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.
Similar content being viewed by others
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
References
L. E. Gerlowski and R. K. Jain. Physiologically based pharmacokinetic modeling: Principles and applications.J. Pharm. Sci. 72:1103–1127 (1983).
R. N. Upton. Regional pharmacokinetics. I Physiological and physiochemical basis.Biopharm. Drug. Dispos. 11:647–662 (1990).
S. Björkman, D. R. Stanski, H. Harashima, R. Dowrie, S. R. Harapat, D. R. Wada, and W. F. Ebling. The tissue distribution of alfentanil and fentanyl in the rat is not blood flow limited.J. Pharmacokin. Biopharm. 21:255–279 (1993).
D. Verotta. An inequality-constrained least squares deconvolution method.J. Pharmacokin. Biopharm. 17:269–287 (1989).
D. J. Cutler. Linear systems analysis in pharmacokinetics.J. Pharmacokin. Biopharm. 6:265–282 (1978).
D. Verotta, L. B. Shiener, W. F. Ebling, and D. R. Stanski. A semiparametric, approach to physiologic flow models.J. Pharmacokin. Biopharm 17:463–489 (1989).
W. F. Ebling, L. Mills-Williams, S. R. Harapat, and D. R. Stanski: High-Performance liquid chromatographic method for determining thiopental concentrations in twelve rat tissues: Application to the physiologic modeling od disposition of barbiturate.J. Chromatog. 490:339–353 (1989).
Y. Igari, T. Sugiyama, S. Awazu, and H. Hanano. Comparative physiologically based pharmacokinetics of hexobarbital, phenobarbital, and thiopental in the rat.J. Pharmacokin. Biopharm. 10:53–75 (1982).
D. Z. D'Arginio and A. Schumitsky. A program package for simulation and parameter estimation in pharmacokinetic systems.Comput. Prog. Biomed. 9:115–134 (1979).
H. Harashima, D. R. Stanski, E. Osaki, and W. F. Ebling. Dose dependent alteration of regional blood flow by thiopental anesthesia in the rat. Implications for physiological flow models of anesthetic disposition. The Sixth Japanese-American Conference on Pharmacokinetics and Biopharmaceutics. Aug. 2–4, Buffalo, NY, 1992.
R. Schessler, K. E. Arfos, and K. Messmer. MIC II: A Program for determination of cardiac output, arterio-venous shunt and regional blood flow using radioactive microsphere method.Comput. Prog. Biomed. 9:19–38 (1979).
M. A. Heyman, B. D. Payne, J. E. Hoffman, and A. M. Randolph. Blood flow measurements with radionuclide-labeled particles.Prog. Cardiovasc. Dis. 20:55–79 (1977).
N. B. Everett, B. Simons, and E. P. Lasher. Distribution of blood (FE59) and plasma (I131) plasma volumes of rats determined by liquid nitrogen freezing.Circ. Res. 4:419–424 (1956).
W. O. Caster, J. Ponecelet, A. B. Simon, and W. D. Armstrong. Tissue weights of the rat: I Normal values determined by dissection and chemical methods.Proc. Soc. Exp. Bio. Med. 91:122–126 (1956).
N. A. Lassen and W. Perl. The volume/flow and mass/flux ratio (mean transit time) II. Bolus injection. InTracer Kinetic Methods in Medical Physiology, Raven Press, New York, 1979, chap. 7.
K. Yamaoka, T. Nakagawa, and T. Uno. Application of Akaike's information criterion (AIC) in the evaluation of linear pharmacokinetic equations.J. Pharmacokin. Biopharm. 6:165–175 (1978).
D. R. Wada, D. R. Stanski, and W. F. Ebling. A PC-based graphical simulator for physiological pharmacokinetic models. The Sixth Japanese-American Conference on Pharmacokinetics and Biopharmaceutics. Aug 2–4, Buffalo, NY, 1992.
M. K. Angelo, K. B. Bischoff, A. B. Prichard and M. A. Presser. A physiological model for the pharmacokinetics of methylene chloride in B6C3F1 mice following IV Administrations.J. Pharmacokin. Biopharm. 12:413–436 (1984).
W. H. Leung. Development and utilization of physiologically based pharmacokinetic models for toxicological applications.J. Toxicol. Environ. Heath 32:247–267 (1991).
F. J. Halford. A critque of intravenous anesthesia in war surgery.Anesthesiology 4:67–69 (1943).
R. C. Adams, and H. K. Gray. Intravenous anesthesia with pentothal sodium in case of gunshot wound associated with accompanying severe traumatic shock and loss of blood: report of a case.Anethesiology 4:70–73 (1943).
M. J. Avram, T. C. Krejcie, and T. K. Henthorn. The relationship of age to the pharmacokinetics of early drug distribution: The concurrent disposition of thiopental and indocyanine green.Anesthesiology 72:403–411 (1990).
D. R. Stanski and P. O. Maitre: Population pharmacokinetics and pharmacodynamics of thiopental: The effect of age revisited.Anesthesiology 72:714–724 (1990).
M. J. Avram, R. Sanghvi, T. K. Henthorn, T. E. Krejcie, A. Shanks, R. J. Fragen, K. A. Howard and D. A. Kaczynski: Determinants of thiopental induction dose requirements.Anesth. Analg. 76:10–17 (1993).
S. Björkman, J. Аkenson, F. Nilsson, K. Messeter, and B. Roth. Ketamine and midazolam decrease cerebral blood flow and consequently their own rate of transport to the brain: An application of mass balance pharmacokinetics with changing regional blood flow.J. Pharmacokin. Biopharm. 20:637–652 (1992).
J. M. Gallo, F. C. Lam, and F. G. Perrier. Moment method for estimation of mass transfer coefficients for physiological pharmacokinetic models.Biopharm. Drug. Dispos.12:127–137 (1991).
J. M. Gallo. Development and application of hybrid physiologically based pharmacokinetic models. Fourth Symposium in Frontiers in Pharmacokinetics and Pharmacodynamics. Little Rock, AK, March 1992.
W. F. Ebling. From Piece-wise to global physiologic models applied to intravenous anesthetics. 4th Symposium in Frontiers in Pharmacokinetics and Pharmacodynamics. Little Rock, AK, March 1992.
C.-H. Chou, A. M. Evnas, G. Fornasini, and M. Rowland. Relationship between lipophilicity and hepatic dispersion and distribution for a homologous series of barbiturates in the isolated perfusedin situ rat liver.Drug Metab. Dispos. 21:933–938 (1993).
Author information
Authors and Affiliations
Additional information
Supported in part by Grant RO1-AG04594 from the National Institute of Aging and the Anesthesia/Pharmacology Research Foundation.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02353622