Parameterization of the size and shape of intracranial saccular aneurysms using Legendre polynomials

Currently, size is used as the predetermining factor to judge whether a saccular aneurysm is likely to rupture. Recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that they enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and finite element analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, an even greater need to quantify regional multiaxial wall stresses, which because of the membrane-like behavior of aneurysms implicates the need for better data on regional surface curvatures. By using a convenient function, such as a Legendre polynomial, a quick, accurate approximation can be made for the size and shape of a saccular aneurysm that allows for stress analysis that surgeons can use to determine if the risk of rupture warrants the risk of treatment

Photogeologic Map of the Perseverance Rover Field Site in Jezero Crater Constructed by the Mars 2020 Science Team

Abstract The Mars 2020 Perseverance rover landing site is located within Jezero crater, a  ∼ 50 km \sim50~\mbox{km} diameter impact crater interpreted to be a Noachian-aged lake basin inside the western edge of the Isidis impact structure. Jezero hosts remnants of a fluvial delta, inlet and outlet valleys, and infill deposits containing diverse carbonate, mafic, and hydrated minerals. Prior to the launch of the Mars 2020 mission, members of the Science Team collaborated to produce a photogeologic map of the Perseverance landing site in Jezero crater. Mapping was performed at a 1:5000 digital map scale using a 25 cm/pixel High Resolution Imaging Science Experiment (HiRISE) orthoimage mosaic base map and a 1 m/pixel HiRISE stereo digital terrain model. Mapped bedrock and surficial units were distinguished by differences in relative brightness, tone, topography, surface texture, and apparent roughness. Mapped bedrock units are generally consistent with those identified in previously published mapping efforts, but this study’s map includes the distribution of surficial deposits and sub-units of the Jezero delta at a higher level of detail than previous studies. This study considers four possible unit correlations to explain the relative age relationships of major units within the map area. Unit correlations include previously published interpretations as well as those that consider more complex interfingering relationships and alternative relative age relationships. The photogeologic map presented here is the foundation for scientific hypothesis development and strategic planning for Perseverance’s exploration of Jezero crater