Modeling chondrocyte patterns by elliptical cluster processes

Superficial zone chondrocytes (CHs) of human joints are spatially organized in distinct horizontal patterns. Among other factors, the type of spatial CH organization within a given articular surface depends on whether the cartilage has been derived from an intact joint or the joint is affected by osteoarthritis (OA). Furthermore, specific variations of the type of spatial organization are associated with particular states of OA. This association may prove relevant for early disease recognition based on a quantitative structural characterization of CH patterns. Therefore, we present a point process model describing the distinct morphology of CH patterns within the articular surface of intact human cartilage. This reference model for intact CH organization can be seen as a first step towards a model-based statistical diagnostic tool. Model parameters are fitted to fluorescence microscopy data by a novel statistical methodology utilizing tools from cluster and principal component analysis. This way, the complex morphology of surface CH patters is represented by a relatively small number of model parameters. We validate the point process model by comparing biologically relevant structural characteristics between the fitted model and data derived from photomicrographs of the human articular surface using techniques from spatial statistics.