Finding the dispersion number (D_N) of the dispersion model from perfused rat and human liver studies

The dispersion number (D_N), which relates to intrahepatic mixing and impacts hepatic clearance (CL_H), is assessed routinely in liver perfusion studies. However, the estimation methods are nonuniform, and estimates for human livers are unknown. Schwab et al (1998) identified D_N estimates for red cells, albumin, sucrose, and water for closed (CBC) (0.31 ± 0.13) and mixed (MBC) boundary conditions (0.22 ± 0.07) (P < .05) from perfused rat livers with inclusion of t₀, transit time of large vessels (4.1 ± 0.7 seconds) and MTT_cath (mean transit time for catheters/injection devices), which defined the nonhepatic transfer function (TF_NH). To address the importance of t₀ and TF_NH, we refitted the digitized data of Schwab by omitting TF_NH, which yielded similar D_N estimates (0.28 ± 0.11 for CBC and 0.21 ± 0.11 for MBC) but a longer time lag (t_lag) (9-10 seconds) that equaled (t₀ + MTT_cath). Fitting without t₀ or t_lag provided much lower D_N estimates (0.020-0.078) for red cells, albumin, and sucrose though less for water (0.263 ± 0.006 for CBC and 0.223 ± 0.006 MBC) due to improper correction of the mean transit time (MTT_corr), rendering a lower CV² (variance/MTT_corr²) and therefore D_N. Notably, fitting of digitized human liver perfusion data without TF_NH (=0) but t_lag (>0) yielded sound D_Ns of 0.31 ± 0.12 for CBC and 0.24 ± 0.12 for MBC and t_lags of 8.3-10.5 seconds, values reminiscent of rat livers. These results suggest that human livers display closely similar D_N values (0.2-0.3) as those of rat livers, with predicted intrinsic clearance values that differ only by 10%-13% between the CBC and MBC to yield the same CL_H. SIGNIFICANCE STATEMENT: Dispersion numbers (D_N) based on fitting liver perfusion data to the dispersion model (DM) requires a time lag (t_lag) or large vessel transit time (t₀), but the nonhepatic transfer function (TF_NH) is not strictly required. Fitting of rat and human liver perfusion data with t_lag provides sound D_Nestimates: 0.26-0.31 and 0.22-0.24, respectively, for closed and mixed boundary conditions (P>.05). These D_N values suggest that the intrinsic clearance (CL_int,DM) values for MBC/CBC differ only by 13% in their prediction of hepatic clearance.