Keng Cheng Ang

Computational modelling of blood flow through curved stenosed arteries

A computational model of three-dimensional blood flow in curved arteries with elliptic stenosis was developed. Two groups of models, (a) different angles of curvature and (b) degrees of stenosis, have been studied under typical conditions for stenosed coronary artery. Useful information on the haemodynamics has been obtained. Results of pressure drop show that the presence of the curvature augments the increased flow resistance due to stenotic lesions. The study also demonstrates the significant presence of secondary flow in a curved artery. In addition, the results have shown that the secondary flow in a curved artery brings about elevated shear stress on the vessel wall. These results indicated that both curvature and stenosis should be considered together by cardiologists to assess or quantify the severity of the stenosis. This study employed a powerful computer-aided design (CAD) package to construct the model and a commercial computational fluid dynamics (CFD) code for the analysis of blood flow in stenosed arteries. The long-term application of this form of research promises to be an effective tool for gaining insights into the pathology of arterial diseases.A computational model of three-dimensional blood flow in curved arteries with elliptic stenosis was developed. Two groups of models, (a) different angles of curvature and (b) degrees of stenosis, have been studied under typical conditions for stenosed coronary artery. Useful information on the haemodynamics has been obtained. Results of pressure drop show that the presence of the curvature augments the increased flow resistance due to stenotic lesions. The study also demonstrates the significant presence of secondary flow in a curved artery. In addition, the results have shown that the secondary flow in a curved artery brings about elevated shear stress on the vessel wall. These results indicated that both curvature and stenosis should be considered together by cardiologists to assess or quantify the severity of the stenosis. This study employed a powerful computer-aided design (CAD) package to construct the model and a commercial computational fluid dynamics (CFD) code for the analysis of blood flow in stenosed arteries. The long-term application of this form of research promises to be an effective tool for gaining insights into the pathology of arterial diseases.

Introducing the boundary element method with MATLAB

The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires complex programming skills beyond the ability of a typical undergraduate. In this article, we present a simple and systematic way of implementing the boundary element method for solving the Laplaces equation using MATLAB, a numerical software package commonly used in undergraduate courses. The examples will demonstrate that a package such as MATLAB serves well in introducing as well as implementing the boundary element method.

Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling – A Case Study

This paper reports an exploratory study which examined how a group of pre-service secondary school mathematics teachers’ knowledge in mathematical modelling was shaped by their independent modelling experiences. It also determined the pre-service teachers’ views on teaching mathematical modelling. The findings show that independent modelling experiences with reflection activities had enabled the pre-service teachers to acquire knowledge on the important elements of modelling activities in the various stages of the modelling process. The pre-service teachers’ views on teaching mathematical modelling were mainly limited to the scientific-humanistic perspective. Implications for these findings on mathematical modelling instructional practice were discussed.

Real-Life Modelling Within a Traditional Curriculum: Lessons from a Singapore Experience

Many mathematics teachers in Singapore are not familiar with designing, implementing and facilitating modelling activities in the classroom. In this chapter, we report an experiment in which a teacher with no experience in mathematical modelling made an attempt to conduct a modelling activity in his mathematics class at a local secondary school. Data in the form of students’ work and feedback, lesson videos and interviews were collected. We examine the reactions from students, and discuss the lessons gained from this experience. From the data collected, it appears that while students were generally motivated in carrying out the task, they had some difficulties handling the mathematics involved and the modelling process. The teacher was able to design a reasonable task, but had some difficulty with classroom implementation of the activity.

Real-life application of a simple continuum traffic flow model

A numerical solution to a simple continuum model for traffic flow is discussed. Real traffic data are used for an in-depth study and the implementation of a finite difference scheme is described in detail. The results show that predicted traffic flow conditions agree well with the observed data provided boundary conditions are treated properly. This modelling exercise provides an excellent example of applying mathematics to a fairly complex real life problem. It serves to provide insight into the processes involved in deterministic modelling using a realistic and relevant example.

A dual-reciprocity boundary element method for steady infiltration problems

Steady water infiltration in homogeneous soils is governed by the Richards equation. This equation can be studied more conveniently by transforming to a type of Helmholtz equation. In this study, a dual-reciprocity boundary element method (DRBEM) is employed to solve the Helmholtz equation numerically. Using the solutions obtained, numerical values of the suction potential are then computed. The proposed method is tested on problems involving infiltration from different types of periodic channels in a homogeneous soil. Moreover, the method is also examined using infiltration from periodic trapezoidal channels in three different types of homogeneous soil. 2010 Mathematics subject classification: 76M15.