A priori identifiability of a one-compartment model with two input functions for liver blood flow measurements

An extended dual-input Kety-Schmidt model can be applied to positron emission tomography data for the quantification of local arterial (f(a)) and local portal-venous blood flow (f(p)) in the liver by freely diffusible tracers (e.g., [15O]H2O). We investigated the a priori identifiability of the three-parameter model (f(a), f(p) and distribution volume (Vd)) under ideal (noise-free) conditions. The results indicate that the full identifiability of the model depends on the form of the portal-venous input function (c(p)(t)), which is assumed to be a sum of m exponentials convolved with the arterial input function (c(a)(t)). When m>or=2, all three-model parameters are uniquely identifiable. For m=1 identifiability of f(p) fails if c(p)(t) coincides with tissue concentration (q(t)/Vd), which occurs if c(p)(t) is generated from an intestinal compartment with transit time Vd/f(a). Any portal input, f(p) c(p)(t), is balanced by the portal contribution, f(p) q(t)/Vd, to the liver efflux, leaving q(t) unchanged by f(p) and only f(a) and Vd are a priori uniquely identifiable. An extension to this condition of unidentifiability is obtained if we leave the assumption of a generating intestinal compartment system and allow for an arbitrary proportionality constant between c(p)(t) and q(t). In this case, only f(a) remains a priori uniquely identifiable. These findings provide important insights into the behaviour and identifiability of the model applied to the unique liver environment.