Timothy Spencer

In silico multi-scale model of transport and dynamic seeding in a bone tissue engineering perfusion bioreactor†

Computer simulations can potentially be used to design, predict, and inform properties for tissue engineering perfusion bioreactors. In this work, we investigate the flow properties that result from a particular poly‐L‐lactide porous scaffold and a particular choice of perfusion bioreactor vessel design used in bone tissue engineering. We also propose a model to investigate the dynamic seeding properties such as the homogeneity (or lack of) of the cellular distribution within the scaffold of the perfusion bioreactor: a pre‐requisite for the subsequent successful uniform growth of a viable bone tissue engineered construct. Flows inside geometrically complex scaffolds have been investigated previously and results shown at these pore scales. Here, it is our aim to show accurately that through the use of modern high performance computers that the bioreactor device scale that encloses a scaffold can affect the flows and stresses within the pores throughout the scaffold which has implications for bioreactor design, control, and use. Central to this work is that the boundary conditions are derived from micro computed tomography scans of both a device chamber and scaffold in order to avoid generalizations and uncertainties. Dynamic seeding methods have also been shown to provide certain advantages over static seeding methods. We propose here a novel coupled model for dynamic seeding accounting for flow, species mass transport and cell advection‐diffusion‐attachment tuned for bone tissue engineering. The model highlights the timescale differences between different species suggesting that traditional homogeneous porous flow models of transport must be applied with caution to perfusion bioreactors. Our in silico data illustrate the extent to which these experiments have the potential to contribute to future design and development of large‐scale bioreactors. Biotechnol. Bioeng. 2013; 110: 1221–1230.

Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile

In order to address the problem of blood flow over the endothelium in small arteries, the near-endothelial region is here studied in more detail. The method used is a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids, named unstructured Lattice Boltzmann equation (ULBE). It is a new scheme based on the idea of placing the unknown fields at the nodes of the mesh and evolving them based on the fluxes crossing the surfaces of the corresponding control volumes. The study shows a significant variation and a high sensitivity of wall shear stress to the height of the endothelium corrugation and the presence of erythrocytes. The latter were modelled as deformable, viscous particles within a fluid continuum.

A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops.

The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, while retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need to be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytical and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences.

Heart rate reduction with ivabradine promotes shear stress-dependent anti-inflammatory mechanisms in arteries

Blood flow generates wall shear stress (WSS) which alters endothelial cell (EC) function. Low WSS promotes vascular inflammation and atherosclerosis whereas high uniform WSS is protective. Ivabradine decreases heart rate leading to altered haemodynamics. Besides its cardio-protective effects, ivabradine protects arteries from inflammation and atherosclerosis via unknown mechanisms. We hypothesised that ivabradine protects arteries by increasing WSS to reduce vascular inflammation. Hypercholesterolaemic mice were treated with ivabradine for seven weeks in drinking water or remained untreated as a control. En face immunostaining demonstrated that treatment with ivabradine reduced the expression of pro-inflammatory VCAM-1 (p<0.01) and enhanced the expression of anti-inflammatory eNOS (p<0.01) at the inner curvature of the aorta. We concluded that ivabradine alters EC physiology indirectly via modulation of flow because treatment with ivabradine had no effect in ligated carotid arteries in vivo, and did not influence the basal or TNFα-induced expression of inflammatory (VCAM-1, MCP-1) or protective (eNOS, HMOX1, KLF2, KLF4) genes in cultured EC. We therefore considered whether ivabradine can alter WSS which is a regulator of EC inflammatory activation. Computational fluid dynamics demonstrated that ivabradine treatment reduced heart rate by 20 % and enhanced WSS in the aorta. In conclusion, ivabradine treatment altered haemodynamics in the murine aorta by increasing the magnitude of shear stress. This was accompanied by induction of eNOS and suppression of VCAM-1, whereas ivabradine did not alter EC that could not respond to flow. Thus ivabradine protects arteries by altering local mechanical conditions to trigger an anti-inflammatory response.

Multi-scale interaction of particulate flow and the artery wall

We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying the widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of particulate flow (blood is not a continuum fluid), and proceed to propose, then validate all the key components in a multiply-coupled, multi-scale modeling strategy (in qualitative terms only, note). Eventually, this strategy should lead to a quantitative, patient-specific understanding of the coupling between particulate flow and the endothelial state.

A many-component lattice Boltzmann equation simulation for transport of deformable particles

We review the analysis of single and N–component lattice Boltzmann methods for fluid flow simulation. Results are presented for the emergent pressure field of a single phase incompressible liquid flowing over a backward–facing step, at moderate Reynolds Number, which is compared with the experimental data of Denham & Patrick (1974 Trans. IChE 52, 361–367). We then access the potential of the N–component method for transport of high volume fraction suspensions of deformable particles in pressure–driven flow. The latter are modelled as incompressible, closely packed liquid drops. We demonstrate the technique by investigating the particles transverse migration in a uniform shear (‘lift’), and profile blunting and chaining.

Endothelial repair in stented arteries is accelerated by inhibition of Rho-associated protein kinase

Aims Stent deployment causes endothelial cells (EC) denudation, which promotes in-stent restenosis and thrombosis. Thus endothelial regrowth in stented arteries is an important therapeutic goal. Stent struts modify local hemodynamics, however the effects of flow perturbation on EC injury and repair are incompletely understood. By studying the effects of stent struts on flow and EC migration, we identified an intervention that promotes endothelial repair in stented arteries. Methods and Results In vitro and in vivo models were developed to monitor endothelialization under flow and the influence of stent struts. A 2D parallel-plate flow chamber with 100 μm ridges arranged perpendicular to the flow was used. Live cell imaging coupled to computational fluid dynamic simulations revealed that EC migrate in the direction of flow upstream from the ridges but subsequently accumulate downstream from ridges at sites of bidirectional flow. The mechanism of EC trapping by bidirectional flow involved reduced migratory polarity associated with altered actin dynamics. Inhibition of Rho-associated protein kinase (ROCK) enhanced endothelialization of ridged surfaces by promoting migratory polarity under bidirectional flow (P < 0.01). To more closely mimic the in vivo situation, we cultured EC on the inner surface of polydimethylsiloxane tubing containing Coroflex Blue stents (65 μm struts) and monitored migration. ROCK inhibition significantly enhanced EC accumulation downstream from struts under flow (P < 0.05). We investigated the effects of ROCK inhibition on re-endothelialization in vivo using a porcine model of EC denudation and stent placement. En face staining and confocal microscopy revealed that inhibition of ROCK using fasudil (30 mg/day via osmotic minipump) significantly increased re-endothelialization of stented carotid arteries (P < 0.05). Conclusions Stent struts delay endothelial repair by generating localized bidirectional flow which traps migrating EC. ROCK inhibitors accelerate endothelial repair of stented arteries by enhancing EC polarity and migration through regions of bidirectional flow.

Anisotropic Medium Approach for the Optical Nonlinearities of Dilute Nitride Superlattices

In this paper we investigate optical nonlinearities in semiconductor superlatitces designed with alternate layers of dilute nitride, GaAsN quantum wells and AlGaAs and barriers. The anisotropic medium approach is used to obtain analytical expressions. The analysis confirms that the nonlinearities increase with anisotropy, extending the anisotropic medium approach to dilute nitride systems.

Analytical expressions for the luminescence of dilute quaternary InAs(N,Sb) semiconductors

Abstract. We calculate the luminescence of the dilute quaternary InAs(N,Sb). The incorporation of N leads to a reduction of the energy gap of the host InAs and Sb acts as a surfactant, improves the N incorporation, and further reduces the bandgap. This is thus extremely relevant for devices operating in the mid-infrared (MIR) spectral range from 3 to 5  μm. In order to describe this system, the theory starts with the band anticrossing model applied to both conduction and the valence band to generate inputs for analytical approximations that lead to luminescence spectra, including plasma screening, bandgap renormalization, and excitonic enhancements. Direct application of the equations leads to good agreement with some recent experimental data.

Lattice Boltzmann method as a computational framework for multiscale haemodynamics

Recent developments of the lattice Boltzmann method for large-scale haemodynamic applications are presented, with special focus on multiscale aspects, including the self-consistent dynamics of suspended biological bodies and their coupling to surface structures, such as the glycocalyx, in the proximity of endothelium using unstructured grids. The description of such multiscale phenomena, each one treated with a suitable variation of the lattice Boltzmann method, opens up new perspectives for a fundamental understanding of the physical mechanisms underlying cardiovascular pathologies, such as plaque growth and the subsequent development of atherosclerotic diseases.