A multi-dimensional integration (MDI) strategy for MR T₂ * mapping

MRI signals are intrinsically multi-dimensional, and signal behavior may be orthogonal among different dimensions. Such dimensional orthogonality can be utilized to eliminate unwanted effects and facilitate mathematical simplicity during image processing for improved outcomes. In this work, we will demonstrate and analyze the principles and performance of a newly developed multi-dimensional integration (MDI) strategy in MR T₂ * mapping. By constructing a complex signal function to extract the inter-echo signal changes, MDI solves an optimization problem by processing all signal dimensions (eg echoes, flip angles and coil channels) in one integrative step. MDI was compared with routine curve fitting methods on noise behavior, quantification accuracy and computational efficiency. All methods were tested and compared on simulation, phantom and knee data. Monte Carlo simulations were performed on simulation and all MRI data to investigate noise propagation from k space to T₂ * maps. For phantom tests, T₂ * values in regions of interest were extracted on a voxel-wise basis and analyzed using a paired t-test between scanning parameters and mapping methods, with p < 0.05 being significantly different. MDI facilitated a straightforward processing procedure, yielding homogeneous, high-signal-to-noise-ratio (SNR) and artifact-free T₂ * maps without explicit coil combination or additional measures. Compared with routine fitting methods, MDI offered significantly (p < 0.05) improved SNR and quantitative accuracy/robustness, with two to three orders higher computational efficiency. MDI also represented low-SNR signals with low T₂ * values, avoiding misinterpretation with long-T₂ * species.