Complex Fluids in Biological Systems (18w5123)


(University of Wisconsin - Madison)

Gwynn Elfring (The University of British Columbia)


The complexity of biological systems, even on the smallest length scales, is staggering. Biological systems are in a continuous state of flux, with interconnected motion and forces spanning over a wide range of length and time scales. These factors pose enormous challenges to mathematical descriptions of the mechanics governing physical processes in biological systems. In particular, fluids in biology are often endowed with highly complex characteristics when viewed as continuous media. With continuing developments of mathematical and numerical machinery for understanding multiscale physical systems, the fields of complex fluids and biological systems are ripe for fruitful cross-pollination. There have already been many successful scientific advances along these lines in numerous areas including: predicting the behaviour of complex biofluids by probing the fluid at the microscopic scale; understanding the motion of biological organisms that interact with complex biological fluids such as mucus; and finally in developing theory for the dynamics of active systems of many organisms (biological or synthetic), but many open questions remain.

The workshop is focused at the intersection of three areas: rheology (the study of the deformation and flow of matter), biolocomotion (swimming and crawling through biological fluids and tissues), and active matter (large systems of active particles and their collective dynamics). This is a particularly vibrant area of multi-disciplinary science, requiring sophisticated mathematical understanding and novel computational techniques to push the field further towards problems of immediate interest for applications in biology, engineering, and human health services. Some of the long term goals of the field are to improve human understanding of fertility and the spread of bacterial infections and diseases. Medical challenges also include detecting and quantifying disruptions in normal material functionality (e.g. dehydrated lung mucus) and to develop new therapies. Fundamental insight gained at the intersection of complex fluids in biological contexts is certain to make a direct impact on these and other important pursuits. But the study of emergent dynamics in large, interacting systems is a fundamental issue in the physical sciences, and lessons learned may impact numerous other scientific fields.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).