A Shape Analysis Algorithm Quantifies Spatial Morphology and Context of 2D to 3D Cell Culture for Novel Quantitation of Phenotypes

Abstract

SUMMARYThis article explains how novel morphological features in cells and organoids can be quantified using the linearized compressed polar coordinates (LCPC) transform, a spatial algorithm that captures properties that traditional metrics, such as area, volume, and surface area, cannot. Best practices for shape orientation and alignment are discussed. Numerous studies have shown that the morphological phenotype of a cell or organoid correlates with its susceptibility to anti-cancer agents. However, traditional methods of measuring phenotype rely on spatial metrics such as area, volume, perimeter, and signal intensity, which work but are limited. These approaches cannot measure many crucial features of spatial context, such as chirality, a property of left- and right-handedness. Volume cannot register chirality because the left and right shoes hold the same volume. Though spatial context in the form of chirality, gravity direction, and polarity axis is intuitive to humans, the traditional metrics used by cell biologists, pathologists, radiologists, and machine learning practitioners to date cannot capture these fundamental notions. The Linearized Compressed Polar Coordinates (LCPC) transform is a novel algorithm that can capture spatial context unlike any other metric. The LCPC transform translates a two-dimensional (2D) contour into a discrete sinusoidal wave by overlaying a grid system that tracks the points of intersection between the contour and the grid lines. It turns the contour into a series of sequential pairs of discrete coordinates, with the independent coordinate (x-coordinate) being consecutive positions in 2D space. Each dependent coordinate (y-coordinate) consists of the distance between an intersection of the contour and gridline to the origin or baseline of the grid system. In the form of a discrete sinusoid wave, the Fast Fourier Transform is then applied to the data. In this way, the shapes of cells in 2D and 3D cell culture are systematically and multidimensionally represented, enabling robust quantitative stratification that will reveal insights into treatment resistance.