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 (fa) and local portal-venous blood flow (fp) in the liver by freely diffusible tracers (e.g., [15O]H2O). We investigated the a priori identifiability of the three-parameter model (fa, fp 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 (cp(t)), which is assumed to be a sum of m exponentials convolved with the arterial input function (ca(t)). When m ⩾ 2, all three-model parameters are uniquely identifiable. For m = 1 identifiability of fp fails if cp(t) coincides with tissue concentration (q(t)/Vd), which occurs if cp(t) is generated from an intestinal compartment with transit time Vd/fa. Any portal input, fp cp(t), is balanced by the portal contribution, fp q(t)/Vd, to the liver efflux, leaving q(t) unchanged by fp and only fa 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 cp(t) and q(t). In this case, only fa remains a priori uniquely identifiable. These findings provide important insights into the behaviour and identifiability of the model applied to the unique liver environment.