Recirculatory Pharmacokinetic Modeling (2012)

In this issue of the journal, Wiltshire et al.1 report the pharmacokinetics and pharmacodynamics of a promising new benzodiazepine, remimazolam (CNS 7056), that has a rapid onset of effect and a short duration of action. As part of the design of their study, and for the convenience of the volunteer subjects, the investigators switched from arterial to venous blood sampling after the initial sampling period. During the crossover of the sampling site, they obtained both arterial and venous blood at the 2-, 3-, and 4-hour sampling times. In analyzing the resultant paired drug concentrations, the authors noted that the venous concentrations were significantly higher than the arterial concentrations at those times. Unfortunately, they had not anticipated these differences and thus did not obtain enough early venous (or later arterial) samples to be able to construct a multicompartmental model using blood from only 1 sampling site. Conventional multicompartmental mammillary pharmacokinetic models cannot account for these arterial-venous concentration differences and, as noted by Fisher and Shafer,2 if the model does not fit the data, the model is wrong. The only recourse for Wiltshire et al. was to analyze their data using a recirculatory pharmacokinetic model. A traditional multicompartmental pharmacokinetic model is a mathematical construct based on characterization of a monotonically decreasing drug concentration versus time relationship with a multiexponential function. Despite its widespread use to describe drug disposition for several decades, this mammillary pharmacokinetic model has been recognized as (somewhat) wrong when used to characterize the early pharmacokinetics of drugs with a rapid onset of action, such as IV-administered anesthetic agents.3 A fundamental problem with the traditional multicompartmental pharmacokinetic model is that it is based on the simplifying assumption that drug is instantaneously and completely mixed within its initial (central) volume of distribution at the time of rapid IV administration. However, the distribution of an IV-administered drug (intercompartmental clearances) by the processes of intravascular mixing, blood flow, and transcapillary diffusion to tissues begins at the moment drug enters the intravascular space.4 As a result of these processes, the apparent distribution volume of a drug expands with time at a rate and to an extent that depend on cardiac output and its distribution, tissue perfusion and affinity for drug, and the relative concentrations of drug in blood and tissues.5 Therefore, the later the first blood samples are obtained after rapid IV administration in a pharmacokinetic study, the larger will be the estimated initial distribution volume of the drug.6 Because a traditional model ignores the complexity of the early distribution processes, it overestimates the actual initial distribution volume, which, along with dose, determines early drug concentrations and the intensity of drug effect.7,8 Recirculatory pharmacokinetic models retain the relative simplicity (compared with a physiologic model) of mammillary models but incorporate descriptions of key physiologic processes that have been recognized as important determinants of IV anesthetic disposition (Figs. 1 and 2).9 A recirculatory model provides a detailed description of the ideal initial distribution volume of the 3-compartment pharmacokinetic model by characterizing drug distribution from the moment of drug administration. On the basis of early arterial drug concentrations of samples obtained frequently after rapid IV administration, a recirculatory pharmacokinetic model provides a detailed characterization of early drug distribution, the front-end kinetics, including the central circulation and pulmonary drug uptake,10 cardiac output (from the first-pass curve, as in dye- or thermal-dilution cardiac output determination) and its distribution, and transit delays. Cardiac output is distributed among 3 parallel pathways, emulating normal physiology. Nondistributive blood flow (estimated from the recirculation peak) is that portion of cardiac output that returns drug to the central circulation after minimal loss to tissues. The balance of cardiac output distributes drug to the rapidly and slowly equilibrating compartments of the traditional compartmental pharmacokinetic model by the process of intercompartmental clearance. Including cardiac output and its regional distribution enables the recirculatory pharmacokinetic model to identify the pharmacokinetic basis of interindividual differences in response to IV anesthetics attributable to age-, sex-, disease-, or drug-induced physiologic perturbations.11 Furthermore, pharmacokinetic models incorporating a description of front-end kinetics can be used to design target-controlled drug infusions that do not result in early drug concentrations that exceed the target because of overestimation of the initial volume of distribution12 and estimate pharmacodynamic parameters with greater precision.13Figure 1: In a 3-compartment pharmacokinetic model, drug is assumed to mix instantaneously within the central or initial volume of distribution (VC) before distribution throughout the remaining apparent volume of distribution. The ideal VC consists of only the central circulation and nondistributive peripheral pathway of the recirculatory pharmacokinetic model (Fig. 2) but the ideal is seldom realized in traditional pharmacokinetic studies. From VC, drug distributes to the rapidly (fast) and slowly equilibrating volumes of distribution (VF and VS, respectively) by intercompartmental clearance (ClF and ClS, respectively), which are volume-independent estimates of drug transfer that are determined by blood flow and transcapillary permeability. The steady-state volume of distribution is the total volume of distribution and, as such, is the sum of VC, VF, and VS. Elimination clearance (ClE) quantifies the irreversible removal of drug from the body or drug metabolism and is not associated with any specific compartment or organ.9Figure 2: The general recirculatory pharmacokinetic model. Cardiac output (CO) flows through the central circulation (VC), which is defined by delay elements, represented generically by rectangles surrounding 4 compartments. Pulmonary tissue volume is a subset of VC. Beyond the central circulation, CO distributes to circulatory and tissue pathways that lump, based on their blood volume to flow ratios or tissue volume to distribution clearance ratios (mean transit times), into the volumes (V) and intercompartmental clearances (Cl) of the nondistributive peripheral pathway (VND, ClND) and the rapidly (fast, VF, ClF) and slowly (VS, ClS) equilibrating tissue volumes. Elimination clearance (ClE) is modeled from the arterial sampling site without being associated with a peripheral circuit. Mixed-venous blood samples can also be modeled. The dotted ellipse surrounds the components of the ideal central volume of a 3-compartment model.9Unlike traditional mammillary models, or their hydraulic model equivalents, recirculatory pharmacokinetic models are more consistent with the way an anesthesiologist thinks about drug distribution after IV administration.14 We do not think in terms of multiexponential decay curves, but we are aware that, among other things, there is a finite transit time resulting in delayed drug delivery to the effect site after IV drug administration (i.e., vein-to-brain circulation time), and poor cardiovascular function (e.g., hypovolemia, low cardiac output) can result in exaggerated drug effect. One of the fundamental aspects of the recirculatory pharmacokinetic model is that it is generally isomorphic with the physiologic system, having organs and tissues arranged in parallel with respect to the blood supply.15,16 In addition, recirculatory models have a definable cardiac output and blood volumes (central and peripheral, arterial and venous). An important aspect of this recirculatory model is that it can be fit to data from arterial and venous blood samples obtained simultaneously.17 However, inherent in a mammillary model is the simplifying assumption that blood sampling occurs only from the initial (central) distribution volume throughout which drug is assumed to be instantaneously and uniformly distributed and is inclusive of the entire blood volume. It is increasingly common for modern pharmacokinetic studies in anesthesia to include early arterial samples but, for convenience, most investigators will obtain later samples (during the elimination phase of drug disposition) from an arm vein, as they did in the present study.1 Although these venous drug concentrations are assumed to differ insignificantly from simultaneously sampled arterial concentrations, this is not always true, as Wiltshire et al.1 discovered. Because drug distribution and redistribution are driven by concentration gradients between blood and tissues, the relative drug concentrations of arterial and venous blood samples, drawn at the same time, depend on the phase of drug disposition and the arterial-venous transit delay.7,8 At steady state, drug concentrations of arterial and venous blood samples drawn at the same time will not be different. However, for tissues that have an affinity for the drug and no barrier to diffusion, early (during the drug distribution phase) venous concentrations will be lower than the concomitant arterial concentration as drug diffuses into the tissue at a rate proportional to the arterial blood-tissue concentration gradient. At later times (e.g., during the elimination phase), venous concentrations will be higher than arterial as drug, again, diffuses down the concentration gradient but this time from tissue to venous blood. Such arterial-venous concentration differences have been reported recently in this journal for morphine-6-glucuronide.18 Chiou8 predicted that drugs with a high volume of distribution, high elimination clearance, or short half-life will have the most pronounced venous-arterial concentration differences during the elimination phase because a large distribution volume represents a large capacity for drug uptake whereas a high elimination clearance contributes to a dramatic lowering of mixed-venous, hence arterial, drug concentrations during the elimination phase of drug disposition. Furthermore, whereas all drug concentrations are assumed to be equal throughout the arterial system, the same is not true for venous blood. The drug concentration in venous blood is dependent on the tissue from which the venous blood elutes. If the organ has a high blood flow to tissue volume ratio, or a barrier to drug diffusion, little drug will be removed from the arterial blood and the organ will appear to be a physiologic shunt (nondistributive blood flow in Figs. 1 and 2). At the other extreme, if the blood is flowing from an organ of elimination, the amount of drug in the venous effluent will be dependent on the efficiency of that organ in removing the drug (extraction ratio). In the middle of these extremes is a tissue bed that has an affinity for the drug and little barrier to diffusion. Mixed venous blood, such as would be sampled from the pulmonary artery, represents the weighted mean venous blood concentration and will equal the arterial concentration if the drug has minimal exchange with pulmonary vasculature or tissue.19 Most drugs encountered in the practice of anesthesia are eliminated (metabolized) by the liver. In this case, hepatic venous blood concentrations will always be lower than arterial concentrations. What, then, would one expect to happen when the mode of drug elimination is metabolism by tissue esterases? As in the case of hepatic metabolism, one would expect the venous blood of the eliminating organ to be lower than the arterial concentration.20 How, then, should we interpret the findings of Wiltshire et al.?1 The tissues of the forearm should contain the esterases responsible for the metabolism of remimazolam and, therefore, one would not expect venous concentrations to exceed arterial21 at any time after drug administration, as they did in the present study.1 Although a recirculatory model enabled Wiltshire et al.1 to model the arterial-venous concentration differences, future studies may be needed to explain the observed higher venous concentrations or to provide a better understanding of the mode of drug elimination. DISCLOSURES Name: Tom C. Krejcie, MD. Contribution: This author helped write the manuscript. Attestation: Tom C. Krejcie approved the final manuscript. Name: Michael J. Avram, PhD. Contribution: This author helped write the manuscript. Attestation: Michael J. Avram approved the final manuscript. This manuscript was handled by: Tony Gin, MD, FRCA, FANZCA.