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Postgraduate Opportunities

Mathematics for Biomedical Engineering - 2009 Summer School

Jointly sponsored by EPSRC and the Institute for Advanced Study (IAS) this is a summer school for doctoral research students and early career researchers that aims to provide knowledge and practical experience of mathematically describing problems encountered in Biomedical Engineering.

To be held at the University of Warwick, 19-24 July, 2009.

The topic for this year's summer school is model validation which will cover the whole spectrum from experimental design through identifiability analysis and parameter estimation to physical experiments and result interpretation.

Further details available at http://www2.warwick.ac.uk/fac/sci/ssimbe/

Postgraduate Research

The Forum promotes multidisciplinary research in the medical arena - in particular work which includes the physical sciences or engineering. The Forum is happy to hear from students who wish to undertake postgraduate study in this area and identify suitable supervisors. A list of possible topics is given below.

MSc in Advanced Biomedical Engineering

In September 2004 the new postgraduate one year MSc in Advanced Biomedical Engineering started. This is open to graduates of any physical science or engineering discipline, or the medical or life science provided sufficient mathematical ability can be demonstrated. The course majors on measurement, modelling, simulation and instrumentation in the biomedical arena.

For further information on the course and how to apply, see www2.warwick.ac.uk/fac/sci/eng/pg/bioeng/

PhD Projects for 2004

Modelling the Dynamics of Human Motion
Time-frequency and Non-linear Time Series Analysis of Heart Rate Variability and/or Lung Function Data
Compartmental modelling of human motion
Modelling bipedal standing
Statistical Modelling of Muscle Activity
Tissue characterisation using MRI
Tissue hyperthermia in the treatment of cancer
Mathematical modelling of the human lung
Modelling of Telemetric Compound Action Potential Data from Cochlear Implants

Modelling the Dynamics of Human Motion

Current models of human joint dynamics are mostly based around simple pin jointed skeletal elements. Such models lack the anatomical and physiological fidelity to have widespread use in the clinical environment. In this project, a new approach will be developed to model joint motion using external sensor measurements of joint motion and detailed information on the anatomy of the joints from MRI scans. Image processing techniques will be used to segment the MRI images to identify both bone and soft tissue structures within the joints selected for study. A variety of different techniques will be used to model the movement of different anatomical elements within the joints and a compartmental modelling shell will be used to combine these to produce a dynamic model. Predictive modelling techniques will be used to relate the positions of both skeletal and soft tissue components to the overall motion of the joint measured by external sensors. To be successful, this project will require a collaboration where physicists, mathematicians and engineers work directly not only with clinicians having expertise in orthopaedics and physical therapy but also with anatomists and physiologists. Improved models of joint motion offer the potential for in-silico testing of new prostheses and the testing of operative procedures for individual patients prior to physical surgery.

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Time-frequency and Non-linear Time Series Analysis of Heart Rate Variability and/or Lung Function Data

Analysis of changes in heart rate can be useful in determining the state of various body functions and disorders. In particular spectral analysis of heart rate variability is used in the assessment of autonomic function. Of special interest is the analysis of the change in autonomic function over time. Similarly, analysis of changes in lung function over time yields valuable information on function and disorders.

Several methods exist for the time-frequency and nonlinear analysis of signals. This project will involve the construction of test-signals and analysis of real signals from heart rate variability and/or lung function data, comparison of several different time series analysis methods and evaluation of their usefulness with respect to the assessment of autonomic and/or lung function. The project will use various computational and simulation tools.

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Compartmental modelling of human motion

Whilst much work has gone into understanding the range of movements of various parts of the human body surprisingly little work has gone into analysing the dynamics of human motion. Compartmental modelling is the standard tool for modelling the dynamics of mechanical and other physical systems and past experience of applying this to anatomical and physiological systems has shown that it is not only a powerful tool for modelling these systems but it also provides a useful framework in which to integrate different modelling techniques to produce a single dynamic model (e.g. 3D computational & statistical). In this project compartmental models of the dynamics of human motion will be developed based on linear and non-linear differential equations and algebraic and discontinuous functions. Initially sample individual joints will be studied to identify the key parameters (e.g. joint structure, range of movement, muscle mass etc.). An essential component of these will be compartmental models of muscle activity which include fatigue. From these models a system classification will be performed with the aim of identifying a small number of generic parameterised human joint models which can be used for different anatomical locations. A variety of techniques including principal components analysis and Tagguchi methods will be used to help identify the generic models, however, the emphasis will be on identifying parameters for this model which have anatomical and physiological meaning and which can be measured non-invasively on a wide variety of subjects, including those with a physical disability. Basic measurements on normal subjects will form an essential component of this research and will include gait lab measurements and measurement of anatomical structures from MRI images as well standard anthrophormetric measures.

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Modelling bipedal standing

In order to achieve bipedal standing, humans activate complex sequences of the postural muscles to both achieve stability and prevent muscle fatigue. In this project we propose to model the dynamics of human standing from the perspective of the sequence of postural activation. Using standard rigid body models of the human as a starting point, models for stability will be developed by integrating information about the patterns of postural muscle activity into these. Measurement of the EMG activity of the postural muscles and the position of body segments in 3D space will be made whilst normal subjects stand on a computer controlled platform that can very rapidly move either forward or backwards. The direction of movement and the time delay between the subject being warned and a movement actually occurring will be a function of a random variable. In addition to improving our knowledge of the biomechanics of human standing, this work will directly aid in the design of both functional electrical stimulation (FES) orthoses designed to improve standing in those with an appropriate functional loss. In addition, it could play a role in the design of lower limb mechanical orthoses.

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Statistical Modelling of Muscle Activity

Human muscle is made a from a large number of fibres whose asynchronous 'twitches' when stimulated sum to allow smooth graduated movements. The large muscles in the arms and legs (e.g. ) are termed prime movers and may have as many as 20,000 fibres. Electromyogram (EMG) studies made during movement record the summed electrical activity associated with the simultaneous twitching of many fibres. Mathematical models of human motion must include models of the muscles that create that motion - in particular they should be able to predict force/extension characteristics together with the onset of fatigue. Compartmental models (for example 'active' pistons) are not suitable for this and models must reflect the activity of individual fibres or groups of fibres. Therefore multi-element models based on statistical distributions to describe patterns of firing will be explored. Until recently it was thought that the pattern of fibre firings was random. However, the work of Hudgins et. al. has shown recently that correlation of the EMG following repeat movements shows a coherence. This finding will be further explored and used to inform the modelling process.

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Tissue characterisation using MRI

NMR spectroscopy provides a method for determining the chemical structure of materials. In medicine the NMR technique is widely used in Magnetic Resonance Imaging to obtain detailed anatomical images of the body. However, whilst these images identify the location of different types of tissue they do not provide a detailed of picture of the structure of that tissue. In the diagnosis of many diseases, including cancer, it is the structure of the tissue which is of importance. Traditionally, cellular structure is determined by microscopy of small samples of tissue removed from the body. Ideally, this invasive procedure should be replaced by a non-invasive one. We have recently shown that it is potentially possible to determine the structure of tissue from MRI measurements by relating information on composition to structure through mathematical models. Our current activities include experimental work both on cell cultures and the theoretical models. The next stage of the work includes looking at ways of characterising the extra-cellular matrix in tissue and determining whether tissue characterisation is possible in low field magnets.

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Tissue hyperthermia in the treatment of cancer

Radiotherapy, which is a standard technique in the treatment of cancers, relies on the cancerous cells having a slightly higher probability of damage to their DNA and a poorer probability of self repair than normal cells when exposed to high energy ionising radiation. Any technique which can increase this differential will improve the success of treatment. It has long been suggested that localised heating of the tumour tissue (termed tissue hyperthermia) will improve the success of the radiotherapy treatment but as yet no practical technique has yet been devised to achieve the required localised heating. In a recent project we have developed a number of promising designs for ultrasound transducers which could produce localised tissue hyperthermia. Within this project we will implement sample transducers and mathematically model them so that their performance can be better understood and optimised. In addition, there is a need to dvelop tissue models to understand the patterns of heating produced when the ultrasound energy is deposited in the tissue.

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Mathematical modelling of the human lung

Mathematical modelling of human organ systems not only supports our understanding of normal physiological processes, but also disease processes and their treatment. We have a long standing interest in modelling the human respiratory system, in particular, the human respiratory system in people suffering from acute disease processes, including acute respiratory distress and a pulmonary embolus. The modelling of the respiratory system is currently limited by our ability to model the disease processes. We have developed a number of theoretical models of the lung which allow us to introduce non-specific lung disease. Results obtained from these models show good correlation with measured data and the published data from other research groups. In this project we will develop these models further to generate improved models of the disease processes and, in particular, the way the nature of the lung damage changes during the course of the disease process. An important element in developing these models will be identifying validation techniques for them using both patient studies and phantoms. In addition, the models will be implemented in a way that allows them to be incorporated into an existing model of artificially ventilated intensive care patients.

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Modelling of Telemetric Compound Action Potential Data from Cochlear Implants

In many profoundly deaf people the hair cells of the inner ear that transduce mechanical sound vibration into electrical signals are damaged or missing. In such cases a device called a cochlear implant can be surgically implanted into the cochlear to replace the function of the hair cells and partially restore hearing. The purpose of the implant is to evoke, with electrical stimulation, a similar pattern of nerve activity to that expected in a healthy ear when subjected to acoustic stimulation.

At present cochlear implants are configured for a particular person in a rather ad hoc fashion and results are dependent on many factors – not least the skill of the individual audiologist. However, new telemetric techniques now enable direct measurements of the compound action potential (CAP) of the cochlear nerve to be made. In principle, if appropriate techniques can be developed, these measurements could be used to optimise in a quantitative and systematic manner the performance of the cochlear implant for a particular subject. It is the development of such techniques that form the basis of this project. We intend to use an information-theoretic and neural modelling approach to make estimates of the amount of speech information encoded direct from telemetric CAP data. Models would then enable the implant to be configured to optimise the information transmitted for an individual subject. Using such a quantitative procedure is likely to improve overall speech comprehension and reduce the great variability in performance experienced across patient groups. This project requires skills in information theory, mathematical modelling, psychophysics and neurophysiology.

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Bacterial genome sequencing will help to open up novel antimicrobial therapies

Bacterial genome sequencing