Auto-Calibrated Parallel Imaging Reconstruction for Arbitrary Trajectories Using ${\bf k}$-Space Sparse Matrices (kSPA)

PBPK model of methotrexate in cerebrospinal fluid ventricles using a combined microdialysis and MRI acquisition

This paper presents a novel hardware solution for solving sparse matrices using emulation technology. The proposed solution introduces a bio-inspired technique, which is Genetic Algorithm (GA) to solve the sparse system of linear equations (SLEs). The proposed solution can be used with any physical system that can be modeled as SLEs. Computations involved in Finite Element Method (FEM) consume too much time, which affects the final time-to-market value. Profiling shows that the most time-consuming part in the simulation process is the solver part which is responsible for solving the resultant SLEs generated from the FEM. The total number of equations may reach thousands or millions of linear equations. Hardware implementation of GA and making a good use of parallelism in implementing the architecture accelerate the time taken by the solver part. Solving the system by classical numerical methods, such as conjugate gradient (CG) implemented in software is performed sequentially, here the architecture allows the parallelism in performing GA operators, such as selection, crossover, and mutation. The parallelism in the proposed architecture is the superiority point which we rely on. The results show that our proposed method to solve the SLEs outperforms the classical CG software implementation on run time and number of equations.

It is known that the main computational costs in the FEM implementation are computing the global system of linear equations (material response computation and stiffness matrix ensemble) and its solution. With the aim of speeding up the total solving boundary value problem time with the help of the developed solver, algorithms of the parallel stiffness matrix ensemble and the system of linear equations solution were implemented. In this paper the results of using GPU to accelerate computations related to the solution of direct boundary value problems of crystal plasticity are present. The existing algorithms for solving the sparse systems of linear equations and parallel ensemble of the global stiffness matrix were implemented on both the CPU and GPU. As a result, a total acceleration of up to 10 times was obtained compared to the software implementation on the CPU.

Introduction. Kron [1] has developed a technique for tearing large, sparse linear systems of algebraic equations into smaller systems, then putting the solutions of these smaller systems together to form the solution of the original problem. This can result in a great savings over solving the whole system in one piece. The trick is to find where to tear so that on the one hand the remaining pieces are small and easily solvable, but on the other hand not so much violence is done to the equations so that the task of putting their solutions back together becomes too difncult. Kron's pro? cedure for solving the pieces and putting their solutions together is based upon representing systems of equations as electric networks. He makes his choice of where to tear from his insight into these networks and the physical processes the equations represent. In the hands of someone such as Kron who has an understanding of the methods and good insight into the prob? lem, this technique has had outstanding success. The widespread use of Kron's technique has perhaps been limited severely for lack of practitioners skilled in this art of determining effective ways of tearing specific problems. Many problems are too large to submit to such insight. It is the purpose of this paper to contribute to the development of procedures which can be performed on a computer for analyzing the structures of the systems of equations themselves as an aid in choosing how to break them up for easier solution. The methods developed here require only that we consider what variables occur in each equation, but not how they appear. Thus, the tech? niques are not limited to linear systems.

Computer subroutines for solving large sparse systems of linear equations usually involve fairly complicated data structures and storage management. In most cases, the user of such subroutines simply wants top solve his problem and does not have to understand how the storage management is done, or how the matrix components are stored. Thus software for solving sparse systems of linear equations should be designed in such a way that it can insulate the user from these considerations, while still allowing the software to be used in a variety of ways.

During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.

Element-by-element iterative solution methods have been shown to be effective for solving large, sparse linear systems of equations with a positive definite stiffness matrix. In this paper the iterative method GMRES will be described. This solution method is also suited for solving nonsymmetric systems of equations. As acceleration technique an element-by-element preconditioner has been employed. Attention is focused mainly on the convergence behaviour of the method. The calculations described in this paper have been performed with the finite element package DIANA.

Fast acquisition in magnetic resonance imaging (MRI) is considered in this paper. Often, fast acquisition is achieved using parallel imaging (pMRI) techniques. It has been shown recently that the combination of pMRI and compressed sensing (CS), which enables exact reconstruction of sparse or compressible signals from a small number of random measurements, can accelerate the speed of MRI acquisition because the number of measurements are much smaller than that by pMRI per se. Also recently in CS, chaos filters were designed to obtain chaotic measurements. This chaotic CS approach potentially offers simpler hardware implementation. In this paper, we combine chaotic CS and pMRI. However, instead of using chaos filters, the measurements are obtained by chaotically undersampling the k-space. MRI image reconstruction is then performed by using nonlinear conjugate gradient optimization. For pMRI, we use the well-known approach SENSE - sensitivity encoding -, which requires an estimation of the sensitivity maps. The performance of the proposed method is analyzed using the point spread function, the transform point spread function, and the reconstruction error measure.

Mild traumatic brain injury (mTBI) sustained in early childhood affects the brain at a peak developmental period and may disrupt sensitive stages of skill acquisition, thereby compromising child functioning. However, due to the challenges of collecting non-sedated neuroimaging data in young children, the consequences of mTBI on young children's brains have not been systematically studied. In typically developing preschool children (of age 3-5years), a brief behavioral-play familiarization provides an effective alternative to sedation for acquiring awake magnetic resonance imaging (MRI) in a time- and resource-efficient manner. To date, no study has applied such an approach for acquiring non-sedated MRI in preschool children with mTBI who may present with additional MRI acquisition challenges such as agitation or anxiety. The present study aimed to compare the effectiveness of a brief behavioral-play familiarization for acquiring non-sedated MRI for research purposes between young children with and without mTBI, and to identify factors associated with successful MRI acquisition. Preschool children with mTBI (n=13) and typically developing children (n=24) underwent a 15-minutes behavioral-play MRI familiarization followed by a 35-minutes non-sedated MRI protocol. Success rate was compared between groups, MRI quality was assessed quantitatively, and factors predicting success were documented. Among the 37 participants, 15 typically developing children (63%) and 10 mTBI (77%) reached the MRI acquisition success criteria (i.e., completing the two first sequences). The success rate was not significantly different between groups (p=.48; 95% CI [-0.36 14.08]; Cramer's V=.15). The images acquired were of high-quality in 100% (for both groups) of the structural images, and 60% (for both groups) of the diffusion images. Factors associated with success included older child age (Β=0.73, p=.007, exp(B)=3.11, 95% CI [1.36 7.08]) and fewer parental concerns (Β=-1.56, p=.02, exp(Β)=0.21, 95% CI [0.05 0.82]) about the MRI procedure. Using brief behavioral-play familiarization allows acquisition of high-quality non-sedated MRI in young children with mTBI with success rates comparable to those of non-injured peers.

Radial encoding is often performed for fast data acquisition in magnetic resonance imaging (MRI). Therefore, the gridding method, which is a kind of algorithm for Fast Fourier Transform, is widely used in fast MRI reconstruction. In this paper, an improved gridding method has been utilized to 2D MRI reconstruction, which precomputes an 1D finely sampled table of a high-accuracy interpolator and then uses separable bilinear interpolation by look-up table. Experimental comparisons are made by assessing the performance of the direct reconstruction, the conventional KB gridding and the proposed method. The experimental results show that the proposed method provides high accuracy, fast computation, and dramatic memory saving.

In many in vivo magnetic resonance imaging (MRI) acquisitions, the image resolution is low and induces considerable segmentation errors with a poor and limited visual interpretation. Acquiring high-resolution images reduces the patient comfort and results in considerable cost because of an increase of the acquisition time. We developed a progressive technique based on multidimensional dual kriging to interpolate 2D and 3D multi-parametric MRI data. The objectives were to (1) optimise kriging parameters for 2D images and 3D volumes interpolation, (2) validate the technique in increasing the image resolution and (3) provide a direct application to 3D non-parametric volumes interpolation and image filtering. We carried out two multi-parametric MRI acquisitions on a bovine tail segment including intervertebral discs from the second to the fourth caudal vertebrae with two different spatial resolutions. We adopted the dual kriging formulation and introduced the technique of progressive kriging, which consists in kriging the given Cartesian data region-by-region. Kriging parameters were optimised to minimise the relative errors. For each MRI sequence, kriging was compared with other interpolation techniques in terms of signal mean within the region of interest, including the zero-padding, the nearest-neighbour, the bilinear and the bicubic techniques. Optimal kriging parameters for transverse relaxation time maps interpolation were a cubic covariance function and a distance of influence of only 1–8 pixels. Our technique was found to be efficient to interpolate the longitudinal and transverse relaxation times, the magnetisation transfer ratio and the apparent diffusion coefficient maps, compared with zero-padding, nearest-neighbour, bilinear and bicubic techniques. Kriging provided relatively high performance and low error, whereas image edges tend to be corrected and better defined compared with other techniques. Progressive dual kriging is a flexible technique that can be optimised to interpolate multidimensional data based on the signal distribution and should open doors to many future applications in medical imaging such as diffusion MRI, image filtering and non-parametric 3D volume reconstruction.

The possibility to perform an early and repeatable assessment of imaging performance is fundamental in the design and development process of new ultrasound (US) probes. Particularly, a more realistic analysis with application-specific imaging targets can be extremely valuable to assess the expected performance of US probes in their potential clinical field of application. The experimental protocol presented in this work was purposely designed to provide an application-specific assessment procedure for newly-developed US probe prototypes based on Capacitive Micromachined Ultrasonic Transducer (CMUT) technology in relation to brain imaging. The protocol combines the use of a bovine brain fixed in formalin as the imaging target, which ensures both realism and repeatability of the described procedures, and of neuronavigation techniques borrowed from neurosurgery. The US probe is in fact connected to a motion tracking system which acquires position data and enables the superposition of US images to reference Magnetic Resonance (MR) images of the brain. This provides a means for human experts to perform a visual qualitative assessment of the US probe imaging performance and to compare acquisitions made with different probes. Moreover, the protocol relies on the use of a complete and open research and development system for US image acquisition, i.e. the Ultrasound Advanced Open Platform (ULA-OP) scanner. The manuscript describes in detail the instruments and procedures involved in the protocol, in particular forthe calibration, image acquisition and registration of US and MR images. The obtained results prove the effectiveness of the overall protocol presented, which is entirely open (within the limits of the instrumentation involved), repeatable, and covers the entire set of acquisition and processing activities for US images.

Bulk motion occurring during the acquisition of magnetic resonance images (MRI) remains a significant limitation in image quality. The paper presents an extension to TRELLIS, a recently developed method of detecting and correcting for bulk motion. Accurate determination of the relative orientations of overlapping strips of k-space is demonstrated. Reconstructions for both simulated and actual MRI acquisitions are presented.

A paradigm for concurrent computing is explored in which a group of autonomous, asynchronous processes shares a common memory space and cooperates to solve a single problem. The processes synchronize with only a few others at a time; barrier synchronization is not permitted except at the beginning and end of the computation. The paradigm maps directly to a shared-memory multiprocessor with efficient synchronization primitives and is applied to the solution of a large, sparse system of linear equations. The algorithm, called pairwise solve (or PSolve), is presented with several variants to address some of the limitations of previous algorithms. On the Alliant FX/8, PSolve is faster than Gaussian elimination and two common sparse matrix algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Super-resolution reconstruction of single anisotropic 3D MR images using residual convolutional neural network