Interpretation of tracer data.
The necessary and sufficient conditions for a particular compartment in an n-compartment system, under certain initial conditions, to be described by two exponential terms have been given by Mann and Gurpide (1969). These conditions are here derived in matrix-vector form, by an essentially algebraic process, under more general initial conditions. The existence of a certain constant is required by the Mann-Gurpide conditions. It is shown that that constant must be one of the real roots of a given matrix. Under certain restrictions, that constant is the unique largest real root of that matrix. Certain obvious sufficient conditions for the Mann-Gurpide conditions to hold are shown to be necessary in the case of symmetrizable systems.
D055592:Biophysical Phenomena; D001703:Biophysics; D008433:Mathematics; D011868:Radioisotopes; D013223:Statistics as Topic
D011868:Radioisotopes