Walid E. Kyriakos

Multi-component apparent diffusion coefficients in human brain†

The signal decay with increasing b‐factor at fixed echo time from brain tissue in vivo has been measured using a line scan Stejskal–Tanner spin echo diffusion approach in eight healthy adult volunteers. The use of a 175 ms echo time and maximum gradient strengths of 10 mT/m allowed 64 b‐factors to be sampled, ranging from 5 to 6000 s/mm2, a maximum some three times larger than that typically used for diffusion imaging. The signal decay with b‐factor over this extended range showed a decidedly non‐exponential behavior well‐suited to biexponential modeling. Statistical analyses of the fitted biexponential parameters from over 125 brain voxels (15 × 15 × 1 mm3 volume) per volunteer yielded a mean volume fraction of 0.74 which decayed with a typical apparent diffusion coefficient around 1.4 µm2/ms. The remaining fraction had an apparent diffusion coefficient of approximately 0.25 µm2/ms. Simple models which might explain the non‐exponential behavior, such as intra‐ and extracellular water compartmentation with slow exchange, appear inadequate for a complete description. For typical diffusion imaging with b‐factors below 2000 s/mm2, the standard model of monoexponential signal decay with b‐factor, apparent diffusion coefficient values around 0.7 µm2/ms, and a sensitivity to diffusion gradient direction may appear appropriate. Over a more extended but readily accessible b‐factor range, however, the complexity of brain signal decay with b‐factor increases, offering a greater parametrization of the water diffusion process for tissue characterization. Copyright

Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP).

A new parallel imaging technique was implemented which can result in reduced image acquisition times in MRI. MR data is acquired in parallel using an array of receiver coils and then reconstructed simultaneously with multiple processors. The method requires the initial estimation of the 2D sensitivity profile of each coil used in the receiver array. These sensitivity profiles are then used to partially encode the images of interest. A fraction of the total number of k‐space lines is consequently acquired and used in a parallel reconstruction scheme, allowing for a substantial reduction in scanning and display times. This technique is in the family of parallel acquisition schemes such as simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE). It extends the use of the SMASH method to allow the placement of the receiver coil array around the object of interest, enabling imaging of any plane within the volume of interest. In addition, this technique permits the arbitrary choice of the set of k‐space lines used in the reconstruction and lends itself to parallel reconstruction, hence allowing for real‐time rendering. Simulated results with a 16‐fold increase in temporal resolution are shown, as are experimental results with a 4‐fold increase in temporal resolution. Magn Reson Med 44:301–308, 2000.

Multi-component apparent diffusion coefficients in human brain : Relationship to spin-lattice relaxation

In vivo measurements of the human brain tissue water signal decay with b‐factor over an extended b‐factor range up to 6,000 s/mm 2 reveal a nonmonoexponential decay behavior for both gray and white matter. Biexponential parametrization of the decay curves from cortical gray (CG) and white matter voxels from the internal capsule (IC) of healthy adult volunteers describes the decay process and serves to differentiate between these two tissues. Inversion recovery experiments performed in conjunction with the extended b‐factor signal decay measurements are used to make separate measurements of the spin‐lattice relaxation times of the fast and slow apparent diffusion coefficient (ADC) components. Differences between the spin‐lattice relaxation times of the fast and slow ADC components were not statistically significant in either the CG or IC voxels. It is possible that the two ADC components observed from the extended b‐factor measurements arise from two distinct water compartments with different intrinsic diffusion coefficients. If so, then the relaxation results are consistent with two possibilities. Either the spin‐lattice relaxation times within the compartments are similar or the rate of water exchange between compartments is “fast” enough to ensure volume averaged T1 relaxation yet “slow” enough to allow for the observation of biexponential ADC decay curves over an extended b‐factor range. Magn Reson Med 44:292–300, 2000.

Fast regularized reconstruction of non-uniformly subsampled parallel MRI data

Parallel MR imaging is an effective approach to reduce MR image acquisition time. Non-uniform subsampling allows one to tailor the subsampling scheme for improved image quality at high acceleration factors. However, non-uniform subsampling precludes fast reconstruction schemes such as SENSE, and is more likely to require a regularized solution than reconstruction of uniformly subsampled data demands. This means that one needs to choose a good regularization parameter, typically requiring multiple expensive system solves. Here, we present an efficient LSQR-Hybrid algorithm which simultaneously addresses the need for rapid regularization parameter selection and fast reconstruction. This algorithm can reconstruct non-uniformly subsampled parallel MRI data, with automatic regularization and good image quality, in a time competitive with Cartesian SENSE

On the regularization of SENSE and Space-RIP in parallel MR imaging

Parallel imaging methods provide accelerated multiple coil MR image acquisitions via reconstruction of sub-sampled k-space data. Currently, analytic comparison between different reconstruction approaches has been hampered by use of different phase encoding paradigms and regularization approaches, historically unique to each method. We present an analysis of the Space-RIP image reconstruction problem that demonstrates the ability to recast the problem in a decoupled form when uniform down-sampling is employed. We show that this decoupled problem is equivalent to the SENSE image reconstruction approach. This approach enables a clear analytic comparison between SENSE and Space-RIP, and we demonstrate the effect of different regularization approaches on image formation in low coil sensitivity regions.

Non-Fourier-encoded parallel MRI using multiple receiver coils.

This paper describes a general theoretical framework that combines non‐Fourier (NF) spatially‐encoded MRI with multichannel acquisition parallel MRI. The two spatial‐encoding mechanisms are physically and analytically separable, which allows NF encoding to be expressed as complementary to the inherent encoding imposed by RF receiver coil sensitivities. Consequently, the number of NF spatial‐encoding steps necessary to fully encode an FOV is reduced. Furthermore, by casting the FOV reduction of parallel imaging techniques as a dimensionality reduction of the k‐space that is NF‐encoded, one can obtain a speed‐up of each digital NF spatial excitation in addition to accelerated imaging. Images acquired at speed‐up factors of 2× to 8× with a four‐element RF receiver coil array demonstrate the utility of this framework and the efficiency afforded by it. Magn Reson Med 52:321–328, 2004.

Projection-based estimation and nonuniformity correction of sensitivity profiles in phased-array surface coils.

To develop a novel approach for calculating the accurate sensitivity profiles of phased‐array coils, resulting in correction of nonuniform intensity in parallel MRI.

Comparison of parallel MRI reconstruction methods for accelerated 3D fast spin-echo imaging.

Parallel MRI (pMRI) achieves imaging acceleration by partially substituting gradient‐encoding steps with spatial information contained in the component coils of the acquisition array. Variable‐density subsampling in pMRI was previously shown to yield improved two‐dimensional (2D) imaging in comparison to uniform subsampling, but has yet to be used routinely in clinical practice. In an effort to reduce acquisition time for 3D fast spin‐echo (3D‐FSE) sequences, this work explores a specific nonuniform sampling scheme for 3D imaging, subsampling along two phase‐encoding (PE) directions on a rectilinear grid. We use two reconstruction methods—2D‐GRAPPA‐Operator and 2D‐SPACE RIP—and present a comparison between them. We show that high‐quality images can be reconstructed using both techniques. To evaluate the proposed sampling method and reconstruction schemes, results via simulation, phantom study, and in vivo 3D human data are shown. We find that fewer artifacts can be seen in the 2D‐SPACE RIP reconstructions than in 2D‐GRAPPA‐Operator reconstructions, with comparable reconstruction times. Magn Reson Med 60:650–660, 2008.

Sampling strategies to enable computationally efficient SPACE-RIP for 3D parallel MR imaging

New MR acquisition techniques are enabling fast acquisition of data from an entire 3D volume. Parallel MR imaging methods can provide additional acceleration to the data acquisition rate. However, the large computational memory requirements associated with 3D imaging requires new efficient reconstruction techniques. This manuscript presents an efficient implementation of SPACE-RIP for the rapid reconstruction of sub-sampled 3D MR data. Uniform sub-sampling effectively decouples the SPACE-RIP linear system of equations into a number of smaller systems which can each be solved independently, thus requiring fewer computational resources. We present a particular phase-encode sampling pattern to capitalize on this effect which allows SPACE-RIP to be computationally competitive with SENSE in 3D imaging, while providing the added benefits of self-calibrated coil sensitivity maps and improved artifact suppression through irregular sub-sampling.

Developments in parallel MRI using SPACE RIP

Parallel acquisition techniques in Magnetic Resonance Imaging (MRI) have recently shown great potential to accelerate the speed of image acquisition. A number of techniques such as SENSE and SMASH have been described thoroughly in the literature, and applied to various dynamic imaging applications. This presentation reports on the state of development of one such technique termed SPACE RIP, its challenges, limitations, and potential applications.