Cramér-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI.

Objective: We extend the traditional framework for estimating subspace bases in quantitative MRI that maximize the preserved signal energy to additionally preserve the Cramer-Rao bound (CRB) of the biophysical ´ parameters and, ultimately, improve accuracy and precision in the quantitative maps.

Methods: To this end, we introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model.

Purpose: To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters.

Theory And Methods: We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model.

Cramér-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI.

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression.

Cramér-Rao bound-informed training of neural networks for quantitative MRI.

Purpose: To improve the performance of neural networks for parameter estimation in quantitative MRI, in particular when the noise propagation varies throughout the space of biophysical parameters.

Theory And Methods: A theoretically well-founded loss function is proposed that normalizes the squared error of each estimate with respective Cramér-Rao bound (CRB)-a theoretical lower bound for the variance of an unbiased estimator. This avoids a dominance of hard-to-estimate parameters and areas in parameter space, which are often of little interest.

Generalized Bloch model: A theory for pulsed magnetization transfer.

Purpose: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water.

Theory And Methods: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools.