ABSTRACT
This chapter introduces some of the basic mathematical approaches that can be used to understand and describe biological systems where nanoscale interactions and nanoscale technology are involved. It outlines some of the challenges involved in the modeling of nanoscale systems. The chapter provides a general framework for choosing a model that is appropriate to the question under consideration. It examines some common mathematical techniques that are particularly effective when applied to model problems related to nanomedicine and nanomedical phenomena. In terms of nano bio-systems, examples of highly restricted flow and diffusion include the passage of material through nanoscale channels in silicon chips and the transport of small molecules across pores in the cell membrane. Mathematical models can be used to gain insight into the underlying mechanisms governing nanoscale properties and behavior. Regardless of the physical laws used, the level of approximation assumed and the degree of experimental “fitting” required, most models involve similar mathematical techniques.
