Convex-Optimization-Based Compartmental Pharmacokinetic Analysis for Prostate Tumor Characterization Using DCE-MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a powerful imaging modality to study the pharmacokinetics in a suspected cancer/tumor tissue. The pharmacokinetic (PK) analysis of prostate cancer includes the estimation of time activity curves (TACs), and thereby, the corresponding kinetic parameters (KPs), and plays a pivotal role in diagnosis and prognosis of prostate cancer. In this paper, we endeavor to develop a blind source separation algorithm, namely convex-optimization-based KPs estimation (COKE) algorithm for PK analysis based on compartmental modeling of DCE-MRI data, for effective prostate tumor detection and its quantification. The COKE algorithm first identifies the best three representative pixels in the DCE-MRI data, corresponding to the plasma, fast-flow, and slow-flow TACs, respectively. The estimation accuracy of the flux rate constants (FRCs) of the fast-flow and slow-flow TACs directly affects the estimation accuracy of the KPs that provide the cancer and normal tissue distribution maps in the prostate region. The COKE algorithm wisely exploits the matrix structure (Toeplitz, lower triangular, and exponential decay) of the original nonconvex FRCs estimation problem, and reformulates it into two convex optimization problems that can reliably estimate the FRCs. After estimation of the FRCs, the KPs can be effectively estimated by solving a pixel-wise constrained curve-fitting (convex) problem. Simulation results demonstrate the efficacy of the proposed COKE algorithm. The COKE algorithm is also evaluated with DCE-MRI data of four different patients with prostate cancer and the obtained results are consistent with clinical observations.