Abstract
Contrast-enhanced magnetic resonance imaging (MRI) is useful to study the infiltration of cells in vivo. This research adopts ultrasmall superparamagnetic iron oxide (USPIO) particles as contrast agents. USPIO particles administered intravenously can be endocytosed by circulating immune cells, in particular, macrophages. Hence, macrophages are labeled with USPIO particles. When a transplanted heart undergoes rejection, immune cells will infiltrate the allograft. Imaged by T(2)(*)-weighted MRI, USPIO-labeled macrophages display dark pixel intensities. Detecting these labeled cells in the image facilitates the identification of acute heart rejection. This paper develops a classifier to detect the presence of USPIO-labeled macrophages in the myocardium in the framework of spectral graph theory. First, we describe a USPIO-enhanced heart image with a graph. Classification becomes equivalent to partitioning the graph into two disjoint subgraphs. We use the Cheeger constant of the graph as an objective functional to derive the classifier. We represent the classifier as a linear combination of basis functions given from the spectral analysis of the graph Laplacian. Minimization of the Cheeger constant based functional leads to the optimal classifier. Experimental results and comparisons with other methods suggest the feasibility of our approach to study the rejection of hearts imaged by USPIO-enhanced MRI.
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