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.
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