Description of immune cell infiltration in solid tumours using spatial statistics and topological data analysis

The increasing digitization of immunohistochemistry slides provides opportunities for pathologists to automate routine tasks and improve current workflows. Techniques for identifying immune cells in biopsies or surgically resected tumours are now widespread, with several open-source or commercial image analysis platforms providing cell identification tools. While these tools can be used to calculate statistics such as the density of immune cells in a given tumour region, a property which correlates with patient prognosis, consideration of spatial statistics and topological analyses which can provide more detailed spatial descriptions of localisation is not widespread. We introduce several spatial statistical descriptors which can be used to describe localisation of immune cells within a tumour, and apply them to macrophage distributions in human IHC images and in simulated datasets. We show that key features of the spherical contact distribution, the pair correlation function, and the J-function vary predictably as the degree of immune cell infiltration from stromal to tumour regions increases in simulated data. Using these statistics, we introduce a new method based on maximum likelihood estimation which combines the strengths of different spatial descriptors to automatically classify macrophage infiltration into tumour nests. We validate our approach by applying it to macrophage distributions from clinical datasets, obtaining infiltration indices which match the qualitative assessments of experienced pathologists. Finally, we demonstrate how topological data analysis can be applied to macrophage distributions in human IHC images and in simulated datasets to enhance these descriptions.