ICMS Newsletter

HIGHLIGHTS OF THE YEAR 1994/5

MATHEMATICS IN MEDICINE RESEARCH PROGRAMME

This year-long programme aimed to bring together mathematicians and medical experts to study problems relevant to certain areas of medical science. The programme was divided into two sections each containing four workshops. Reports on the three workshops in 1994 appeared in the last edition of ICMS News (Heart Modelling ; The Lung and Cardiovascular System ; Biomechanics). There was widespread interest in each of the remaining workshops with participants coming from both the mathematical and medical communities. In addition, ICMS sponsored a Science Festival Lecture by Professor Roy Anderson, FRS on Mathematical Models in Infectious Disease Control.

Support for this programme had been received from a number of sources including the following organisations:

WORKSHOP 4 : WOUND HEALING

10 - 13 January 1995

Speakers:

E H Sage (Seattle, Washington), J Davidson (Vanderbilt), W Lindblad (Wayne State), P Maini (Oxford), J Sherratt (Warwick), R Clark (StonyBrook)

The New Year saw the resumption of the ICMS Research Programme "Mathematics in Medicine" which got off to a flying start with a workshop devoted to wound healing. The programme attracted some 35 participants from various fields of research including mathematics, biology, surgery and biochemistry.

The first day of the workshop was Tuesday, 10 January and was devoted to the theme of angiogenesis, a process which involves the formation of blood vessels and which is crucial to successful wound healing. This process also occurs in such pathological conditions as tumour growth and arthritis. Professor Helen Sage (University of Washington, Seattle) opened the proceedings with an immensely informative overview on the different stages of angiogenesis. David West (Liverpool) then gave a summary of the important roles of chemicals such as hyaluronan which modulate and to some extent control angiogenesis. The afternoon session was devoted to mathematical modelling of angiogenesis in tumour growth and wound healing (M Chaplain, H Byrne, Bath) and was completed by a very stimulating lecture by Frank Arnold on applications of catastrophe theory to tissue repair.

The Wednesday had a strong biological theme to it with a focus on the key cellular events involved in wound healing such as cell migration, cell-extracellular matrix interactions, and critical events involved in nascent granulation tissue. Three superb expository talks were given by Jeffrey Davidson, Bill Linblad and Richard Clark. During the afternoon session interesting presentations were given by I Hopkinson on the role of collagen in wound healing, W Bardsley on the quantitative analysis of wound healing data and A Fitzgerald on fibroblast migration in Dupuytren's disease. The day was rounded off by a very stimulating discussion entitled Can Mathematical Modelling Heal Wounds? which anticipated the next day's talks.

Thursday focused on mathematical models of wound healing beginning with an excellent overview talk by Philip Maini (Oxford) followed by a highly polished, more specific talk on corneal wound healing by Jonathan Sherratt (Warwick). The afternoon session saw contributions from Luke Olsen on mathematical models for fibro contractive diseases, D Semrov on inverse parameter determination and J Fitzpatrick on the analysis of rodent wound contraction.

The morning of Friday 13th saw the end of the workshop with a lovely review of scarring in foetal and adult wound healing given by Roisin McCallion (Manchester) followed by the mathematical modelling of scar formation by P Dale (Oxford).

WORKSHOP 5 : TUMOUR GROWTH AND DEVELOPMENT

13 - 17 February 1995

Speakers:

R Jain (Harvard), R Sutherland (SRI International), J Adam (Old Dominion), H Acker (Dortmund), W Mueller-Klieser (Mainz), R Lefever (Brussels), V Kuznetsov (Moscow), J Freyer (Los Alamos).

February saw the biggest workshop yet with over 40 people in attendance and standing room only in 14 India Street for most of the week. Unfortunately, Professor Judah Folkman could not make the workshop due to health problems. However, M Chaplain (Bath) and B Sleeman (Dundee) opened up the workshop with two talks giving a comprehensive overview of the mathematical modelling of solid tumour growth and development. The afternoon session saw two very interesting contributed talks by S Cross (Sheffield) concerning the fractal nature of the boundaries of invasive cancers and D Cameron (Edinburgh) on modelling the tumour response and re-growth during chemotherapy for primary breast cancer. Tuesday 14th was dominated by the charismatic presence of Professor Rakesh Jain (Harvard) who provided good value for money and held the audience spellbound as he gave a superlative overview of his 15 years of research in the field in the equivalent of 4 plenary lectures. This was a truly stunning performance and the highlight of the week. The day was rounded off by a contributed talk by C. Rowlatt and then a very stimulating discussion session prompted by Professor Jain's marvellous exposition.

Wednesday 15th was Multicellular Spheroid day and the participants were treated to three excellent talks on various aspects of multicellular spheroid growth and development by three of the leading researchers in the world in this field. R Sutherland (SRI International) presented his work concerning gene expression and how this affects growth in multicellular spheroids, R Acker (Dortmund) on metabolism and cell activities and W Mueller-Klieser (Mainz) on diffusion fields in multicellular spheroids. The afternoon session was rounded off by J Freyer (Los Alamos) and Z Bajzer (Mayo Clinic) who gave contributions on the mathematical modelling of multicellular spheroids and also M Marusic who talked on fitting nonlinear models for tumour growth to data.

The morning of Thursday 16th was devoted to the immune response to cancer with two excellent talks on aspects of the mathematical modelling of the immune system by R Lefever (Brussels) and V Kuznetsov (Moscow). Oliver Scott finished the morning off with a fine talk concerning tumour immunity which led to a fruitful discussion session. Thursday afternoon was taken as break.

Friday morning saw the workshop brought to a close with two contributed talks by A Perumpanani (Oxford) with a mathematical model of tumour invasion and by J-H Mao (Glasgow) with a stochastic model for tumorigenesis in mice. Finally, John Adam (Old Dominion) wound-up the proceedings with one of the best and most humorous finishing talks to be heard for a long time entitled Mathematical Models of Tumour Growth: A Speculative Overview.

SPECIAL LECTURE: PROFESSOR ROY ANDERSON FRS

Mathematics Models in Infectious Disease Control: from Henry to the Formulation of Public Health Policy

Edinburgh International Science Festival, 6 April 1995.

Professor Anderson has a very prominent position in UK medical science, both in research and administration. He is the Linacre Professor of Zoology at Oxford, and a Governor of the Wellcome Trust. With Robert May he co-authored Infectious Diseases of Humans: Dynamics and Control. His lecture was a brilliant account of the role of mathematical models of infection in understanding both childhood diseases such as measles, rubella and pertussis, and the new global menace of Aids. Particular emphasis was placed on the relevance of the theory to basic public health issues such as the design mass vaccination programmes.

WORKSHOP 6: CHEMOTHERAPY

10 - 12 April 1995

Speakers:

G Webb (Vanderbilt), Z Agur (Oxford), O Arino (Pau), S Michelson (Syntex Discovery Research), L Pilz (Heidelberg).

April saw the arrival of the chemotherapy workshop with Monday 10th being devoted to mathematical modelling. The participants were treated to two very informative overview talks concerning the mathematical modelling of various aspects of chemotherapy by Glenn Webb (Vanderbilt) on qualitative features of mathematical models of chemotherapy and by Zvia Agur (Weizman Institute) on insight into chemotherapy and the cell cycle gained from mathematical modelling. The afternoon session consisted of contributed talks by H Byrne and M Chaplain (Bath).

Tuesday 11th opened with a very colourful and lively talk by Seth Michelson (Syntex Research) concerning modelling the activity and reversal of the P-glycoprotein pump and multidrug resistance. Lothar Pilz (Heidelberg) then gave a fine exposition of his work concerning the modelling of the growth and control of cell colonies using stochastic techniques. The afternoon session consisted of two talks from "locals" D Cameron and D Jodrell who presented contributed talks on the modelling of chemotherapy in breast tumours and the optimising of chemotherapy administration in individual patients respectively.

Wednesday 12th saw the workshop brought to a close with first a plenary lecture by Ovide Arino (Pau) who gave an excellent overview of his work concerning structured cell population models and then a captivating presentation by Philip Arundel (Zeneca) on a problem in control theory applied to the identification of key parameters in intravenous infusions.

WORKSHOP 7: IMAGE ANALYSIS

12 - 16 June 1995

Speakers:

J Demongeot (Grenoble), K Mardia (Leeds), C Jennison (Bath), V A Kuznetsov (Moscow), A Ivshina (Moscow), B Sleeman (Dundee).

The final workshop of the summer was devoted to Image Analysis and attracted participants from several fields of research including medicine, mathematics, industry and statistics. Six plenary talks were given on a wide variety of topics and there was much helpful and fruitful discussion.

K Mardia (Leeds) gave the first plenary talk on Monday afternoon on statistical issues in image warping for shape change, followed by Chris Jennison (Bath) who gave presentation on models and algorithms of statistical image analysis.

Brian Sleeman (Dundee) opened the proceedings on Tuesday with a talk on the location and reconstruction of solid tumours from the X-ray transform. V Kuznetsov (Moscow) then rounded the morning off with a talk on the recognition of fuzzy sets with applications in immunology, cytology and oncology. The afternoon session was devoted to discussions on the previous days' topics.

Dr A Ivshina (Moscow) gave the first talk of Wednesday concerning the structure of lymphocyte subpopulations in the blood and applying the syndrome-disease approach for staging human osteosarcoma. Professor Jacques Demongeot (Grenoble) finished off the workshop with a wonderfully Gallic presentation of his research into medical imaging techniques at the Medical Image Centre, Grenoble, using spline interpolation and transform techniques.

WORKSHOP 8: CELL KINETICS

28 November - 1 December

Speakers:

D Appleton (Newcastle), G Bocharov (Moscow), H Byrne (Bath), D Cameron (Western General Hospital, Edinburgh), A Columbano (Italy), L Mallucci (King's College, London), B Sleeman (Leeds), G Zajicek (Israel).

The final workshop of the ICMS year long programme Mathematics in Medicine took place during the week 27 November - 1 December. The workshop was devoted to Cell Kinetics and once again attracted a very good mix of biomathematicians, clinicians and experimentalists. The discussion sessions were therefore highly fruitful and productive.

The workshop opened on Tuesday 28 with a talk by Dr David Appleton entitled An Overview of Models of Cell Proliferation. This got the workshop off to a very good start and the talk was animated by Dr Appleton illustrating his models using various can-openers of assorted shapes and sizes. The second talk of the morning session was presented by Dr Mark Chaplain and dealt with mathematical models of Growth Inhibitory and Growth Promoting Factors within Multicellular Spheroids. Several (theoretical) reaction-diffusion models were presented with some recent results from experiments carried out at the John Radcliffe hospital used to illustrate the theory.

Professor Brian Sleeman gave a very stimulating presentation during the afternoon session presenting new results obtained from models of cell aggregation. Explicit solutions of simplified systems were presented which were very good approximations to the full nonlinear system. The afternoon session finished off with a one hour discussion session on questions which had arisen during the day's proceedings.

Professor Amadeo Columbano gave the first talk of Wednesday with a beautiful overview of his experimental research into the various transcription factors and growth factors involved in liver regeneration and mitogen-induced hyperplasia. Dr Helen Byrne completed the morning session with a nicely counter-balanced theoretical presentation on the mathematical modelling of apoptosis and necrosis. The afternoon session opened with Dr David Cameron presenting clinical and experimental results of the roles of apoptosis, necrosis and mitosis in breast cancer. Given the themes of the two morning talks, and the latter talk, once again the day's proceedings were finished off with a very stimulating discussion session in which clinicians, theoreticians and experimentalists all fully participated.

Thursday, the scheme of Wednesday was in a sense reversed with two theoretical talks sandwiching an experimental talk. Professor Gennadi Bocharov presented some of his mathematical modelling of cell proliferation which consisted of highly nonlinear coupled ordinary differential equations with delay-terms. Professor L Malluci then completed then morning session with a presentation of his experimental research into the control of cell-cycle in normal cells and induction of apoptosis in leukaemia cells by a growth inhibitory factor. During the afternoon, Drs Usher and Henderson presented a mathematical model of chemotherapy scheduling in the presence and absence of drug resistance.

The final talk of the workshop was presented on Friday morning by Professor Gershom Zajicek who presented his mathematical model of the so-called "streaming-tissue". This model was very general and quite controversial in its approach and application and so provided for a very useful final discussion session which generated both heat and light.


LONDON MATHEMATICAL SOCIETY SPITALFIELDS DAY

Biomathematics

10 June 1995

With the support of the London Mathematical Society we were able to mount a series of talks giving a rich sample of some of the topics covered during the year's work on Mathematics and Medicine. The meeting was attended by both mathematicians and medical practitioners from Scotland and the North of England. The author's abstracts are printed here in order to convey better the scale of the ideas addressed at the meeting.

Jonathan Sherratt (Warwick)

Mathematical Models of Wound Healing

Wound healing is a fundamental issue in clinical medicine, and despite extensive experimental research, many aspects of the process are only partially understood. Contributions of mathematical modelling were described.

Wounds to the outer (epidermal) layer of adult skin heal by the cells at the wound edge crawling inwards, while simultaneously dividing to provide a source of new cells. In the context of the cornea of the eye, improved speed of healing is a vital objective. A model which focuses on cell division during healing, is used to make quantitative predictions on increasing the speed of healing by chemical manipulation. In embryonic skin, recent experiments suggest that epidermal wounds heal by a quite different mechanism, namely the contraction of a cable of filamentous actin at the wound edge. A model for the formation of this cable based on the balance of elastic and traction forces within the skin gives predictions which compare well with experiments and also suggests a mechanism for the formation of the cable.

Healing disorders occur in a small but significant minority of the population, and are usually associated with the contraction process in the inner (dermal) layer of the skin. It is these contraction forces that produce the wrinkling commonly seen around a healing wound. The role of contraction in dermal wound healing can be explored using a partial differential equation model and gives an explanation of a bifunction into an abnormal mode. A second issue associated with dermal repair is the formation of a scar at the end of the healing process. Remarkably, foetal wounds do not scar, and recent experiments have shown that this difference is controlled by the levels of chemical regulators during healing. The prospects for scarless healing in adult wounds was discussed using a model.

Tim J Pedley (Leeds)

Flow and Mass Transport in the Lungs and Cardiovascular System

The talk explored some topics which had featured at the earlier one-week workshop.

The study of flow in collapsible tubes is applicable to blood flow in arteries under a cuff and in veins above the heart, to airflow in the bronchi during forced expiration and to urine flow in the urethra. Laboratory experiments reveal the characteristics of a complex non-linear dynamical system and progress in the mathematical modelling of the observed phenomena was described.

Time-dependent flow in tubes of complex, three-dimensional geometry model blood flow in arteries. The distribution of viscous wall shear stress (WSS) in arteries is related to the distribution of atherosclerosis, so the difficulties in predicting WSS in individuals are potentially important. It is found that the WSS distribution is very sensitive to geometrical and temporal perturbations.

Airway closure as a consequence of surface tension instability is almost certainly responsible for normal expiratory gas trapping in adults and may be the cause of respiratory failure in some premature babies. Models for the underlying cause of airway closure, and potential methods for relieving it, were described.

Martin Nowak (Oxford)

Evolutionary Dynamics of HIV

Recent investigations have made it possible to obtain quantitative estimates for the dynamics of HIV infections: in an infected individual free virus and infected cells turn over with a half-life time of about two days. This implies a daily production of at least 10^9 virus particles. The human immunodeficiency virus evolves rapidly during infections which enables the virus to evade from immunological pressure. The immune response selects for virus diversity which makes it increasingly difficult for the immune system to control the virus. In this context HIV infections can be seen as evolutionary processes on the time scale of several years. New results were presented that describe the escape dynamics of HIV from cytotoxic T cell responses which are directed against multiple epitopes of the virus.

Robert M May (Oxford)

Spatial Chaos and its Role in Ecology and Evolution

Very simple and fully deterministic mathematical models which incorporate rules for movement on some spatial lattice can generate an extremely diverse array of spatial patterns, including spiral waves, apparently static but inhomogeneous "crystal lattices", and spatial chaos. Many examples were given, ranging from the population dynamics of host parasitoid and other systems, to evolutionary games (Prisoner's Dilemma, Hawk-dove) played among "territory holders", and the lecture ended with speculation on the implications of the work and on its likely future directions.

WORKSHOPS & CONFERENCES

SEVERAL COMPLEX VARIABLES

An ICMS Instructional Conference: 19 March - 1 April 1995

Organisers:

S Krantz (St Louis), N Sibony (Orsay), T Bailey (Edinburgh), E Rees (Edinburgh).

This was the third in the series of successful ICMS Instructional conferences in topics related to analysis. R Narasimhan (Chicago) gave a series of introductory lectures beginning at One Complex Variable and this was built on by three other short courses in the first week:

In the second week some more advanced courses were given: In addition to the main programme, there were examples sessions and other opportunities for the 57 participants to interact with the speakers and with each other. This very successful event was supported by the EC HCM programme which enabled participants from many different European countries to attend.

STATISTICS AND NEURAL NETWORKS

19 - 21 April 1995

Organisers:

M Titterington (Glasgow), J W Kay (BioSS).

This two-day workshop brought together statisticians and a few mathematicians interested in the theory and methodology underlying Artificial Neural Network(ANN) models, along with leading members of the mainstream ANN community. ANN models have been much used in recent years as the basis of methodology for pattern recognition and classification, optimization, flexible nonlinear prediction, and in a variety of applications such as image processing, speech recognition, character recognition and many others. Many of these areas are of interest to statisticians, who have developed sometimes different, sometimes very similar, methodology, such as projection pursuit regression, nonparametric regression, nonparametric density estimation and latent structure analysis. The principal aim of the Workshop was to continue a growing movement to stimulate cross-fertilisation between the two communities. More specifically, the stated objectives were as follows.

The programme included talks by ANN world experts and by internationally known statisticians. The individual speakers were Professors L Breiman (Berkeley), P J Brown (Kent), D J Hand (Open University), T Hastie (Stanford), N Intrator (Tel Aviv), M Jordan (MIT), J W Kay (BioSS), D Lowe (Aston), D J Ripley (Oxford). Two special features were the series of lively case-study presentations at the end of the first day and the concluding discussion session at the end of the second day. The case-study presentations were made by the winners of a pre- advertised 'competition', the individuals involved being H Brown (Edinburgh), R P W Duin (Delft), E B Martin and A J Morris (Newcastle) and B Yuhas (AT&T Bell Labs). Attendance was limited to about 50 participants, made up of the two organisers, the 16 invited speakers, 10 UK including the five competition winners, 19 invited participants, 8 research students and a very small number of additional places, filled by responders to a dra! matically over-subscribed call for expressions of interest.

It was decided to exploit the presence in Edinburgh of so many experts in what is currently an area of considerable general interest by following the Workshop by a one-day Open Meeting. This meeting was to be aimed at a slightly less specialised audience, and it turned out to be well attended with the 150-seat Wolfson Lecture Theatre of the Royal Society of Edinburgh virtually filled to capacity. All the feedback from the participants in these events has been enthusiastic.

WORKSHOP ON MULTIBODIES

5 - 6 June 1995

Speakers:

H Le Dret (Paris VI), R Ohayon (CNAM, Paris), V G Maz'ya (Linkoping), H W Mackenzie (Pilkington Technology Management), D Vassiliev (Sussex), V A Kozlov (Linkoping), M Bernadou (INRIA), G P Panasenko (Saint-Etienne), A B Movchan (Bath) and J Periaux (Avions Marcel Dassault).

Organisers:

P G Ciarlet (Paris VI), H Le Dret (Paris VI) and J M Ball (Heriot-Watt).

A multibody is any engineering structure that is formed by joining together parts that have different dimensions. Thus rods or plates either fitted together or joined onto a solid three-dimensional object constitute a multibody. The junction problems that occur in a multibody are susceptible to mathematical modelling, and recent mathematical advances are leading to an improved understanding of how the different parts of a multibody interact statically and dynamically. The workshop was regarded as very useful and instructive by those who attended. From the theoretical point of view it brought together leading representatives of the French and Russian schools, whose approaches are somewhat different. While the participation from industry was smaller than hoped for, one industrial participant said that the workshop had "opened his eyes" to what mathematics could do in this area. The input from industry was equally valuable for the academic participants as a source of new problems and insights.

UNESCO 50TH ANNIVERSARY CELEBRATIONS

ICMS is proud to have been chosen by UNESCO to organise events to celebrate the 50th anniversary of UNESCO in November 1995. UNESCO had expressed the wish to hold a high-level scientific event in the UK in recognition of the fact that it was the UK that at UNESCO's inception proposed the inclusion of science in its charter. After an approach to UNESCO by the James Clerk Maxwell Foundation, ICMS organised two prestigious events: a lecture by Professor Sir Roger Penrose and a workshop on Fluid Mechanics.

PROFESSOR SIR ROGER PENROSE

SHADOWS OF THE MIND

8 November 1995

Sir Roger Penrose, FRS, Rouse Ball Professor of Mathematics at Oxford University, has in recent years been at the centre of an intense debate on the nature of consciousness, and in particular on the limitations of existing theories, whether of computation or of fundamental physics, for explaining consciousness. His popular appeal, and the intrinsic interest of the theme, were confirmed when tickets for this prestigious event were snapped up on the day of release. This necessitated arrangements, using video conferencing facilities, to bring the lecture to an overflow audience.

The problem of consciousness is perennial, and can currently be approached from many points of view, philosophical or scientific. The introduction, and the concluding vote of thanks were given respectively by a philosopher and a scientist, two of ICMS's staunchest supporters, Professor Sir Stewart Sutherland, FBA, Principal of The University of Edinburgh, and Professor Alistair MacFarlane, FRS, Principal of Heriot-Watt University. Here it became evident that there is no problem of two cultures in Edinburgh, as each speaker, in a scholarly and witty way, articulated the significance of Sir Roger's grand theme.

The plenary talk itself made it quite obvious why Sir Roger is so much in demand. Even for those (presumably few) for whom Sir Roger's two books are absolutely familiar, there were basic new points, both theoretical (on the need for new physical theory) and more speculative (on the computational significance of various neurological entities), all delivered in a relaxed style. The volume (and diversity) of questions fielded by Sir Roger was clear evidence of the universal appeal of the topic. There were even requests for autographs.

The lecture was attended by The Lord Provost of Edinburgh and Dr Albert Sasson, Assistant Director General UNESCO, and many distinguished guests. ICMS is grateful to the Lord Provost and The City of Edinburgh District Council for providing a reception after the lecture.

WORKSHOP ON NEW MATHEMATICAL DEVELOPMENTS IN FLUID MECHANICS

6-10 November 1995

The workshop formed part of the 50th Anniversary celebrations of the founding of UNESCO and was funded by grants from UNESCO and EPSRC.

The workshop lived up to all expectations, and provided an exciting overview of current progress towards a more fundamental understanding of the governing equations of fluid mechanics. The workshop was built around three lecture courses, each of three lectures, by P Constantin (Chicago) on Statistical Navier-Stokes Equations, by P L Lions (Paris) on The Compressible Navier-Stokes Equations, and by A J Majda (New York) on Turbulent Diffusion,Vortices, and Singularities in Fluids. Invited lectures were given by Y Brenier (Paris), S Childress (New York, joint session with the North British Differential Equations Symposium), M J P Cullen (Meteorological Office), M Farge (Paris), E Grenier (Paris), K Kirchgaessner (Stuttgart), D Lohse (Marburg) and F Waleffe (MIT). Shorter contributed lectures were given by S K Venkatesan (Calcutta), I Roulstone (Meteorological Office) and A S Vasudeva Murthy (Bangalore). The topics covered included problems from meteorology, turbulence, dynamo theory and sonoluminescence.

The Scientific Committee consisted of the three principal speakers, J T Stuart (Imperial College) and J M Ball (Heriot-Watt). The workshop was attended by 47 persons, and was notable for the lively nature of the scientific exchanges. The bulk of the UNESCO grant was used to enable talented researchers from developing countries to participate in the workshop, of whom two were from Argentina, four from India and two from Senegal.

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Chris Eilbeck / Heriot-Watt University/ chris@ma.hw.ac.uk