This grant supports the travel of both students and early career researchers to attend the meeting entitled, "Coupled Processes in Continuum Mechanics Motivated by Biological Phenomena," being held at Michigan State University in October 2011. Such processes involve biomechanical effects related to bearing load, swelling, growing, and remodeling that are coupled to biochemical effects related to transport of ionic species, electrical transduction, and chemical reaction. Such processes operate on a variety of time and length scales, and are severely compromised upon transitioning from in-vivo operation to in-vitro examination. The meeting will address the underlying partial differential equation formulations, the variational structure of equilibrium and steady state models, the treatment of dissipative phenomena, and the handling of multiple time and space scales including consistent coupling to atomistic treatments in the fast and small limit at which the continuum assumption breaks down.
The meeting, to be held on the campus of Michigan State University, is organized under the auspices of both the Society for Natural Philosophy (the 49th such annual meeting since 1963) and the Institute for Mathematics and its Applications (under its Participating Institution program). These organizations are noted for bringing together mathematicians, engineers, biologists, and physical scientists in a workshop atmosphere for the purpose of exploring new directions in mathematical modeling. The focus of this meeting is on coupled biological processes such as those governed by a combination of mechanical and chemical factors. A more sophisticated modeling treatment of these processes is essential to transforming scientific understanding into cost effective medical care. For example, recent ideas for modeling swelling in the context of continuum mechanics show great promise for a more accurate description of soft tissue response in both normal function (birth) and abnormal function (edema, asthma). More accurate mathematical models for describing such processes provide useful analytical tools that contribute to the creation of improved diagnostic procedures and medical therapies.
A three day workshop was held on the campus of Michigan State University in October of 2011 on the subject of building and analyzing mathematical models for the simulation of biological processes. The main tool for this purpose is continuum mechanics, which allows one to account for force balance, heat transfer, chemical reaction, and other complex physical processes upon the biological system. While continuum mechanics was originally developed over a century ago for the analyis of complex engineering structures, it has now become a standard tool for understanding complex biological systems from an engineering perspective. The workshop, which was open to the general scientific community, brought together about fifty researchers from diverse scientific backgrounds (mathematics, engineering, chemistry and biology) and numerous different countries (USA, United Kingdom, India, Italy). NSF support for this workshop was specifically devoted to making it possible for early career scientists to attend. New mathematical models for several phenomena were put forward, debated, and analyzed. These included: (1) the locomotion of kineson along microtubules, (2) the interaction of nanoparticles with biological systems, (3) active mechanosensing at the cellular level, (4) activation of muscle fibers, (5) brain neuromechanics, and (6) cell and tissue mechanical interaction during growth. Outcomes included identification of: strengths and weaknesses of the various models, steps needed so as to allow these models to be used in conjunction with other analysis procedures, and promising computational methods so as to allow their wider implementation. More generally, the workshop is anticipated to foster long term beneficial interactions within the US scientific community.
