Convex analysis for separation of functional patterns in DCE-MRI: A longitudinal study to antiangiogenic therapy

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can characterize vascular heterogeneity, and has potential utility in assessment of the efficacy of angiogenesis inhibitors in cancer treatment. Due to the heterogeneous nature of tumor microvasculature, the measured signals can be represented as the mixture of the permeability images corresponding to different perfusion rates. We recently reported a hybrid convex analysis of mixture framework for unmixing of non-negative yet dependent angiogenic permeability distributions (APDs) and perfusion time activity curves (TACs). In our last work, we presented an underlying theory to infer the concept that the TACs can be identified by finding the lateral edges of an observation-constructed convex pyramid when the well-grounded points exist for all APDs. For fulfilling this concept, a hybrid method including non-negative clustered component analysis, convex analysis, and least-squares fitting with non-negativity constraints was developed. In this paper, we use computer simulations to validate the performance of our reported framework, and further apply it to three sets of real DCE-MRI data, before and during the treatment period, for assessing the response to antiangiogenic therapy. The experimental results are not only surprisingly meaningful in biology and clinic, but also capable of reflecting the efficacy of angiogenesis inhibitors in cancer treatment.