Tangential curvatures are a key geometric feature of tissue folds in the human cerebral cortex. In the brain, these smoother and firmer bends are called gyri and sulci and form distinctive curved tissue patterns imposing a mechanical stimulus on neuronal networks. This stimulus is hypothesized to be essential for proper brain cell function but lacks in most standard neuronal cell assays. A variety of soft lithographic micropatterning techniques can be used to integrate round geometries in cell assays. Most microfabricated patterns, however, focus only on a small set of defined curvatures. In contrast, curvatures in the brain span a wide physical range, leaving it unknown which precise role distinct curvatures may play on neuronal cell signaling. Here we report a hydrogel-based multi-curvature design consisting of over twenty bands of distinct parallel curvature ranges to precisely engineer neuronal networks' growth and signaling under patterns of arcs. Monitoring calcium and mitochondrial dynamics in primary rodent neurons grown over two weeks in the multi-curvature patterns, we found that static calcium signaling was locally attenuated under higher curvatures ( k > 0.01 μm −1 ). In contrast, to randomize growth, transient calcium signaling showed higher synchronicity when neurons formed networks in confined multi-curvature patterns.more »
Manipulating elastic waves via engineered spatial curvature profiles
We investigate curved surfaces operating as geodesic lenses for elastic waves. Consistently with findings in optics, we show that wave propagation occurs along rays that correspond to the geodesics of the curved surfaces, and we establish the geometric equivalence between Gaussian curvature and refractive index. This equivalence is formulated for flexural waves in curved shells by showing that, in the short wavelength limit, the ray equation corresponds to the classical equation of geodesics. We leverage this result to identify a non-Euclidean transformation that maps the geometric profile of a isotropic curved waveguide into a spatially varying refractive index distribution for a planar waveguide. These theoretical predictions are validated first through numerical simulations, and subsequently through experiments on 3D printed curved membranes with different curvature distributions. Numerical and experimental findings confirm that focal regions and caustic networks are correctly predicted based on geodesic evaluations. Our results form the basis for the design of curved profiles that correspond to spatial distributions of the refractive index and induce focal points by forcing waves to propagate along predefined trajectories. The findings of this study also suggest curvature as an attractive alternative to strategies based on the local tailoring of material properties and geometrical patterns more »
- Editors:
- Fromme, Paul; Su, Zhongqing
- Award ID(s):
- 2217543
- Publication Date:
- NSF-PAR ID:
- 10383169
- Journal Name:
- SPIE Smart Structures + Nondestructive Evaluation
- Volume:
- 12048
- Page Range or eLocation-ID:
- 1204805
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1117/12.2612573
