Scaling of organ subunits in adult mammals and birds: a model

Members of one class of organs--including kidney and lung--consist chiefly of repeating units, or subunits, similar in size and shape. Across species, both the number and size of repeating units may increase with increasing organ size. A simple model is proposed, relating the scaling of unit-size and unit-number to that of organ volume. The model makes three structural assumptions, the crucial one, biologically speaking, being that the numerical density of repeating units scales as does organ surface-to-volume ratio. Data were collected from the literature bearing on the number, diameter, total surface area and total volume of such repeating units (i.e., alveoli, air capillaries, renal tubules and glomeruli), for avian and mammalian lung and for mammalian kidney, each as a function of organ size. These data, after log-log transformation, were submitted to standard linear least squares regression analysis. The resultant slopes for nine different regression lines are in good agreement with the model predictions. This finding suggests, surprisingly, that organ scale-up, at least for selected organs, expressed in terms of repeating units, as a function of organ volume, in mammals and birds, and conceivably in other phyla, may be based on a small number of elementary structural principles.