APPLICATION OF THE DISPERSION MODEL FOR DESCRIPTION OF THE OUTFLOW DILUTION PROFILES OF NONELIMINATED REFERENCE INDICATORS IN RAT-LIVER PERFUSION STUDIES

The dispersion model (DM) is a stochastic model describing the distrib ution of blood-borne substances within organ vascular beds. It is base d on assumptions of concurrent convective and random-walk (pseudodiffu sive) movements in the direction of flow, and is characterized by the mean transit time ((t) over bar) and the dispersion number (inverse Pe clet number), D-N. The model is used with either closed (reflective) b oundary conditions at the inflow and the outflow point (Danckwerts con ditions) or a closed condition at the inflow and an open (transparent) condition at the outflow (mixed conditions). The appropriateness of D M was assessed with outflow data from single-pass perfused rat liver m ultiple indicator dilution (MID) experiments, with varying lengths of the inflow and outflow catheters. The studies were performed by inject ion of bolus doses of Cr-51-labeled red blood cells (vascular indicato r), I-125-labeled albumin and [C-14] sucrose (interstitual indicators) , and [H-3](2)O (whole tissue indicator) into the portal vein at a per fusion rate of 12 ml/min. The outflow profiles based on the DM were co nvolved with the transport function of the catheters, then fitted to t he data. A fairly good fit was obtained for most of the MID curve, wit h the exception of the late-in-time data (prolonged tail) beyond 3 x ( t) over bar. The fitted D(N)s were found to differ among the indicator s, and not with the length of the inflow and outflow catheters. But th e differences disappeared when a delay parameter, t(0) = 4.1 +/- 0.7 s ec ((x) over bar +/- SD), was included as an additional fitted paramet er for all of the indicators except water. Using the short catheters, the average D-N for the model with delay was 0.31 +/- 0.13 for closed and 0.22 +/- 0.07 for mixed boundary conditions, for all reference ind icators. Mean transit times and the variances of the fitted distributi ons were always smaller than the experimental ones (on average, by 6.8 +/- 3.7% and 58 +/- 19%, respectively). In conclusion, the DM is a re asonable descriptor of dispersion for the early-in-time data and not t he late-in-time data. The existence of a common D-N for all nonelimina ted reference indicators suggests that intrahepatic dispersion depends only on the geometry of the vasculature rather than the diffusional p rocesses. The role of the nonsinusoidal (''large'') vessels can be par tly represented by a simple delay.