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Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs

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Abstract

An assumption of previous models of hepatic elimination is that there is negligible axial diffusion in the liver. We show, by construction of a stochastic model and analysis of published data, that compounds which are readily diffusible and partitioned into hepatocytes may undergo axial tissue diffusion. The compounds most likely to be affected by axial tissue diffusion are the lipophilic drugs for which the cell membranes provide little resistance and which are highly extracted, thereby creating steep concentration gradients along the sinusoid at steady state. This phenomenon greatly modifies the availability of the compound under conditions of altered hepatic blood flow and protein binding. For moderately diffusible compounds, these relationships are similar to those predicted by the simplistic venous-equilibrium model. Hence, the paradoxical ability of the venous-equilibrium model to describe the steady-state kinetics of lipophilic drugs such as lidocaine, meperidine, and propranolol may be finally resolved. The effects of axial tissue diffusion and vascular dispersion on hepatic availability of drugs are compared. Vascular dispersion is of major importance to the availability of poorly diffusible compounds, whereas axial tissue diffusion becomes increasingly dominant for highly diffusive and partitioned substances.

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Abbreviations

A :

Surface area of contact between hepatocytes and sinusoidal plasma

c :

Concentration of compound

C :

Dimensionless concentration of compound

Cl H :

Hepatic clearance

Cl int :

Intrinsic clearance of liver or sinusoid

C ss :

Steady-state concentration

Cu ss :

Steady-state unbound concentration

cv :

Coefficient of variation

¯D N :

Dispersion coefficient

D N :

Dispersion number

D App :

Apparent dimensionless diffusion coefficient

D :

Dimensionless diffusion coefficient

¯D :

True diffusion coefficient

E :

Hepatic extraction fraction

F :

Hepatic availability

F * :

Fractional appearance

fu :

Fraction unbound

k :

First-order rate constant of metabolism

K :

Partition coefficient of unbound drug

L :

Length of sinusoid

n :

Number of sinusoidal classes

P in :

Influx permeability coefficient

P ef :

Efflux permeability coefficient

Q :

Hepatic blood flow

Qs :

Sinusoidal blood flow

R :

Remainder term in Bass equation

R o :

Constant rate of oral administration

R N :

Dimensionless efficiency number

t :

Time

¯t :

Mean residence time

t s :

Residence time of sinusoidal class

V :

Volume

v :

Sinusoidal blood velocity

x :

Distance along sinusoid

z :

Dimensionless distance along sinusoid

b:

Blood

d:

Drug (when discerning between drug and metabolite)

het:

In the presence of axial heterogeneity of metabolism

i :

Pertaining to the ith class of sinusoid

in:

Going into the liver

m:

Metabolite

met:

Sinusoidal section of metabolism of a particular compound

out:

Coming out of liver

t:

Tissue

u:

Unbound

α i :

Fraction of sinusoids in the rth flow class

Β i :

Fraction of sinusoids in the rth residence time class

δ :

Partial derivative

ɛ :

Coefficient of variation of sinusoidal metabolism and flow

ξ :

Fraction of sinusoid active in metabolism

σ2 :

Variance of the log-normal distribution

Ω:

Density function

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  1. Department of Medicine, University of Queensland, Princess Alexandra Hospital, 4102, Woolloongabba, Qld., Australia

    Laurent P. Rivory, Michael S. Roberts & Susan M. Pond

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  1. Laurent P. Rivory
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  2. Michael S. Roberts
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This study was supported by the National Health and Medical Research Council of Australia.

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Rivory, L.P., Roberts, M.S. & Pond, S.M. Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs. Journal of Pharmacokinetics and Biopharmaceutics 20, 19–61 (1992). https://doi.org/10.1007/BF01143185

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