Improving computation of cardiovascular relative pressure fields from velocity MRI.

PURPOSE: To evaluate a multigrid-based solver for the pressure Poisson equation (PPE) with Galerkin coarsening, which works directly on the specified domain, for the computation of relative pressure fields from velocity MRI data. MATERIALS AND METHODS: We compared the proposed structure-defined Poisson solver to other popular Poisson solvers working on unmodified rectangular and modified quasirectangular domains using synthetic and in vitro phantoms in which the mathematical solution of the pressure field is known, as well as on in vivo MRI velocity measurements of aortic blood flow dynamics. RESULTS: All three PPE solvers gave accurate results for convex computational domains. Using a rectangular or quasirectangular domain on a more complicated domain, like a c-shape, revealed a systematic underestimation of the pressure amplitudes, while the proposed PPE solver, working directly on the specified domain, provided accurate estimates of the relative pressure fields. CONCLUSION: Popular iterative approaches with quasirectangular computational domains can lead to significant systematic underestimation of the pressure amplitude. We suggest using a multigrid-based PPE solver with Galerkin coarsening, which works directly on the structure-defined computational domain. This solver provides accurate estimates of the relative pressure fields for both simple and complex geometries with additional significant improvements with respect to execution speed.

Phase sensitive reconstruction for water/fat separation in MR imaging using inverse gradient.

This paper presents a novel method for phase unwrapping for phase sensitive reconstruction in MR imaging. The unwrapped phase is obtained by integrating the phase gradient by solving a Poisson equation. An efficient solver, which has been made publicly available, is used to solve the equation. The proposed method is demonstrated on a fat quantification MRI task that is a part of a prospective study of fat accumulation. The method is compared to a phase unwrapping method based on region growing. Results indicate that the proposed method provides more robust unwrapping. Unlike region growing methods, the proposed method is also straight-forward to implement in 3D.

A Bayesian approach for stochastic white matter tractography.

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.

A new strategy for respiration compensation, applied toward 3D free-breathing cardiac MRI.

In thorax and abdomen imaging, image quality may be affected by breathing motion. Cardiac MR images are typically obtained while the patient holds his or her breath, to avoid respiration-related artifacts. Although useful, breath-holding imposes constraints on scan duration, which in turn limits the achievable resolution and SNR. Longer scan times would be required to improve image quality, and effective strategies are needed to compensate for respiratory motion. A novel approach at respiratory compensation, targeted toward 3D free-breathing cardiac MRI, is presented here. The method aims at suppressing the negative effects of respiratory-induced cardiac motion while capturing the heart's beating motion. The method is designed so that the acquired data can be reconstructed in two different ways: First, a time series of images is reconstructed to quantify and correct for respiratory motion. Then, the corrected data are reconstructed a final time into a cardiac-phase series of images to capture the heart's beating motion. The method was implemented, and initial results are presented. A cardiac-phase series of 3D images, covering the entire heart, was obtained for two free-breathing volunteers. The present method may prove especially useful in situations where breath-holding is not an option, for example, for very sick, mentally impaired or infant patients.

Affine and deformable registration based on polynomial expansion.

This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.