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.

Identifying chondrogenesis strategies for tissue engineering of articular cartilage.

A key step in the tissue engineering of articular cartilage is the chondrogenic differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells). Chondrogenesis is regulated by transforming growth factor- (TGF-), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications aim to maximise the yield of differentiated MSCs.

Optimal control of diffuser shapes for non-uniform flow.

A simplified model is used to identify the diffuser shape that maximises pressure recovery for several classes of non-uniform inflow. We find that optimal diffuser shapes strike a balance between not widening too soon, as this accentuates the non-uniform flow, and not staying narrow for too long, which is detrimental for wall drag. Three classes of non-uniform inflow are considered, with the axial velocity varying across the width of the diffuser entrance.

Inducing chondrogenesis in MSC/chondrocyte co-cultures using exogenous TGF-β: a mathematical model.

The differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells), or chondrogenesis, is a key step in the tissue engineering of articular cartilage, where the motility and high proliferation rate of MSCs used as seed cells are exploited. Chondrogenesis is regulated by transforming growth factor-beta (TGF-β), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications require the complete differentiation of an initial population of MSCs, and two common strategies used to achieve this in vitro are (1) co-culture the MSCs with chondrocytes, which constitutively produce TGF-β; or (2) add exogenous TGF-β.

Stem Cell Differentiation as a Non-Markov Stochastic Process.

Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage.

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.

Stochastic modelling of membrane filtration.

Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances and deposition on the membrane surface. In this paper, we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores.

Computational modelling of placental amino acid transfer as an integrated system.

Placental amino acid transfer is essential for fetal development and its impairment is associated with poor fetal growth. Amino acid transfer is mediated by a broad array of specific plasma membrane transporters with overlapping substrate specificity. However, it is not fully understood how these different transporters work together to mediate net flux across the placenta.

Extracellular Matrix Deposition in Engineered Micromass Cartilage Pellet Cultures: Measurements and Modelling.

This article explores possible mechanisms governing extracellular matrix deposition in engineered cartilaginous cell pellets. A theoretical investigation is carried out alongside an experimental study measuring proteoglycan and collagen volume fractions within murine chondrogenic (ATDC-5) cell pellets. The simple mathematical model, which adopts a nutrient-dependent proteoglycan production rate, successfully reproduces the periphery-dominated proteoglycan deposition, characteristic of the growth pattern observed experimentally within pellets after 21 days of culture.

Integration of computational modeling with membrane transport studies reveals new insights into amino acid exchange transport mechanisms.

Uptake of system L amino acid substrates into isolated placental plasma membrane vesicles in the absence of opposing side amino acid (zero-trans uptake) is incompatible with the concept of obligatory exchange, where influx of amino acid is coupled to efflux. We therefore hypothesized that system L amino acid exchange transporters are not fully obligatory and/or that amino acids are initially present inside the vesicles. To address this, we combined computational modeling with vesicle transport assays and transporter localization studies to investigate the mechanisms mediating [(14)C]L-serine (a system L substrate) transport into human placental microvillous plasma membrane (MVM) vesicles.

Computational modelling of amino acid exchange and facilitated transport in placental membrane vesicles.

Placental amino acid transport is required for fetal development and impaired transport has been associated with poor fetal growth. It is well known that placental amino acid transport is mediated by a broad array of specific membrane transporters with overlapping substrate specificity. However, it is not fully understood how these transporters function, both individually and as an integrated system.

Pore geometry regulates early stage human bone marrow cell tissue formation and organisation.

Porous architecture has a dramatic effect on tissue formation in porous biomaterials used in regenerative medicine. However, the wide variety of 3D structures used indicates there is a clear need for the optimal design of pore architecture to maximize tissue formation and ingrowth. Thus, the aim of this study was to characterize initial tissue growth solely as a function of pore geometry.

Review: Modelling placental amino acid transfer--from transporters to placental function.

Amino acid transfer to the fetus is dependent on several different factors. While these factors can be understood in isolation, it is still not possible to predict the function of the system as a whole. In order to do this an integrated approach is required which incorporates the interactions between the different determinants of amino acid transfer.

The design of microfluidic affinity chromatography systems for the separation of bioanalytes.

The analytical (numerical) design of planar microfluidic affinity chromatography devices, which consist of multiple separation lanes and multiple, different surface-immobilised receptor patterns in each lane, is described. The model is based on the analytical solution of the transport-reaction equations in microfluidic systems of low Gratz number and for injection of small analyte plugs. The results reveal a simple approach for the design of microfluidic affinity chromatography devices tailored to the separation of bioanalytes, where receptors with high binding affinity are available.

A fluid mechanical explanation of the spontaneous reattachment of a previously detached Descemet membrane.

Descemet membrane detachment (DMD) is a rare but potentially serious surgical complication that arises most often during cataract surgery. A recent study (Couch, S. M.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods.

Computational modelling of amino acid transfer interactions in the placenta.

Amino acid transfer from mother to fetus via the placenta plays a critical role in normal development, and restricted transfer is associated with fetal growth restriction. Placental amino acid transfer involves the interaction of 15 or more transporters and 20 amino acids. This complexity means that knowing which transporters are present is not sufficient to predict how they operate together as a system.

A continuum model for the development of tissue-engineered cartilage around a chondrocyte.

The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. We propose a continuum multispecies model for the development of cartilage around a single chondrocyte. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components.

Design criteria for a printed tissue engineering construct: a mathematical homogenization approach.

Cartilage tissue repair procedures currently under development aim to create a construct in which patient-derived cells are seeded and expanded ex vivo before implantation back into the body. The key challenge is producing physiologically realistic constructs that mimic real tissue structure and function. One option with vast potential is to print strands of material in a 3D structure called a scaffold that imitates the real tissue structure; the strands are composed of gel seeded with cells and so provide a template for cartilaginous tissue growth.

Experimental-computational evaluation of human bone marrow stromal cell spreading on trabecular bone structures.

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading.

Stochasticity and the molecular mechanisms of induced pluripotency.

The generation of induced pluripotent stem cells from adult somatic cells by ectopic expression of key transcription factors holds significant medical promise. However, current techniques for inducing pluripotency rely on viral infection and are therefore not, at present, viable within a clinical setting. Thus, there is now a need to better understand the molecular basis of stem cell pluripotency and lineage specification in order to investigate alternative methods to induce pluripotency for clinical application.

Modelling the formation of necrotic regions in avascular tumours.

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material.

Elastohydrodynamics of the eyelid wiper.

This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface.

Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration.

Limited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions.

Modelling the cell cycle and cell movement in multicellular tumour spheroids.

This paper analyses a recent mathematical model of avascular tumour spheroid growth which accounts for both cell cycle dynamics and chemotactic driven cell movement. The model considers cells to exist in one of two compartments: proliferating and quiescent, as well as accounting for necrosis and apoptosis. One particular focus of this paper is the behaviour created when proliferating and quiescent cells have different chemotactic responses to an extracellular nutrient supply.