Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis

An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:

$$B_1 (t) = int_{t_2 = - infty }^infty {int_{t_1 = - infty }^infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$