Past Junior Applied Mathematics Seminar

18 October 2011
13:15
Abstract

Motivated by the study of micro-vascular disease, we have been investigating the relationship between the structure of capillary networks and the resulting blood perfusion through the muscular walls of the heart. In order to derive equations describing effective fluid transport, we employ an averaging technique called homogenisation, based on a separation of length scales. We find that the tissue-scale flow is governed by Darcy's Law, whose coefficients we are able to explicitly calculate by averaging the solution of the microscopic capillary-scale equations. By sampling from available data acquired via high-resolution imaging of the coronary capillaries, we automatically construct physiologically-realistic vessel networks on which we then numerically solve our capillary-scale equations. By validating against the explicit solution of Poiseuille flow in a discrete network of vessels, we show that our homogenisation method is indeed able to efficiently capture the averaged flow properties.

  • Junior Applied Mathematics Seminar
21 June 2011
13:15
Abstract

Bacteria are ubiquitous on Earth and perform many vital roles in addition to being responsible for a variety of diseases. Locomotion allows the bacterium to explore the environment to find nutrient-rich locations and is also crucial in the formation of large colonies, known as biofilms, on solid surfaces immersed in the fluid. Many bacteria swim by turning corkscrew-shaped flagella. This can be studied computationally by considering hydrodynamic forces acting on the bacterium as the flagellum rotates. Using a boundary element method to solve the Stokes flow equations, it is found that details of the shape of the cell and flagellum affect both swimming efficiency and attraction of the swimmer towards flat no-slip surfaces. For example, simulations show that relatively small changes in cell elongation or flagellum length could make the difference between an affinity for swimming near surfaces and a repulsion. A new model is introduced for considering elastic behaviour in the bacterial hook that links the flagellum to the motor in the cell body. This model, based on Kirchhoff rod theory, predicts upper and lower bounds on the hook stiffness for effective swimming.

  • Junior Applied Mathematics Seminar
7 June 2011
13:15
Abstract

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterised by a high proviral load and risk of developing ATL, an aggressive blood cancer, or HAM/TSP, a progressive neurological and inflammatory disease. Infected individuals typically mount a large, chronically activated HTLV-I-specific CTL response, yet the virus has developed complex mechanisms to evade host immunity and avoid viral clearance. Moreover, identification of determinants to the development of disease has thus far been elusive.

 This model is based on a recent experimental hypothesis for the persistence of HTLV-I infection and is a direct extension of the model studied by Li and Lim (2011). A four-dimensional system of ordinary differential equations is constructed that describes the dynamic interactions among viral expression, infected target cell activation, and the human immune response. Focussing on the particular roles of viral expression and host immunity in chronic HTLV-I infection offers important insights to viral persistence and pathogenesis.

  • Junior Applied Mathematics Seminar
8 March 2011
13:15
Sophie Kershaw
Abstract

How best to use the cellular Potts model? This is a boundary dynamic method for computational cell-based modelling, in which evolution of the domain is achieved through a process of free energy minimisation. Historically its roots lie in statistical mechanics, yet in modern day it has been implemented in the study of metallic grain growth, foam coarsening and most recently, biological cells. I shall present examples of its successful application to the Steinberg cell sorting experiments of the early 1960s, before examining the specific case of the colorectal crypt. This scenario highlights the somewhat problematic nuances of the CPM, and provides useful insights into the process of selecting a cell-based framework that is suited to the complex biological tissue of interest.

  • Junior Applied Mathematics Seminar
22 February 2011
13:15
Yi Ming Lai
Abstract
&nbsp;We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modelling<br />populations of neurons. In particular, we use the example of a interacting<br />populations of excitatory and inhibitory neurons (E-I networks). As each<br />network consists of a large but finite number of neurons that fire<br />stochastically, we can study the effect of this intrinsic noise using a master<br />equation formulation. In the parameter regime where each E-I network acts as a<br />limit cycle oscillator, we combine phase reduction and averaging to study the<br />stationary distribution of phase differences in an ensemble of uncoupled E-I<br />oscillators, and explore how the intrinsic noise disrupts synchronization due<br />to a common external noise source.<pre> </pre>
  • Junior Applied Mathematics Seminar
25 January 2011
13:15
Hermes Gadelha
Abstract

Abstract: Flagella and cilia are ubiquitous in biology as a means of motility and critical for male gametes migration in reproduction, to mucociliary clearance in the lung, to the virulence of devastating parasitic pathogens such as the Trypanosomatids, to the filter feeding of the choanoflagellates, which are constitute a critical link in the global food chain. Despite this ubiquity and importance, the details of how the ciliary or flagellar waveform emerges from the underlying mechanics and how the cell, or the environs, may control the beating pattern by regulating the axoneme is far from fully understood. We demonstrate in this talk that mechanics and modelling can be utilised to interpret observations of axonemal dynamics, swimming trajectories and beat patterns for flagellated motility impacts on the science underlying numerous areas of reproductive health, disease and marine ecology. It also highlights that this is a fertile and challenging area of inter-disciplinary research for applied mathematicians and demonstrates the importance of future observational and theoretical studies in understanding the underlying mechanics of these motile cell appendages.

  • Junior Applied Mathematics Seminar
30 November 2010
13:15
Almut Eisentrager
Abstract
<p>In a healthy human brain, cerebrospinal fluid (CSF), a water-like liquid, fills a system of cavities, known as ventricles, inside the brain and also surrounds the brain and spinal cord. Abnormalities in CSF dynamics, such as hydrocephalus, are not uncommon and can be fatal for the patient. We will consider two types of models for the so-called infusion test, during which additional fluid is injected into the CSF space at a constant rate, while measuring the pressure continuously, to get an insight into the CSF dynamics of that patient.</p> <p>&nbsp;</p> <p>In compartment type models, all fluids are lumped into compartments, whose pressure and volume interactions can be modelled with compliances and resistances, equivalent to electric circuits. Since these models have no spatial variation, thus cannot give information such as stresses in the brain tissue, we also consider a model based on the theory of poroelasticity, but including strain-dependent permeability and arterial blood as a second fluid interacting with the CSF only through the porous elastic solid.</p>
  • Junior Applied Mathematics Seminar
16 November 2010
13:15
Chris Lustri
Abstract
We investigate the behaviour of free-surface waves on time-varying potential flow in the limit as the Froude number becomes small. These waves are exponentially small in the Froude number, and are therefore inaccessible to ordinary asymptotic methods. As such, we demonstrate how exponential asymptotic techniques may be applied to the complexified free surface in order to extract information about the wave behaviour on the free surface, using a Lagrangian form of the potential flow equations. We consider the specific case of time-varying flow over a step, and demonstrate that the results are consistent with the steady state case.
  • Junior Applied Mathematics Seminar
2 November 2010
13:15
Athanasios Tsanas
Abstract
<p>This work demonstrates how we can extract clinically useful patterns</p><p>extracted from time series data (speech signals) using nonlinear signal<br /> processing and how to exploit those patterns using robust statistical<br /> machine learning tools, in order to estimate remotely and accurately<br /> average Parkinson's disease symptom severity.&nbsp;</p> <p>&nbsp;</p>
  • Junior Applied Mathematics Seminar
19 October 2010
13:15
Abstract
<p>We explore two different threading approaches on a graphics processing<br /> unit (GPU) exploiting two different characteristics of the current GPU<br /> architecture. The fat thread approach tries to minimise data access time<br /> by relying on shared memory and registers potentially sacrificing<br /> parallelism. The thin thread approach maximises parallelism and tries to<br /> hide access latencies. We apply these two approaches to the parallel<br /> stochastic simulation of chemical reaction systems using the stochastic<br /> simulation algorithm (SSA) by Gillespie. In these cases, the proposed<br /> thin thread approach shows comparable performance while eliminating the<br /> limitation of the reaction system's size.</p><p>Link to paper:&nbsp;</p> <p><a target="_blank" href="http://people.maths.ox.ac.uk/erban/papers/paperCUDA.pdf">http://people.maths.ox.ac.uk/erban/papers/paperCUDA.pdf</a></p>
  • Junior Applied Mathematics Seminar

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