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Register a new userAn Efficient Method for Multi-Parameter Mapping in Quantitative MRI using B-Spline Interpolation
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Added by
Willem Van Valenberg
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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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, 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. 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 ($T_1,T_2,B_1^+$) by, on average, an order of magnitude. In effect, the applied dictionary was reduced from 1.47 GB to 464 KB. 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.
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Optimizing k-space sampling trajectories is a challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction algorithm and sampling trajectories jointly concerning image reconstruction quality. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and enable multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct the potential eddy-current effect introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in-vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 20x acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.
Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.
The use of wireless implanted medical devices (IMDs) is growing because they facilitate continuous monitoring of patients during normal activities, simplify medical procedures required for data retrieval and reduce the likelihood of infection associated with trailing wires. However, most of the state-of-the-art IMDs are passive and offline devices. One of the key obstacles to an active and online IMD is the infeasibility of real-time, high-quality video broadcast from the IMD. Such broadcast would help develop innovative devices such as a video-streaming capsule endoscopy (CE) pill with therapeutic intervention capabilities. State-of-the-art IMDs employ radio-frequency electromagnetic waves for information transmission. However, high attenuation of RF-EM waves in tissues and federal restrictions on the transmit power and operable bandwidth lead to fundamental performance constraints for IMDs employing RF links, and prevent achieving high data rates that could accomodate video broadcast. In this work, ultrasonic waves were used for video transmission and broadcast through biological tissues. The proposed proof-of-concept system was tested on a porcine intestine ex vivo and a rabbit in vivo. It was demonstrated that using a millimeter-sized, implanted biocompatible transducer operating at 1.1-1.2 MHz, it was possible to transmit endoscopic video with high resolution (1280 pixels by 720 pixels) through porcine intestine wrapped with bacon, and to broadcast standard definition (640 pixels by 480 pixels) video near real-time through rabbit abdomen in vivo. A media repository that includes experimental demonstrations and media files accompanies this paper. The accompanying media repository can be found at this link: https://bit.ly/3wuc7tk.
Recently, deep learning methods have been proposed for quantitative susceptibility mapping (QSM) data processing: background field removal, field-to-source inversion, and single-step QSM reconstruction. However, the conventional padding mechanism used in convolutional neural networks (CNNs) can introduce spatial artifacts, especially in QSM background field removal and single-step QSM which requires inference from total fields with extreme large values at the edge boundaries of volume of interest. To address this issue, we propose an improved padding technique which utilizes the neighboring valid voxels to estimate the invalid voxels of feature maps at volume boundaries in the neural networks. Studies using simulated and in-vivo data show that the proposed padding greatly improves estimation accuracy and reduces artifacts in the results in the tasks of background field removal, field-to-source inversion, and single-step QSM reconstruction.
For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with variable density, AMP encounters convergence problems. In response we present an algorithm based on Orthogonal AMP constructed specifically for variable density partial Fourier sensing matrices. For the first time in this setting a state evolution has been observed. A practical advantage of state evolution is that Steins Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with no free parameters. We empirically evaluate the effectiveness of the parameter-free algorithm on simulated data and find that it converges over 5x faster and to a lower mean-squared error solution than Fast Iterative Shrinkage-Thresholding (FISTA).
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