biostudies-literatureVipond OCancer Research UKNational Institute for Health Research (NIHR)Jean Shanks FoundationRoyal SocietyRCUK | Engineering and Physical Sciences Research CouncilEngineering and Physical Sciences Research Councile2102166118https://www.ebi.ac.uk/biostudies/studies/S-EPMC8522280biostudies-literatureUnknown118(41)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 spherProceedings of the National Academy of Sciences of the United States of AmericaMultiparameter persistent homology landscapes identify immune cell spatial patterns in tumors.PMC8522280EP/R005125/1N/AC5255/A18085EP/R018472/1UF150238EP/T001968/1RGFEA201074ACF-2013-13-018EP/N509711/1Bull JAHarrington HAVipond OMacklin PSByrne HMPugh CWTillmann UfalseMultiparameter persistent homology landscapes identify immune cell spatial patterns in tumors.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 spher2021-01-01T00:00:00Z2021 Oct2025-04-04T22:43:38.461Z2025-04-04T22:43:38.461ZS-EPMC85222803462549110.1073/pnas.2102166118