Shape component analysis: structure-preserving dimension reduction on biological shape spaces

A robust unsupervised machine-learning method to quantify the morphological heterogeneity of cells and nuclei

Cell morphology encodes essential information on many underlying biological processes. It is commonly used by clinicians and researchers in the study, diagnosis, prognosis, and treatment of human diseases. Quantification of cell morphology has seen tremendous advances in recent years. However, effectively defining morphological shapes and evaluating the extent of morphological heterogeneity within cell populations remain challenging. Here we present a protocol and software for the analysis of cell and nuclear morphology from fluorescence or bright-field images using the VAMPIRE algorithm ( https://github.com/kukionfr/VAMPIRE_open ). This algorithm enables the profiling and classification of cells into shape modes based on equidistant points along cell and nuclear contours. Examining the distributions of cell morphologies across automatically identified shape modes provides an effective visualization scheme that relates cell shapes to cellular subtypes based on endogenous and exogenous cellular conditions. In addition, these shape mode distributions offer a direct and quantitative way to measure the extent of morphological heterogeneity within cell populations. This protocol is highly automated and fast, with the ability to quantify the morphologies from 2D projections of cells seeded both on 2D substrates or embedded within 3D microenvironments, such as hydrogels and tissues. The complete analysis pipeline can be completed within 60 minutes for a dataset of ~20,000 cells/2,400 images.

Evaluation of methods for generative modeling of cell and nuclear shape

MOTIVATION

Cell shape provides both geometry for, and a reflection of, cell function. Numerous methods for describing and modeling cell shape have been described, but previous evaluation of these methods in terms of the accuracy of generative models has been limited.

RESULTS

Here we compare traditional methods and deep autoencoders to build generative models for cell shapes in terms of the accuracy with which shapes can be reconstructed from models. We evaluated the methods on different collections of 2D and 3D cell images, and found that none of the methods gave accurate reconstructions using low dimensional encodings. As expected, much higher accuracies were observed using high dimensional encodings, with outline-based methods significantly outperforming image-based autoencoders. The latter tended to encode all cells as having smooth shapes, even for high dimensions. For complex 3D cell shapes, we developed a significant improvement of a method based on the spherical harmonic transform that performs significantly better than other methods. We obtained similar results for the joint modeling of cell and nuclear shape. Finally, we evaluated the modeling of shape dynamics by interpolation in the shape space. We found that our modified method provided lower deformation energies along linear interpolation paths than other methods. This allows practical shape evolution in high dimensional shape spaces. We conclude that our improved spherical harmonic based methods are preferable for cell and nuclear shape modeling, providing better representations, higher computational efficiency and requiring fewer training images than deep learning methods.

AVAILABILITY AND IMPLEMENTATION

All software and data is available at http://murphylab.cbd.cmu.edu/software.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.