Effect of tortuous extracellular pathways on resistance measurements

There are many instances in which we are limited to measuring macroscopic quantities such as a bulk flow or an average field. In biology, wer are frequently interested in using such macroscopic measurements, for example, the total current from a tissue, to determine the microscopic properties of the cells or tubules of the tissue. The microstructure of the tissue will generally increase the resistance to flow over what would be measured in an unstructured medium. This paper derives a fairly general expression for the relationship between effective resistance to macroscopic flow and the specific resistance of the medium conducting the microscopic flow. This expression, called a tortuosity factor, is defined entirely in terms of measurable morphometric and geometric parameters of the tissue.