A Novel Statistical Optimization Algorithm for Estimating Perfusion Curves in Susceptibility Contrast-Enhanced MRI

Abstract

Dynamic susceptibility contrast-enhanced magnetic resonance imaging is an important tool for evaluating intravascular indicator dynamics, which in turn is valuable for understanding brain physiology and pathophysiology. This procedure usually involves fitting a gamma-variate function to observed concentration-time curves in order to eliminate undesired effects of recirculation and the leakage of contrast agents. Several conventional curve-fitting approaches are routinely applied. The nonlinear optimization methods typically are computationally expensive and require reliable initial values to guarantee success, whereas a logarithmic linear least-squares (LL-LS) method is more stable and efficient, and does not suffer from the initial-value problem, but it can show degraded performance, especially when a few data or outliers are present. In this paper, we demonstrate, that the original perfusion curve-fitting problem can be transformed into a gamma-distribution-fitting problem by treating the concentration-time curves as a random sample from a gamma distribution with time as the random variable. A robust maximum-likelihood estimation (MLE) algorithm can then be readily adopted to solve this problem. The performance of the proposed method is compared with the nonlinear Levenberg-Marquardt (L-M) method and the LL-LS method using both synthetic and real data. The results show that the performance of the proposed approach is far superior to those of the other two methods, while keeping the advantages of the LL-LS method, such as easy implementation, low computational load, and dispensing with the need to guess the initial values. We argue that the proposed method represents an attractive alternative option for assessing intravascular indicator dynamics in clinical applications. Moreover, we also provide valuable suggestions on how to select valid data points and set the initial values in the two traditional approaches (LL-LS and nonlinear L-M methods) to achieve more reliable estimations.