Abstract
Two assumptions inherent in common tracer techniques of determining the order of steady state compartmental systems are examined: (i) that experimental access to the compartmental system is adequate to reveal all compartments, and (ii) that the compartments can be counted by resolving tracer transients into sums of non-positive exponentials.
Linear systems theory is applied to a matrix formalization of the tracer kinetics to derive necessary and sufficient conditions under which assumption (i) is valid. Examples of how to test for adequate experimental access are given for general classes of compartmental systems, as well as for specific structures. Both direct insertion and “natural” absorption of tracer into a system are considered.
General methods of obtaining linear system order are related to the tracer analysis of compartmental systems. Assumption (ii) is valid only when the characteristic roots of the tracer system matrix are non-positive, real, and distinct. These roots are always non-positive; necessary and sufficient conditions on the compartmental structure are described under which they are also real and distinct. Also, the relations between the number of exponentials in a tracer transient and compartmental system order are derived for general compartmental structures.