Mathematical modelling and the consequent analysis of problems arising in the Biomedical  Sciences  is increasingly becoming a major research interest. 

Indeed, the great scientific revolution of this century is going to be the mathematical formalisation of phenomena in the Life Sciences, much as the revolution of the past two centuries was the development of the above approach in the Physical Sciences. To quote J E Cohen [1]: Mathematics is Biology’s next microscope, only better; Biology is Mathematics’ next Physics, only better.

The Italian community of mathematicians has decided to join efforts in facing the enormous challenges posed by such problems, by founding, in 1997, CIMAB, a national centre aimed at coordinating all  major scientific competences in the area of Mathematical Biology and  their diverse applications. It now includes seven universities (Florence, Milan, Naples, Torino University and Torino Politecnico, Trento, Urbino) and two National Research Council  (IAC and IASI) centres, as well as individual researchers from other institutions including the IEO. We are aware that only by breaking down the academic and disciplinary silos will science be able to grow in order to resolve the enormous challenging problems raised by the Biomedical Sciences.  

It is now becoming common to be aware that the heuristic or evidence based experimental approach, which is the traditional investigative method in the Biological Sciences, should be complemented by a mathematical modelling approach. The latter can be used as a hypothesis-testing, and indeed, hypothesis-generating, tool which can help to direct experimental research, while the results of experiments help to refine the modelling.  The ultimate goal of CIMAB is to use mathematical models together with their computer simulations to support biomedical research to design new therapeutic strategies.

The main contribution that Mathematics can offer includes, because of its specific peculiarities, the following: 

a)  a better  semantic  understanding  of  the phenomenon, in terms of  entities and relationships among them,  followed by  its  syntactic  representation, in terms of mathematical structures, i.e. its mathematical model; 

b)  the finding of solutions, possibly  quantitative, of  the mathematical models which on one hand  offer  an  interpretation of available data,  and on the other hand  offer   predictions  of possible  behaviours by varying  some parameters, or the state of the system at the beginning,  and also its external conditions; 

c) validation of models based on real data, which includes  the identification of the main parameters, is part of the  mathematical approach to the analysis.

In addition to the above we cannot ignore the impact of sophisticated mathematical and statistical methods in medical diagnostics; let us just think of the  methods for  reconstruction and  analysis of biomedical images obtained by non invasive techniques, such as TAC, NMR.   The area of acquisition, processing  and analysis of biomedical images is in itself  a ground for  challenging problems  for   mathematics and  computational sciences.

One of the major contributions of  Mathematical and Computational Biology is  the ability to  provide simulations, and  related visualization in a set of scenarios that would be  impossible in wet  laboratories, because of financial,  temporal  or even ethical constraints.  We are then facing the emergence of new paradigms that allocate computational experiments, based on mathematical models  (in silico experiments  -  dry experiments)  side to side with in vitro or in vivo experiments (wet experiments).

Mathematicians have become very aware that existing mathematical methods are not sufficient for the special  complexity of biological systems, since  the  variety and  the evolution  of  biological systems  and their intrinsic complexity and multiscale  structure make them a lot more complex  than  non biological systems.

An open problem is thus the development of innovative mathematical theories and methods capable of bridging different scales, from   genes to cells, organs to organisms. Methods to reduce complexity, both analytical and computational, should be able to capture information at the micro-level of individuals (genes, cells, vessels, etc.) which are responsible for the emergence of  complex behaviour  on a  larger scale (organs, organisms, etc.).

With the aim of encouraging interaction between mathematicians and researchers in Biomedical Sciences, CIMAB has organized the Workshop MathCell2010, that will be held in Rome on the14-15 December 2010 (web site: http://ctpde.iac.rm.cnr.it/MathCell2010/). Participation is free, but online registration is kindly required. As far as the topic of cancer research goes,  this  workshop will focus  on the modelling and simulation of the complexity of cancer phenomena covering the whole path from the molecular (genetic) scale to that of tissues, through the description, by mathematical actions, at the cellular scale. The final, and main, objective of the modelling is focused on the optimization of therapeutic actions.

It is worth stressing that the workshop cannot aim to cover the whole variety of issues in the field, but simply to capture, out of the selected topics and speakers, the main issues related to the modelling of cancer phenomena with special focus on multi-scale aspects. Specifically the talks will deal with issues such as neo-angiogenesis and biomechanics of tumours. The hope is to cover sufficient material to motivate, on one side more mathematicians to develop a research activity in the field  which  also includes highly challenging analytic problems, while on the other side the hope is to attract the attention  of  the biomedical community towards a proficient cooperation aiming  to improve  the quality of  human  life, being aware  that  the solution of  such tremendous problems  can be reached only by a  close collaboration of  mathematicians, physicists, engineers and computer scientists  with  biologists and clinicians.   Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development.

 Interestingly, Alberts et al [2] observe that ‘the emphasis given to cancer research has profoundly benefited a much wider area of medical knowledge than that of cancer alone’, explaining that ‘the effort to combat cancer has driven many fundamental discoveries in cell biology’.   

The workshop will also cover topics concerning the regenerating tissues and the biofilms. From the mathematical modelling point of view, these biological phenomena share some open problems with the tumour growth, and we believe in the interest of the mutual interaction of these investigation.

The main speeches will be delivered during the Opening session by Prof G McVie (IEO), Prof M Chaplain  (University of Dundee), and Prof L Preziosi (CIMAB-Politecnico Torino).

Vincenzo Capasso, Professor

Probability and Mathematical Statistics

Director of CIMAB

President-elect of the European Academy of Sciences

Department of Mathematics

Universita’  degli Studi di Milano

Via  Saldini 50

20133  MILANO, Italy

e-mail:  vincenzo.capasso@unimi.it

------------

[1] Cohen JE (2004) PLoS Biol 2 (12) e439 doi:10.1371/journal.pbio.0020439

[2] Alberts  B  et al (2002)  Molecular Biology of the Cell 4th edn (New York: Garland Science)