Método de elementos finitos aplicado à microscopia de desfocalização

Abstract

Defocusing microscopy is a technique that has been used at the Physics Laboratory of Biological Systems at UFMG to characterize transparent objects, such as cells and waveguides. Through it we can obtain morphological and biomechanical parameters of living cells using only an optical microscope operating in bright field. From two defocused images, it is possible to perform the 3D reconstruction of the sample by solving two differential equations. Despite being quite convenient for the study of biological samples, the application of the technique is limited by the computational cost of data analysis. This work aimed to find a more efficient way to perform the 3D reconstruction. For this, we develop Python programs that take two defocused images as input and return the cell thickness and asymmetry. For the asymmetry calculation, the most time-consuming part of the process, the programs use the finite element method through the Fenics platform. We performed tests for three different situations: reconstruction of simulated phase objects, reconstruction of a red blood cell and reconstruction of a cardiomyocyte. For the first two cases, we were able to compare the results obtained here with those obtained by the methods that had already been established in previous works. The main result of this work was the substantial decrease in the time needed to perform the reconstruction. The new programs take around 10 s to perform cell reconstruction starting from images with 128×128 pixels while, for the methodology prior to this work, the process took around 7200 s on similar hardware. Finally, we were able to perform the reconstruction of a cardiomyocyte, a considerably larger cell, also in about 10 s. These results indicate that the finite element method is a good alternative for the asymmetry calculation, returning results quickly even for higher resolution images. These results open perspectives for the use of defocusing microscopy to study dynamic cellular processes.