Purpose: To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account. Methods: A predictive model for the undersampling error leveraging on perturbation theory was exploited to optimize the MRF flip angle sequence for improved robustness against undersampling artifacts. In this framework parameter maps from a previously acquired MRF scan were used as reference. Sequences were optimized for different sequence lengths, smoothness constraints and undersampling factors. Numerical simulations and in vivo measurements in eight healthy subjects were performed to assess the effect of the performed optimization. The optimized MRF sequences were compared to a conventionally shaped flip angle pattern and an optimized pattern based on the Cramér–Rao lower bound (CRB). Results: Numerical simulations and in vivo results demonstrate that the undersampling errors can be suppressed by flip angle optimization. Analysis of the in vivo results show that a sequence optimized for improved robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors in (Formula presented.) : (Formula presented.) and (Formula presented.) : (Formula presented.) compared to the conventional ((Formula presented.) : (Formula presented.), (Formula presented.) : (Formula presented.)) and CRB-based ((Formula presented.) : (Formula presented.), (Formula presented.) : (Formula presented.)) sequences. Conclusion: The proposed method is able to optimize the MRF flip angle pattern such that significant mitigation of the artifacts from strong k-space undersampling in MRF is achieved.

Purpose: To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues. Methods: The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference. Results: The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0% (Formula presented.) 5.8% with the conventional, two-step approach to 9.6% (Formula presented.) 3.9% and 9.6% (Formula presented.) 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN). Conclusion: The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method.

Objective: To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries. Materials and methods: High-dimensional MRF dictionaries were simulated and embedded into a lower-dimensional space using t-distributed stochastic neighbor embedding (t-SNE). The embeddings were visualized via colors as a surrogate for location in low-dimensional space. First, we illustrate this technique on three different MRF sequences. We then compare the resulting embeddings and the color-coded dictionary maps to these obtained with a singular value decomposition (SVD) dimensionality reduction technique. We validate the t-SNE approach with measures based on existing quantitative measures of encoding capability using the Euclidean distance. Finally, we use t-SNE to visualize MRF sequences resulting from an MRF sequence optimization algorithm. Results: t-SNE was able to show clear differences between the color-coded dictionary maps of three MRF sequences. SVD showed smaller differences between different sequences. These findings were confirmed by quantitative measures of encoding. t-SNE was also able to visualize differences in encoding capability between subsequent iterations of an MRF sequence optimization algorithm. Discussion: This visualization approach enables comparison of the encoding capability of different MRF sequences. This technique can be used as a confirmation tool in MRF sequence optimization.

Purpose: To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions. Methods: A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian noise images. Each multichannel training example contains a simulated sampling mask, complex coil sensitivity maps, and two regularization parameter maps. The trained model was integrated in the preconditioned conjugate gradient (PCG) method as part of the split Bregman CS method. The acceleration performance was compared with that of a circulant PI-CS preconditioner for varying undersampling factors, number of coil elements and anatomies. Results: The learned preconditioner reduces the number of PCG iterations by a factor of 4, yielding a similar acceleration as an efficient circulant preconditioner. The method generalizes well to different sampling schemes, coil configurations and anatomies. Conclusion: It is possible to learn adaptable preconditioners for PI and CS reconstructions that meet the performance of state-of-the-art preconditioners. Further acceleration could be achieved by optimizing the network architecture and the training set. Such a preconditioner could also be integrated in fully learned reconstruction methods to accelerate the training process of unrolled networks.

Purpose: To design a low-cost, portable permanent magnet-based MRI system capable of obtaining in vivo MR images within a reasonable scan time. Methods: A discretized Halbach permanent magnet array with a clear bore diameter of 27 cm was designed for operation at 50 mT. Custom-built gradient coils, RF coil, gradient amplifiers, and RF amplifier were integrated and tested on both phantoms and in vivo. Results: Phantom results showed that the gradient nonlinearity in the y-direction and z-direction was less than 5% over a 15-cm FOV and did not need correcting. For the x-direction, it was significantly greater, but could be partially corrected in postprocessing. Three-dimensional in vivo scans of the brain of a healthy volunteer using a turbo spin-echo sequence were acquired at a spatial resolution of 4 × 4 × 4 mm in a time of about 2 minutes. The T₁-weighted and T₂-weighted scans showed a good degree of tissue contrast. In addition, in vivo scans of the knee of a healthy volunteer were acquired at a spatial resolution of about 3 × 2 × 2 mm within 12 minutes to show the applicability of the system to extremity imaging. Conclusion: This work has shown that it is possible to construct a low-field MRI unit with hardware components costing less than 10 000 Euros, which is able to acquire human images in vivo within a reasonable data-acquisition time. The system has a high degree of portability with magnet weight of approximately 75 kg, gradient and RF amplifiers each 15 kg, gradient coils 10 kg, and spectrometer 5 kg.

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 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 $(\boldsymbol {T}_{\boldsymbol {1}},\boldsymbol {T}_{\boldsymbol {2}})$ , proton density $\left ({\boldsymbol {PD} }\right)$ , receiver phase ( $\boldsymbol {\varphi }_{\boldsymbol {0}}$ ), transmit field inhomogeneity ( $\boldsymbol {B}_{\boldsymbol {1}}^{\boldsymbol {+}}$ ), and slice profile. Parameter maps were compared with 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 ( $\boldsymbol {T}_{\boldsymbol {1}},\boldsymbol {T}_{\boldsymbol {2}},\boldsymbol {B}_{\boldsymbol {1}}^{\boldsymbol {+}}$ ) by - on average - an order of magnitude. In effect, the applied dictionary was reduced from .47GB$ to $464KB$. Furthermore, the proposed method was equally robust against undersampling artifacts as dictionary matching. Dictionary fitting with B-spline interpolation reduces the computational and memory costs of dictionary-based methods and is therefore a promising method for multi-parametric mapping.