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 $R_2^{\ast }$ 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 $R_2^{\ast }$ and R₂.

Methods

Spin- and gradient-echo (SAGE) data were simulated across $T_2^{\ast }$ 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 $R_2^{\ast }$ and R₂, as well as cerebral blood volume (CBV), were compared with the standard NLSQ approach.

Results

Across all fitting methods, $T_2^{\ast }$ was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.87, CV ≤ 0.08) SNR. Except for short $T_2^{\ast }$ 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 $R_2^{\ast }$ and R₂ estimates were similar to NLSQ, and there were no differences in $R_2^{\ast }$ 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 $R_2^{\ast }$- (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).

Conclusions

LLSQ reliably fit for $R_2^{\ast }$ and R₂ in simulated and in vivo data. Use of LLSQ methods reduced the computational demand, enabling rapid estimation of $R_2^{\ast }$ and R₂.