Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). However, state-of-the-art...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of mathematical biology 2024, Vol.86 (11), p.128, Article 128
Main Authors: Stolz, Bernadette J., Dhesi, Jagdeep, Bull, Joshua A., Harrington, Heather A., Byrne, Helen M., Yoon, Iris H. R.
Format: Article
Language:English
Subjects:
Biomedical data
Blood vessels
Cell Biology
Computational Biology
Computer Simulation
Data analysis
Data collection
Homology
Humans
Immune system
Life Sciences
Macrophages
Macrophages - immunology
Macrophages - pathology
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Medical imaging
Models, Biological
Neoplasms - immunology
Neoplasms - pathology
Original
Original Article
Phenotypes
Spatial analysis
Spatial data
Topology
Tumor cells
Tumor microenvironment
Tumor Microenvironment - immunology
Tumors
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). However, state-of-the-art data collection techniques now generate exquisitely detailed multispecies data, prompting a need for methods that can examine and quantify the relations among them. Such heterogeneous data types arise in many contexts, ranging from biomedical imaging, geospatial analysis, to species ecology. Here, we propose two methods for encoding spatial relations among different data types that are based on Dowker complexes and Witness complexes. We apply the methods to synthetic multispecies data of a tumor microenvironment and analyze topological features that capture relations between different cell types, e.g., blood vessels, macrophages, tumor cells, and necrotic cells. We demonstrate that relational topological features can extract biological insight, including the dominant immune cell phenotype (an important predictor of patient prognosis) and the parameter regimes of a data-generating model. The methods provide a quantitative perspective on the relational analysis of multispecies spatial data, overcome the limits of traditional PH, and are readily computable.
ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-024-01353-6