A mathematical model for the biodegradation of magnesium is developed in this study to inspect the corrosion behaviour of biodegradable implants. The aim of this study was to provide a suitable framework for the assessment of the corrosion rate of magnesium which includes the process of formation/dissolution of the protective film. The model is intended to aid the design of implants with suitable geometries. The level-set method is used to follow the changing geometry of the implants during the corrosion process. A system of partial differential equations is formulated based on the physical and chemical processes that occur at the implant-medium boundary in order to simulate the effect of the formation of a protective film on the degradation rate. The experimental data from the literature on the corrosion of a high-purity magnesium sample immersed in simulated body fluid is used to calibrate the model. The model is then used to predict the degradation behaviour of a porous orthopaedic implant. The model successfully reproduces the precipitation of the corrosion products on the magnesium surface and the effect on the degradation rate. It can be used to simulate the implant degradation and the formation of the corrosion products on the surface of biodegradable magnesium implants with complex geometries.

Bioengineering of tissues and organs has the potential to generate functional replacement organs. However, achieving the full-thickness vascularization that is required for long-term survival of living implants has remained a grand challenge, especially for clinically sized implants. During the pre-vascular phase, implanted engineered tissues are forced to metabolically rely on the diffusion of nutrients from adjacent host-tissue, which for larger living implants results in anoxia, cell death, and ultimately implant failure. Here it is reported that this challenge can be addressed by engineering self-oxygenating tissues, which is achieved via the incorporation of hydrophobic oxygen-generating micromaterials into engineered tissues. Self-oxygenation of tissues transforms anoxic stresses into hypoxic stimulation in a homogenous and tissue sizeindependent manner. The in situ elevation of oxygen tension enables the sustained production of high quantities of angiogenic factors by implanted cells, which are offered a metabolically protected pro-angiogenic microenvironment. Numerical simulations predict that self-oxygenation of living tissues will effectively orchestrate rapid full-thickness vascularization of implanted tissues, which is empirically confirmed via in vivo experimentation. Self-oxygenation of tissues thus represents a novel, effective, and widely applicable strategy to enable the vascularization living implants, which is expected to advance organ transplantation and regenerative medicine applications.

A variety of natural or synthetic calcium phosphate (CaP)-based scaffolds are currently produced for dental and orthopaedic applications. These scaffolds have been shown to stimulate bone formation due to their biocompatibility, osteoconductivity and osteoinductivity. The release of the Ca 2+ ions from these scaffolds is of great interest in light of the aforementioned properties. It can depend on a number of biophysicochemical phenomena such as dissolution, diffusion and degradation, which in turn depend on specific scaffold characteristics such as composition and morphology. Achieving an optimal release profile can be challenging when relying on traditional experimental work alone. Mathematical modelling can complement experimentation. In this study, the in vitro dissolution behaviour of four CaP-based scaffold types was investigated experimentally. Subsequently, a mechanistic finite element method model based on biophysicochemical phenomena and specific scaffold characteristics was developed to predict the experimentally observed behaviour. Before the model could be used for local Ca 2+ ions release predictions, certain parameters such as dissolution constant (k dc ) and degradation constant (k sc ) for each type of scaffold were determined by calibrating the model to the in vitro dissolution data. The resulting model showed to yield release characteristics in satisfactory agreement with those observed experimentally. This suggests that the mathematical model can be used to investigate the local Ca 2+ ions release from CaP-based scaffolds.