Computed tomography perfusion (CTp) is an emerging functional imaging technology that provides a quantitative assessment of the passage of fluid through blood vessels. Tissue perfusion plays a critical role in oncology due to the proliferation of networks of new blood vessels typical of cancer angiogenesis, which triggers modifications to the vasculature of the surrounding host tissue. In this article, we consider a Bayesian semiparametric model for the analysis of functional data. This method is applied to a study of four interdependent hepatic perfusion CT characteristics that were acquired under the administration of contrast using a sequence of repeated scans over a period of 590 seconds. More specifically, our modeling framework facilitates borrowing of information across patients and tissues. Additionally, the approach enables flexible estimation of temporal correlation structures exhibited by mappings of the correlated perfusion biomarkers and thus accounts for the heteroskedasticity typically observed in those measurements, by incorporating change-points in the covariance estimation. This method is applied to measurements obtained from regions of liver surrounding malignant and benign tissues, for each perfusion biomarker. We demonstrate how to cluster the liver regions on the basis of their CTp profiles, which can be used in a prediction context to classify regions of interest provided by future patients, and thereby assist in discriminating malignant from healthy tissue regions in diagnostic settings.