3D solid of SARS-CoV-2 viral particles applied Legendre polynomials from Tomography Fourier analysis

Abstract

We show the construction of 3D solids (volumetric 3D models) of SARS-CoV-2 viral particles from the tomographic studies (videos) of SARS-CoV-2-infected tissues. To this aim, we propose a video analysis (tomographic images) by frames (medical images of the virus), which we set as our metadata. We optimize the frames by means of Fourier analysis, which induces a periodicity with simple structure patterns to minimize noise filtering and to obtain an optimal phase of the objects in the image, focusing on the SARS-CoV-2 cells to obtain a medical image under study phase (MIS) (process repeated over all frames). We build a Python algorithm based on Legendre polynomials called “2DLegendre_Fit,” which generates (using multilinear interpolation) intermediate images between neighboring MIS phases. We used this code to generate m images of size M × M , resulting in a matrix with size M × M × M (3D solid). Finally, we show the 3D solid of the SARS-CoV-2 viral particle as part of our results in several videos, subsequently rotated and filtered to identify the glicoprotein spike protein, membrane protein, envelope, and the hemagglutinin esterase. We show the algorithms in our proposal along with the main MATLAB functions such as FourierM and Results as well as the data required for the program execution in order to reproduce our results.