spatialFDA - a tool for spatial multi-sample comparisons

Author(s): Martin Emons,Mark Robinson

Affiliation(s): University of Zurich



With the more widespread use of spatial omics, scientists have been able to analyse cells in their tissue environment. Often diseases show changes in cellular interactions compared to healthy tissue and the comparison of such changes in space are of interest. There are various metrics to quantify cellular interactions, but most of them do not incorporate a mechanism to have them compared across samples. Existing methods to compare spatial arrangements of cells are most often limited to comparing scalar metrics across conditions or samples. Our new framework, spatialFDA, takes a different approach by maintaining the “functional” aspect of various spatial metrics (such as Ripley’s $K$ or nearest-neighbourhood functions) that are widely used tools in geospatial analysis. We calculate one curve per region of interest (e.g. field of view) and depending on the experimental design, may obtain several curves per experimental unit (e.g., sample). Instead of compressing these functions into scalar values, spatialFDA compares the entire curves between conditions using additive mixed models with functional responses. These models compare the curves at each radius $r$ and allow for a correct estimation of random effects between samples. The estimated coefficients of these models are themselves functions over a user defined radius-range. This allows for a spatial interpretation of the effect that covariates have on the spatial curves between conditions. We show that spatialFDA can be used to find biologically meaningful differential co-localisation of cell types with spatial interpretation of the estimated coefficients while controlling for sample-level variability. spatialFDA is to be integrated into the Bioconductor framework to allow easy to use calculations of spatial heterogeneity and subsequent comparison using functional data analysis.