Rapid simultaneous estimation of relaxation rates using multi-echo, multi-contrast MRI

Abstract

PurposeMulti-echo, multi-contrast methods are increasingly used in dynamic imaging studies to simultaneously quantify R2∗ and R2. To overcome the computational challenges associated with nonlinear least squares (NLSQ) fitting, we propose a generalized linear least squares (LLSQ) solution to rapidly fit R2∗ and R2. MethodsSpin- and gradient-echo (SAGE) data were simulated across T2∗ and T2 values at high (200) and low (20) SNR. Full (four-parameter) and reduced (three-parameter) parameter fits were implemented and compared with both LLSQ and NLSQ fitting. Fit data were compared to ground truth using concordance correlation coefficient (CCC) and coefficient of variation (CV). In vivo SAGE perfusion data were acquired in 20 subjects with relapsing-remitting multiple sclerosis. LLSQ R2∗ and R2, as well as cerebral blood volume (CBV), were compared with the standard NLSQ approach. ResultsAcross all fitting methods, T2∗ was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.87, CV ≤ 0.08) SNR. Except for short T2∗ values (5–15 ms), T2 was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.99, CV ≤ 0.03) SNR. In vivo, LLSQ R2∗ and R2 estimates were similar to NLSQ, and there were no differences in R2∗ across fitting methods at high SNR. However, there were some differences at low SNR and for R2 at high and low SNR. In vivo NLSQ and LLSQ three parameter fits performed similarly, as did NLSQ and LLSQ four-parameter fits. LLSQ CBV nearly matched the standard NLSQ method for R2∗- (0.97 ratio) and R2-CBV (0.98 ratio). Voxel-wise whole-brain fitting was faster for LLSQ (3–4 min) than NLSQ (16–18 h). ConclusionsLLSQ reliably fit for R2∗ and R2 in simulated and in vivo data. Use of LLSQ methods reduced the computational demand, enabling rapid estimation of R2∗ and R2.