Search for: All records

This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and new Minkowski problems studied in convex geometry, PDEs, and harmonic analysis, and structured in a conceptual framework of the Brunn-Minkowski theory, its extensions, and related subjects. 

The emergence of engineered living materials (ELMs) has led to the development of functional composites by combining living microorganisms with nonliving components, particularly hydrogels. Hydrogels, which mimic the extracellular matrix, support microbial growth by providing essential nutrients and promoting cell adhesion, making them ideal for ELM production. However, hydrogel-based materials often face challenges in three-dimensional printing due to poor structural integrity and limited printability, frequently requiring additional processes, precise control, and/or material modifications to enhance their printing performance. This study focuses on developing a microorganism-laden gelatin microgel and gelatin solution-based composite bioink for self-supported printing of ELMs, enhanced via microbial-induced calcium carbonate precipitation. Gelatin microgels are utilized as rheology modifiers, enabling the yield-stress fluid behavior of the bioink for improved printability and postprinting shape retention, while transglutaminase enzymatically cross-links printed structures completely, resulting in good printability. Furthermore, Sporosarcina pasteurii in the bioink enables calcium carbonate deposition during postprinting culturing, forming robust, biomineralized structures. Fabricated samples are found to have significant successful mineral deposition with over 50 wt% calcium carbonate content, and they exhibit compressive strengths of up to 1.4 MPa. This approach offers a cost-effective, energy-efficient method for creating high-strength, biocompatible biocomposites with potential applications such as bone tissue engineering, coral restoration, and sustainable building development. 

Abstract Versatile printing of polymers, metals, and composites always calls for simple, economic approaches. Here we present an approach to three-dimensional (3D) printing of polymeric, metallic, and composite materials at room conditions, based on the polymeric vapor-induced phase separation (VIPS) process. During VIPS 3D printing (VIPS-3DP), a dissolved polymer-based ink is deposited in an environment where nebulized non-solvent is present, inducing the low-volatility solvent to be extracted from the filament in a controllable manner due to its higher chemical affinity with the non-solvent used. The polymeric phase is hardened in situ as a result of the induced phase separation process. The low volatility of the solvent enables its reclamation after the printing process, significantly reducing its environmental footprint. We first demonstrate the use of VIPS-3DP for polymer printing, showcasing its potential in printing intricate structures. We further extend VIPS-3DP to the deposition of polymer-based metallic inks or composite powder-laden polymeric inks, which become metallic parts or composites after a thermal cycle is applied. Furthermore, spatially tunable porous structures and functionally graded parts are printed by using the printing path to set the inter-filament porosity as well as an inorganic space-holder as an intra-filament porogen. 

Vascularization is essential for realizing thick and functional tissue constructs that can be utilized for in vitro study platforms and in vivo grafts. The vasculature enables the transport of nutrients, oxygen, and wastes and is also indispensable to organ functional units such as the nephron filtration unit, the blood–air barrier, and the blood–brain barrier. This review aims to discuss the latest progress of organ-like vascularized constructs with specific functionalities and realizations even though they are not yet ready to be used as organ substitutes. First, the human vascular system is briefly introduced and related design considerations for engineering vascularized tissues are discussed. Second, up-to-date creation technologies for vascularized tissues are summarized and classified into the engineering and cellular self-assembly approaches. Third, recent applications ranging from in vitro tissue models, including generic vessel models, tumor models, and different human organ models such as heart, kidneys, liver, lungs, and brain, to prevascularized in vivo grafts for implantation and anastomosis are discussed in detail. The specific design considerations for the aforementioned applications are summarized and future perspectives regarding future clinical applications and commercialization are provided. 

Abstract Three-dimensional (3D) bioprinting has emerged as a powerful engineering approach for various tissue engineering applications, particularly for the development of 3D cellular structures with unique mechanical and/or biological properties. For the jammed gelatin microgel-gelatin solution composite bioink, comprising a discrete phase of microgels (enzymatically gelled gelatin microgels) and a cross-linkable continuous gelatin precursor solution-based phase containing transglutaminase (TG), its rheological properties and printability change gradually due to the TG enzyme-induced cross-linking process. The objective of this study is to establish a direct mapping between the printability of the gelatin microgel-gelatin solution based cross-linkable composite bioink and the TG concentration and cross-linking time, respectively. Due to the inclusion of TG in the composite bioink, the bioink starts cross-linking once prepared and is usually prepared right before a printing process. Herein, the bioink printability is evaluated based on the three metrics: injectability, feature formability, and process-induced cell injury. In this study, the rheological properties such as the storage modulus and viscosity have been first systematically investigated and predicted at different TG concentrations and times during the cross-linking process using the first-order cross-linking kinetics model. The storage modulus and viscosity have been satisfactorily modeled as exponential functions of the TG concentration and time with an experimentally calibrated cross-linking kinetic rate constant. Furthermore, the injectability, feature formability, and process-induced cell injury have been successfully correlated to the TG concentration and cross-linking time via the storage modulus, viscosity, and/or process-induced shear stress. By combing the good injectability, good feature formability, and satisfactory cell viability zones, a good printability zone (1.65, 0.61, and 0.31 h for the composite bioinks with 1.00, 2.00, and 4.00% w/v TG, respectively) has been established during the printing of mouse fibroblast-based 2% gelatin B microgel-3% gelatin B solution composite bioink. This printability zone approach can be extended to the use of other cross-linkable bioinks for bioprinting applications.