Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay

In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by analyzing the characteristic equation. For Turing–Hopf bifurcation, we derive the truncated third-order normal form based on the work of Jiang et al. [11], which is topologically equivalent to the original equation, and theoretically reveal system exhibits abundant spatial, temporal and spatiotemporal patterns, such as semistable spatially inhomogeneous periodic solutions, as well as tristable patterns of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. Especially, we theoretically explain the phenomenon that time delay inhibits the formation of heterogeneous steady patterns, found by S. Lee, E. Gaffney and N. Monk [The influence of gene expression time delays on Gierer–Meinhardt pattern formation systems, Bull. Math. Biol., 72(8):2139–2160, 2010.

The 3-dimensional printing for dental tissue regeneration: the state of the art and future challenges

Tooth loss or damage poses great threaten to oral and general health. While contemporary clinical treatments have enabled tooth restoration to a certain extent, achieving functional tooth regeneration remains a challenging task due to the intricate and hierarchically organized architecture of teeth. The past few decades have seen a rapid development of three-dimensional (3D) printing technology, which has provided new breakthroughs in the field of tissue engineering and regenerative dentistry. This review outlined the bioactive materials and stem/progenitor cells used in dental regeneration, summarized recent advancements in the application of 3D printing technology for tooth and tooth-supporting tissue regeneration, including dental pulp, dentin, periodontal ligament, alveolar bone and so on. It also discussed current obstacles and potential future directions, aiming to inspire innovative ideas and encourage further development in regenerative medicine