Cookies on this website

We use cookies to ensure that we give you the best experience on our website. If you click 'Accept all cookies' we'll assume that you are happy to receive all cookies and you won't see this message again. If you click 'Reject all non-essential cookies' only necessary cookies providing core functionality such as security, network management, and accessibility will be enabled. Click 'Find out more' for information on how to change your cookie settings.

Significance Quantifying and comparing complex spatial biological datasets is crucial for medical applications and remains an active area of research. As datasets become more heterogeneous and complicated, so must the methods that are used to understand them. Multiparameter topology is built upon the assumption that the shape of data depends on multiple parameters, such as scale, outliers, or other parameters (e.g., cell density and oxygen levels in the case of tumors). A key difficulty encountered in multiparameter persistent homology (MPH) is interpreting and comparing data. The present work uses statistical MPH landscapes to overcome this difficulty and quantifies differences in synthetic data of immune cell infiltration as well as clinical tumor histology data of T cells, macrophages, and hypoxia.

Original publication




Journal article


Proceedings of the National Academy of Sciences


Proceedings of the National Academy of Sciences

Publication Date