A new free-surface stabilization algorithm for geodynamical modelling:Theory and numerical tests

The surface of the solid Earth is effectively stress free in its subaerial portions, and hydrostatic beneath the oceans. Unfortunately, this type of boundary condition is difficult to treat computationally, and for computational convenience, numerical models have often used simpler approximations that do not involve a normal stress-loaded, shear-stress free top surface that is free to move. Viscous flow models with a computational free surface typically confront stability problems when the time step is bigger than the viscous relaxation time. The small time step required for stability (<2. Kyr) makes this type of model computationally intensive, so there remains a need to develop strategies that mitigate the stability problem by making larger (at least ~10 Kyr) time steps stable and accurate. Here we present a new free-surface stabilization algorithm for finite element codes which solves the stability problem by adding to the Stokes formulation an intrinsic penalization term equivalent to a portion of the future load at the surface nodes. Our algorithm is straightforward to implement and can be used with both Eulerian or Lagrangian grids. It includes α and β parameters to respectively control both the vertical and the horizontal slope-dependent penalization terms, and uses Uzawa-like iterations to solve the resulting system at a cost comparable to a non-stress free surface formulation. Four tests were carried out in order to study the accuracy and the stability of the algorithm: (1) a decaying first-order sinusoidal topography test, (2) a decaying high-order sinusoidal topography test, (3) a Rayleigh-Taylor instability test, and (4) a steep-slope test. For these tests, we investigate which α and β parameters give the best results in terms of both accuracy and stability. We also compare the accuracy and the stability of our algorithm with a similar implicit approach recently developed by Kaus et al. (2010). We find that our algorithm is slightly more accurate and stable for steep slopes, and also conclude that, for longer time steps, the optimal α controlling factor for both approaches is ~2/3, instead of the 1/2 Crank-Nicolson parameter inferred from a linearized accuracy analysis. This more-implicit value coincides with the velocity factor for a Galerkin time discretization applied to our penalization term using linear shape functions in time

Neuropsychological Outcome and Diffusion Tensor Imaging in Complicated versus Uncomplicated Mild Traumatic Brain Injury

This study examined whether intracranial neuroimaging abnormalities in those with mild traumatic brain injury (MTBI) (i.e., “complicated” MTBIs) are associated with worse subacute outcomes as measured by cognitive testing, symptom ratings, and/or diffusion tensor imaging (DTI). We hypothesized that (i) as a group, participants with complicated MTBIs would report greater symptoms and have worse neurocognitive outcomes than those with uncomplicated MTBI, and (ii) as a group, participants with complicated MTBIs would show more Diffusion Tensor Imaging (DTI) abnormalities. Participants were 62 adults with MTBIs (31 complicated and 31 uncomplicated) who completed neurocognitive testing, symptom ratings, and DTI on a 3T MRI scanner approximately 6-8 weeks post injury. There were no statistically significant differences between groups on symptom ratings or on a broad range of neuropsychological tests. When comparing the groups using tract-based spatial statistics for DTI, no significant difference was found for axial diffusivity or mean diffusivity. However, several brain regions demonstrated increased radial diffusivity (purported to measure myelin integrity), and decreased fractional anisotropy in the complicated group compared with the uncomplicated group. Finally, when we extended the DTI analysis, using a multivariate atlas based approach, to 32 orthopedic trauma controls (TC), the findings did not reveal significantly more areas of abnormal DTI signal in the complicated vs. uncomplicated groups, although both MTBI groups had a greater number of areas with increased radial diffusivity compared with the trauma controls. This study illustrates that macrostructural neuroimaging changes following MTBI are associated with measurable changes in DTI signal. Of note, however, the division of MTBI into complicated and uncomplicated subtypes did not predict worse clinical outcome at 6-8 weeks post injury

Dynamic Morphometric Changes in Degenerative Lumbar Spondylolisthesis : A Pilot Study of Upright Magnetic Resonance Imaging

The objectives of this study were to (a) develop a standing MRI imaging protocol, tolerable to symptomatic patients with degenerative spondylolisthesis (DLS), and (b) to evaluate the morphometric changes observed in DLS patients in both supine and standing postures. Patients with single level, Meyerding grade 1 DLS undergoing surgery at a single institution between November 2015 to May 2017 were consented. Patients were imaged in the supine and standing positions in a 0.5T vertically open MRI scanner (MROpen, Paramed, Genoa, Italy) with sagittal and axial T2 images. The morphometric parameters measured were: cross-sectional area of the thecal sac (CSA), lateral recess height, disc height, degree of anterolisthesis, disc angle, lumbar lordosis, the presence of facet effusion and restabilization signs. Measures from both postures were compared using paired T-test. Associations of posture with the magnitude of change in the various measurements was determined using Pearson correlation or paired T-test when appropriate. All fourteen patients (mean age 64.4 years) included tolerated standing for the time required for image acquisition. All measurements with the exception of lumbar lordosis and disk height showed a statistically significant difference between the postures (p <0.05). In the standing position, CSA and lateral recess height were reduced by 28% and 50%, respectively. There was no relationship between the change in CSA of the thecal sac and any measures. Standing images acquired in an upright MRI scanner demonstrated postural changes associated with Meyerding grade 1 DLS and images acquisition was tolerated in all patients.Medicine, Faculty ofOrthopaedic Surgery, Department ofRadiology, Department ofReviewedFacultyResearcherOthe