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References
Characterization of pressure distribution in penetrating traumatic brain injuries
Severe impacts to the head commonly lead to localized brain damage. Such impacts may also give rise to temporary pressure changes that produce secondary injuries in brain volumes distal to the impact site. Monitoring pressure changes in a clinical setting is difficult; detailed studies into the effect of pressure changes in the brain call for the development and use of animal models. The aim of this study is to characterize the pressure distribution in an animal model of penetrating traumatic brain injuries (pTBI). This data may be used to validate mathematical models of the animal model and to facilitate correlation studies between pressure changes and pathology. Pressure changes were measured in rat brains while subjected to pTBI for a variety of different probe velocities and shapes; pointy, blunt, and flat. Experiments on ballistic gel samples were carried out to study the formation of any temporary cavities. In addition, pressure recordings from the gel experiments were compared to values recorded in the animal experiments. The pTBI generated short lasting pressure changes in the brain tissue; the pressure in the contralateral ventricle (CLV) increased to 8 bar followed by a drop to 0.4 bar when applying flat probes. The pressure changes in the periphery of the probe, in the Cisterna Magna, and the spinal canal, were significantly less than those recorded in the CLV or the vicinity of the skull base. Highspeed videos of the gel samples revealed the formation of spherically shaped cavities when flat and spherical probes were applied. Pressure changes in the gel were similar to those recorded in the animals, although amplitudes were lower in the gel samples. We concluded cavity expansion rate rather than cavity size correlated with pressure changes in the gel or brain secondary to probe impact. The new data can serve as validation data for finite element models of the trauma model and the animal and to correlate physical measurements with secondary injuries.
Covariant Lyapunov vectors of a quasi-geostrophic baroclinic model: analysis of instabilities and feedbacks
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly nonlinear theories can be constructed using higher order expansion terms. While these methods undoubtedly have great value for elucidating the relevant physical processes, they are unable to follow the dynamics of a turbulent atmosphere. We provide a first example of the extension of classical stability analysis to a nonlinearly evolving quasi-geostrophic flow. The so-called covariant Lyapunov vectors (CLVs) provide a covariant basis describing the directions of exponential expansion and decay of perturbations to the nonlinear trajectory of the flow. We use such a formalism to re-examine the basic barotropic and baroclinic processes of the atmosphere with a quasi-geostrophic beta-plane two-layer model in a periodic channel driven by a forced meridional temperature gradient T. We explore three settings of T, representative of relatively weak turbulence, well-developed turbulence and intermediate conditions. We construct the Lorenz energy cycle for each CLV describing the energy exchanges with the background state. A positive baroclinic conversion rate is a necessary but not sufficient condition for instability. Barotropic instability is present only for a few very unstable CLVs for large values of T. Slowly growing and decaying hydrodynamic Lyapunov modes closely mirror the properties of the background flow. Following the classical necessary conditions for barotropic/baroclinic instability, we find a clear relationship between the properties of the eddy fluxes of a CLV and its instability. CLVs with positive baroclinic conversion seem to form a set of modes for constructing a reduced model of the atmospheric dynamics.