Recent Trends in Biomathematics - from theory to the clinic
by Zvia Agur

Attending recent conferences in North America and Europe, one could note the increasing committment of biomathematicians to the effort of understanding and improving the therapy of adverse human diseases. Possibly, the AIDS pandemic and the overwhelming realisation that very intricate dynamics are involved in host-virus interactions, played a decisive role in finally bridging the gap between biomedicine on the one hand, and biomathematics on the other. It appears that the significance of these dynamics, and the necessity to study them by biomathematical tools, can no longer be overlooked. The need to sharpen these tools, and to check their suitability for solving ad-hoc medical problems, motivated three conferences I attended last Spring as well as future conferences that are now under organisation.

Solving real-life problems.

The fourth SIAM Conference of Application of Dynamical Systems, which took place in mid-May 1997, at Snowbird, Utah, under the co-chairmanship of Mary Silber and Steve Strogatz, had mathematical biology as one of its principal themes. Within these auspices Michael Mackey organised a mini-symposium: "Mathematics and Medicine: From the Laboratory to the Clinic". This mini-sympsium raised a considerable interest, suggesting that a major item on the agenda of the theorists now is to increase involvement with decision-making in medicine. The aim of the mini-symposium was to illustrate, via concrete examples, the contributions that applied mathematics can make in the interpretation of laboratory and clinical data from a modelling perspective, the pitfalls that await the unwary modeler who chooses to ignore these data, and the richness of new mathematics that can arise from consideration of realistic models in the biomedical sciences. The examples, carefully selected from cancer chemotherapy, the control of cardiac activity and feedback control of the pupil light reflex, mark a shift in focus in biomathematics, from developing pure theories to solving real-life clinical problems.

The need for joint endeavour in mathematical biomedicine

A similar shift in focus characterised the Shanks Conference on Mathematical Models in Medical and Health Sciences held at Vanderbilt University, May 28-31, 1997. Here, rather than demonstrating selected highlights, the organisers of the conference presented the broad scope of mathematical biomedicine, and the wealth of current modelling work in this area, ranging from the use of non-linear finite difference equations through ordinary differential equations and differential delay equations. Special sessions were held on cancer modelling, optimisation and control, medical imaging, cure models in survival analysis, epidemic models, models of immunology and models of cell population dynamics. The participants came from universities, medical research institutes, medical clinics, pharmaceutical companies and included mathematicians, bioengineers, cell biologists, physicians, and medical researchers from various subfields. Hopefully, the efforts invested in gathering such a variety of experts, all thriving to solve similar medical problems, will ripen and carry fruits in the foreseeable future.

Sharpening the tools

The Shanks lecturer this year was Martin Nowak, who pinpointed the role of mathematical modelling in parameter estimation in AIDS. A week later, at the St. Flour Summer school, Glenn Webb elegantly illustrated the sensitivity of different estimates to the caveats of the specific models. By carefully analysing several modelling approaches, Webb pointed at their embarrassingly different resulting conclusions.

Presently, in almost every specific modelling situation, little is known about the mathematical properties of the model. Thus, contradicting predictions of alternative models describing the same systems are not easily reconciled. A notion that surfaced during the Spring meetings is that the recent trends in Biomathematics call for a definition of strict criteria of acceptability of the mathematical models. Indeed, it seems only natural that new conceptual problems arise when a field takes new directions. Now there is a need to evaluate the existing tools in terms of reliability and efficacy.

An effective attempt in this direction was made at the school "Biology and Mathematics of Cell Proliferation, held in early June, 1997, in the mediaeval town, Saint-Flour, which is located in the most handsome landscape of the Cantal region in the Massif Central, France. The school was organised by Ovide Arino, with support from the French Society for Theoretical Biology, the INSERM, the Ministry of Foreign Affairs and the University of Pau. The school was unique in the choice of the superb location, the warm atmosphere at the "Old Seminary," and the very international collection of enthusiastic students and teachers, who quickly became one big family. Most notably, the school made a serious attempt to put together up-to-date mathematical methods of branching processes, semi-group theory, reaction-diffusion processes and non-linear dynamics, with their application to quantifiable chromosomal changes, cell proliferation, principles of cytometry, cell kinetics parameter estimation, tumor invasion and cell-cycle analysis.

The international conferences on mathematical population dynamics (MPD) were initiated by Dave Axelrod, Marek Kimmel and Ovide Arino. Since the first conference in this series, which was held at the University of Mississippi in 1986 there has been a growing interest in these conferences and they have become a major event in the area of biomathematics. Recently, it was suggested that in future MPD conferences special attention will be given to strengthening the links of biomathematics to clinical policy-making. This decision was motivated by the desire to reflect the current tendencies in our field, and to contribute to its maturation process. Thus, in the 5th International Conference on Mathematical Population Dynamics, to be held at Zakopane, Poland, June 21-26 1998 (Andrzej Swierniak being the main organiser) an attempt will be made to discuss controversial interdisciplinary issues, such as parameter estimation in AIDS, the efficacy of screening trials in breast cancer, the growth law of solid tumors, etc.

In spite of the enthusiasm about the new avenues in biomathematics, our integration within the biomedical community is still far from being complete. A few of our more celebrated models are "famous for their famousness", and many of us are aware of the dangers in basing predictions on shaky models, especially when these are applied to the clinic. At the same time, it is our duty to encourage experimentalists to carefully examine the arguments of individual theoretical studies. It seems to me that by taking pains to state each and every assumption the model is based on, as well as the caveats in the analysis, and the limitations of the conclusions, we will be able to move more rapidly from the margins into the well illuminated centre of science.

Return to the Table of Contents