BMEN 630 or Math 774 - Viscous Flows in Biology
A unifying theme in biological fluid dynamics is the interaction of solid structures with a surrounding viscous fluid. This course introduces students to the fundamental equations of incompressible fluid mechanics as well as computational tools that are used to analyze these systems. In addition, several applications are discussed including cell-adhesion in blood vessels, sperm motility in the reproductive tract and the process of pulmonary airway-reopening. Topics covered include: derivations of fundamental equations, scaling and dimensional Analysis, model problems (biological and non-biological), lubrication theory analysis, and an introduction to computational methods (immersed boundary methods, boundary element methods). Applications include: flow over immersed objects (e.g. cells), evaluations of flow fields and stresses, flow through irregular geometries, convection-diffusion interactions, time-dependent flows and surface tension flows.
BMEN 633 - Fluid Mechanics for Biomedical Engineers
This course covers general intermediate/advanced fluid mechanics principles. Issues pertinent to the study of biofluid mechanics are emphasized. Topics studied include kinematic principles, Navier-Stokes equations, boundary conditions for viscous flows, basic solutions to steady and unsteady Navier-Stokes equations and interfacial phenomena. Whenever possible, problems of a biological nature are used as examples. These topics include blood rheology, mechanics of the circulation, microcirculation effects, arterial wave propagation and the transport of suspended solutes.
BMEN 667 - Pulmonary Mechanics
This course is designed to provide a survey of mechanical models of the pulmonary system. Topics covered include intermediate fluid mechanics principles, pulmonary anatomy, lung statics, ventilation/perfusion relationships, convection fields in the lung, Taylor dispersion, mucus transport and interfacial pulmonary flows. Students are expected to choose a pulmonary mechanics topic to analyze and present to the class.
BMEN 682 - Fundamentals of Mathematical Modeling and Analysis of Biological Systems
This course, originally developed as part of the Lilly Foundation Teaching Fellowship I was awarded in 1992-93, teaches mathematical modeling methods with a motivation towards understanding biological systems. Mathematical techniques studied include compartmental systems, ordinary differential equations, local analysis, stability analysis, dimensional analysis, scaling, and regular perturbation methods. Student learn and use Mathematica (Wolfram Research) to develop and analyze models using the techniques described above. This creates a laboratory atmosphere, which is useful in developing the students’ mathematical and physical intuition. In addition, the students work on individual and group projects, which they present to the class. Recent projects have included the analysis of AIDS population growth, Taylor dispersion, insulin regulation, enzyme kinetics and fisheries.