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

Purpose: Multi-echo, multi-contrast methods are increasingly used in dynamic imaging studies to simultaneously quantify R * 2 and R 2 . To overcome the computational challenges associated with nonlinear least squares (NLSQ) fitting, we propose a generalized linear least squares (LLSQ) solution to rapidly fit R * 2 and R 2 . Methods: Spin- and gradient-echo (SAGE) data were simulated across T * 2 and T 2 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 relapsingremitting multiple sclerosis. LLSQ R * 2 and R 2 , as well as cerebral blood volume (CBV), were compared with the standard NLSQ approach. Results: Across all fitting methods, T * 2 was well-fit at high (CCC = 1, CV = 0) and low (CCC >= 0.87, CV <= 0.08) SNR. Except for short T * 2 values (5 - 15 ms), T 2 was well-fit at high (CCC = 1, CV = 0) and low (CCC >= 0.99, CV <= 0.03) SNR. In vivo, LLSQ R * 2 and R 2 estimates were similar to NLSQ, and there were no differences in R * 2 across fitting methods at high SNR. However, there were some differences at low SNR and for R 2 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 R * 2- (0.97 ratio) and R 2-CBV (0.98 ratio). Voxel-wise whole-brain fitting was faster for LLSQ (3 - 4 min) than NLSQ (16 - 18 h). Conclusions: LLSQ reliably fit for R * 2 and R 2 in simulated and in vivo data. Use of LLSQ methods reduced the computational demand, enabling rapid estimation of R * 2 and R 2 .