Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors

Abstract

Highly resolved spatial data of complex systems encode rich and nonlinear information. Quantification of heterogeneous and noisy data—often with outliers, artifacts, and mislabeled points—such as those from tissues, remains a challenge. The mathematical field that extracts information from the shape of data, topological data analysis (TDA), has expanded its capability for analyzing real-world datasets in recent years by extending theory, statistics, and computation. An extension to the standard theory to handle heterogeneous data is multiparameter persistent homology (MPH). Here we provide an application of MPH landscapes, a statistical tool with theoretical underpinnings. MPH landscapes, computed for (noisy) data from agent-based model simulations of immune cells infiltrating into a spheroid, are shown to surpass existing spatial statistics and one-parameter persistent homology. We then apply MPH landscapes to study immune cell location in digital histology images from head and neck cancer. We quantify intratumoral immune cells and find that infiltrating regulatory T cells have more prominent voids in their spatial patterns than macrophages. Finally, we consider how TDA can integrate and interrogate data of different types and scales, e.g., immune cell locations and regions with differing levels of oxygenation. This work highlights the power of MPH landscapes for quantifying, characterizing, and comparing features within the tumor microenvironment in synthetic and real datasets.

Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning

“…In addition, ongoing advances in ODE modeling combined with tissue level simulations also show promise. For example, mathematical models of metabolism and cell proliferation indicated new molecular targets (48) and such multicellular models can further predict outcomes such as necrosis and growth arrest (49), cancer cell migration (50), and immune cell invasion (51). It can be envisioned that the computational efforts described herein can contribute to proposed Digital Twins for personalized medicine in cancer (52).…”

A Topological Data Analytic Approach for Discovering Biophysical Signatures in Protein Dynamics

“…Another natural extension would be to apply the SINATRA Pro pipeline to other data types used to study variation in 3D protein structures such as cryogenic electron microscopy (cryo-EM), nuclear magnetic resonance (NMR) ensembles, and X-ray crystallography (i.e., electron density) data. Previous work has already shown that topological characteristics computed on tumors from magnetic resonance images (MRIs) have the potential to be powerful predictors of survival times for patients with glioblastoma multiforme (GBM) [17,51] and other cancer subtypes [52][53][54]; however, it has also been noted that the efficacy of current topological summaries decreases when heterogeneity between two phenotypic classes is driven by minute differences [13]. For example, cryo-EM images can look quick similar even for two proteins harboring different mutations.…”

Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images

“…This stability result is illustrated by the good agreement between the output of the flooding filtration (loops) when applied to the two sets of annotations from the STARE dataset. In future work, we plan to implement extended persistence and multiparameter persistence to determine whether they provide more robust quantification of VSIs [44,45].…”