Topological classification of tumour-immune interactions and dynamics

Area of Science:

• Computational Biology
• Cancer Research
• Topology

Background:

• Tumour progression involves complex interactions between tumour and immune cells, leading to diverse behaviours like elimination, equilibrium, and escape.
• Early-stage tumours share similar cell configurations, making prediction of malignant behaviour challenging using conventional methods.

Purpose of the Study:

• To develop and evaluate a novel topological approach for analyzing time-series spatial data of cell locations to predict malignant tumour behaviour.
• To assess the efficacy of different topological vectorizations in predicting the formation of perivascular niches as a proxy for metastasis.

Main Methods:

• Utilized four specialized topological vectorizations: persistence images of Vietoris-Rips and radial filtrations (static), and persistence images for zigzag filtrations and persistence vineyards (time-dependent).
• Generated synthetic data from an agent-based model simulating tumour-immune cell interactions.
• Employed logistic regression to compare the predictive performance of topological summaries against simpler markers (tumour cell count, macrophage phenotype ratio) at various time steps.

Main Results:

• Both static and time-dependent topological methods accurately identified perivascular niche formation earlier than traditional markers.
• Dimension 0 persistence on macrophage data showed superior performance in early prediction, especially when incorporating time-dependent analysis.
• Topological measures capturing tumour shape (tortuosity, punctures) were more effective at intermediate and later stages of tumour development.

Conclusions:

• Topological data analysis offers a powerful and sensitive tool for early prediction of tumour metastasis by revealing intricate spatial patterns.
• Time-dependent topological methods, particularly persistence on macrophage spatial arrangements, provide significant advantages for early-stage cancer detection.
• The study highlights the potential of topology in understanding tumour heterogeneity and guiding therapeutic strategies.