Magnetically driven formation of 3D freestanding soft bioscaffolds.

3D soft bioscaffolds have great promise in tissue engineering, biohybrid robotics, and organ-on-a-chip engineering applications. Though emerging three-dimensional (3D) printing techniques offer versatility for assembling soft biomaterials, challenges persist in overcoming the deformation or collapse of delicate 3D structures during fabrication, especially for overhanging or thin features. This study introduces a magnet-assisted fabrication strategy that uses a magnetic field to trigger shape morphing and provide remote temporary support, enabling the straightforward creation of soft bioscaffolds with overhangs and thin-walled structures in 3D. We demonstrate the versatility and effectiveness of our strategy through the fabrication of bioscaffolds that replicate the complex 3D topology of branching vascular systems. Furthermore, we engineered hydrogel-based bioscaffolds to support biohybrid soft actuators capable of walking motion triggered by cardiomyocytes. This approach opens new possibilities for shaping hydrogel materials into complex 3D morphologies, which will further empower a broad range of biomedical applications.

Microfibrous Scaffolds Guide Stem Cell Lumenogenesis and Brain Organoid Engineering.

3D organoids are widely used as tractable in vitro models capable of elucidating aspects of human development and disease. However, the manual and low-throughput culture methods, coupled with a low reproducibility and geometric heterogeneity, restrict the scope and application of organoid research. Combining expertise from stem cell biology and bioengineering offers a promising approach to address some of these limitations. Here, melt electrospinning writing is used to generate tuneable grid scaffolds that can guide the self-organization of pluripotent stem cells into patterned arrays of embryoid bodies. Grid geometry is shown to be a key determinant of stem cell self-organization, guiding the position and size of emerging lumens via curvature-controlled tissue growth. Two distinct methods for culturing scaffold-grown embryoid bodies into either interconnected or spatially discrete cerebral organoids are reported. These scaffolds provide a high-throughput method to generate, culture, and analyze large numbers of organoids, substantially reducing the time investment and manual labor involved in conventional methods of organoid culture. It is anticipated that this methodological development will open up new opportunities for guiding pluripotent stem cell culture, studying lumenogenesis, and generating large numbers of uniform organoids for high-throughput screening.

Emergent collective organization of bone cells in complex curvature fields.

Individual cells and multicellular systems respond to cell-scale curvatures in their environments, guiding migration, orientation, and tissue formation. However, it remains largely unclear how cells collectively explore and pattern complex landscapes with curvature gradients across the Euclidean and non-Euclidean spectra. Here, we show that mathematically designed substrates with controlled curvature variations induce multicellular spatiotemporal organization of preosteoblasts. We quantify curvature-induced patterning and find that cells generally prefer regions with at least one negative principal curvature. However, we also show that the developing tissue can eventually cover unfavorably curved territories, can bridge large portions of the substrates, and is often characterized by collectively aligned stress fibers. We demonstrate that this is partly regulated by cellular contractility and extracellular matrix development, underscoring the mechanical nature of curvature guidance. Our findings offer a geometric perspective on cell-environment interactions that could be harnessed in tissue engineering and regenerative medicine applications.

Curvature Induced by Deflection in Thick Meta-Plates.

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

The local and global geometry of trabecular bone.

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. STATEMENT OF SIGNIFICANCE: The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface curvatures and Minkowski functionals, which are the most fundamental local and global shape quantifiers. Our results show that these shape metrics are sensitive to differences between bone types and unify traditional metrics within a single mathematical framework. This geometrical framework could also be useful to design bone-mimicking scaffolds and understand geometry-driven tissue growth.

Substrate curvature as a cue to guide spatiotemporal cell and tissue organization.

Recent evidence clearly shows that cells respond to various physical cues in their environments, guiding many cellular processes and tissue morphogenesis, pathology, and repair. One aspect that is gaining significant traction is the role of local geometry as an extracellular cue. Elucidating how geometry affects cell and tissue behavior is, indeed, crucial to design artificial scaffolds and understand tissue growth and remodeling. Perhaps the most fundamental descriptor of local geometry is surface curvature, and a growing body of evidence confirms that surface curvature affects the spatiotemporal organization of cells and tissues. While well-defined in differential geometry, curvature remains somewhat ambiguously treated in biological studies. Here, we provide a more formal curvature framework, based on the notions of mean and Gaussian curvature, and summarize the available evidence on curvature guidance at the cell and tissue levels. We discuss the involved mechanisms, highlighting the interplay between tensile forces and substrate curvature that forms the foundation of curvature guidance. Moreover, we show that relatively simple computational models, based on some application of curvature flow, are able to capture experimental tissue growth remarkably well. Since curvature guidance principles could be leveraged for tissue regeneration, the implications for geometrical scaffold design are also discussed. Finally, perspectives on future research opportunities are provided.