Complexity in applying spatial analysis to describe heterogeneous air-trapping in thoracic imaging data

In this paper we consider a novel approach to analyzing medical images by applying a concept typically employed in geospatial studies. For certain diseases, such as asthma, there is a relevant distinction between the heterogeneity of constriction in airways for patients compared to healthy individuals. In order to describe such heterogeneities quantitatively, we utilize spatial correlation in the realm of lung computer tomography (CT). Specifically, we apply the approximate profile-likelihood estimator (APLE) to simulated lung air-trapping data selected based on potential interest to pulmonologists, and we explore reference values obtainable through this statistic. Results indicate that APLE values are independent of air-trapping values, and can provide useful insight into spatial patterns of these values within the lungs in situations where other common metrics, such as the coefficient of variation, reveal little. The APLE relies on a neighborhood weights matrix to define spatial relatedness of considered regions, and among a few weight structures explored, a working optimal choice seems to be one based on the inverse distance squared between regions of interest. The application yields a new method to help analyze the degree of heterogeneity in lung CT images, which can be generalized to other medical images as well.