Computational fluid dynamics for improved bioreactor design and 3D culture

The complex relationship between the hydrodynamic environment and surrounding tissues directly impacts on the design and production of clinically useful grafts and implants. Tissue engineers have generally seen bioreactors as 'black boxes' within which tissue engineering constructs (TECs) are cultured. It is accepted that a more detailed description of fluid mechanics and nutrient transport within process equipment can be achieved by using computational fluid dynamics (CFD) technology. This review discusses applications of CFD for tissue engineering-related bioreactors -- fluid flow processes have direct implications on cellular responses such as attachment, migration and proliferation. We conclude that CFD should be seen as an invaluable tool for analyzing and visualizing the impact of fluidic forces and stresses on cells and TECs.

Parallel linear system solution and its application to railway power network simulation

The Streaming SIMD extension (SSE) is a special feature embedded in the Intel Pentium III and IV classes of microprocessors. It enables the execution of SIMD type operations to exploit data parallelism. This article presents improving computation performance of a railway network simulator by means of SSE. Voltage and current at various points of the supply system to an electrified railway line are crucial for design, daily operation and planning. With computer simulation, their time-variations can be attained by solving a matrix equation, whose size mainly depends upon the number of trains present in the system. A large coefficient matrix, as a result of congested railway line, inevitably leads to heavier computational demand and hence jeopardizes the simulation speed. With the special architectural features of the latest processors on PC platforms, significant speed-up in computations can be achieved.

A review of simulation models for railway systems

With the advances in computer hardware and software development techniques in the past 25 years, digital computer simulation of train movement and traction systems has been widely adopted as a standard computer-aided engineering tool [1] during the design and development stages of existing and new railway systems. Simulators of different approaches and scales are used extensively to investigate various kinds of system studies. Simulation is now proven to be the cheapest means to carry out performance predication and system behaviour characterisation. When computers were first used to study railway systems, they were mainly employed to perform repetitive but time-consuming computational tasks, such as matrix manipulations for power network solution and exhaustive searches for optimal braking trajectories. With only simple high-level programming languages available at the time, full advantage of the computing hardware could not be taken. Hence, structured simulations of the whole railway system were not very common. Most applications focused on isolated parts of the railway system. It is more appropriate to regard those applications as primarily mechanised calculations rather than simulations. However, a railway system consists of a number of subsystems, such as train movement, power supply and traction drives, which inevitably contains many complexities and diversities. These subsystems interact frequently with each other while the trains are moving; and they have their special features in different railway systems. To further complicate the simulation requirements, constraints like track geometry, speed restrictions and friction have to be considered, not to mention possible non-linearities and uncertainties in the system. In order to provide a comprehensive and accurate account of system behaviour through simulation, a large amount of data has to be organised systematically to ensure easy access and efficient representation; the interactions and relationships among the subsystems should be defined explicitly. These requirements call for sophisticated and effective simulation models for each component of the system. The software development techniques available nowadays allow the evolution of such simulation models. Not only can the applicability of the simulators be largely enhanced by advanced software design, maintainability and modularity for easy understanding and further development, and portability for various hardware platforms are also encouraged. The objective of this paper is to review the development of a number of approaches to simulation models. Attention is, in particular, given to models for train movement, power supply systems and traction drives. These models have been successfully used to enable various ‘what-if’ issues to be resolved effectively in a wide range of applications, such as speed profiles, energy consumption, run times etc.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Patient-specific computational biomechanics for simulating adolescent scoliosis surgery : predicted vs clinical correction for a preliminary series of six patients

Scoliosis is a spinal deformity that requires surgical correction in progressive cases. In order to optimize surgical outcomes, patient-specific finite element models are being developed by our group. In this paper, a single rod anterior correction procedure is simulated for a group of six scoliosis patients. For each patient, personalised model geometry was derived from low-dose CT scans, and clinically measured intra-operative corrective forces were applied. However, tissue material properties were not patient-specific, being derived from existing literature. Clinically, the patient group had a mean initial Cobb angle of 47.3 degrees, which was corrected to 17.5 degrees after surgery. The mean simulated post-operative Cobb angle for the group was 18.1 degrees. Although this represents good agreement between clinical and simulated corrections, the discrepancy between clinical and simulated Cobb angle for individual patients varied between -10.3 and +8.6 degrees, with only three of the six patients matching the clinical result to within accepted Cobb measurement error of +-5 degrees. The results of this study suggest that spinal tissue material properties play an important role in governing the correction obtained during surgery, and that patient-specific modelling approaches must address the question of how to prescribe patient-specific soft tissue properties for spine surgery simulation.

Numerical simulation of flow in a photocatalytic reactor containing baffles

In this study a new immobilized flat plate photocatalytic reactor for wastewater treatment has been investigated using computational fluid dynamics (CFD). The reactor consists of a reactor inlet, a reactive section where the catalyst is coated, and outlet parts. For simulation, the reactive section of the reactor was modelled with an array of baffles. In order to optimize the fluid mixing and reactor design, this study attempts to investigate the influence of baffles with differing heights on the flow field of the flat plate reactor. The results obtained from the simulation of a baffled flat plate reactor hydrodynamics for differing baffle heights for certain positions are presented. Under the conditions simulated, the qualitative flow features, such as the distribution of local stream lines, velocity contours, and high shear region, boundary layers separation, vortex formation, and the underlying mechanism are examined. At low and high Re numbers, the influence of baffle heights on the distribution of species mass fraction of a model pollutant are also highlighted. The simulation of qualitative and quantitative properties of fluid dynamics in a baffled reactor provides valuable insight to fully understand the effect of baffles and their role on the flow pattern, behaviour, and features of wastewater treatment using a photocatalytic reactor.

CFD Simulation of turbulence promoters in a water treatment reactor

A new immobilized flat plate photocatalytic reactor for wastewater treatment has been proposed in this study to avoid subsequent catalyst removal from the treated water. The reactor consists of an inlet, reactive section where catalyst is coated and an outlet parts. In order to optimize the fluid mixing and reactor design, this study aims to investigate the influence of baffles and its arrangement on the flat plate reactor hydrodynamics using computational fluid dynamics (CFD) simulation. For simulation, an array of baffles acting as turbulence promoters is inserted in the reactive zone of the reactor. In this regard, results obtained from the simulation of a baffled- flat plate photoreactor hydrodynamics for different baffle positions, heights and intervals are presented utilizing RNG k-ε turbulence model. Under the conditions simulated, the qualitative flow features, such as the development and separation of boundary layers, vortex formation, the presence of high shear regions and recirculation zones, and the underlying mechanism are examined. The influence of various baffle sizes on the distribution of pollutant concentration is also highlighted. The results presented here indicate that the spanning of recirculation increases the degree of interfacial distortion with a larger interfacial area between fluids which results in substantial enhancement in fluid mixing. The simulation results suggest that the qualitative and quantitative properties of fluid dynamics in a baffled reactor can be obtained which provides valuable insight to fully understand the effect of baffles and its arrangements on the flow pattern, behaviour, and feature.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.