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The Kerr and Kerr-de Sitter metrics share remarkable local geometric properties in four dimensions. Gibbons et al. found a generalization of the Kerr-de Sitter metric to higher dimensions, to which the local characterization above cannot be applied. One viable approach to characterize this family is to understand the behaviour of these metrics at future null infinity. We review Friedrich's and Fefferman-Graham formalisms to discuss the asymptotic initial value problem of ([Formula: see text])-vacuum spacetimes in arbitrary dimensions and study their properties: geometric identification and conformal equivalence of data, Killing initial data and conformal equivalence of boundary conformal Killing vectors (CKV). These results are used to review a recent characterization of Kerr-de Sitter in terms of its asymptotic data, namely conformal flatness at [Formula: see text] together with a canonical TT tensor constructed from specific CKV at [Formula: see text]. Allowing for arbitrary CKV defines the (larger) Kerr-de Sitter-like class. All these metrics can be obtained explicitly as limits or analytic extensions of Kerr-de Sitter. The Kerr-de Sitter-like class is also characterized by the property of being Kerr-Schild and fulfilling a certain falloff condition. In addition, in five dimensions, this class corresponds to all algebraically special metrics with non-degenerate optical matrix. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

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For physical-based compression therapeutic modalities, especially compression stockings (CSs), their pressure performances are necessarily evaluated by the standardized cylinder leg mannequins before biological applications. However, the insufficient pressure supply caused by morphological shape diversities between circular leg mannequins and irregular bio-bodies limits the clinical effectiveness and user compliance of CSs. Therefore, an operable and efficiency approach for optimization bio-design and digital development of CSs with enhanced compression performances needs to be proposed. The present study has adopted three-dimensional (3D) body scanning and reverse engineering technologies for lower limb cross-sectional geometric characterization and morphological classification. The irregularity of biological leg circumferential slices was determined and clustered as four levels relating to individual curvature variations. Sequentially, a new pressure prediction model was constructed through characterized geometric variations for bio-based bodies, then its acceptability was validated with good agreement by wearing trials (mean prediction accuracy was 2.53 ± 0.52 mmHg). Thus, the digital pressure reshaped development guidance was obtained based on the classified irregular levels and established pressure prediction models. Consequently, this study provides a novel reliable optimization bio-design solution for manufacturing of therapeutic compression textiles and facilitates the medical efficacy and precision of compression therapy in practical use.

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The gap fraction (GF) of vegetative canopies is an important property related to the contained bulk of reproductive elements and woody facets within the tree crown volume. This work was developed from the perspectives of porous media theory and computer graphics techniques, considering the vegetative elements in the canopy as a solid matrix and treating the gaps between them as pores to guide volume-based GFvol calculations. Woody components and individual leaves were extracted from terrestrial laser scanning data. The concept of equivalent leaf thickness describing the degrees of leaf curling and drooping was proposed to construct hexagonal prisms properly enclosing the scanned points of each leaf, and cylinder models were adopted to fit each branch segment, enabling the calculation of the equivalent leaf and branch volumes within the crown. Finally, the volume-based GFvol of the tree crown following the definition of the void fraction in porous media theory was calculated as one minus the ratio of the total plant leaf and branch volume to the canopy volume. This approach was tested on five tree species and a forest plot with variable canopy architecture, yielding an estimated maximum volume-based GFvol of 0.985 for a small crepe myrtle and a minimal volume-based GFvol of 0.953 for a sakura tree. The 3D morphology of each compositional element in the tree canopy was geometrically defined and the canopy was considered a porous structure to conduct GFvol calculations based on multidisciplinary theory.

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Fruit cells are living irregular three-dimensional (3D) transparent objects which makes them challenging to determine their real 3D size and shape through only two-dimensional (2D) images using the existing biological microscope. This study deals with a newly self-developed biological microscope including a microscope imaging system, a light source system, a stage and a support base for the 3D size characterization of fruit single cells. The main design concept is based on two optical path systems set up at the front (x-axis) and bottom (z-axis) directions of a transparent chamber containing single cells that allow the front view and bottom view of the single cell to be observed. Performance indicators such as mass, size, observation range, objective magnification, total magnification, focal range, focal accuracy, and resolution of the developed biological microscope were estimated. Finally, the 3D geometry size of single tomato cells was measured by the new biological microscope to demonstrate the relative ease at which accurate real 3D geometry information of single fruit cells could be obtained, which echoes its scientific value.

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Intracranial aneurysm projected posteriorly is associated with high risk of aneurysm rupture. In order to investigate the biomechanical mechanisms for the adverse event, three-dimension intracranial cerebral aneurysms were constructed based on clinical data, and we numerically compared effect of location, position, size, and shape of aneurysm on hemodynamic conditions including velocity, pressure, and wall shear stress (WSS). The numerical results showed that the aneurysm projected posteriorly even at small sizes led to abnormal hemodynamic environment, which was featured by a local high pressure and stress concentration near aneurysm neck area. Moreover, the one located at the proximal A1 segment and ellipsoidal aneurysm would further worse local hemodynamic environment, causing high local stresses. These findings indicated the potential mechanical mechanism for high rupture rate of the aneurysms projected posteriorly, underscoring importance of early and accurate diagnosis and promptly treatment for improved the clinical outcome, even if these aneurysms are of small sizes.

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Automated tools for landmarking the internal carotid artery (ICA) bends have the potential for efficient and objective medical image-based morphometric analysis. The two existing algorithms rely on numerical approximations of curvature and torsion of the centerline. However, input parameters, original source code, comparability, and robustness of the algorithms remain unknown. To address the former two, we have re-implemented the algorithms, followed by sensitivity analyses. Of the input parameters, the centerline smoothing had the least impact resulting in 6-7 bends, which is anatomically realistic. In contrast, centerline resolution showed to completely over- and underestimated the number of bends varying from 3 to 33. Applying the algorithms to the same cohort revealed a variability that makes comparison of results between previous studies questionable. Assessment of robustness revealed how one algorithm is vulnerable to model smoothness and noise, but conceptually independent of application. In contrast, the other algorithm is robust and consistent, but with limited general applicability. In conclusion, both algorithms are equally valid albeit they produce vastly different results. We have provided a well-documented open-source implementation of the algorithms. Finally, we have successfully performed this study on the ICA, but application to other vascular regions should be performed with caution.

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This work presents a computational framework to perform a systematic and comprehensive assessment of the morphometry of coronary arteries from in vivo medical images. The methodology embraces image segmentation, arterial vessel representation, characterization and comparison, data storage, and finally analysis. Validation is performed using a sample of 48 patients. Data mining of morphometric information of several coronary arteries is presented. Results agree to medical reports in terms of basic geometric and anatomical variables. Concerning geometric descriptors, inter-artery and intra-artery correlations are studied. Data reported here can be useful for the construction and setup of blood flow models of the coronary circulation. Finally, as an application example, similarity criterion to assess vasculature likelihood based on geometric features is presented and used to test geometric similarity among sibling patients. Results indicate that likelihood, measured through geometric descriptors, is stronger between siblings compared with non-relative patients. Copyright © 2016 John Wiley & Sons, Ltd.

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