Comparison of analytical and numerical analysis of the reference region model for DCE-MRI

Abstract

This study compared three methods for analyzing DCE-MRI data with a reference region (RR) model: a linear least-square fitting with numerical analysis (LLSQ-N), a nonlinear least-square fitting with numerical analysis (NLSQ-N), and an analytical analysis (NLSQ-A). The accuracy and precision of estimating the pharmacokinetic parameter ratios KR and VR, where KR is defined as a ratio between the two volume transfer constants, Ktrans,TOI and Ktrans,RR, and VR is the ratio between the two extracellular extravascular volumes, ve,TOI and ve,RR, were assessed using simulations under various signal-to-noise ratios (SNRs) and temporal resolutions (4, 6, 30, and 60s). When no noise was added, the simulations showed that the mean percent error (MPE) for the estimated KR and VR using the LLSQ-N and NLSQ-N methods ranged from 1.2% to 31.6% with various temporal resolutions while the NLSQ-A method maintained a very high accuracy (<1.0×10−4 %) regardless of the temporal resolution. The simulation also indicated that the LLSQ-N and NLSQ-N methods appear to underestimate the parameter ratios more than the NLSQ-A method. In addition, seven in vivo DCE-MRI datasets from spontaneously occurring canine brain tumors were analyzed with each method. Results for the in vivo study showed that KR (ranging from 0.63 to 3.11) and VR (ranging from 2.82 to 19.16) for the NLSQ-A method were both higher than results for the other two methods (KR ranging from 0.01 to 1.29 and VR ranging from 1.48 to 19.59). A temporal downsampling experiment showed that the averaged percent error for the NLSQ-A method (8.45%) was lower than the other two methods (22.97% for LLSQ-N and 65.02% for NLSQ-N) for KR, and the averaged percent error for the NLSQ-A method (6.33%) was lower than the other two methods (6.57% for LLSQ-N and 13.66% for NLSQ-N) for VR. Using simulations, we showed that the NLSQ-A method can estimate the ratios of pharmacokinetic parameters more accurately and precisely than the NLSQ-N and LLSQ-N methods over various SNRs and temporal resolutions. All simulations were validated with in vivo DCE MRI data.