Biological Fluid Dynamics in Morphogenesis

North Carolina State University, Raleigh NC

Investigators

Abstract

This research will develop models of the mechanical aspects of shape change in (1) cylindrical fiber-reinforced hydrostats, (2) pattern formation by traction forces in mesenchymal tissues during development and remodeling, and (3) glandular branching morphogenesis. In this Stokesian multiphase area of biological fluid dynamics, there is no inertia, but there are forces across interfaces and transfers of forces between the fluids and fibers embedded in the fluids. In some applications, the models have multiple viscous fluids separated by active interfaces, and in others, the models have a single fluid whose motion and material properties are coupled with the motion of contractile fibers. The models will be used to gain a better understanding of the anisotropic behavior of cylindrical hydrostats (trunks, tentacles, and tongues). They will be used to increase understanding of the mechanical instabilities and pattern formation which can emerge when cells modify their extracellular matrix by moving through it or pulling on it. They will also be used to help define the developmental implications of mechanical hypotheses about how branched tubular structures (like lungs) form in the body. Some results will generate interpretations of theories, some will suggest experiments to test the implications of theories, and some will suggest industrial applications of biomechanical principles. The project will also develop the finite difference numerical methods necessary to solve the partial differential equations arising from modeling the physical forces in these tissues. The development of robust three-dimensional algorithms for the solution of biological fluid dynamics problems will be key to the effective modeling of dozens of problems in the mechanics of cell motion and tissue remodeling. This project involves several biomedical problems in the dynamics of tissues. At all stages of an organism's existence there are mechanical forces at work. How does a completely round egg get to be a very complicated-looking human being, with limbs and eyes and ducts and glands and a wrinkled brain? There are genes that switch on and off, but that is not the whole story. An airplane has switches too, but to understand how it really works, we need to study fluid mechanics - the physical forces that lift, stabilize, and occasionally disturb the craft. Fluid dynamics is equally relevant to biology. As an organism - or part of it - is growing, it creates physical forces, and is shaped by physical forces. The science of Tissue Dynamics is relatively new, and requires expertise in many areas. A biological modeler, a numerical analyst, a developmental biologist, and an industrial researcher have teamed up to study the biomechanics of tissues which are changing their shape, size, strength, orientation, and function. Results of the work should increase our understanding of processes in developmental biology, wound healing, cancer, vascular health and disease, and many other areas of biomedicine involving tissues. This grant is made under the Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology. This is a joint competition sponsored by the Division of Mathematical Sciences (DMS) at the National Science Foundation and the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health.