Fast determination of coarse-grained cell anisotropy and size in epithelial tissue images using Fourier transform

Abstract

Mechanical strain and stress play a major role in biological processes such as wound healing or morphogenesis. To assess this role quantitatively, fixed or live images of tissues are acquired at a cellular precision in large fields of views. To exploit these data, large numbers of cells have to be analyzed to extract cell shape anisotropy and cell size. Most frequently, this is performed through detailed individual cell contour determination, using so-called segmentation computer programs, complemented if necessary by manual detection and error corrections. However, a coarse grained and faster technique can be recommended in at least three situations. First, when detailed information on individual cell contours is not required, for instance in studies which require only coarse-grained average information on cell anisotropy. Second, as an exploratory step to determine whether full segmentation can be potentially useful. Third, when segmentation is too difficult, for instance due to poor image quality or too large a cell number. We developed a user-friendly, Fourier transform-based image analysis pipeline. It is fast (typically 10 4 cells per minute with a current laptop computer) and suitable for time, space or ensemble averages. We validate it on one set of artificial images and on two sets of fully segmented images, one from a Drosophila pupa and the other from a chicken embryo; the pipeline results are robust. Perspectives include in vitro tissues, non-biological cellular patterns such as foams, and xyz stacks.

Shaping the zebrafish myotome by intertissue friction and active stress

“…See SI Appendix , SI Methods and Table S1 for further details (N=30 embryos and n=41 somites). ( B ) Fourier transform image analysis method (42) provides cell elongation field, with anisotropy represented by ellipsoids ( SI Appendix , SI Methods ). Cell elongation is along the major axis of the ellipse.…”

“…We quantified muscle elongation dynamics using a Fourier transform method to analyze the evolution in cellular anisotropy (Fig. 2 B and C ) (42). We find signatures of future slow muscle elongation prior to segmentation, and these cells rapidly extend over the next 100 min (Fig.…”

Cell shape anisotropy and motility constrain self-organised feather pattern fidelity in birds

“…To quantify cell density, we counted the number DAPI-stained cell nuclei within 3 squares of 100μm 2 distributed along the antero-posterior axis on focal plans of confocal images at epidermal or dermal levels (n=3 per species). To extract coarse-grained cell anisotropy we used our published Fourier transform (FT) based program (available on GitHub 22 ) on images segmented in 256×256 pixel interrogation boxes with 50% overlap, as follows: we applied to each box a multiplying function to avoid singularities in the FT due to boundaries and computed the FT using the MATLAB fast FT algorithm (fft2.m). Resulting Fourier space patterns were binarised by retaining only the 5% brightest pixels yielding filled ellipses with correct aspect ratio, and inertia matrices were computed and diagonalised.…”

“…Resulting Fourier space patterns were binarised by retaining only the 5% brightest pixels yielding filled ellipses with correct aspect ratio, and inertia matrices were computed and diagonalised. This allowed extracting pattern anisotropy defined by (where L maj and L min are respectively major and minor axes of the ellipse), a dimensionless number equal to zero when the pattern is isotropic and whose value corresponding to average elongation of cells within a given interrogation box is represented by the length and orientation of a bar (shown in red in Figures; see 22 for further details). Primordia and inter-primordia regions were manually defined as groups of 4 interrogation boxes using stains mentioned above.…”

“… (a) Left panels show confocal views at 40X of 100μm 2 magnifications of phalloïdin-stained inter-primordia regions in the embryonic dermis of each species at stages Co, Cd and Di. Primordia emergence involves dynamic changes in the anisotropy of average cell shapes, which we extracted using Fourier transform and represented by red bars ( 22 and see methods; bar length is equal to measured anisotropy and bar direction is that of cell elongation). Right panel schemes represent the dynamic evolution of pattern array fidelity from stages Cd to Di in segments/areas for each species (see Fig.…”