title: A priori identifiability of a one-compartment model with two input functions for liver blood flow measurements.
abstract: 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.
authors.affiliation: Nuclear Medicine, University of Leipzig, Germany.
authors.forename: Georg A
authors.initials: GA
authors.lastname: Becker
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Müller-Schauenburg
authors.forename: Mary E
authors.initials: ME
authors.lastname: Spilker
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Machulla
authors.forename: Morand
authors.initials: M
authors.lastname: Piert
mesh_terms: D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology; D003198:Computer Simulation; D006499:Hepatic Artery / Q000000981:diagnostic imaging / Q000502:physiology; D006503:Hepatic Veins / Q000000981:diagnostic imaging / Q000502:physiology; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008099:Liver / Q000098:blood supply* / Q000000981:diagnostic imaging* / Q000378:metabolism; D008102:Liver Circulation / Q000502:physiology*; D008111:Liver Function Tests / Q000379:methods*; D008954:Models, Biological; D011865:Radioisotope Dilution Technique; D011877:Radionuclide Imaging; D019275:Radiopharmaceuticals / Q000493:pharmacokinetics; D013552:Swine
chemical_list: D019275:Radiopharmaceuticals