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

LaCoDe:A Lagrangian two-dimensional thermo-mechanical code for large-strain compressible visco-elastic geodynamical modeling

We present LaCoDe (Lagrangian Compressible Deformation), a MATLAB solver for the Stokes equations for compressible non-Newtonian visco-elastic flow in two dimensions, based on a Lagrangian formulation of the Finite Element Method. The incompressible Boussinesq approximation is a widespread assumption in numerical models of lithospheric deformation, thus potentially masking a significant contribution of mechanisms linked to volumetric changes that occur in the asthenospheric mantle and the lithosphere. LaCoDe employs a compressible formulation of the Stokes equations designed to address such volume-changing processes. First, we provide a description of the equations governing the deformation of Earth rocks and detailed overview of the algorithm, its numerical implementation, treatment of the non-linearities rising from the compressible formulation and ineleastic deformation, and the remeshing algorithm that tracks and transfers the physical fields from a highly-distorted mesh to a high-quality one. LaCoDe is then benchmarked by comparing numerical results to analytical solutions for the bending of a thin elastic beam under a constant uniform load, flow around a rigid inclusion, Rayleigh-Taylor instability, stress build-up in a visco-elastic Maxwell body, and Couette flow with viscous heating. The Rayleigh-Taylor instability test is further used to demonstrate the accuracy of the remeshing algorithm. The importance of including volumetric strain for geodynamic processes is illustrated by two numerical experiments: i) volumetric-strain inducing phase changes in amagmatic slow-spreading ridges, and ii) subducting slabs.</p

Duration of androgen deprivation therapy with postoperative radiotherapy for prostate cancer: a comparison of long-course versus short-course androgen deprivation therapy in the RADICALS-HD randomised trial

Background Previous evidence supports androgen deprivation therapy (ADT) with primary radiotherapy as initial treatment for intermediate-risk and high-risk localised prostate cancer. However, the use and optimal duration of ADT with postoperative radiotherapy after radical prostatectomy remains uncertain. Methods RADICALS-HD was a randomised controlled trial of ADT duration within the RADICALS protocol. Here, we report on the comparison of short-course versus long-course ADT. Key eligibility criteria were indication for radiotherapy after previous radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to add 6 months of ADT (short-course ADT) or 24 months of ADT (long-course ADT) to radiotherapy, using subcutaneous gonadotrophin-releasing hormone analogue (monthly in the short-course ADT group and 3-monthly in the long-course ADT group), daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as metastasis arising from prostate cancer or death from any cause. The comparison had more than 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 75% to 81% (hazard ratio [HR] 0·72). Standard time-to-event analyses were used. Analyses followed intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov , NCT00541047 . Findings Between Jan 30, 2008, and July 7, 2015, 1523 patients (median age 65 years, IQR 60–69) were randomly assigned to receive short-course ADT (n=761) or long-course ADT (n=762) in addition to postoperative radiotherapy at 138 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 8·9 years (7·0–10·0), 313 metastasis-free survival events were reported overall (174 in the short-course ADT group and 139 in the long-course ADT group; HR 0·773 [95% CI 0·612–0·975]; p=0·029). 10-year metastasis-free survival was 71·9% (95% CI 67·6–75·7) in the short-course ADT group and 78·1% (74·2–81·5) in the long-course ADT group. Toxicity of grade 3 or higher was reported for 105 (14%) of 753 participants in the short-course ADT group and 142 (19%) of 757 participants in the long-course ADT group (p=0·025), with no treatment-related deaths. Interpretation Compared with adding 6 months of ADT, adding 24 months of ADT improved metastasis-free survival in people receiving postoperative radiotherapy. For individuals who can accept the additional duration of adverse effects, long-course ADT should be offered with postoperative radiotherapy. Funding Cancer Research UK, UK Research and Innovation (formerly Medical Research Council), and Canadian Cancer Society