A unified theory for estimation of cardiac output, volumes of distribution and renal clearance from indicator dilution curves

The non-compartmental steady-state volume of distribution revisited

The lack in the literature of a simple, yet general and complete derivation of the widely used equation for non-compartmental calculation of steady-state volume of distribution is pointed out. It is demonstrated that the most frequently cited references contain an overly simplified explanation. The logical gap consists in doubly defining the same quantities without a proof the definitions are equivalent. Two alternative solutions are proposed: analytical derivation and hydrodynamic analogy. It is shown, that the problem can be analyzed in a purely macroscopic framework by utilizing the integral mean value of the function, without the need to resort to statistical distributions.

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.

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.

Relationships between steady state blood concentrations and cardiac output during intravenous infusions

The blood concentration of a drug at steady state can be calculated from the ratio of infusion rate over the total body drug clearance. When the blood is assumed to be a homogenous pool, the clearance is not usually referenced to any particular site within the circulation. In contrast, in recirculating systems, the relative sites of an infusion, the lungs and organs of elimination, and dilution in the cardiac output, produce concentration gradients in the blood. Equations that describe the relationship between the steady state concentrations of a drug in arterial, pulmonary artery, mixed venous and eliminating organ (e.g. liver or kidney) blood and the intrinsic clearance of the drug in the lungs and the eliminating organ were derived analytically. The concentrations at all sites were shown to be cardiac output dependent with the following exceptions: (1) in arterial blood, when the drug is highly extracted by the lungs, and (2) in eliminating organ blood when there is no lung clearance of the drug. The arterial and pulmonary artery concentrations will be least affected by cardiac output in the absence of lung clearance, and if the intrinsic clearance in the eliminating organ is substantially less than cardiac output.

Dynamics of drug distribution. I. Role of the second and third curve moments

Conventionally, the dynamics of distribution in the body is evaluated by the so-called distribution half-life (e.g., t1/2, alpha); but then the mean time of the distribution process is underestimated due to the influence of elimination. By contrast, information about the dynamics of distribution contained in drug disposition curves can be extracted by the second and third curve moments, parameters that are related to the variance (VDRT) and skewness (SDRT) of residence time distributions; whereas the equilibrium state characterized by the volume of distribution (Vss), is determined by the mean residence time (MDRT) or the first curve moment. The approach represents a general noncompartmental analysis that is independent of a detailed structural model or a particular disposition function. Two parameters are introduced to characterize the dynamics of drug distribution: (i) the degree of departure of the system from "well-mixed" behavior of instantaneous distribution equilibrium (related to VDRT) and (ii) the mean time until equilibration is achieved (mean equilibration time, MEQT), which additionally depends on SDRT. Both parameters are quantitative measures of the dynamics of distribution and display explicit physical significance in terms of distribution within the corresponding noneliminating system. It is further shown that the so-called "distribution phase" in biexponential disposition curves is related to a monoexponential mixing curve of its corresponding noneliminating system with an equilibration or mixing half-time, t1/2,M = t1/2,alpha (V beta/Vss*), where Vss* denotes the distribution volume of the noneliminating system. The results are applied to mixing and disposition curves measured for acetaminophen in liver-ligated and intact rats, respectively.

Theorems on log-convex disposition curves in drug and tracer kinetics

Conventionally, analysis of the dynamic behaviour of substances in the whole organism is based on the multiexponential paradigm (compartmental model). Alternatively the use of power functions has been proposed. In this paper a unified view is developed investigating the implications of observed log-convexity of disposition (clearance) curves. Using a non-compartmental approach it is proved that the disposition residence time distribution corresponding to a log-convex impulse response (blood concentration-time curve) belongs to the DFR (decreasing failure rate) class, implying that (1) the disposition curve has an exponential tail and (2) the relative dispersion of residence times is greater than or equal to one. This class of disposition curves includes multiexponential and power functions as special cases. In terms of the underlying biophysical principles the DFR property is discussed as a consequence of a dominant role of passive distribution processes of particles in the organism. The paper also deals with the corresponding properties of a recirculatory model using renewal theoretic concepts.

A note on the rôle of generalized inverse Gaussian distributions of circulatory transit times in pharmacokinetics

Based on a stochastic pharmacokinetical model (which mirrors topological properties of the circulatory system) it is shown by reinterpreting results of Wise (1974) that if the transit times of circulating drug molecules have a generalized inverse Gaussian distribution the corresponding residence times are gamma distributed. The condition that the probability of elimination of a drug molecule in a single circulatory passage is sufficiently small appears to be valid for most drugs. Thus theoretical evidence is given for fitting blood concentration-time curves following bolus injection of a single dose by power functions of time.

Hemodynamic influences upon the variance of disposition residence time distribution of drugs

A recirculation model of drug disposition is used to interpret the physiological meaning of the variance of residence time distribution (VDRT). The pharmacokinetic parameter VDRT is determined by the means and variances of the transfer times across the organs, as well as by the respective blood flow and extraction ratios. The model is illustrated for a specified distribution of organ transit times assuming flow limited mass transport. Based on data from the literature, the influence of changes in cardiac output and its regional distribution on the variance of recirculation and residence times, respectively, is predicted for lidocaine. Thereby the study is focused on the effect of certain cardiovascular states (shock, hypoxia, exercise, sympathomimetic drugs). Unlike pharmacokinetic parameters derived from the zeroth and first curve moments, the relative residence time dispersion is found to be affected by a redistribution of the blood flow among the noneliminating organs. The equations presented allow a simple and rapid calculation of clinically relevant pharmacokinetic parameters from physiological and physicochemical data.

Modelling of initial distribution of drugs following intravenous bolus injection

Based on a recirculatory pharmacokinetic model, a physiologically realistic definition of the initial distribution volume has been developed to characterize the overall distribution process occurring shortly after rapid bolus injection of a drug. This apparent volume of distribution, which refers to the peak right atrial blood concentration, depends on the cardiac output and basic pharmacokinetic parameters usually derived from the whole blood concentration vs time curve. The initial distribution process appears to be affected by changes in the variance of the distribution of residence times of the drug in the body. The influence of the site and time of early blood sampling on the estimated initial distribution volume is discussed. This relatively simple a priori model should prove useful in predicting to a first approximation the principal characteristics of the initial distribution process.

Moments of physiological transit time distributions and the time course of drug disposition in the body

Characterizing the tissue distribution kinetics of drugs by physiological and physico-chemical parameters and using a circulatory model the time course of blood concentration after intravenous injection is predicted for linear pharmacokinetic systems. The interrelationships between the first three (zero to second) moments of the distribution functions of organ transfer times, circulation times and residence times of drug molecules in the body are described. Utilizing literature data the model is applied to the analysis of lidocain kinetics in humans.