A diffusion gradient optimization framework for spinal cord diffusion tensor imaging.

The uncertainty in the estimation of diffusion model parameters in diffusion tensor imaging (DTI) can be reduced by optimally selecting the diffusion gradient directions utilizing some prior structural information. This is beneficial for spinal cord DTI, where the magnetic resonance images have low signal-to-noise ratio and thus high uncertainty in diffusion model parameter estimation. Presented is a gradient optimization scheme based on D-optimality, which reduces the overall estimation uncertainty by minimizing the Rician Cramer-Rao lower bound of the variance of the model parameter estimates. The tensor-based diffusion model for DTI is simplified to a four-parameter axisymmetric DTI model where diffusion transverse to the principal eigenvector of the tensor is assumed isotropic. Through simulations and experimental validation, we demonstrate that an optimized gradient scheme based on D-optimality is able to reduce the overall uncertainty in the estimation of diffusion model parameters for the cervical spinal cord and brain stem white matter tracts.

Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm.

Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement.

Multiple echo NMR velocimetry: fast and localized measurements of steady and pulsatile flows in small channels.

The understanding of fluid transport in miniaturized flow devices is an important component in the design of flow cells, micromixers, and microreactors. In this manuscript, we employ NMR in the form of a voxel-selective multiple modulation multiple echo sequence (MMMEV) to monitor average velocities in individual microchannels inside a six-channel network. The technique produces average velocities which are consistent with the imposed flow rates. In addition, we take advantage of the short acquisition time (32 ms per velocity component) of the technique to quantitatively track the time evolution of the fluid velocity in a pulsatile flow phantom.

An inverse problem for reduced-encoding MRI velocimetry in potential flow.

We propose a computational technique to reconstruct internal physiological flows described by sparse point-wise MRI velocity measurements. Assuming that the viscous forces in the flow are negligible, the incompressible flow field can be obtained from a velocity potential that satisfies Laplace's equation. A set of basis functions each satisfying Laplace's equation with appropriately defined boundary data is constructed using the finite-element method. An inverse problem is formulated where higher resolution boundary and internal velocity data are extracted from the point-wise MRI velocity measurements using a least-squares method. From the results we obtained with approximately 100 internal measurement points, the proposed reconstruction method is shown to be effective in filtering out the experimental noise at levels as high as 30%, while matching the reference solution within 2%. This allows the reconstruction of a high-resolution velocity field with limited MRI encoding.

Synchronized EPI phase contrast velocimetry in a mixing reactor.

Notwithstanding its widespread use in cardiovascular and functional MRI studies, Echo Planar Imaging (EPI) has only recently been subjected to systematic validation studies. Most velocity measurement studies employing such ultrafast MRI methods involve the use of phantoms characterized by rigid or deformable solid motion. The current implementation involves a rotating phantom (angular velocity up to 10.5 rpm) with a superimposed swirling liquid flow (with axial velocities ranging between 0.145 and 0.27 cm/s) of water doped with copper sulfate. The standard implementation of single-shot EPI with phase contrast velocity encoding allows the complete mapping of the Eulerian velocity field in slices perpendicular to the rotation axis following a subtractive procedure requiring the synchronized acquisition of each velocity component on each selected transverse slice during two revolutions of the rotor. The image acquisition time is 100 ms (per velocity component) at each 64 x 64 slice. In addition to acquiring full-field velocity data for future direct comparisons with other techniques, EPI is employed here for the first time to reconstruct the three-dimensional flow field between the blades of a partitioned pipe mixer.