Emergent Differential Organization of Airway Smooth Muscle Cells on Concave and Convex Tubular Surface

Airway smooth muscle cells (ASMCs) exist in a form of helical winding bundles within the bronchial airway wall. Such tubular tissue provides cells with considerable curvature as a physical constraint, which is widely thought as an important determinant of cell behaviors. However, this process is difficult to mimic in the conventional planar cell culture system. Here, we report a method to develop chips with cell-scale tubular (concave and convex) surfaces from fused deposition modeling 3D printing to explore how ASMCs adapt to the cylindrical curvature for morphogenesis and function. Results showed that ASMCs self-organized into two distinctively different patterns of orientation on the concave and convex surfaces, eventually aligning either invariably perpendicular to the cylinder axis on the concave surface or curvature-dependently angled on the convex surface. Such oriented alignments of the ASMCs were maintained even when the cells were in dynamic movement during migration and spreading along the tubular surfaces. Furthermore, the ASMCs underwent a phenotype transition on the tubular (both concave and convex) surfaces, significantly reducing contractility as compared to ASMCs cultured on a flat surface, which was reflected in the changes of proliferation, migration and gene expression of contractile biomarkers. Taken together, our study revealed a curvature-induced pattern formation and functional modulation of ASMCs in vitro, which is not only important to better understanding airway smooth muscle pathophysiology, but may also be useful in the development of new techniques for airway disease diagnosis and therapy such as engineering airway tissues or organoids.

Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics

Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions that the second fundamental form is parallel with respect to the induced connection and the normal connection is compatible with a metric on the transversal bundle. Both connections are induced by a canonical transversal plane bundle, which is defined by certain symmetry conditions. The obtained surfaces are always products of an ellipse and a conical planar curve.

Growth and survival performance of the West African mangrove oyster, Crassostrea tulipa cultivated by suspension and bottom culture methods in the Densu Estuary, Ghana

This study compares the efficacy of suspension and bottom culture methods of the West African mangrove oyster, Crassostrea tulipa, on recycled oyster shell cultches in connection with some environmental factors in the Densu Estuary, Ghana, from December 2017 to July 2018. Oyster spat grew up to 5.56 ± 0.10 cm SH for suspension and 4.60 ± 0.14 cm SH for bottom culture on the convex surfaces of oyster shell cultches, whereas oysters cultured on the concave surfaces by suspension and bottom cultured measured 5.59 ± 0.14 cm SH and 4.68 ± 0.14 cm SH, respectively. There was a significant difference (F = 36.26, p = 0.001) between the growth rate of oysters cultured on convex surfaces of cultches by suspension (0.80 ± 0.23 cm/month) and bottom culture (1.02 ± 0.24 cm/month). The growth rate of cultured oysters on concave surfaces of cultches by suspension (1.00 ± 0.24 cm/month) was significantly better (F = 22.32, p < 0.001) than the bottom approach (0.81 ± 0.23 cm/month). Before the extermination of oysters cultured on the bottom in July 2018, there was no significant difference in the survival of oysters cultured by suspension and bottom methods on the convex (χ2 = 0.06, p = 0.99) and concave surfaces (χ2 = 0.19, p = 0.99). Of the physico-chemical factors monitored, oyster growth and survival were significantly influenced by DO (p = 0.004; 0.039) and salinity (p = 0.027; 0.012), respectively. Suspension culture approach should be preferred over the bottom culture, especially for water bodies with low bulk density.

PARAMETER-UNIFORM ESTIMATES IN THE METRIC OF A FAMILY OF CLOSED CONVEX SURFACES WITH A GIVEN GAUSSIAN CURVATURE

The paper provides a proof of the boundedness of the solution of a family of Monge-Ampere differential one-parameter equations. The obtained result is used in the study of the unique solvability of the differential equation under study.

Nonlinear Optimization Method for Transmission Error of Hypoid Gear Machined by the Duplex Helical Method

In this study, synchronous cutting of concave and convex surfaces for hypoid gear was achieved using a duplex helical method. Precise, nonlinear optimization of the transmission error driven by machine tool parameters was performed to reduce the vibration noise of the gear pair. First, the transmission error curve and contact path of the tooth surface of the initial pinion were solved using tooth contact analysis. Second, according to the preset parabolic transmission error curve, the initial gear was used to generate the target pinion, which coincided with the contact path of the initial pinion. Finally, a deviation correction model of the discrete points, corresponding to the contact paths on the concave and convex surfaces of the target and initial pinions, was established. This model was solved using the Levenberg–Marquard algorithm with the trust region strategy, to obtain optimized machine tool parameters. Synchronous optimization of the transmission errors of concave and convex surfaces of the pinion was achieved by correcting the deviations of the contact points. The effectiveness of the proposed method was verified by a numerical example and by performing a contact area rolling test.