The application of kinematic equations for the study of cell turnover

Cell turnover in renewing populations is accompanied by cell displacement from a site where cells are formed to a location where they are eliminated. Cell displacement reflects genuine streaming, proceeding along a trajectory denominated as tissue radius. In the sagittally sectioned gastro-intestinal crypt the radius extends along one of its cell columns. In each column the cell locations are numbered so that the crypt origin resides at location 1. Since the cell proceeds from the first location and outward, given two locations i and j such that j greater than i, the cell at j is older or more differentiated than the cell at location i, or more generally, state j represents the future state of i while state i represents a past stage for j. Cell displacement on the radius depends solely upon cell production and the acceleration of a cell through location i equals the cell production rate there. Its velocity may be represented by kinematic equations which in the present context acquire dual meaning: either describing cell displacement, or cell production associated with cell displacement. Cell velocities may be derived by following a labelled cell with time or from density distributions of labelled cells along the tissue radius. The first approach is essentially kinematic, while the second regards the density distribution as an analog of mechanical work and since work involves displacement, velocity (and cell production) is derivable from the density distribution. The two estimates are denominated here as time and space estimates. The second approach is essentially morphological, and may be applied during routine examination of histopathological slide and even be computerized.(ABSTRACT TRUNCATED AT 250 WORDS)