Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data

Abstract

Modern fluorescence microscopy enables fast 3D imaging of biological and inert systems alike. In many studies, it is important to detect the surface of objects and quantitatively characterize its local geometry, including its mean curvature. We present a fully automated algorithm to determine the location and curvatures of an object from 3D fluorescence images, such as those obtained using confocal or light-sheet microscopy. The algorithm aims at reconstructing surface labelled objects with spherical topology and mild deformations from the spherical geometry with high accuracy, rather than reconstructing arbitrarily deformed objects with lower fidelity. Using both synthetic data with known geometrical characteristics and experimental data of spherical objects, we characterize the algorithm's accuracy over the range of conditions and parameters typically encountered in 3D fluorescence imaging. We show that the algorithm can detect the location of the surface and obtain a map of local mean curvatures with relative errors typically below 2% and 20%, respectively, even in the presence of substantial levels of noise. Finally, we apply this algorithm to analyse the shape and curvature map of fluorescently labelled oil droplets embedded within multicellular aggregates and deformed by cellular forces.

A fluid-to-solid jamming transition underlies vertebrate body axis elongation

“…, where H b and H a are the mean curvatures of the droplet at the intersection of the two principal axis with the ellipsoid and γ is the droplet's interfacial tension ( Fig. 1d), as previously established for droplet with arbitrary deformations 21,35 . The mean curvatures H b and H a are given by H b = b/a 2 and H a = 1/2a + a/(2b 2 ), with b and a being the long and short semi-axis of the fitted ellipse ( Fig.…”

“…Confocal sections through the middle of a ferrofluid droplet were obtained by confocal microscopy, as described above. We then used a custom-made MATLAB code (adapted from a previously published code 35 ) to obtain the coordinates of the droplet contour (segmentation) and measure the in-plane curvature κ(s) along the droplet contour, with s being the arclength along the contour. We first applied a gaussian lowpass filter on the original raw image.…”

Stress-driven tissue fluidization physically segments vertebrate somites

“…2a,b; Methods; Supplementary Movies 3 and 4). To do so, we captured a 3D timelapse of each droplet, quantified its deformations using automated 3D reconstruction and analysis software 38,39 (Fig. 2c; Methods), and obtained both cell-scale and supracellular (tissue-scale) stresses after calibrating the droplet in situ and in vivo (Fig.…”

STRESS, an automated geometrical characterization of deformable particles forin vivomeasurements of cell and tissue mechanical stresses

“…Once the point cloud that represents the deformed particle's surface has been determined, there are several approaches to characterize its geometry. We previously developed a methodology to obtain the surface mean curvature map from local quadratic fits [18] (Fig. 1F).…”

“…However, approximate methods have been recently developed to obtain mechanical stresses using gel microbeads from their surface deformations and the bead stiffness [17]. While different analysis methods exist to reconstruct the geometry of the probes in 3D [12,17,18], an automated and and reliable tool to obtain stresses in 3D and time, as well as to analyze their spatiotemporal characteristics, is lacking.…”