The influence of resolution on the predictive power of spatial heterogeneity measures as biomarkers of liver fibrosis.

Spatial heterogeneity of cells in liver biopsies can be used as biomarker for disease severity of patients. This heterogeneity can be quantified by non-parametric statistics of point pattern data, which make use of an aggregation of the point locations. The method and scale of aggregation are usually chosen ad hoc, despite values of the aforementioned statistics being heavily dependent on them. Moreover, in the context of measuring heterogeneity, increasing spatial resolution will not endlessly provide more accuracy. The question then becomes how changes in resolution influence heterogeneity indicators, and subsequently how they influence their predictive abilities. In this paper, cell level data of liver biopsy tissue taken from chronic Hepatitis B patients is used to analyze this issue. Firstly, Morisita-Horn indices, Shannon indices and Getis-Ord statistics were evaluated as heterogeneity indicators of different types of cells, using multiple resolutions. Secondly, the effect of resolution on the predictive performance of the indices in an ordinal regression model was investigated, as well as their importance in the model. A simulation study was subsequently performed to validate the aforementioned methods. In general, for specific heterogeneity indicators, a downward trend in predictive performance could be observed. While for local measures of heterogeneity a smaller grid-size is outperforming, global measures have a better performance with medium-sized grids. In addition, the use of both local and global measures of heterogeneity is recommended to improve the predictive performance.

Measures of spatial heterogeneity in the liver tissue micro-environment as predictive factors for fibrosis score.

The organization and interaction between hepatocytes and other hepatic non-parenchymal cells plays a pivotal role in maintaining normal liver function and structure. Although spatial heterogeneity within the tumor micro-environment has been proven to be a fundamental feature in cancer progression, the role of liver tissue topology and micro-environmental factors in the context of liver damage in chronic infection has not been widely studied yet. We obtained images from 110 core needle biopsies from a cohort of chronic hepatitis B patients with different fibrosis stages according to METAVIR score. The tissue sections were immunofluorescently stained and imaged to determine the locations of CD45 positive immune cells and HBsAg-negative and HBsAg-positive hepatocytes within the tissue. We applied several descriptive techniques adopted from ecology, including Getis-Ord, the Shannon Index and the Morisita-Horn Index, to quantify the extent to which immune cells and different types of liver cells co-localize in the tissue biopsies. Additionally, we modeled the spatial distribution of the different cell types using a joint log-Gaussian Cox process and proposed several features to quantify spatial heterogeneity. We then related these measures to the patient fibrosis stage by using a linear discriminant analysis approach. Our analysis revealed that the co-localization of HBsAg-negative hepatocytes with immune cells and the co-localization of HBsAg-positive hepatocytes with immune cells are equally important factors for explaining the METAVIR score in chronic hepatitis B patients. Moreover, we found that if we allow for an error of 1 on the METAVIR score, we are able to reach an accuracy of around 80%. With this study we demonstrate how methods adopted from ecology and applied to the liver tissue micro-environment can be used to quantify heterogeneity and how these approaches can be valuable in biomarker analyses for liver topology.