Estimating T₁ from multichannel variable flip angle SPGR sequences

Abstract

Quantitative estimation of T1 is a challenging but important task inherent to many clinical applications. The most commonly used paradigm for estimating T1 in vivo involves performing a sequence of spoiled gradient-recalled echo acquisitions at different flip angles, followed by fitting of an exponential model to the data. Although there has been substantial work comparing different fitting methods, there has been little discussion on how these methods should be applied for data acquired using multichannel receivers. In this note, we demonstrate that the manner in which multichannel data is handled can have a substantial impact on T1 estimation performance and should be considered equally as important as choice of flip angles or fitting strategy.

Maximum likelihood reconstruction for magnetic resonance fingerprinting

“…Equation (12) has a separable structure, i.e., with a fixed value of θ, it reduces to a linear least-squares problem with respect to ρ. A class of algorithms based on variable projection Zhao et al Page 6 (VARPRO) [14]- [18] can efficiently solve this type of problems. The VARPRO method expresses the update for { } as follows 1 : (13) and (14) Note that it can be shown that solving (13) and (14) together can yield the same set of optimal solutions as (12) (see [15] for more details).…”

“…Although (13) is more amenable to generic nonlinear optimization methods, applying these methods still involves Bloch simulations, which can be time consuming. Inspired by [16]- [18] and the idea from MR fingerprinting [1], here we bypass this issue by reformulating (13) as a discrete optimization problem. More specifically, we discretize the feasible search space of θ n into a finite set of parameters , with which we use Bloch simulations to generate a dictionary that contains all possible signal evolutions, i.e.,…”

“…estimation formalism. To solve the resulting optimization problem, a novel solution algorithm, based on variable splitting (VS) [9]- [11], alternating direction method of multipliers (ADMM) [11]- [13], and variable projection (VARPRO) methods [14]- [18], is described. The proposed algorithm features a unique variable splitting strategy that separates the Bloch equation based physical model from the data model.…”

Model-Based MR Parameter Mapping With Sparsity Constraints: Parameter Estimation and Performance Bounds

“…Systematic experimental study are needed to further evaluate the practical utility of the proposed method. In this case, some practical issues also need to be taken into account, such as the generalization to multichannel acquisitions [66] and compensation of effects from sequence imperfection [67]. …”

Fast quantitative MRI as a nonlinear tomography problem

“…In this work, they are calculated by first order forward finite difference approximations. We point out that the VARPRO method has many applications and has even been used to solve different MR problems before [15–17]. …”