Multiscale modelling and homogenisation of fibre-reinforced hydrogels for tissue engineering.

Tissue engineering aims to grow artificial tissues to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected 3D-printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is distributed throughout the construct.

A mathematical model for cell infiltration and proliferation in a chondral defect.

We develop a mathematical model to describe the regeneration of a hydrogel inserted into an ex vivo osteochondral explant. Specifically we use partial differential equations to describe the evolution of two populations of cells that migrate from the tissue surrounding the defect, proliferate, and compete for space and resources within the hydrogel. The two cell populations are chondrocytes and cells that infiltrate from the subchondral bone.

Reinforcement of hydrogels using three-dimensionally printed microfibres.

Despite intensive research, hydrogels currently available for tissue repair in the musculoskeletal system are unable to meet the mechanical, as well as the biological, requirements for successful outcomes. Here we reinforce soft hydrogels with highly organized, high-porosity microfibre networks that are 3D-printed with a technique termed as melt electrospinning writing. We show that the stiffness of the gel/scaffold composites increases synergistically (up to 54-fold), compared with hydrogels or microfibre scaffolds alone.

A stochastic model for early placental development.

In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo.

The role of inflammation resolution speed in airway smooth muscle mass accumulation in asthma: insight from a theoretical model.

Despite a large amount of in vitro data, the dynamics of airway smooth muscle (ASM) mass increase in the airways of patients with asthma is not well understood. Here, we present a novel mathematical model that describes qualitatively the growth dynamics of ASM cells over short and long terms in the normal and inflammatory environments typically observed in asthma. The degree of ASM accumulation can be explained by an increase in the rate at which ASM cells switch between non-proliferative and proliferative states, driven by episodic inflammatory events.