The Poisson's ratio and elastic modulus are two parameters determining the elastic behavior of biomaterials. While the effects of elastic modulus on the cell response is widely studied, very little is known regarding the effects of the Poisson's ratio. The micro-architecture of meta-biomaterials determines not only the Poisson's ratio but also several other parameters that also influence cell response, such as porosity, pore size, and effective elastic modulus. It is, therefore, very challenging to isolate the effects of the Poisson's ratio from those of other micro-architectural parameters. Here, we computationally design meta-biomaterials with controlled Poisson's ratios, ranging between -0.74 and +0.74, while maintaining consistent porosity, pore size, and effective elastic modulus. The 3D meta-biomaterials were additively manufactured at the micro-scale using two-photon polymerization (2PP), and were mechanically evaluated at the meso‑scale. The response of murine preosteoblasts to these meta-biomaterials was then studied using in vitro cell culture models. Meta-biomaterials with positive Poisson's ratios resulted in higher metabolic activity than those with negative values. The cells could attach and infiltrate all meta-biomaterials from the bottom to the top, fully covering the scaffolds after 17 days of culture. Interestingly, the meta-biomaterials exhibited different cell-induced deformations (e.g., shrinkage or local bending) as observed via scanning electron microscopy. The outcomes of osteogenic differentiation (i.e., Runx2 immunofluorescent staining) and matrix mineralization (i.e., Alizarin red staining) assays indicated the significant potential impact of these meta-biomaterials in the field of bone tissue engineering, paving the way for the development of advanced bone meta-implants. Statement of significance: We studied the influence of Poisson's ratio on bone cell response in meta-biomaterials. While elastic modulus effects are well-studied, the impact of Poisson's ratio, especially negative values found in architected biomaterials, remains largely unexplored. The complexity arises from intertwined micro-architectural parameters, such as porosity and elastic modulus, making it challenging to isolate the Poisson's ratio. To overcome this limitation, this study employed rational computational design to create meta-biomaterials with controlled Poisson's ratios, alongside consistent effective elastic modulus, porosity, and pore size. The study reveals that two-photon polymerized 3D meta-biomaterials with positive Poisson's ratios displayed higher metabolic activity, while all the developed meta-biomaterials supported osteogenic differentiation of preosteoblasts as well as matrix mineralization. The outcomes pave the way for the development of advanced 3D bone tissue models and meta-implants.

Emerging 4D printing techniques have enabled the realization of smart materials whose shape or properties can change with time. Two important phenomena play important roles in the 4D printing of shape memory polymeric materials. First, the anisotropic deformation of the printed filaments due to residual stresses can be harnessed to create out-of-plane shape transformations. Second, the unavoidable formation of micro-defects during the printing processes often affects the programmability of the printed object. Here, we propose a design approach that harnesses these two effects occurring during fused deposition modeling to create tailor-made curved geometries from initially 2D flat disks. We first determined the size and distribution of the imperfections formed within printed structures by varying two printing parameters namely the printing speed and the number of printed materials. Spatially varying the printing speed and combining polylactic acid filaments with a softer material without shape memory properties allowed us to cover a variety of shapes from negative to positive values of the mean and Gaussian curvature. We propose an analytical model to calculate the magnitude of the maximum out-of-plane deformation from the anisotropic expansion factor of the constituting microstructures. Furthermore, we develop computational models to predict the complex shape-changing of thermally actuated 4D printed structures given the distribution of rationally introduced imperfections and we demonstrate the potential applications of such defect-based metamaterials in drug delivery systems.

4D (bio-)printing endows 3D printed (bio-)materials with multiple functionalities and dynamic properties. 4D printed materials have been recently used in biomedical engineering for the design and fabrication of biomedical devices, such as stents, occluders, microneedles, smart 3D-cell engineered microenvironments, drug delivery systems, wound closures, and implantable medical devices. However, the success of 4D printing relies on the rational design of 4D printed objects, the selection of smart materials, and the availability of appropriate types of external (multi-)stimuli. Here, this work first highlights the different types of smart materials, external stimuli, and design strategies used in 4D (bio-)printing. Then, it presents a critical review of the biomedical applications of 4D printing and discusses the future directions of biomedical research in this exciting area, including in vivo tissue regeneration studies, the implementation of multiple materials with reversible shape memory behaviors, the creation of fast shape-transformation responses, the ability to operate at the microscale, untethered activation and control, and the application of (machine learning-based) modeling approaches to predict the structure–property and design–shape transformation relationships of 4D (bio)printed constructs.

Mechanical and morphological design parameters, such as stiffness or porosity, play important roles in creating orthopedic implants and bone substitutes. However, we have only a limited understanding of how the microarchitecture of porous scaffolds contributes to bone regeneration. Meta-biomaterials are increasingly used to precisely engineer the internal geometry of porous scaffolds and independently tailor their mechanical properties (e.g., stiffness and Poisson's ratio). This is motivated by the rare or unprecedented properties of meta-biomaterials, such as negative Poisson's ratios (i.e., auxeticity). It is, however, not clear how these unusual properties can modulate the interactions of meta-biomaterials with living cells and whether they can facilitate bone tissue engineering under static and dynamic cell culture and mechanical loading conditions. Here, we review the recent studies investigating the effects of the Poisson's ratio on the performance of meta-biomaterials with an emphasis on the relevant mechanobiological aspects. We also highlight the state-of-the-art additive manufacturing techniques employed to create meta-biomaterials, particularly at the micrometer scale. Finally, we provide future perspectives, particularly for the design of the next generation of meta-biomaterials featuring dynamic properties (e.g., those made through 4D printing).

Magneto-/ electro-responsive polymers (MERPs) are a class of stimuli-responsive materials that are actuated when triggered by external magnetic/ electric fields. MERPs exhibit rapid, reversible, and safe multi-functional and dynamic (i.e., changing with time) properties, which can effectively be manipulated at different length scales. These features make MERPs very attractive particularly in biomedical engineering (e.g., drug delivery systems and tissue engineering), soft matter engineering (e.g., soft robotics), and structural design of smart materials with unprecedented properties (e.g., complex shape morphing). Due to the recent progress in the design and development of MERPs, here, we highlighted the current advances in fabricating MERPs using various manufacturing methods including 3D/ 4D printing and conventional techniques. We also summarized the methods used for the characterization of MERPs and discussed their important structure-property relationship. We also highlighted the potential applications of MERPs in biomedical engineering, soft robotic, and the design of smart materials and systems. MERPs show great potentials for creating smart materials with predictable dynamic properties. More studies are necessary to investigate the biological responses of MERP both in-vivo and in-vitro, which is essential for biomedical engineering applications.

The authors regret to inform that unfortunately, there is a minor typo in the original version of the article. Authors apologize for this shortcoming and are aimed to report the correct data herein. In Table 1 of the original manuscript, a6 must be considered to be equal with +2.71 (instead of −2.71). The authors would like to apologise for any inconvenience caused.