Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated... Show moreQuantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching the measured signal with a precomputed signal dictionary on a discrete parameter grid (i.e. lookup table) as used in MR Fingerprinting. However, accurate estimation requires discretizing each parameter with a high resolution and consequently high computational and memory costs for dictionary generation, storage, and matching. Here, we reduce the required parameter resolution by approximating the signal between grid points through B-spline interpolation. The interpolant and its gradient are evaluated efficiently which enables a least-squares fitting method for parameter mapping. The resolution of each parameter was minimized while obtaining a user-specified interpolation accuracy. The method was evaluated by phantom and in-vivo experiments using fully-sampled and undersampled unbalanced (FISP) MR fingerprinting acquisitions. Bloch simulations incorporated relaxation effects (T-1, T-2), proton density (PD), receiver phase ( phi(0)), transmit field inhomogeneity (B-1(+)), and slice profile. Parametermapswere comparedwith those obtained from dictionary matching, where the parameter resolution was chosen to obtain similar signal (interpolation) accuracy. For both the phantom and the in-vivo acquisition, the proposed method approximated the parameter maps obtained through dictionary matching while reducing the parameter resolution in each dimension (T-1, T-2, B-1(+)) by - on average - an order of magnitude. In effect, the applied dictionary was reduced from 1.47GB to 464KB. Furthermore, the proposed method was equally robust against undersampling artifacts as dictionarymatching. Dictionary fittingwith B-spline interpolation reduces the computational and memory costs of dictionary-based methods and is therefore a promising method for multi- parametric mapping. Show less
A novel mathematical model describes spatial-temporal drug distribution within one or more brain units, which are cubic representations of a piece of brain tissue with brain capillaries at the... Show moreA novel mathematical model describes spatial-temporal drug distribution within one or more brain units, which are cubic representations of a piece of brain tissue with brain capillaries at the edges. The brain unit can be considered a highly representative building block of the brain in terms of drug distribution. While the focus of the model is on drug distribution within the brain ECF, the model includes descriptions of drug concentrations within the blood plasma, drug distribution via brain capillary blood flow, drug transport across the blood-brain barrier (BBB) by passive paracellular and transcellular transport as well as active transport, brain ECF diffusion, brain ECF bulk flow, non-specific binding of the drug to brain tissue, and drug target binding kinetics. We study the model with analytical methods and numerical simulations. This allows us to examine the integrated effect of the individual processes important to drug distribution and effect on the local concentration-time profiles of free and (non-)specifically bound drug. Moreover, the model allows us to generate a local distribution profile of a drug within the brain. In addition, the impact of disease-induced changes in brain-specific properties on the concentrations of drug within the brain ECF is assessed. Show less
Stochastic gradient descent (SGD) is commonly used to solve (parametric) image registration problems. In the case of badly scaled problems, SGD, however, only exhibits sublinear convergence... Show moreStochastic gradient descent (SGD) is commonly used to solve (parametric) image registration problems. In the case of badly scaled problems, SGD, however, only exhibits sublinear convergence properties. In this paper, we propose an efficient preconditioner estimation method to improve the convergence rate of SGD. Based on the observed distribution of voxel displacements in the registration, we estimate the diagonal entries of a preconditioning matrix, thus rescaling the optimization cost function. The preconditioner is efficient to compute and employ and can be used for mono-modal as well as multi-modal cost functions, in combination with different transformation models, such as the rigid, the affine, and the B-spline model. Experiments on different clinical datasets show that the proposed method, indeed, improves the convergence rate compared with SGD with speedups around 2 similar to 5 in all tested settings while retaining the same level of registration accuracy. Show less
Klinkenberg, D.; Hahne, S.J.M.; Woudenberg, T.; Wallinga, J. 2018
