytes has important physiological significance. Based on elastic substrate technique, this paper develops a set of algorithms for high-efficiency cellular traction recovery. By applying a gradient-based digital image correlation method to track randomly distributed fluorescence microbeads on the deformed substrate induced by single cardiac myocyte, high-resolution substrate displacement field can readily be obtained. By using a numerical algorithm based on the integral Boussinesq solution, cell-substrate tractions are reconstructed in a stable and reliable manner. Finally, spatiotemporal dynamics of a single cardiac myocyte is investigated as it adheres to a polyacrylamide elastic substrate.

Mechanical behavior study of single cell contraction by digital image correlation technique

Precise determination of cellular traction forces has important significance in assessing cellular mechanical characteristic on micro/nano scale. Elastic substrate method is a useful way to study cellular traction forces, in which the cells are cultured on elastic gel substrate marked by randomly embedding fluorescent microbeads and they exert mechanical forces on the film to cause deformation of the substrate material. In this paper, we investigate the acquisition of deformation field induced by single cardiac myocyte by using digital image correlation (DIC) technique. In view of the fact that cellular force restoration is essentially an ill-posed inverse problem, which implies that the force reconstruction is susceptible to the input displacement noise, we develop a novel optimal filtering scheme in two-dimensional Fourier space to restrain displacement noise amplification. Experiments of traction force recovery for a real cardiac myocyte indicate the optimal scheme in combination with the DIC method enables us to reconstruct cellular traction fields with high accuracy.

CD4+ T Cell Counting by Impedance Measurement on a Chip with Fluidic Electrodes

Abstract A practical label-free method for counting CD4+ T cells is proposed on the basis of a microfluidic chip with fluidic electrodes. With the help of hydrodynamic focusing, two sheath flows of KCl solution, serving as electric conductors to replace solid metal electrodes, are used to squeeze the cell suspension. By measuring the electrical impedances between the fluidic electrodes, a linear relationship is found between the logarithmic value of cell concentration and the impedance value (R2 = 0.97). The detection limit of CD4+ T lymphocytes reaches as low as ∼10 cells·µL−1, Both the CD4+ T cell concentration of the nude mice group and that of the normal group were counted to further test the function of the chip system, which indicated that there existed significant differences between these groups, showing the approach is valid for identifying immunodeficiency.