A 3D numerical study of the collateral capacity of the circle of Willis with anatomical variation in the posterior circulation

Background The Circle of Willis (CoW) is the most important collateral pathway of the cerebral artery. The present study aims to investigate the collateral capacity of CoW with anatomical variation when unilateral internalcarotid artery (ICA) is occluded. Methods Basing on MRI data, we have reconstructed eight 3D models with variations in the posterior circulation of the CoW and set four different degrees of stenosis in the right ICA, namely 24%, 43%, 64% and 79%, respectively. Finally, a total of 40 models are performed with computational fluid dynamics simulations. All of the simulations share the same boundary condition with static pressure and the volume flow rate (VFR) are obtained to evaluate their collateral capacity. Results As for the middle cerebral artery (MCA) and the anterior cerebral artery (ACA), the transitional-type model possesses the best collateral capacity. But for the posterior cerebral artery (PCA), unilateral stenosis of ICA has the weakest influence on the unilateral posterior communicating artery (PCoA) absent model. We also find that the full fetal-type posterior circle of Willis is an utmost dangerous variation which must be paid more attention. Conclusion The results demonstrate that different models have different collateral capacities in coping stenosis of unilateral ICA and these differences can be reflected by different outlets. The study could be used as a reference for neurosurgeon in choosing the best treatment strategy.

Oxygen transport in a three-dimensional microvascular network incorporated with early tumour growth and preexisting vessel cooption: Numerical simulation study

We propose a dynamic mathematical model of tissue oxygen transport by a preexisting three-dimensional microvascular network which provides nutrients for an in situ cancer at the very early stage of primary microtumour growth. The expanding tumour consumes oxygen during its invasion to the surrounding tissues and cooption of host vessels. The preexisting vessel cooption, remodelling and collapse are modelled by the changes of haemodynamic conditions due to the growing tumour. A detailed computational model of oxygen transport in tumour tissue is developed by considering (a) the time-varying oxygen advection diffusion equation within the microvessel segments, (b) the oxygen flux across the vessel walls, and (c) the oxygen diffusion and consumption with in the tumour and surrounding healthy tissue. The results show the oxygen concentration distribution at different time points of early tumour growth. In addition, the influence of preexisting vessel density on the oxygen transport has been discussed. The proposed model not only provides a quantitative approach for investigating the interactions between tumour growth and oxygen delivery, but also is extendable to model other molecules or chemotherapeutic drug transport in the future study.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Impact of coronary tortuosity on coronary pressure: Numerical simulation study

Background: Coronary tortuosity (CT) is a common coronary angiographic finding. Whether CT leads to an apparent reduction in coronary pressure distal to the tortuous segment of the coronary artery is still unknown. The purpose of this study is to determine the impact of CT on coronary pressure distribution by numerical simulation. Methods: 21 idealized models were created to investigate the influence of coronary tortuosity angle (CTA) and coronary tortuosity number (CTN) on coronary pressure distribution. A 2D incompressible Newtonian flow was assumed and the computational simulation was performed using finite volume method. CTA of 30°, 60°, 90°, 120° and CTN of 0, 1, 2, 3, 4, 5 were discussed under both steady and pulsatile conditions, and the changes of outlet pressure and inlet velocity during the cardiac cycle were considered. Results: Coronary pressure distribution was affected both by CTA and CTN. We found that the pressure drop between the start and the end of the CT segment decreased with CTA, and the length of the CT segment also declined with CTA. An increase in CTN resulted in an increase in the pressure drop. Conclusions: Compared to no-CT, CT can results in more decrease of coronary blood pressure in dependence on the severity of tortuosity and severe CT may cause myocardial ischemia.

Numerical modelling of particle deposition in idealized porous channels

This project provides a steppingstone to comprehend the mechanisms that govern particulate fouling in metal foam heat exchangers. The method is based on development of an advanced Computational Fluid Dynamics model in addition to performing analytical validation. This novel method allows an engineer to better optimize heat exchanger designs, thereby mitigating fouling, reducing energy consumption caused by fouling, economize capital expenditure on heat exchanger maintenance, and reduce operation downtime. The robust model leads to the establishment of an alternative heat exchanger configuration that has lower pressure drop and particulate deposition propensity.

Bias reduction using stochastic approximation

The paper studies stochastic approximation as a technique for bias reduction. The proposed method does not require approximating the bias explicitly, nor does it rely on having independent identically distributed (i.i.d.) data. The method always removes the leading bias term, under very mild conditions, as long as auxiliary samples from distributions with given parameters are available. Expectation and variance of the bias-corrected estimate are given. Examples in sequential clinical trials (non-i.i.d. case), curved exponential models (i.i.d. case) and length-biased sampling (where the estimates are inconsistent) are used to illustrate the applications of the proposed method and its small sample properties.

Numerical studies of gypsum plasterboard and MGO board lined LSF walls exposed to fire

Fire resistance of cold-formed light gauge steel frame (LSF) wall systems is enhanced by lining them with single or multiple layers of wall boards with varying thermal properties. These wall boards are gypsum plasterboards or Magnesium Oxide (MgO) boards produced by different manufacturers. Thermal properties of these boards appear to show considerable variations and this can lead to varying fire resistance levels (FRL) for their wall systems. Currently FRLs of wall systems are determined using full scale fire tests, but they are time consuming and expensive. Recent research studies on the fire performance of LSF wall systems have used finite element studies to overcome this problem, but they were developed based on 1-D and 2-D finite element platform capable of performing either heat transfer or structural analysis separately. Hence in this research a 3-D finite element model was developed first for LSF walls lined with gypsum plasterboard and cavity insulation materials. Accurate thermal properties of these boards are essential for finite element modelling, and thus they were measured at both ambient and elevated temperatures. This experimental study included specific heat, relative density and thermal conductivity of boards. The developed 3-D finite element model was then validated using the available fire tests results of LSF walls lined with gypsum plasterboard, and is being used to investigate the fire performance of different LSF wall configurations. The tested MgO board exhibited significant variations in their thermal properties in comparison to gypsum plasterboards with about 50% loss of its initial mass at about 500 ºC compared to 16% for gypsum plasterboards. Hence the FRL of MgO board lined LSF wall systems is likely to be significantly reduced. This paper presents the details of this research study on the fire performance of LSF wall systems lined with gypsum plasterboard and MgO board including the developed 3-D finite element models, thermal property tests and the results.

Numerical modelling of deformation behaviour of red blood cells in microvessels using the coupled SPH-DEM method

This thesis developed an advanced computational model to investigate the motion and deformation properties of red blood cells in capillaries. The novel model is based on the meshfree particle methods and is capable of modelling the large deformation of red blood cells moving through blood vessels. The developed model was employed to simulate the deformation behaviour of healthy and malaria infected red blood cells as well as the motion of red blood cells in stenosed capillaries.

Numerical studies on CFRP strengthened steel circular members under marine environment

The durability of carbon fibre reinforced polymer (CFRP) strengthened steel circular hollow section (CHS) members has now become a real challenge to researchers. In addition, various parameters that may affect the durability of such members have not been revealed yet. This paper presents brief experimental results and the first finite element (FE) approach of CFRP strengthened steel CHS beams conditioned in simulated sea water, along with an accelerated corrosion environment at ambient (24 OC ± 4 OC) and 50 OC temperatures. The beams were loaded to failure under four-point bending. It was found that the strength and stiffness reduced significantly after conditioning in an accelerated corrosion environment. Numerical simulation is implemented using the ABAQUS static general approach. A cohesive element was utilised to model the interface element and an 8-node quadrilateral in-plane general-purpose continuum shell was used to model CFRP elements. A mixed mode cohesive law was deployed for all the three components of stresses in the proposed FE approach, which were one normal component and two shear components. The validity of the FE models was ascertained by comparing the ultimate load and load vs deflection response from experimental results. A range of parametric studies were conducted to investigate the effects of bond length, adhesive types, thickness and diameter of tubes. The results of parametric studies indicated that the adhesive with high tensile modulus performed better and durability design factors varied from section to section.

Experimental and numerical investigation of the behaviour of CFRP strengthened CHS beams subjected to bending

This paper presents the results of an experimental and numerical program to investigate the circular hollow section (CHS) beams, strengthened using Carbon Fibre Reinforced Polymer (CFRP) sheets. The circular hollow shaped steel beams bonded with different CFRP layer orientations were tested under four-point bending. The mid-span deflection, service load and failure load were recorded. The LHL (where L, first inner longitudinal layer, H, second hoop layer and L, third outer longitudinal layer) and LLH (where L, first inner longitudinal layer, L, second longitudinal layer and H, third outer hoop layer) layer oriented strengthened beams perform slightly better than HHL (where H, first inner hoop layer, H, second hoop layer and L, third outer longitudinal layer) layer oriented strengthened beams. The LHL and LLH layer oriented treated beams showed very similar structural behaviour. Numerical analyses were then conducted on the CFRP strengthened steel CHS beams. The validity of the models has been assessed by comparing the failure loads and mid-span deflections. The effects of various parameters such as bond length, section types, tensile modulus of CFRP, adhesive layer thickness and adhesive types have been studied.

Experimental and numerical investigation of strain-rate-dependent behavior of kangaroo shoulder cartilage

This thesis introduces a new animal model, kangaroo, to biomechanical investigations of shoulder cartilage research. It examines the effect of cartilage structure and constituents on tissue behavior and its adaptation to mechanical loading. In doing so, the study explains the relationship of tissue's functional behaviors to its structure and constituents which has important implications for tissue engineering strategies catering joint specific cartilage tissue generation.

Natural convection in rectangular cavities at high Rayleigh number

Natural convection in rectangular two-dimensional cavities with differentially heated side walls is a standard problem in numerical heat transfer. Most of the existing studies has considered the low Ra laminar regime. The general thrust of the present research is to investigate higher Ra flows extending into the unsteady and turbulent regimes where the physics is not fully understood and appropriate models for turbulence are not yet established. In the present study the Boussinesq approximation is being used, but the theoretical background and some preliminary results have been obtained[1] for flows with variable properties.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

Numerical study on the surface depression of the concrete runway pavement under impact load

Airport runway pavement always subjected to huge impact loading due to the hard landing of aircraft on the pavement surface. Therefore runway pavements should have sufficient impact resistance capability to avoid damage causing by hard impact like surface deflection in downward or penetration since the repair works is cumbersome within the operating condition of airport and also increases the service life cost of the pavement structure. Several research works have been carried out on airport runway pavement to measure the present condition of pavement and also to predict future performance of it. However, most of the works are confined by pavement response under moving aircraft loading. Nevertheless, no comprehensive research work is yet conducted to identify the controlling factors which might have significant effect in changing the common pavements damage like surface penetration depth under impact of aircraft. Therefore, a 3D FE study is conducted to determine some effective factors in controlling the top surface penetration depth of runway pavement. Among the exterior factors, mass of the impactor, velocity of the impactor, impact angle and boundary conditions are selected and as interior factors, thickness of the runway pavement, compressive strength and density of materials used in the runway pavement are selected.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.