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

David H. Nguyen; Michael Bruck; Jennifer M. Rosenbluth

doi:10.3791/71066

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Method Article

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

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DOI:

10.3791/71066

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July 21st, 2026

David H. Nguyen¹ , Michael Bruck² , Jennifer M. Rosenbluth³^,⁴

¹Tissue Spatial Geometrics Lab, ²Department of Medicine, University of California, San Francisco, ³Department of Medicine, University of California, San Francisco, ⁴Chan Zuckerberg Biohub - San Francisco

Summary

This 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.

Abstract

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 be used to register chirality because the left and right shoes have 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 sequence of pairs of discrete coordinates, with the independent coordinate (x-coordinate) corresponding to 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.

Introduction

Three-dimensional (3D) organoid culture has proven superior to two-dimensional (2D) cell culture in mimicking in vivo biology¹^,². Organoids have become indispensable in cancer research for screening for effective treatments and for gaining insights into disease progression³^,⁴^,⁵^,⁶. While it is well known in cancer biology that distinctions in morphology correlate with distinct biological behavior of cells and tissues, the field relies on traditional shape metrics that are lim....