Theory of transport in linear biological systems: I. Fundamental integral equation

The conditions under which the output,γ b (t), of a biological system is related to the input,γ a (t), by an integral equation of the typeγ b (t) = ∫ 0 t γ a (ω)w(t−ω)dω, where ω(t) is a transport functioncharacteristic of the system, are analyzed in detail. Methods of solving this type of integral equation are briefly discussed. The theory is then applied to problems in tracer kinetics in which input and output are sums of exponentials, and explicit formulae, which are applicable whether or not the pool is uniformly mixed, are derived for “turnover time” and “pool” size.