Cell culture has become an indispensable tool to help uncover fundamental biophysical and biomolecular mechanisms by which cells assemble into tissues and organs, how these tissues function, and how that function becomes disrupted in disease. Cell culture is now widely used in biomedical research, tissue engineering, regenerative medicine, and industrial practices. Although flat, two-dimensional (2D) cell culture has predominated, recent research has shifted toward culture using three-dimensional (3D) structures, and more realistic biochemical and biomechanical microenvironments. Nevertheless, in 3D cell culture, many challenges remain, including the tissue-tissue interface, the mechanical microenvironment, and the spatiotemporal distributions of oxygen, nutrients, and metabolic wastes. Here, we review 2D and 3D cell culture methods, discuss advantages and limitations of these techniques in modeling physiologically and pathologically relevant processes, and suggest directions for future research.

Kirigami, a modified form of origami which includes paper cutting, has been used to improve material stretchability and compliance. However, this technique is so far underexplored in patterning piezoelectric materials towards developing efficient and mechanically flexible thin-film energy generators. Motivated by existing kirigami-based applications, we introduce interdigitated cuts to polyvinylidene fluoride (PVDF) films to evaluate the effect on voltage generation and stretchability. Our results from theoretical analysis, numerical simulations, and experimental tests show that kirigami PVDF films exhibit an extended strain range while still maintaining significant voltage generation compared to films without cuts. Various cutting patterns were studied, and it was found that films with denser cuts have a larger voltage output. This kirigami design can enhance the properties of existing piezoelectric materials and help to integrate tunable PVDF generators into biomedical devices.

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Helices are ubiquitous building blocks in natural and engineered systems. Previous studies showed that helical ribbon morphology can result from anisotropic driving forces and geometric misorientation between the principal axes of the driving forces and the geometric axes. However, helical ribbon shapes induced by elastic modulus anisotropy have not been systematically examined even though most natural and engineered structures are made of composite materials with anisotropic mechanical properties. We build on a previously developed model using continuum elasticity and stationarity principles to predict helical ribbon shapes induced by material anisotropy under both isotropic and anisotropic pre-stretching conditions. Results from finite element analysis and table-top experiments showed that the principal curvatures, chirality, and helix angles can be further tuned in anisotropic ribbons under both isotropic and anisotropic pre-stretching conditions. This work can promote programmable design and fabrication of curved structures and devices.

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