Pharmacokinetic curve fitting using numerical inverse Laplace transformation

Beta blockade increases pulmonary and systemic transit time heterogeneity: evaluation based on indocyanine green kinetics in healthy volunteers

Knowledge of factors influencing the heterogeneity of blood transit times is important in cardiovascular physiology. The aim of the study was to investigate the effect of beta-adrenergic blockade on blood transit time dispersion in awake, anxious volunteers. Recirculatory modelling of the disposition of intravascular markers using parametric forms for transit time distributions, such as the inverse Gaussian distribution, provides the opportunity to estimate the systemic and pulmonary transit time dispersion in vivo. The latter is determined by the flow heterogeneity in the microcirculatory network. Using this approach, we have analysed indocyanine green (ICG) disposition data obtained in four subjects by frequent early arterial blood sampling before and after beta-adrenergic blockade by propranolol. Propranolol decreased cardiac output from 9·3 ± 2·8 l min^-1 to 3·5 ± 0·47 l min^-1 (P<0·05). This reduction was accompanied by a 4·5 ± 0·6-fold and 2·1 ± 0·3-fold increase (P<0·001) in the relative dispersion (dimensionless variance) of blood transit times through the systemic and pulmonary circulation, respectively.

A physiologically based model of hepatic ICG clearance: interplay between sinusoidal uptake and biliary excretion

Although indocyanine green (ICG) has long been used for the assessment of liver function, the respective roles of sinusoidal uptake and canalicular excretion in determining hepatic ICG clearance remain unclear. Here this issue was addressed by incorporating a liver model into a minimal physiological model of ICG disposition that accounts of the early distribution phase after bolus injection. Arterial ICG concentration-time data from awake dogs under control conditions and from the same dogs while anesthetized with 3.5% isoflurane were subjected to population analysis. The results suggest that ICG elimination in dogs is uptake limited since it depends on hepatocellular uptake capacity and on biliary excretion but not on hepatic blood flow. Isoflurane caused a 63% reduction in cardiac output and a 33% decrease in the ICG biliary excretion rate constant (resulting in a 26% reduction in elimination clearance) while leaving unchanged the sinusoidal uptake rate. The terminal slope of the concentration-time curve, K, correlated significantly with elimination clearance. The model could be useful for assessing the functions of sinusoidal and canalicular ICG transporters.

Cardiac output and systemic transit time dispersion as determinants of circulatory mixing time: a simulation study

A new approach to characterize the kinetics of intravascular mixing process is presented. The mixing time, defined as the time required for achieving 95% homogeneity, is calculated by numerical simulations using a circulatory model applied to the intravascular marker indocyanine green (ICG). The results suggest that the mixing time is determined by cardiac output and the relative dispersion of transit time distribution across the systemic circulation, whereby the rate of mixing increases with increasing cardiac output and decreasing transit time dispersion, and vice versa. The estimation of plasma volume from simulated ICG dilution data using the backextrapolation method shows that slow mixing is accompanied by an overestimation of blood volume. This error may be negligible for mixing times of less than approximately 3 min but high in disease states characterized by low cardiac output and/or high transit time dispersion. In view of the role of transit time dispersion as determinant of intravascular mixing, it would be interesting to know more about the effect of disease states on systemic transit time dispersion.

A minimal physiological model of thiopental distribution kinetics based on a multiple indicator approach

Currently available models of thiopental disposition kinetics using only plasma concentration-time data neglect the influence of intratissue diffusion and provide no direct information on tissue partitioning in individual subjects. Our approach was based on a lumped-organ recirculatory model that has recently been applied to unbound compounds. The goal was to find the simplest model that accounts for the heterogeneity in tissue partition coefficients and accurately describes initial distribution kinetics of thiopental in dogs. To ensure identifiability of the underlying axially distributed capillary-tissue exchange model, simultaneously measured disposition data of the vascular indicator, indocyanine green, and the marker of whole body water, antipyrine, were analyzed together with those of thiopental. A model obtained by grouping the systemic organs in two subsystems containing fat and nonfat tissues, successfully described all data and allowed an accurate estimation of model parameters. The estimated tissue partition coefficients were in accordance with those measured in rats. Because of the effect of tissue binding, the diffusional equilibration time characterizing intratissue distribution of thiopental is longer than that of antipyrine. The approach could potentially be used in clinical pharmacokinetics and could increase our understanding of the effect of obesity on the disposition kinetics of lipid-soluble drugs.

Mechanistic modeling of digoxin distribution kinetics incorporating slow tissue binding

This study aims to develop a mechanistic pharmacokinetic model that accounts for the kinetics of tissue binding in order to evaluate the effect of slow binding of digoxin to skeletal muscular Na(+)/K(+)-ATPase in humans. The approach is based on a minimal circulatory model with a systemic transit time density function that accounts for vascular mixing, transcapillary permeation and extravascular binding of the drug. The model parameters were estimated using previously published disposition data of digoxin in healthy volunteers and physiological distribution volumes taken from the literature. A time constant of the binding process of 34min was estimated indicating that receptor binding and not permeation clearance is the rate-limiting step of the distribution process. Model simulations suggest that up- or downregulation of sodium pumps, typically observed under physiological or pathophysiological conditions, could be detected with this method. The model allows a quantitative prediction of the effect of changes in skeletal muscular sodium pump activity on plasma levels of digoxin.

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.

Cytoplasmic binding and disposition kinetics of diclofenac in the isolated perfused rat liver

1. The binding kinetics of diclofenac to hepatocellular structures were evaluated in the perfused rat liver using the multiple indicator dilution technique and a stochastic model of organ transit time density. 2. The single-pass, in situ rat liver preparation was perfused with buffer solution (containing 2% albumin) at 30 ml min(-1). Diclofenac and [(14)C]-sucrose (extracellular reference) were injected simultaneously as a bolus dose into the portal vein (six experiments in three rats). An analogous series of experiments was performed with [(14)C]-diclofenac and [(3)H]-sucrose. 3. The diclofenac outflow data were analysed using three models of intracellular distribution kinetics, assuming (1) instantaneous distribution and binding (well-mixed model), (2) 'slow' binding at specific intracellular sites after instantaneous distribution throughout the cytosol (slow binding model), and (3) 'slowing' of cytoplasmic diffusion due to instantaneous binding (slow diffusion model). 4. The slow binding model provided the best description of the data. The rate constants for cellular influx and sequestration were 0.126+/-0. 026 and 0.013+/-0.009 s(-1), respectively. The estimated ratio of cellular initial distribution volume to extracellular volume of 2.82 indicates an almost instantaneous distribution in the cellular water space, while the corresponding ratio of 5.54 estimated for the apparent tissue distribution volume suggests a relatively high hepatocellular binding. The non-instantaneous intracellular equilibration process was characterized by time constants of the binding and unbinding process of 53.8 and 49.5 s, respectively. The single-pass availability of diclofenac was 86%. The results obtained with [(14)C]-diclofenac and [(3)H]-sucrose were not statistically different.

Notes on the inverse Gaussian distribution and choice of boundary conditions for the dispersion model in the analysis of local pharmacokinetics

The dispersion model has been widely used to analyze local pharmacokinetics in the organs and the tissues since the 1980's. However, an ambiguity still remains in selecting the boundary conditions which are necessary to solve the basic equation of the model. In this note, theoretical considerations are given to this problem and we present here some deficiencies of the mixed boundary conditions. It seems that theoretical confusion exists in the literature for the mixed boundary conditions. It is well-known that the solution of the dispersion model with a bolus input is the inverse Gaussian distribution for the mixed boundary conditions. However, it is rarely recognized that the inverse Gaussian distribution requires an open boundary at either the inlet or the outlet. For the analysis of local pharmacokinetics, the use of the classical Danckwerts (or closed) boundary conditions is recommended.