Mathematical modelling of atheroma plaque formation and development in coronary arteries

Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier–Stokes equations and Darcy''s law for fluid dynamics, convection–diffusion–reaction equations for modelling the mass balance in the lumen and intima, and the Kedem–Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.     

The application of principles of soil mechanics to the modelling of pastes

This paper presents a simple model of the stress-strain behaviour of pastes made from non-damaging particles. It is based on an earlier model by Chandler and Macphee (Cem Concr Res 33:265–270, 2003) and Sands and Chandler (accepted for publication in Géotechnique) which is de-dimensionalised to reduce the number of model parameters and facilitate their establishment. The model is first tested against the results of experimental work on sands by Oka et al. (Géotechnique 49(5):661–680, 1999) and very successful simulations of torsion tests on hollow cylinders are obtained by finding the most suitable values of two adjustable parameters. The model is also checked against mechanical tests performed on a number of simple pastes. An experimental procedure used for the tests on various compositions of pastes is presented, together with the results of the tests and simulations using the model. Good agreement is achieved with the model, showing that some recent developments in soil models might provide a guide to developing and improving models for dense granular pastes operating in the frictional regime.     

The use of the generalized Waring process in modelling informetric data

Summary Although its use in informetrics dates back at least to 1987, data analysed in a recent paper by Shan et al. (2004) has rekindled interest in the generalized Waring distribution (GWD). The purpose of this note is to show that for many purposes, the distribution is best motivated via a familiar informetric scenario of a population of “sources” producing “items” over time leading to a stochastic process from which the univariate, bivariate and multivariate forms of the GWD are natural consequences. Earlier work and possible future applications are highlighted. Many of the results are due to Irwin and Xekalaki while much of the material on the Waring process has been previously available in an unpublished research report by the author (Burrell, 1991).     

The influence of the cohesive process zone in hydraulic fracturing modelling

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions.     

Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow

A multiphysics mathematical model to simulate drug delivery in idealized and patient-specific coronary arteries is presented. Blood is modeled as an incompressible Navier–Stokes fluid, the arterial wall as a linear poroelastic medium, and the drug transport is described by a scalar advection-diffusion equation. The drug compound is released into the bloodstream, carried by the flow, deposited onto the endothelium, penetrates into the wall, and is transported within the arterial wall. NURBS-based isogeometric analysis is employed to describe the geometry and discretize the fluid-solid interaction equations.     

A multiscale and multiphysics numerical framework for modelling of hygrothermal ageing in laminated composites

In this work, a numerical framework for modelling of hygrothermal ageing in laminated composites is proposed. The model consists of a macroscopic diffusion analysis based on Fick's second law coupled with a multiscale FE² stress analysis in order to take microscopic degradation mechanisms into account. Macroscopic material points are modelled with a representative volume element with random fibre distribution. The resin is modelled as elasto‐plastic with damage, and cohesive elements are included at the fibre/matrix interfaces. The model formulations and the calibration of the epoxy model using experimental results are presented in detail. A study into the representative volume element size is conducted, and the framework is demonstrated by simulating the ageing process of a unidirectional specimen immersed in water. The influence of transient swelling stresses on microscopic failure is investigated, and failure envelopes of dry and saturated micromodels are compared. Copyright © 2017 John Wiley & Sons, Ltd.     

The modelling of the freezing process in fine-grained porous media: Application to the frost heave estimation

The solution of the moving-boundary problem, related to heat- and mass-transfer processes in freezing, fine-grained, porous media under phase-transition conditions is presented. It is assumed that a freezing zone, characterized by a wide temperature range of phase transitions, is formed. Therefore a three-zone model is developed. The preservation of the term ∂L/∂t(L is the ice content) in the system of equations has made it possible to determine the ice distribution within the frozen and the freezing zones. For loamy soils the dependence of the freezing process on the characteristic parameters, the Stefan and Lewis numbers, was analyzed. It was found that increasing the enthalpy of phase transition, i.e., decreasing the Stefan number Ste, resulted in diminution of the frozen zone but, at the same time, the ice content within this zone increased. Intensification of the migration process, i.e., increasing the Lewis number Le, also led to diminution of the frozen zone, in which the ice content and, consequently, the total moisture (including ice) were increased. For large Lewis numbers the freezing zone was observed to decrease. When the water migration process is absent (Le = 0), the calculations, which were based on the described model show that in the course of freezing the redistribution takes place only between moisture and ice contents. The total moisture remains constant and equal to the initial water content. The theoretical conceptions and results derived from the analytical solution are in agreement with experimental findings. The presented model predicts the freezing process in porous media and satisfactorily reflects observed phenomena. The utilization of the considered problem solution to the prediction of the frost heave phenomenon in soils freezing processes shown that the calculated frost heave curve matches the experimental results very closely indicating that the model can well reproduce the frost heaving process associated with the freezing. Propagation of the freezing front in the test is predicted the experimental results with reasonable accuracy.     

The use of magnetic techniques in the development of a hydrogenation process

Finely divided Raney Nickel is widely used as a hydrogenation catalyst in the chemical industry and in the refining or hardening of oils and fats. Catalyst removal from process streams is usually carried out by filtration or by centrifugation. Catalyst recycle is difficult owing to the abrasive and pyrophoric nature of the catalyst, general solids handling problems and the propensity of the catalyst to form blockages in linework and in processing equipment. This paper describes the development of a novel design of reactor using magnetic techniques to overcome these problems. An electromagnetic coil is used at the end of a batch to induce sufficient magnetism within the Nickel particles suspended in the process liquor to cause flocculation or agglomeration of the catalyst particles into clusters. These agglomerates settle much faster than the original finely divided material and within minutes most of the catalyst settles out on the base of the vessel. The slight haze of catalyst which remains is removed using an external HGMS unit which is backflushed into the reactor by the following charge. Settled catalyst is easily resuspended by an agitator. Alternative ways of applying the magnetic flocculation technique are described and ways of improving the HGMS unit are discussed.     

液位控制器和PLC在工艺流程中的应用

简述液位控制器在化妆品生产工艺流程中的应用及 PL C在同类设备改进中的使用实例     

Dispersion of carbon nanofibres in a low viscosity resin by calendering process to manufacture multiscale composites by VARIM

The use of mechanical processes, such as calendering, is an interesting method to disperse carbon nanofibres because this technique avoids the use of organic solvents needed in chemical methods. Variations of the process are used by researchers, and further study of the effect of the calendering parameters is still needed. For this reason, the effectiveness of the dispersion of several percentages of carbon nanofibres (0.5–3 wt.%) in epoxy resin using different parameters of the calendering process has been studied in this work. Carbon nanofibres/epoxy nanocomposites and non-cured nanoreinforced mixtures have been characterised. This study showed that the dispersion was enhanced with a Sequential method. Density and thermomechanical properties of nanocomposites manufactured by the selected calendering method were evaluated. The viscosity of the CNF/epoxy mixtures at different percentages of nanoreinforcement was adequate to use them as a matrix in multiscale reinforced composites.     

Dispersion of carbon nanofibres in a low viscosity resin by calendering process to manufacture multiscale composites by VARIM

The use of mechanical processes, such as calendering, is an interesting method to disperse carbon nanofibres because this technique avoids the use of organic solvents needed in chemical methods. Variations of the process are used by researchers, and further study of the effect of the calendering parameters is still needed. For this reason, the effectiveness of the dispersion of several percentages of carbon nanofibres (0.5–3 wt.%) in epoxy resin using different parameters of the calendering process has been studied in this work. Carbon nanofibres/epoxy nanocomposites and non-cured nanoreinforced mixtures have been characterised. This study showed that the dispersion was enhanced with a Sequential method. Density and thermomechanical properties of nanocomposites manufactured by the selected calendering method were evaluated. The viscosity of the CNF/epoxy mixtures at different percentages of nanoreinforcement was adequate to use them as a matrix in multiscale reinforced composites.     

Predictions of crack propagation using a variational multiscale approach and its application to fracture in laminated fiber reinforced composites

Predictions of crack propagation is a valuable resource for ensuring structural integrity and damage tolerance of aerospace structures. Towards that end, a variational multiscale approach to predict mixed mode in-plane cohesive crack propagation is presented here. To demonstrate applicability and to provide validation of the finite element based predictive methodology, a comparative study of the numerical results with the corresponding experimental observations of crack propagation in laminated fiber reinforced composite panels is presented.     

Potential and limits of functional modelling in the CAD process

This paper gives a survey of the beginning and newest computer-aided functional modelling by German researchers. The basic principles of functional modelling are established and a representative function model is illustrated by the example of an emergency power unit. Some important methods for computer-aided modelling according to the function model are explained in detail. Following this the limits of functional modelling are outlined by describing the working arrangements of working principles using a flowchart representation of the function structure.     

Fuzzy regression approach to process modelling and optimization of epoxy dispensing

Epoxy dispensing is one of the popular processes to perform microchip encapsulation for chip-on-board (COB) packages. However, determination of proper process parameters setting for optimal quality of the encapsulation is difficult due to the complex behaviour of the encapsulant during dispensing and the uncertainties caused by fuzziness of epoxy dispensing systems. In conventional regression models, deviations between the observed values and the estimated values are supposed to be in probability distribution. However, when data is irregular, the obtained regression model has an unnaturally wide possibility range. In fact, these deviations in some processes such as epoxy dispensing can be regarded as system fuzziness that can be dealt with properly using fuzzy regression method. In this paper, a fuzzy regression approach with fuzzy intervals to process modelling of epoxy dispensing for microchip encapsulation is described. Two fuzzy regression models relating three process parameters and two quality characteristics respectively for epoxy dispensing were developed. They were then introduced to formulate a fuzzy multi-objective optimization problem. A fuzzy linear programming technique was employed to formulate the optimization model. By solving the model, an optimal setting of process parameters can be obtained. Validation experiments were conducted to evaluate the effectiveness of the proposed approach to process modelling and optimization of epoxy dispensing for microchip encapsulation.     

The development of an inherent safety approach to the prevention of domino accidents

The severity of industrial accidents in which a domino effect takes place is well known in the chemical and process industry. The application of an inherent safety approach for the prevention of escalation events leading to domino accidents was explored in the present study. Reference primary scenarios were analyzed and escalation vectors were defined. Inherent safety distances were defined and proposed as a metric to express the intensity of the escalation vectors. Simple rules of thumb were presented for a preliminary screening of these distances. Swift reference indices for layout screening with respect to escalation hazard were also defined. Two case studies derived from existing layouts of oil refineries were selected to understand the potentialities coming from the application in the methodology. The results evidenced that the approach allows a first comparative assessment of the actual domino hazard in a layout, and the identification of critical primary units with respect to escalation events. The methodology developed also represents a useful screening tool to identify were to dedicate major efforts in the design of add-on measures, optimizing conventional passive and active measures for the prevention of severe domino accidents.     

Formation of water-in-oil emulsions and application to oil spill modelling

Water-in-oil mixtures were grouped into four states or classes: stable, mesostable, unstable, and entrained water. Of these, only stable and mesostable states can be characterized as emulsions. These states were established according to lifetime, visual appearance, complex modulus, and differences in viscosity. Water content at formation was not an important factor. Water-in-oil emulsions made from crude oils have different classes of stability as a result of the asphaltene and resin contents, as well as differences in the viscosity of the starting oil. The different types of water-in-oil classes are readily distinguished simply by appearance, as well as by rheological properties. A review of past modelling efforts to predict emulsion formation showed that these older schemes were based on first-order rate equations that were developed before extensive work on emulsion physics took place. These results do not correspond to either laboratory or field results. The present authors suggest that both the formation and characteristics of emulsions could be predicted using empirical data. If the same oil type as already studied is to be modelled, the laboratory data on the state and properties can be used directly. In this paper, a new numerical modelling scheme is proposed and is based on empirical data and the corresponding physical knowledge of emulsion formation. The density, viscosity, saturate, asphaltene and resin contents are used to compute a class index which yields either an unstable or entrained water-in-oil state or a mesostable or stable emulsion. A prediction scheme is given to estimate the water content and viscosity of the resulting water-in-oil state and the time to formation with input of wave height.     

Wavelet-based analysis of multiscale phenomena: application to material porosity and identification of dominant scales

The paper presents a general process that utilizes wavelet analysis in order to link information on material properties at several scales. In the particular application addressed analytically and numerically, multiscale porosity is the source of material structure or heterogeneity, and the wavelet-based analysis of multiscale information shows clearly its role on properties such as resistance to mechanical failure. Furthermore, through the statistical properties of the heterogeneity at a hierarchy of scales, the process clearly identifies a dominant scale or range of scales. Special attention is paid to porosity appearing at two distinct scales far apart from each other since this demonstrates the process in a lucid fashion. Finally, the paper suggests ways to extend the process to general multiscale phenomena, including time scaling.     

Statistical modelling of the variation in advanced process technologies using a multi-level partitioned response

The advances in semiconductor processing technologies have led to the need for a detailed understanding and stringent control of the variations in device performance. Statistical techniques provide methods, such as response surface modelling (RSM), to measure, characterise and model the variations, thus enabling an understanding and identification of the impact of these on both yield and performance of the devices and circuits built from advanced process technologies. The construction of response surface (RS) models, however, has been restricted to only a few variables, due to the number of TCAD simulations and hence the statistical analyses required for fitting sufficiently accurate models. The problem of modelling a large number of manufacturing process parameters is addressed by partitioning the parameters and subsequently building multi-level RS models which can analyse and predict the process variability. This approach greatly reduces (by approximately two to three orders of magnitude) the large number of TCAD simulations necessary to fit the RS models. The application of multi-level partitioned RSM is demonstrated on a 65 nm CMOS technology. With the device dimensions shrinking and the impact of manufacturing process variations becoming dominant on the device performance, the proposed approach plays a vital role in design for manufacturability. The variability information obtained from these models is important not only to control and optimise the process variation but also to quantify its effects on device and circuits designs.