Quantifying spatial heterogeneity in dynamic contrast-enhanced MRI parameter maps

Dynamic contrast-enhanced MRI is becoming a standard tool for imaging-based trials of anti-vascular/angiogenic agents in cancer. So far, however, biomarkers derived from DCE-MRI parameter maps have largely neglected the fact that the maps have spatial structure and instead focussed on distributional summary statistics. Such statistics-e.g., biomarkers based on median values-neglect the spatial arrangement of parameters, which may carry important diagnostic and prognostic information. This article describes two types of heterogeneity biomarker that are sensitive to both parameter values and their spatial arrangement. Methods based on Rényi fractal dimensions and geometrical properties are developed, both of which attempt to describe the complexity of DCE-MRI parameter maps. Experiments using simulated data show that the proposed biomarkers are sensitive to changes that distribution-based summary statistics cannot detect and demonstrate that heterogeneity biomarkers could be applied in the drug trial setting. An experiment using 23 DCE-MRI parameter maps of gliomas-a class of tumour that is graded on the basis of heterogeneity-shows that the proposed heterogeneity biomarkers are able to differentiate between low- and high-grade tumours.