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Application of the Dispersion Model for Description of the Outflow Dilution Profiles of Noneliminated Reference Indicators in Rat Liver Perfusion Studies

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Abstract

The dispersion model (DM) is a stochastic model describing the distribution of blood-borne substances within organ vascular beds. It is based on assumptions of concurrent convective and random-walk (pseudodiffusive) movements in the direction of flow, and is characterized by the mean transit time \(\left( {\overline {\text{t}} } \right)\) and the dispersion number (inverse Peclet number), DN. The model is used with either closed (reflective) boundary conditions at the inflow and the outflow point (Danckwerts conditions) or a closed condition at the inflow and an open (transparent) condition at the outflow (mixed conditions). The appropriateness of DM was assessed with outflow data from single-pass perfused rat liver multiple indicator dilution (MID) experiments, with varying lengths of the inflow and outflow catheters. The studies were performed by injection of bolus doses of 51Cr-labeled red blood cells (vascular indicator),125I-labeled albumin and [14C] sucrose (interstitual indicators), and [3H]2O (whole tissue indicator) into the portal vein at a perfusion rate of 12 ml/min. The outflow profiles based on the DM were convolved with the transport function of the catheters, then fitted to the data. A fairly good fit was obtained for most of the MID curve, with the exception of the late-in-time data (prolonged tail) beyond \(3 \times \overline {\text{t}}\). The fitted DNs were found to differ among the indicators, and not with the length of the inflow and outflow catheters. But the differences disappeared when a delay parameter, t0=4.1 ± 0.7 sec \(\left( {\overline x \pm SD} \right)\), was included as an additional fitted parameter for all of the indicators except water. Using the short catheters, the average DNfor the model with delay was 0.31 ± 0.13 for closed and 0.22 ± 0.07 for mixed boundary conditions, for all reference indicators. Mean transit times and the variances of the fitted distributions were always smaller than the experimental ones (on average, by 6.8 ± 3.7% and 58 ± 19%, respectively). In conclusion, the DM is a reasonable descriptor of dispersion for the early-in-time data and not the late-in-time data. The existence of a common DN for all non-eliminated reference indicators suggests that intrahepatic dispersion depends only on the geometry of the vasculature rather than the diffusional processes. The role of the nonsinusoidal (“large”) vessels can be partly represented by a simple delay.

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  1. McGill University Medical Clinic, Montreal General Hospital, Montreal, Quebec, H3G 1A4, Canada

    Andreas J. Schwab

  2. Department of Pharmaceutical Sciences, Faculty of Pharmacy, University of Toronto, Toronto, M5S 2S2, Canada

    Wanping Geng & K. Sandy Pang

  3. University Medical Clinic, Montreal General Hospital, Montreal, Quebec, Canada

    Andreas J. Schwab

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Schwab, A.J., Geng, W. & Pang, K.S. Application of the Dispersion Model for Description of the Outflow Dilution Profiles of Noneliminated Reference Indicators in Rat Liver Perfusion Studies. J Pharmacokinet Pharmacodyn 26, 163–181 (1998). https://doi.org/10.1023/A:1020557706994

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