Deciphering the diversity and sequence of extracellular matrix and cellular spatial patterns in lung adenocarcinoma using topological data analysis

Extracellular matrix (ECM) organization influences cancer development and progression. It modulates the invasion of cancer cells and can hinder the access of immune cells to cancer cells. Effective quantification of ECM architecture and its relationship to the position of different cell types is, therefore, important when investigating the role of ECM in cancer development. Using topological data analysis (TDA), particularly persistent homology and Dowker persistent homology, we develop a novel analysis pipeline for quantifying ECM architecture, spatial patterns of cell positions, and the spatial relationships between distinct constituents of the tumour microenvironment. We apply the pipeline to 44 surgical specimens of lung adenocarcinoma from the lung TRACERx study stained with picrosirius red and haematoxylin. We show that persistent homology effectively encodes the architectural features of the tumour microenvironment. Inference using pseudo-time analysis and spatial mapping to centimetre scale tissues suggests a gradual and progressive route of change in ECM architecture, with two different end states. Dowker persistent homology enables the analysis of spatial relationship between any pair of constituents of the tumour microenvironment, such as ECM, cancer cells, and leukocytes. We use Dowker persistent homology to quantify the spatial segregation of cancer and immune cells over different length scales. A combined analysis of both topological and non-topological features of the tumour microenvironment indicates that progressive changes in the ECM are linked to increased immune exclusion and reduced oxidative metabolism. ### Competing Interest Statement The authors express their sincere thanks to The Mark Foundation for Cancer Research who have generously supported this work and funded the contributions of I.H.R.Y. in full and of E.C. D.N. and H.M.B. in part (MFCR ASPIRE 2022 0384). E.S. and R.J. receive funding from the European Research Council (ERC Advanced Grant CAN ORGANISE Grant agreement number 101019366). E.S. and A.R. are supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001144 FC001003), the UK Medical Research Council (FC001144 FC001003), and the Wellcome Trust (FC001144 FC001003). C.S. is a Royal Society Napier Research Professor (RSRP\R\210001). His work is supported by the Francis Crick Institute that receives its core funding from Cancer Research UK (CC2041); the UK Medical Research Council (CC2041); and the Wellcome Trust (CC2041). C.S. is funded by Cancer Research UK (TRACERx (C11496/A17786); PEACE (C416/A21999) and CRUK Cancer Immunotherapy Catalyst Network); Cancer Research UK Lung Cancer Centre of Excellence (C11496/A30025); the Rosetrees Trust; Butterfield and Stoneygate Trusts; NovoNordisk Foundation (ID16584); Royal Society Professorship Enhancement Award (RP/EA/180007 & RF\ERE\231118); National Institute for Health Research (NIHR) University College London Hospitals Biomedical Research Centre; the Cancer Research UK University College London Centre; Experimental Cancer Medicine Centre; the Breast Cancer Research Foundation (US) (BCRF-22-157); Cancer Research UK Early Detection and Diagnosis Primer Award (Grant EDDPMA Nov21/100034); and The Mark Foundation for Cancer Research Aspire Award (Grant 21 029 ASP). C.S. was also supported by a Stand Up To Cancer LUNGevity American Lung Association Lung Cancer Interception Dream Team Translational Research Grant (Grant Number: SU2C AACR DT23 17 to S.M. Dubinett and A.E. Spira). Stand Up To Cancer is a division of the Entertainment Industry Foundation. Research grants are administered by the American Association for Cancer Research, the Scientific Partner of SU2C. CS is in receipt of an ERC Advanced Grant (PROTEUS) from the European Research Council under the European Union Horizon 2020 research and innovation programme (grant agreement no. 835297). DISCLOSURES E.S. consults for Phenomic AI and Theolytics and receives research support from Novartis; MSD; and AstraZeneca. C.S. acknowledges grants from AstraZeneca; Boehringer Ingelheim; Bristol Myers Squibb; Pfizer; Roche-Ventana; Invitae (previously Archer Dx Inc; collaboration in minimal residual disease sequencing technologies); Ono Pharmaceutical; and Personalis. He is Chief Investigator for the AZ MeRmaiD 1 and 2 clinical trials and is the Steering Committee Chair. He is also Co Chief Investigator of the NHS Galleri trial funded by GRAIL and a paid member of the GRAIL Scientific Advisory Board. He receives consultant fees from Achilles Therapeutics (also SAB member); Bicycle Therapeutics (also a SAB member); Genentech; Medicxi; China Innovation Centre of Roche (CICoR) formerly Roche Innovation Centre Shanghai; Metabomed (until July 2022); Relay Therapeutics SAB member; Saga Diagnostics SAB member and the Sarah Cannon Research Institute. C.S has received honoraria from Amgen; AstraZeneca; Bristol Myers Squibb; GlaxoSmithKline; Illumina; MSD; Novartis; Pfizer; and Roche Ventana. C.S. has previously held stock options in Apogen Biotechnologies and GRAIL and currently has stock options in Epic Bioscience; Bicycle Therapeutics; and has stock options and is cofounder of Achilles Therapeutics. Patents: C.S declares a patent application (PCT/US2017/028013) for methods for lung cancer detection; targeting neoantigens (PCT/EP2016/059401); identifying patient response to immune checkpoint blockade (PCT/EP2016/071471); methods for lung cancer detection (US20190106751A1); identifying patients who respond to cancer treatment (PCT/GB2018/051912); determining HLA LOH (PCT/GB2018/052004); predicting survival rates of patients with cancer (PCT/GB2020/050221); methods for systems and tumour monitoring (PCT/EP2022/077987). C.S. is an inventor on a European patent application (PCT/GB2017/053289) relating to assay technology to detect tumour recurrence. This patent has been licensed to a commercial entity and under their terms of employment C.S is due a revenue share of any revenue generated from such license(s).