Tiling mechanisms of the compound eye through geometrical tessellation

Tilling patterns are observed in many biological structures. Hexagonal tilling, commonly observed in the compound eyes of wild-type Drosophila, is dominant in nature; this dominance can probably be attributed to physical restrictions such as structural robustness, minimal boundary length, and space filling efficiency. Surprisingly, tetragonal tiling patterns are also observed in some Drosophila small eye mutants and aquatic crustaceans. Herein, geometrical tessellation is shown to determine the ommatidial tiling patterns. In small eye mutants, the hexagonal pattern is transformed into a tetragonal pattern as the relative positions of neighboring ommatidia are stretched along the dorsal-ventral axis. Hence, the regular distribution of ommatidia and their uniform growth collectively play an essential role in the establishment of tetragonal and hexagonal tiling patterns in compound eyes.

Energy-conserving model of hexagonal pattern in Rayleigh-Bénard convection

We have constructed an energy-conserving sixteen mode dynamical system to model hexagonal pattern in Rayleigh-Bénard convection of Boussinesq fluids with symmetric stress-free thermally conducting boundaries. The model shows stable roll pattern at the onset of convection. Hexagon is found to appear in the system via sausage and (or) stationary rhombus patterns. Both up and down hexagons arise periodically or chaotically with roll, sausage and rhombus patterns. Hexagonal patterns exist for all values of the Prandtl number, 1 ≤ Pr ≤ 5 explored here. However the pattern is more prominent for small Pr and k < kc , where k denotes the wave number. The plot of Nusselt number matches with previous theoretical result. In dissipationless limit, the total energy and the unavailable energy are constants though the kinetic energy, the potential energy and the available energy vary with time. The derived model does not diverge for large values of Rayleigh number Ra.

The New Useful High-Resolution Computed Tomography Finding for Diagnosing Fibrotic Hypersensitivity Pneumonitis: “Hexagonal Pattern”: A Single-Center Retrospective Study

Background Centrilobular nodules, ground-glass opacity (GGO), mosaic attenuation, air trapping, and three-density pattern were reported as high-resolution computed tomography (HRCT) findings characteristic of fibrotic hypersensitivity pneumonitis (HP). However, it is often difficult to differentiate fibrotic HP from idiopathic pulmonary fibrosis (IPF). In fibrotic HP, the HRCT sometimes shows tortoiseshell-like interlobular septal thickening that extends from the subpleural lesion to the inner layers. This finding is called “hexagonal pattern,” and this study is focused on the possibility that such finding is useful for differentiating fibrotic HP from IPF. Methods This study included patients with multidisciplinary discussion (MDD) diagnosis of fibrotic HP or IPF undergoing surgical lung biopsy between January 2015 and December 2017 in Kanagawa Cardiovascular and Respiratory Center. Two radiologists have evaluated the HRCT findings without clinical and pathological information. Results A total of 23 patients were diagnosed with fibrotic HP by MDD and 48 with IPF. Extensive GGO, centrilobular nodules, and hexagonal pattern were more frequent findings in fibrotic HP than in IPF. No significant difference was observed between the two groups in the presence or absence of mosaic attenuation, air trapping, or three-density pattern. In the multivariate logistic regression, the presence of extensive GGO and hexagonal pattern was associated with increased odds ratio of fibrotic HP. The sensitivity and specificity of the diagnosis of fibrotic HP in the presence of the hexagonal pattern were 69.6% and 87.5%, respectively. Conclusion Hexagonal pattern is a useful finding for differentiating fibrotic HP from IPF.

Study of the effectiveness of transpupillary hexagonal pattern retinal laser coagulation in the treatment of active ROP stages

Цель. Изучить эффективность гексагональной паттерновой лазеркоагуляции сетчатки (ЛКС) при активной ретинопатии недоношенных (РН) в сравнении с матричной паттерновой ЛКС. Материал и методы. С 2017 по 2019 гг. в Калужском филиале МНТК транспупиллярная ЛКС была проведена у 142-х младенцев (161 глаз) с активными стадиями РН. Всем пациентам лазерное лечение проводилось на паттерновой системе «Integrе Pro Scan» 561 нм (Ellex, Австралия). В основной группе выполняли ЛКС с использованием паттерна гексагональной формы (суммарно 7 аппликатов) – 69 детей. В контрольной группе ЛКС проводили с использованием матричных паттернов 3*3 (суммарно 9 аппликатов) – 73 младенца. Межспотовое расстояние в основной группе было увеличено на 0,25 диаметра коагулята по сравнению с контрольной. Результаты. Гексагональная паттерновая ЛКС обеспечила регресс заболевания при 3-«пороговой» стадии на 112 глазах (97%), при задней агрессивной РН на стадии ранних клинических проявлений – на 10 глазах (86%), на стадии манифестации – на 6 глазах (75%). Регресс заболевания при проведении стандартной паттерновой ЛКС с использованием квадратной матричной решетки на 3-«пороговой» стадии был отмечен на 109 глазах (96%), при задней агрессивной РН на стадии ранних клинических проявлений – на 8 глазах (80%), на стадии манифестации – на 4 глазах (66,7%). Длительность лазерного лечения, суммарная энергетическая нагрузка, частота использования одиночных импульсов в основной группе были значительно меньше, чем в контрольной. Заключение. Гексагональная паттерновая ЛКС обеспечивает высокую эффективность лазерного лечения активной РН и позволяет сократить продолжительность сеанса лечения по сравнению с матричной паттерновой ЛКС. Уменьшение плотности гексагональной ЛКС по сравнению с матричной приводит к уменьшению суммарной энергетической нагрузки на сетчатку глаза недоношенного ребенка с сохранением высокой клинической эффективности метода.

Modelling Groundwater Hydraulics to Design a Groundwater Level Monitoring Network for Sustainable Management of Fresh Groundwater Lens in Lower Indus Basin, Pakistan

The over-extraction of groundwater from thin fresh groundwater lenses is a threat to the livelihood of farmers in the Lower Indus Basin (LIB). It is essential to monitor and regulate this pumping to sustain fresh groundwater lenses. In this study, we applied a modelling approach in combination with geostatistical analysis to identify the critical locations to monitor the groundwater levels for sustaining fresh groundwater in the LIB. Our approach included four steps: (i) simulating temporal heads using a calibrated hydrogeological model; (ii) sampling monitoring locations using a hexagonal pattern of sampling; (iii) applying principal component analysis (PCA) of the temporal head observations, and selecting high scoring locations from the PCA; and (iv) minimizing the observation points to represent the water level contours. The calibrated model was able to replicate the hydro-dynamic behavior of the study area, with a root mean square of 0.95 and an absolute residual mean of 0.74 m. The hexagonal pattern of spatial sampling resulted in a 195 point network, but PCA reduced this network to 135 points and contour classification reduced it even further to 59 points. The 195, 135, and 59 point networks represented the water levels with average standard errors of 0.098, 0.318, and 0.610 m, respectively. Long-term simulations with increased pumping showed that the water levels would best be assessed by 195 monitoring points, although 135 and 59 points would represent the depleting area but would not capture the water logging area.