Flow and transport in tissue engineering scaffolds: A network modelling approach

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Tissue engineers aim to grow functional tissues in the laboratory. One approach is to seed cells on a porous biomaterial scaffold, which is then cultured in a flow perfusion bioreactor. Such bioreactors enhance the transport of nutrients and growth factors to the cells by convection, and provide mechanical loads to mechanosensitive tissues. In this paper, we adopt a network modelling approach to provide insight into the nature of the flow, nutrient transport and cell distribution through the porous scaffold. The approach resolves flow and nutrient transport at the pore scale, and thus enables the local cellular environment to be determined. We demonstrate how this method can be used to study the impact of scaffold geometry (e.g. porosity, connectivity) on the cellular environment, and hence provide insight into the optimum culture conditions required to obtain functional tissues.This study is funded by the EPSRC

Multiphase modelling of the effect of fluid shear stress on cell yield and distribution in a hollow fibre membrane bioreactor

We present a simplified two-dimensional model of fluid flow, nutrient transport and cell distribution in a hollow fibre membrane bioreactor, with the aim of exploring how fluid flow can be used to control the distribution and yield of a cell population which is sensitive to both fluid shear stress and nutrient concentration. The cells are seeded in a scaffold in a layer on top of the hollow fibre, only partially occupying the extracapillary space. Above this layer is a region of free-flowing fluid which we refer to as the upper fluid layer. The flow in the lumen and upper fluid layer is described by the Stokes equations, whilst the flow in the porous fibre membrane is assumed to follow Darcy’s law. Porous mixture theory is used to model the dynamics of and interactions between the cells, scaffold and fluid in the cell–scaffold construct. The concentration of a limiting nutrient (e.g. oxygen) is governed by an advection–reaction–diffusion equation in each region. Through exploitation of the small aspect ratio of each region and asymptotic analysis, we derive a coupled system of partial differential equations for the cell volume fraction and nutrient concentration. We use this model to investigate the effect of mechanotransduction on the distribution and yield of the cell population, by considering cases in which cell proliferation is either enhanced or limited by fluid shear stress and by varying experimentally controllable parameters such as flow rate and cell–scaffold construct thickness

Mathematical modelling of nanoparticle delivery to vascular tumours

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The goal of any cancer therapy is to achieve efficient, tissue-specific targeting of drugs to cancer cells. However, most anticancer agents act on healthy and malignant tissue alike, potentially resulting in side effects to healthy tissue. This has motivated the development of treatment strategies that are cancer-cell specific; one approach uses biomimetic polymer vesicles (BPV) to deliver chemotherapeutic drugs into cells before releasing them. BPVs are synthetic membrane enclosed, nanometre-sized structures, and provide ideal drug delivery vectors because specific targeting to cancer cells can be achieved by coating with tumourspecific molecules. We present several mathematical models covering a wide range of length-scales pertinent to BPV-mediated delivery protocols and focus on capturing the in vivo environment by evaluating the impact of the underlying vascular structure upon the governing transport mechanisms. Firstly, we present models of specific binding of BPVs to cancer cells. Subsequently we examine the implications of these model outputs in the contexts of both discrete capillary architectures and higher level homogenized-models that track blood and BPV transport at the tissue scale (both intra- and extra-tumorally). Numerical solutions are discussed, and recommendations are presented on that optimal integration of the models to generate quantitative predictions associated with BPV treatment efficacy

Mathematical modelling of cell layer growth in a hollow fibre bioreactor

Generating autologous tissue grafts of a clinically useful volume requires efficient and controlled expansion of cell populations harvested from patients. Hollow fibre bioreactors show promise as cell expansion devices, owing to their potential for scale-up. However, further research is required to establish how to specify appropriate hollow fibre bioreactor operating conditions for expanding different cell types. In this study we develop a simple model for the growth of a cell layer seeded on the outer surface of a single fibre in a perfused hollow fibre bioreactor. Nutrient-rich culture medium is pumped through the fibre lumen and leaves the bioreactor via the lumen outlet or passes through the porous fibre walls and cell layer, and out via ports on the outer wall of the extra-capillary space. Stokes and Darcy equations for fluid flow in the fibre lumen, fibre wall, cell layer and extra-capillary space are coupled to reaction–advection–diffusion equations for oxygen and lactate transport through the bioreactor, and to a simple growth law for the evolution of the free boundary of the cell layer. Cells at the free boundary are assumed to proliferate at a rate that increases with the local oxygen concentration, and to die and detach from the layer if the local fluid shear stress or lactate concentration exceed critical thresholds. We use the model to predict operating conditions that maximise the cell layer growth for different cell types. In particular, we predict the optimal flow rate of culture medium into the fibre lumen and fluid pressure imposed at the lumen outlet for cell types with different oxygen demands and fluid shear stress tolerances, and compare the growth of the cell layer when the exit ports on the outside of the bioreactor are open with that when they are closed. Model simulations reveal that increasing the inlet flow rate and outlet fluid pressure increases oxygen delivery to the cell layer and, therefore, the growth rate of cells that are tolerant to high shear stresses, but may be detrimental for shear-sensitive cells. The cell layer growth rate is predicted to increase, and be less sensitive to the lactate tolerance of the cells, when the exit ports are opened, as the radial flow through the bioreactor is enhanced and the lactate produced by the cells cleared more rapidly from the cell layer

Interpretation of ambiguous situations: evidence for a dissociation between social and physical threat in Williams syndrome

There is increasing evidence that Williams syndrome (WS) is associated with elevated anxiety that is non-social in nature, including generalised anxiety and fears. To date very little research has examined the cognitive processes associated with this anxiety. In the present research, attentional bias for non-social threatening images in WS was examined using a dot-probe paradigm. Participants were 16 individuals with WS aged between 13 and 34 years and two groups of typically developing controls matched to the WS group on chronological age and attentional control ability respectively. The WS group exhibited a significant attention bias towards threatening images. In contrast, no bias was found for group matched on attentional control and a slight bias away from threat was found in the chronological age matched group. The results are contrasted with recent findings suggesting that individuals with WS do not show an attention bias for threatening faces and discussed in relation to neuroimaging research showing elevated amygdala activation in response to threatening non-social scenes in WS

A preliminary study of genetic factors that influence susceptibility to bovine tuberculosis in the British cattle herd

Associations between specific host genes and susceptibility to Mycobacterial infections such as tuberculosis have been reported in several species. Bovine tuberculosis (bTB) impacts greatly the UK cattle industry, yet genetic predispositions have yet to be identified. We therefore used a candidate gene approach to study 384 cattle of which 160 had reacted positively to an antigenic skin test (‘reactors’). Our approach was unusual in that it used microsatellite markers, embraced high breed diversity and focused particularly on detecting genes showing heterozygote advantage, a mode of action often overlooked in SNP-based studies. A panel of neutral markers was used to control for population substructure and using a general linear model-based approach we were also able to control for age. We found that substructure was surprisingly weak and identified two genomic regions that were strongly associated with reactor status, identified by markers INRA111 and BMS2753. In general the strength of association detected tended to vary depending on whether age was included in the model. At INRA111 a single genotype appears strongly protective with an overall odds ratio of 2.2, the effect being consistent across nine diverse breeds. Our results suggest that breeding strategies could be devised that would appreciably increase genetic resistance of cattle to bTB (strictly, reduce the frequency of incidence of reactors) with implications for the current debate concerning badger-culling

Genome wide association mapping of grain arsenic, copper, molybdenum and zinc in rice (Oryza sativa L.) grown at four international field sites

Peer reviewedPublisher PD

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in fow based on a modifed viscoelastic fuid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear fow, we fx the parameters for VWF’s unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000 s−1 . We then use the theoretical model to predict VWF’s behaviour in two complex fows where experimental data are challenging to obtain: pure elongational fow and stenotic arterial fow. In pure elongational fow, our model predicts that VWF is 50% unfolded at approximately 2000 s−1 , matching the established hypothesis that VWF unfolds at lower shear rates in elongational fow than in shear fow. We demonstrate the sensitivity of this elongational fow prediction to the value of maximum VWF length used in the model, which varies signifcantly across experimental studies, predicting that VWF can unfold between 2000 and 3200 s−1 depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational fow structures in the centre of the artery compared to high shear regions near the arterial walls