Quasi Monte Carlo-based isotropic distribution of gradient directions for improved reconstruction quality of 3D EPR imaging

Ultrafast multiple paramagnetic species EPR imaging using a total variation based model

An EPR spectrum or an EPR sinogram for imaging contains information about all the paramagnetic species that are in the analyzed sample. When only one species is present, an image of its spatial repartition can be reconstructed from the sinogram by using the well-known Filtered Back-Projection (FBP). However, in the case of several species, the FBP does not allow the reconstruction of the images of each species from a standard acquisition. One has to use for this spectral-spatial imaging whose acquisition can be very long. A new approach, based on Total Variation minimization, is proposed in order to efficiently extract the spatial repartitions of all the species present in a sample from standard imaging data and therefore drastically reduce the acquisition time. Experiments have been carried out on Tetrathiatriarylmethyl, nitroxide and DPPH.

Development of a fast-scan EPR imaging system for highly accelerated free radical imaging

PURPOSE

In continuous wave EPR imaging, the acquisition of high-quality images was previously limited by the requisite long acquisition times of each image projection that was typically greater than 1 second. To accelerate the process of image acquisition facilitating greater numbers of projections and higher image resolution, instrumentation was developed to greatly accelerate the magnetic field scan that is used to obtain each EPR image projection.

METHODS

A low-inductance solenoidal coil for field scanning was used along with a spherical solenoid air core magnet, and scans were driven by triangular symmetric waves, allowing forward and reverse spectrum acquisition as rapid as 3.8 ms. The uniform distribution of projections was used to optimize the contribution of projections for 3D image reconstruction.

RESULTS

Using this fast-scan EPR system, high-quality EPR images of phantoms and perfused rat hearts were performed using trityl or nanoparticulate LiNcBuO (lithium octa-n-butoxy-substituted naphthalocyanine) probes with fast-scan EPR imaging at L-band, achieving spatial resolutions of up to 250 micrometers in 1 minute.

CONCLUSION

Fast-scan EPR imaging can greatly facilitate the efficient and precise mapping of the spatial distribution of free radical and other paramagnetic probes in living systems.

A Spatiotemporal-Constrained Sorting Method for Motion-Robust 4D-MRI: A Feasibility Study

PURPOSE

To develop a spatiotemporal-constrained sorting technique for motion-robust 4 dimensional-magnetic resonance imaging.

METHODS AND MATERIALS

This sorting method implemented 2 new approaches for 4-dimensional imaging: (1) an optimized sparse k-space acquisition trajectory with self-gating signal derivation, and (2) a retrospective k-space sorting for reconstruction using a novel spatiotemporal-constrained strategy to minimize breathing variation-induced motion artifacts. Such sorting was regularized by a spatiotemporal index. Volumetric reconstruction was implemented iteratively with a secnd-order total generalized variation penalty. The proposed method was evaluated and compared with the conventional phase-sorting and amplitude-sorting methods in 2 studies. In a computer simulation study, 6 abdominal motion scenarios, including 2 cosine and 4 patient breathing motion patterns, were studied. Reconstruction accuracy was evaluated quantitatively in reference to the ground truth by average image relative error (IRE) in 10 phases and target Dice similarity coefficients (DSCs) in end-of-exhalation/inhalation phases. In addition, the proposed method was evaluated using a custom-made motion phantom. Reconstruction accuracy was evaluated by motion range measurement and image quality comparison in both fast and slow breathing motions.

RESULTS

In the simulation study, stitching motion artifacts in restricted images were lessened using the proposed method compared with those using the conventional methods. The average IRE and target DSC (end-of-exhalation/inhalation) were 0.031 and 0.95/0.94, respectively, suggesting better motion reconstruction accuracy than the phase-sorted method (IRE, 0.057; DSC, 0.89/0.89) and the amplitude-sorted method (IRE, 0.048; DSC, 0.91/0.88). In the phantom study, the moving target reconstructed by the proposed method demonstrated better rendering with less edge blurring. With fast breathing motion, the range measured using the proposed method was more accurate than that of the phase-sorted method and was comparable to the result of amplitude-sorted method and ground truths.

CONCLUSIONS

Preliminary results suggested that the proposed sorting technique could reconstruct high-quality images and accurate motion estimation with reduced artifacts in 4 dimensional-magnetic resonance imaging.

Pseudometrically constrained centroidal voronoi tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and three-dimensional radial MRI

PURPOSE

The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role in image quality when the raw data and image data are related through the Fourier relationship. Currently, it is extremely challenging to generate large and uniform antipodally symmetric point sets suitable for three-dimensional radial MRI. A novel approach is proposed to solve this long-standing problem in a unique and optimal way.

METHODS

The proposed method is based on constrained centroidal Voronoi tessellations of the upper hemisphere with a novel pseudometric.

RESULTS

The time complexity of the proposed tessellations was shown to be effectively linear, i.e., on the order of the number of sampling measurements. For small sample size, the proposed method was comparable with the state-of-the-art method (a direct iterative minimization of the electrostatic potential energy of a collection of electrons antipodal-symmetrically distributed on the unit sphere) in terms of the sampling uniformity. For large sample size, in which the state-of-the-art method is infeasible, the reconstructed images from the proposed method has less streak and ringing artifacts, when compared with those of the commonly used methods.

CONCLUSION

This work proposed a unique and optimal approach to solving a long-standing problem in generating uniform sampling points for three-dimensional radial MRI.

Maximally spaced projection sequencing in electron paramagnetic resonance imaging

Electron paramagnetic resonance imaging (EPRI) provides 3D images of absolute oxygen concentration (pO₂) in vivo with excellent spatial and pO₂ resolution. When investigating such physiologic parameters in living animals, the situation is inherently dynamic. Improvements in temporal resolution and experimental versatility are necessary to properly study such a system. Uniformly distributed projections result in efficient use of data for image reconstruction. This has dictated current methods such as equal-solid-angle (ESA) spacing of projections. However, acquisition sequencing must still be optimized to achieve uniformity throughout imaging. An object-independent method for uniform acquisition of projections, using the ESA uniform distribution for the final set of projections, is presented. Each successive projection maximizes the distance in the gradient space between itself and prior projections. This maximally spaced projection sequencing (MSPS) method improves image quality for intermediate images reconstructed from incomplete projection sets, enabling useful real-time reconstruction. This method also provides improved experimental versatility, reduced artifacts, and the ability to adjust temporal resolution post factum to best fit the data and its application. The MSPS method in EPRI provides the improvements necessary to more appropriately study a dynamic system.

EPR image based oxygen movies for transient hypoxia

Chronic hypoxia strongly affects the malignant state and resistance to therapy for tumors. Transient hypoxia has been hypothesized, but not proven to be more deleterious. Electron paramagnetic resonance imaging (EPRI) provides non-invasive, quantitative imaging of static pO₂ in vivo. Dynamic EPRI produces pO₂ movies, enabling non-invasive assessment of in vivo pO₂ changes, such as transient hypoxia. Recent developments have been made to enable Dynamic EPRI. Maximally spaced projection sequencing has been implemented to allow for more accurate and versatile acquisition of EPRI data when studying dynamic systems. Principal component analysis filtering has been employed to enhance SNR. Dynamic EPRI studies will provide temporally resolved oxygen movies necessary to perform in vivo studies of physiologically relevant pO₂ changes in tumors. These oxygen movies will allow for the localization/quantification of transient hypoxia and will therefore help to disentangle the relationship between chronic and transient hypoxia, in order to better understand their roles in therapeutic optimization and outcome.

Compressed sensing of spatial electron paramagnetic resonance imaging

PURPOSE

To improve image quality and reduce data requirements for spatial electron paramagnetic resonance imaging (EPRI) by developing a novel reconstruction approach using compressed sensing (CS).

METHODS

EPRI is posed as an optimization problem, which is solved using regularized least-squares with sparsity promoting penalty terms, consisting of the l1 norms of the image itself and the total variation of the image. Pseudo-random sampling was employed to facilitate recovery of the sparse signal. The reconstruction was compared with the traditional filtered back-projection reconstruction for simulations, phantoms, isolated rat hearts, and mouse gastrointestinal (GI) tracts labeled with paramagnetic probes.

RESULTS

A combination of pseudo-random sampling and CS was able to generate high-fidelity EPR images at high acceleration rates. For three-dimensional (3D) phantom imaging, CS-based EPRI showed little visual degradation at nine-fold acceleration. In rat heart datasets, CS-based EPRI produced high quality images with eight-fold acceleration. A high resolution mouse GI tract reconstruction demonstrated a visual improvement in spatial resolution and a doubling in signal-to-noise ratio (SNR).

CONCLUSION

A novel 3D EPRI reconstruction using compressed sensing was developed and offers superior SNR and reduced artifacts from highly undersampled data.

Uniform spinning sampling gradient electron paramagnetic resonance imaging

PURPOSE

To improve the quality and speed of electron paramagnetic resonance imaging (EPRI) acquisition by combining a uniform sampling distribution with spinning gradient acquisition.

THEORY AND METHODS

A uniform sampling distribution was derived for spinning gradient EPRI acquisition (uniform spinning sampling, USS) and compared to the existing (equilinear spinning sampling, ESS) acquisition strategy. Novel corrections were introduced to reduce artifacts in experimental data.

RESULTS

Simulations demonstrated that USS puts an equal number of projections near each axis whereas ESS puts excessive projections at one axis, wasting acquisition time. Artifact corrections added to the magnetic gradient waveforms reduced noise and correlation between projections. USS images had higher SNR (85.9 ± 0.8 vs. 56.2 ± 0.8) and lower mean-squared error than ESS images. The quality of the USS images did not vary with the magnetic gradient orientation, in contrast to ESS images. The quality of rat heart images was improved using USS compared to that with ESS or traditional fast-scan acquisitions.

CONCLUSION

A novel EPRI acquisition which combines spinning gradient acquisition with a uniform sampling distribution was developed. This USS spinning gradient acquisition offers superior SNR and reduced artifacts compared to prior methods enabling potential improvements in speed and quality of EPR imaging in biological applications.

A simple scheme for generating nearly uniform distribution of antipodally symmetric points on the unit sphere

A variant of the Thomson problem, which is about placing a set of points uniformly on the surface of a sphere, is that of generating uniformly distributed points on the sphere that are endowed with antipodal symmetry, i.e., if x is an element of the point set then -x is also an element of that point set. Point sets with antipodal symmetry are of special importance to many scientific and engineering applications. Although this type of point sets may be generated through the minimization of a slightly modified electrostatic potential, the optimization procedure becomes unwieldy when the size of the point set increases beyond a few thousands. Therefore, it is desirable to have a deterministic scheme capable of generating this type of point set with near uniformity. In this work, we will present a simple deterministic scheme to generate nearly uniform point sets with antipodal symmetry.

Analytically exact spiral scheme for generating uniformly distributed points on the unit sphere

The problem of constructing a set of uniformly-distributed points on the surface of a sphere, also known as the Thomson problem, has a long and interesting history, which dates back to J.J. Thomson in 1904. A particular variant of the Thomson problem that is of great importance to biomedical imaging is that of generating a nearly uniform distribution of points on the sphere via a deterministic scheme. Although the point set generated through the minimization of electrostatic potential is the gold standard, minimizing the electrostatic potential of one thousand points (or charges) or more remains a formidable task. Therefore, a deterministic scheme capable of generating efficiently and accurately a set of uniformly-distributed points on the sphere has an important role to play in many scientific and engineering applications, not the least of which is to serve as an initial solution (with random perturbation) for the electrostatic repulsion scheme. In the work, we will present an analytically exact spiral scheme for generating a highly uniform distribution of points on the unit sphere.

Random volumetric MRI trajectories via genetic algorithms

A pseudorandom, velocity-insensitive, volumetric k-space sampling trajectory is designed for use with balanced steady-state magnetic resonance imaging. Individual arcs are designed independently and do not fit together in the way that multishot spiral, radial or echo-planar trajectories do. Previously, it was shown that second-order cone optimization problems can be defined for each arc independent of the others, that nulling of zeroth and higher moments can be encoded as constraints, and that individual arcs can be optimized in seconds. For use in steady-state imaging, sampling duty cycles are predicted to exceed 95 percent. Using such pseudorandom trajectories, aliasing caused by under-sampling manifests itself as incoherent noise. In this paper, a genetic algorithm (GA) is formulated and numerically evaluated. A large set of arcs is designed using previous methods, and the GA choses particular fit subsets of a given size, corresponding to a desired acquisition time. Numerical simulations of 1 second acquisitions show good detail and acceptable noise for large-volume imaging with 32 coils.

Improvement of temporal resolution for three-dimensional continuous-wave electron paramagnetic resonance imaging

This paper describes improved temporal resolution for three-dimensional (3D) continuous-wave electron paramagnetic resonance (EPR) imaging. To improve temporal resolution, the duration of magnetic filed scanning that is used to obtain an EPR spectrum for each projection was reduced to 40 ms. The Helmholtz coil pair for field scanning was driven by triangular waves. The uniform distribution of projections was also used to reduce the number of projections for 3D image reconstruction. The reduction reaction of 4-hydroxy-2,2,6,6-tetramethyl-piperidinooxy with ascorbic acid was visualized by improved 3D EPR imaging techniques with a temporal resolution of 5.8 s.

Development and testing of a CW-EPR apparatus for imaging of short-lifetime nitroxyl radicals in mouse head

This article describes a method for reducing the acquisition time in three-dimensional (3D) continuous-wave electron paramagnetic resonance (CW-EPR) imaging. To visualize nitroxyl spin probes, which have a short lifetime in living organisms, the acquisition time for a data set of spectral projections should be shorter than the lifetime of the spin probes. To decrease the total time required for data acquisition, the duration of magnetic field scanning was reduced to 0.5s. Moreover, the number of projections was decreased by using the concept of a uniform distribution. To demonstrate this faster data acquisition, two kinds of nitroxyl radicals with different decay rates were measured in mice. 3D EPR imaging of 4-hydroxy-2,2,6,6-tetramethylpiperidine-d17-1-15N-1-oxyl in mouse head was successfully carried out. 3D EPR imaging of nitroxyl spin probes with a half-life of a few minutes was achieved for the first time in live animals.

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging

In continuous wave (CW) electron paramagnetic resonance imaging (EPRI), high quality of reconstruction in a limited acquisition time is a high priority. It has been shown for the case of 3D EPRI, that a uniform distribution of the projection data generally enhances reconstruction quality. In this work, we have suggested two data acquisition techniques for which the gradient orientations are more evenly distributed over the 4D acquisition space as compared to the existing methods. The first sampling technique is based on equal solid angle partitioning of 4D space, while the second technique is based on Fekete points estimation in 4D to generate a more uniform distribution of data. After acquisition, filtered backprojection (FBP) is applied to carry out the reconstruction in a single stage. The single-stage reconstruction improves the spatial resolution by eliminating the necessity of data interpolation in multi-stage reconstructions. For the proposed data distributions, the simulations and experimental results indicate a higher fidelity to the true object configuration. Using the uniform distribution, we expect about 50% reduction in the acquisition time over the traditional method of equal linear angle acquisition.