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From piecewise to full physiologic pharmacokinetic modeling: Applied to thiopental disposition in the rat

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Abstract

Physiologically based pharmacokinetic modeling procedures employ anatomical tissue weight, blood flow, and steady tissue/blood partition data, often obtained from different sources, to construct a system of differential equations that predict blood and tissue concentrations. Because the system of equations and the number of variables optimized is considerable, physiologic modeling frequently remains a simulation activity where fits to the data are adjusted by eye rather than with a computer-driven optimization algorithm. We propose a new approach to physiological modeling in which we characterize drug diposition in each tissue separately using constrained numerical deconvolution. This technique takes advantage of the fact that the drug concentration time course, CT(t), in a given tissue can be described as the convolution of an input function with the unit disposition function (UDF T) of the drug in the tissue, (i.e., C T (t)=(C a (t)Q r )*UDF r (t) whereC a(t) is the arterial concentration,Q T is the tissue blood flow and * is the convolution operator). The obtained tissue unit disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug injected into the tissue in the absence of recirculation. From theUDF, a parametric model for the intratissue disposition of each tissue can be postulated. Using as input the product of arterial concentration and blood flow, this submodel is fit separately utilizing standard nonlinear regression programs. In a separate step, the entire body is characterized by reassembly of the individuals submodels. Unlike classical physiologic modeling the fit for a given tissue is not dependent on the estimates obtained for other tissues in the model. Additionally, because this method permits examination of individualUDF s, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat.

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Abbreviations

Variable:

Description and Units

Dose :

Administered dose, (μg)

A :

Dose normalized preexponential arterial time course coefficient (ml−1)

λ:

Exponential coefficient of arterial concentration time course (min−1)

τ:

Infusion duration (min)

t :

Time (min)

C :

Drug concentration in region, (μg/g region) or (μg/ml region)

Q :

Regional blood flow velocity, (ml/min per tissue)

J :

Flux of drug to tissue (μg/min per g)

Hct :

Hematocrit

K p :

Tissue to blood partition coefficient (ml blood/gm tissue)

ρ:

blood to plasma partition coefficient (ml plasma/ml blood)

δ:

Density of blood (g/ml blood)

UDF :

Unit disposition function of tissue

AUC UDF :

Area under the unit disposition function (min)

AUM UDF :

First moment of the unit disposition function (min2)

MST :

Mean sojourn time of drug across tissue (min)

X :

Mass of drug tissue or compartment (μg)

k :

Intratissue microrate constant (min−1)

V :

Apparent volume (ml/g tissue)

WT :

Tissue weight (g)

T:

Total tissue T

m :

Mesenteric organm

n :

Number of mesenteric organs excluding liver, or number of exponential phases in arterial concentration time course

i :

Tissue compartmenti or disposition phasei

ij :

From compartmenti to compartmentj, 0 denotes outside the tissue or body

p:

Arterial plasma

a:

Arterial blood

v:

Venous blood

Vasc:

Tissue capillary space

Paren:

Parencymal space

HA:

Hepatic artery

Portal:

Portal vein

Hepatic:

Total liver

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Authors and Affiliations

  1. Department of Pharmaceutics, State University of New York at Buffalo, 14260-1200, Buffalo, New York

    William F. Ebling

  2. Veterans Administration Medical Center, Stanford University School of Medicine, Anesthesia Service [112-A], 3801 Miranda Drive, 94304, Palo Alto, California

    William F. Ebling

  3. Department of Anesthesia, Stanford University School of Medicine, 94305-5117, Palo Alto, California

    D. Russell Wada & Donald R. Stanski

Authors
  1. William F. Ebling
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  2. D. Russell Wada
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  3. Donald R. Stanski
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Additional information

Supported in part by Grant RO1-AG04594 from the National Institute of Aging and the Anesthesia/Pharmacology Research Foundation.

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Ebling, W.F., Wada, D.R. & Stanski, D.R. From piecewise to full physiologic pharmacokinetic modeling: Applied to thiopental disposition in the rat. Journal of Pharmacokinetics and Biopharmaceutics 22, 259–292 (1994). https://doi.org/10.1007/BF02353622

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