Publications by Year: 2008

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.

Characterizing diffusion of gases and liquids within pores is important in understanding numerous transport processes and affects a wide range of practical applications. Previous measurements of the pulsed gradient stimulated echo (PGSTE) signal attenuation, E(q), of water within nerves and impermeable cylindrical microcapillary tubes showed it to be exquisitely sensitive to the orientation of the applied wave vector, q, with respect to the tube axis in the high-q regime. Here, we provide a simple three-dimensional model to explain this angular dependence by decomposing the average propagator, which describes the net displacement of water molecules, into components parallel and perpendicular to the tube wall, in which axial diffusion is free and radial diffusion is restricted. The model faithfully predicts the experimental data, not only the observed diffraction peaks in E(q) when the diffusion gradients are approximately normal to the tube wall, but their sudden disappearance when the gradient orientation possesses a small axial component. The model also successfully predicts the dependence of E(q) on gradient pulse duration and on gradient strength as well as tube inner diameter. To account for the deviation from the narrow pulse approximation in the PGSTE sequence, we use Callaghan’s matrix operator framework, which this study validates experimentally for the first time. We also show how to combine average propagators derived for classical one-dimensional and two-dimensional models of restricted diffusion (e.g. between plates, within cylinders) to construct composite three-dimensional models of diffusion in complex media containing pores (e.g. rectangular prisms and/or capped cylinders) having a distribution of orientations, sizes, and aspect ratios. This three-dimensional modeling framework should aid in describing diffusion in numerous biological systems and in a myriad of materials sciences applications.

Two strategies are widely used in parallel MRI to reconstruct subsampled multicoil image data. SENSE and related methods employ explicit receiver coil spatial response estimates to reconstruct an image. In contrast, coil-by-coil methods such as GRAPPA leverage correlations among the acquired multicoil data to reconstruct missing k-space lines. In self-referenced scenarios, both methods employ Nyquist-rate low-frequency k-space data to identify the reconstruction parameters. Because GRAPPA does not require explicit coil sensitivities estimates, it needs considerably fewer autocalibration signals than SENSE. However, SENSE methods allow greater opportunity to control reconstruction quality though regularization and thus may outperform GRAPPA in some imaging scenarios. Here, we employ GRAPPA to improve self-referenced coil sensitivity estimation in SENSE and related methods using very few auto-calibration signals. This enables one to leverage each methods’ inherent strength and produce high quality self-referenced SENSE reconstructions.

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, delta, is comparable to the diffusion time, Delta. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Delta/delta, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Delta/delta approximately 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long delta the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Delta/delta approximately 1 the diffraction peaks are shifted to even higher q-values, even when delta is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Delta/delta approximately 1.

We consider a general double pulsed field gradient experiment with arbitrary experimental parameters and calculate an exact expression for the NMR signal attenuation from restricted geometries, which is valid at long wavelengths, i.e., when the product of the gyromagnetic ratio of the spins, the pulsed gradients’ duration, and their magnitude is small compared to the reciprocal of the pore size. It is possible to observe microscopic anisotropy within the pore space induced by the boundaries of the pore, which can be used to differentiate restricted from free or multicompartmental diffusion and to estimate a characteristic pore dimension in the former case. Explicit solutions for diffusion taking place between parallel plates as well as in cylindrical and spherical pores are provided. In coherently packed cylindrical pores, it is possible to measure simultaneously the cylinders’ orientation and diameter using small gradient strengths. The presence of orientational heterogeneity of cylinders is addressed, and a scheme for differentiating microscopic from ensemble anisotropy is proposed.

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.

In MRI, macroscopic boundaries lead to a diffusion-related increase in signal intensity near them—an effect commonly referred to as edge-enhancement. In diffusion-weighted imaging protocols where the signal attenuation due to diffusion results predominantly from the application of magnetic field gradients, edge-enhancement will depend on the orientation of these diffusion gradients. The resulting diffusion anisotropy can be exploited to map the direction normal to the macroscopic boundary. Simulations suggest that the hypothesized anisotropy may be within observable limits even when the voxel contains no boundary itself—hence, the name remote-anisotropy. Moreover, for certain experimental parameters there may be significant phase cancellations within the voxel that may lead to an edge detraction effect. When this is avoided, the eigenvector corresponding to the smallest eigenvalue of the diffusion tensor obtained from diffusion-tensor imaging can be used to create surface-normal maps conveniently. Experiments performed on simple geometric constructs as well as real tissue demonstrate the feasibility of using the edge-enhancement mechanism to map orientations orthogonal to macroscopic surfaces, which may be used to assess the integrity of tissue and organ boundaries noninvasively.

Segmentation involves separating an object from the background in a given image. The use of image information alone often leads to poor segmentation results due to the presence of noise, clutter or occlusion. The introduction of shape priors in the geometric active contour (GAC) framework has proved to be an effective way to ameliorate some of these problems. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, using level-sets. Following the work of Leventon et al., we propose to revisit the use of PCA to introduce prior knowledge about shapes in a more robust manner. We utilize kernel PCA (KPCA) and show that this method outperforms linear PCA by allowing only those shapes that are close enough to the training data. In our segmentation framework, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description permits to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, occlusions, or smearing.

This paper proposes a novel method to apply the standard graph cut technique to segmenting multimodal tensor valued images. The Riemannian nature of the tensor space is explicitly taken into account by first mapping the data to a Euclidean space where non-parametric kernel density estimates of the regional distributions may be calculated from user initialized regions. These distributions are then used as regional priors in calculating graph edge weights. Hence this approach utilizes the true variation of the tensor data by respecting its Riemannian structure in calculating distances when forming probability distributions. Further, the non-parametric model generalizes to arbitrary tensor distribution unlike the Gaussian assumption made in previous works. Casting the segmentation problem in a graph cut framework yields a segmentation robust with respect to initialization on the data tested.

Richly labeled images representing several sub-structures of an organ occur quite frequently in medical images. For example, a typical brain image can be labeled into grey matter, white matter or cerebrospinal fluid, each of which may be subdivided further. Many manipulations such as interpolation, transformation, smoothing, or registration need to be performed on these images before they can be used in further analysis. In this work, we present a novel multi-shape representation and compare it with the existing representations to demonstrate certain advantages of using the proposed scheme. Specifically, we propose label space, a representation that is both flexible and well suited for coupled multi-shape analysis. Under this framework, object labels are mapped to vertices of a regular simplex, e.g. the unit interval for two labels, a triangle for three labels, a tetrahedron for four labels, etc. This forms the basis of a convex linear structure with the property that all labels are equally spaced. We will demonstrate that this representation has several desirable properties: algebraic operations may be performed directly, label uncertainty is expressed equivalently as a weighted mixture of labels or in a probabilistic manner, and interpolation is unbiased toward any label or the background. In order to demonstrate these properties, we compare label space to signed distance maps as well as other implicit representations in tasks such as smoothing, interpolation, registration, and principal component analysis.