SPF: A Spatial and Functional Data Analytic Approach to cell Imaging data

Abstract

The tumor microenvironment (TME), which characterizes the tumor and its surroundings, plays a critical role in understanding cancer development and progression. Recent advances in imaging techniques enable researchers to study spatial structure of the TME at a single-cell level. Investigating spatial patterns and interactions of cell subtypes within the TME provides useful insights into how cells with different biological purposes behave, which may consequentially impact a subject's clinical outcomes. We utilize a class of well-known spatial summary statistics, the K-function and its variants, to explore inter-cell dependence as a function of distances between cells. Using techniques from functional data analysis, we introduce an approach to model the association between these summary spatial functions and subject-level outcomes, while controlling for other clinical scalar predictors such as age and disease stage. In particular, we leverage the additive functional Cox regression model (AFCM) to study the nonlinear impact of spatial interaction between tumor and stromal cells on overall survival in patients with non-small cell lung cancer, using multiplex immunohistochemistry (mIHC) data. The applicability of our approach is further validated using a publicly available Multiplexed Ion beam Imaging (MIBI) triple-negative breast cancer dataset.

FunSpace: A functional and spatial analytic approach to cell imaging data using entropy measures

“…In other words, if K i is too large, i.e., w ik gets close to 0, leading to no point being observed resulting in indefined entropy. Provided the sparse observed entropies for each individual, fitting SPI i directly into a model as functional covariates as in (31) is not feasible. Therefore, we utilize the approach proposed by Yao et al (32) to address the sparseness in the observed data through functional principal components (FPC) analysis targeting sparse and irregularly spaced data points.…”

DenVar: density-based variation analysis of multiplex imaging data

“…In recent years, various technologies are being used for probing single-cell spatial biology, for example, multiparameter immunofluorescence ( Bataille et al , 2006 ), imaging mass cytometry ( Ali et al , 2020 ), multiplex immunohistochemistry (mIHC) ( Tan et al , 2020 ; Vu et al , 2021 ) and multiplexed ion beam imaging (MIBI) ( Angelo et al , 2014 ; Seal et al , 2021 ). These technologies, often referred to as multiplex tissue imaging, offer the potential for researchers to explore the basis of many different biological mechanisms.…”