Bayesian functional spatial partitioning for boundary surface lesion detection using 3D MRI

Multi-parametric magnetic resonance imaging (mpMRI) plays a critical role in the detection and localization of prostate cancer (PCa). 3D mpMRI represents prostate anatomy as a volume assembled from multiple 2D slices, providing richer information for lesion detection and localization than analysis based on a single slice alone. Existing statistical 3D approaches often struggle to ensure spatial contiguity of detected regions and may fail to capture the complex geometry of cancer boundaries. In addition, our motivating application uses 3D prostate mpMRI data from a single-site study, where the limited sample size can make deep learning approaches less practical for reliable training of high-dimensional 3D models. To address these challenges, we develop BFSP-3D, a Bayesian functional spatial partitioning method for automatic lesion detection in 3D imaging data. The proposed method employs a transformation from Cartesian to spherical coordinates to flexibly represent smooth 3D lesion boundaries. An adaptive Metropolis–Hastings algorithm is used to jointly estimate the boundary surface and the parameters of the underlying Gaussian process. Simulation studies demonstrate that BFSP-3D is robust to varying spatial configurations and lesion shapes. We illustrate the method using 3D mpMRI data of the prostate.