A vectorized Levenberg-Marquardt model fitting algorithm for efficient post-processing of cardiac T1 mapping MRI

Abstract

Purpose: T₁ mapping is an emerging MRI research tool to assess diseased myocardial tissue. Recent research has been focusing on the image acquisition protocol and motion correction, yet little attention has been paid to the curve fitting algorithm.

Methods: After nonrigid registration of the image series, a vectorized Levenberg-Marquardt (LM) technique is proposed to improve the robustness of the curve fitting algorithm by allowing spatial regularization of the parametric maps. In addition, a region-based initialization is proposed to improve the initial guess of the T₁ value. The algorithm was validated with cardiac T₁ mapping data from 16 volunteers acquired with saturation-recovery (SR) and inversion-recovery (IR) techniques at 3T, both pre- and post-injection of a contrast agent. Signal models of T₁ relaxation with 2 and 3 parameters were tested.

Results: The vectorized LM fitting showed good agreement with its pixel-wise version but allowed reduced calculation time (60 s against 696 s on average in Matlab with 256 × 256 × 8(11) images). Increasing the spatial regularization parameter led to noise reduction and improved precision of T₁ values in SR sequences. The region-based initialization was particularly useful in IR data to reduce the variability of the blood T₁.

Conclusions: We have proposed a vectorized curve fitting algorithm allowing spatial regularization, which could improve the robustness of the curve fitting, especially for myocardial T₁ mapping with SR sequences.

Keywords: Cardiac MR; Curve fitting; MR parameter mapping; Relaxometry; T(1) mapping.