Simple elimination models: Theoretical estimates of the effect of variations in elimination rates

This paper analyses the effect of variations in the elimination rates of four elimination models. Three types of variations are studied: (1) a periodic change between two elimination rates; (2) changes between two elimination rates at random times; and (3), an elimination rate varying smoothly in time, generated by having the elimination rate vary exponentially with temperature and a sinusoidally varying temperature. The elimination process is described by four different models: (1) a single compartment; (2) two compartments in parallel; (3) two compartments in series; and (4) the Goldstein-Elwood model. It is shown that for all 12 cases, the solutions can be given the same form as with constant elimination rates through reinterpretation of the parameters. As a special case, the use of elimination methods to estimate respiration is discussed and a possible source of error is pointed out.