Modelling of initial distribution of drugs following intravenous bolus injection

The Performance of an Artificial Neural Network Model in Predicting the Early Distribution Kinetics of Propofol in Morbidly Obese and Lean Subjects

BACKGROUND

Induction of anesthesia is a phase characterized by rapid changes in both drug concentration and drug effect. Conventional mammillary compartmental models are limited in their ability to accurately describe the early drug distribution kinetics. Recirculatory models have been used to account for intravascular mixing after drug administration. However, these models themselves may be prone to misspecification. Artificial neural networks offer an advantage in that they are flexible and not limited to a specific structure and, therefore, may be superior in modeling complex nonlinear systems. They have been used successfully in the past to model steady-state or near steady-state kinetics, but never have they been used to model induction-phase kinetics using a high-resolution pharmacokinetic dataset. This study is the first to use an artificial neural network to model early- and late-phase kinetics of a drug.

METHODS

Twenty morbidly obese and 10 lean subjects were each administered propofol for induction of anesthesia at a rate of 100 mg/kg/h based on lean body weight and total body weight for obese and lean subjects, respectively. High-resolution plasma samples were collected during the induction phase of anesthesia, with the last sample taken at 16 hours after propofol administration for a total of 47 samples per subject. Traditional mammillary compartment models, recirculatory models, and a gated recurrent unit neural network were constructed to model the propofol pharmacokinetics. Model performance was compared.

RESULTS

A 4-compartment model, a recirculatory model, and a gated recurrent unit neural network were assessed. The final recirculatory model (mean prediction error: 0.348; mean square error: 23.92) and gated recurrent unit neural network that incorporated ensemble learning (mean prediction error: 0.161; mean square error: 20.83) had similar performance. Each of these models overpredicted propofol concentrations during the induction and elimination phases. Both models had superior performance compared to the 4-compartment model (mean prediction error: 0.108; mean square error: 31.61), which suffered from overprediction bias during the first 5 minutes followed by under-prediction bias after 5 minutes.

CONCLUSIONS

A recirculatory model and gated recurrent unit artificial neural network that incorporated ensemble learning both had similar performance and were both superior to a compartmental model in describing our high-resolution pharmacokinetic data of propofol. The potential of neural networks in pharmacokinetic modeling is encouraging but may be limited by the amount of training data available for these models.

Quantifying rates of glucose production in vivo following an intraperitoneal tracer bolus

Aberrant regulation of glucose production makes a critical contribution to the impaired glycemic control that is observed in type 2 diabetes. Although isotopic tracer methods have proven to be informative in quantifying the magnitude of such alterations, it is presumed that one must rely on venous access to administer glucose tracers which therein presents obstacles for the routine application of tracer methods in rodent models. Since intraperitoneal injections are readily used to deliver glucose challenges and/or dose potential therapeutics, we hypothesized that this route could also be used to administer a glucose tracer. The ability to then reliably estimate glucose flux would require attention toward setting a schedule for collecting samples and choosing a distribution volume. For example, glucose production can be calculated by multiplying the fractional turnover rate by the pool size. We have taken a step-wise approach to examine the potential of using an intraperitoneal tracer administration in rat and mouse models. First, we compared the kinetics of [U-¹³C]glucose following either an intravenous or an intraperitoneal injection. Second, we tested whether the intraperitoneal method could detect a pharmacological manipulation of glucose production. Finally, we contrasted a potential application of the intraperitoneal method against the glucose-insulin clamp. We conclude that it is possible to 1) quantify glucose production using an intraperitoneal injection of tracer and 2) derive a "glucose production index" by coupling estimates of basal glucose production with measurements of fasting insulin concentration; this yields a proxy for clamp-derived assessments of insulin sensitivity of endogenous production.

Exploration of PBPK Model-Calculation of Drug Time Course in Tissue Using IV Bolus Drug Plasma Concentration-Time Profile and the Physiological Parameters of the Organ

An uncommon innovative consideration of the well-stirred linear physiologically based pharmacokinetic model and the drug plasma concentration-time profile, which is measured in routine intravenous bolus pharmacokinetic study, was applied for the calculation of the drug time course in human tissues. This cannot be obtained in the in vivo pharmacokinetic study. The physiological parameters of the organ such as organ tissue volume, organ blood flow rate, and its vascular volume were used in the calculation. The considered method was applied to calculate the time course of midazolam, alprazolam, quinidine, and diclofenac in human organs or tissues. The suggested method might be applied for the prediction of drug concentration-time profile in tissues and consequently the drug concentration level in the targeted tissue, as well as the possible undesirable toxic levels in other tissues.

Applications of minimal physiologically-based pharmacokinetic models

Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue (usually total body weight) volumes, fractions (f ( d )) of cardiac output with Fick's Law of Perfusion, tissue/blood partitioning (K ( p )), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mammillary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated K ( p ) values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common K ( p ) and f ( d ) values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.

Performance evaluation of paediatric propofol pharmacokinetic models in healthy young children

BACKGROUND

The performance of eight currently available paediatric propofol pharmacokinetic models in target-controlled infusions (TCIs) was assessed, in healthy children from 3 to 26 months of age.

METHODS

Forty-one, ASA I-II children, aged 3-26 months were studied. After the induction of general anaesthesia with sevoflurane and remifentanil, a propofol bolus dose of 2.5 mg kg(-1) followed by an infusion of 8 mg kg(-1) h(-1) was given. Arterial blood samples were collected at 1, 2, 3, 5, 10, 20, 40, and 60 min post-bolus, at the end of surgery, and at 1, 3, 5, 30, 60, and 120 min after stopping the infusion. Model performance was visually inspected with measured/predicted plots. Median performance error (MDPE) and the median absolute performance error (MDAPE) were calculated to measure bias and accuracy of each model.

RESULTS

Performance of the eight models tested differed markedly during the different stages of propofol administration. Most models underestimated propofol concentration 1 min after the bolus dose, suggesting an overestimation of the initial volume of distribution. Six of the eight models tested were within the accepted limits of performance (MDPE<20% and MDAPE<30%). The model derived by Short and colleagues performed best.

CONCLUSIONS

Our results suggest that six of the eight models tested perform well in young children. Since most models overestimate the initial volume of distribution, the use for TCI might result in the administration of larger bolus doses than necessary.

A note on population analysis of dissolution-absorption models using the inverse Gaussian function

Because conventional absorption models often fail to describe plasma concentration-time profiles following oral administration, empirical input functions such as the inverse Gaussian function have been successfully used. The purpose of this note is to extend this model by adding a first-order absorption process and to demonstrate the application of population analysis using maximum likelihood estimation via the EM algorithm (implemented in ADAPT 5). In one example, the analysis of bioavailability data of an extended-release formulation, as well as the mean dissolution times estimated in vivo and in vitro with the use of the inverse Gaussian function, is well in accordance, suggesting that the inverse Gaussian function indeed accounts for the in vivo dissolution process. In the other example, the kinetics of trapidil in patients with liver disease, the absorption/dissolution parameters are characterized by a high interindividual variability. Adding a first-order absorption process to the inverse Gaussian function improved the fit in both cases.

A non-Markovian model for calcium kinetics in the body

We present a new generalized compartmental model for calcium kinetics as measured by tracer concentration in blood plasma. The parameter measuring incorporation of calcium in bone discriminates between different levels of physical development in female teenagers and between teenagers and adults.

Pharmacokinetics and electrophysiological effects of intravenous ajmaline

The pharmacokinetics of ajmaline were studied in 10 patients with suspected paroxysmal atrioventricular block who received a 1 mg/kg intravenous dose over 2 minutes for diagnostic purposes (ajmaline test). Plasma concentration decay followed a triexponential time course with a final half-life much longer (7.3 +/- 3.6 hours) than that previously found by other investigators (about 15 minutes). Mean total plasma clearance and renal clearance were 9.76 ml/min/kg and 0.028 ml/min/kg, respectively. Although most of the dose was eliminated through the extrarenal route (only 3.5% of the intravenous dose was recovered in urine), no fluorescent metabolites could be detected either in plasma or urine. The steady-state volume of distribution averaged 6.17 L/kg, and plasma protein binding ranged between 29 and 46%. Three patients developed a transient atrioventricular block after ajmaline administration. In the remainder, the drug prolonged atrio-His bundle (AH interval), His bundle-ventricular (HV interval) and intraventricular (QRS interval) conduction times. Corrected ventricular repolarisation time (QTc interval) showed less marked changes, which were biphasic at times. The mean maximum ajmaline-induced increase in HV interval was 98%, in QRS was 58%, in AH was 30%, and in QTc was 17%. In most cases the time course of electrocardiographic changes lagged behind that of plasma concentrations, suggesting a delayed equilibrium of plasma concentrations with the site of action (hysteresis). Despite that, the pharmacokinetic-pharmacodynamic model, which accounted for hysteresis, failed to fit the experimental data adequately.(ABSTRACT TRUNCATED AT 250 WORDS)

Analysis of arterial-venous blood concentration difference of drugs based on recirculatory theory with fast inverse Laplace transform (FILT)

An arterial and venous blood (or plasma) concentration difference of drugs across the lung of rats was evaluated based on the recirculatory concept. The recirculatory system is given by the combination of the transfer functions for the pulmonary and the systemic circulations and is described by a Laplace-transformed equation, i.e., an image equation. For the manipulation of the image equations, the fast inverse Laplace transform (FILT) was adopted and MULTI(FILT) was used for the simultaneous curve fitting to estimate the pharmacokinetic parameters in the recirculatory model. Metoprolol as a test drug and cephalexin as a control drug were infused respectively into the femoral vein for 30 min, and arterial and venous blood samples were collected simultaneously through the cannula at the femoral artery and at right atrium during and after the infusion. Exponential functions were assumed for the weight functions through both the pulmonary and systemic circulations. Results of the curve fitting showed that the single-pass extraction ratio through the pulmonary circulation (Ep) of metoprolol was about 0.2, whereas that of cephalexin was negligible. The mean transit times through the pulmonary circulation (tp) of metoprolol and cephalexin were both about 0.5 min, which is small. The single-pass extraction ratios through the systemic circulation (Es) of metoprolol and cephalexin were both about 0.1, and the mean transit times through the systemic circulation (ts) were 11.5 min and 8.2 min, respectively.

Pharmacokinetics from a dynamical systems point of view

The pharmacological action of many drugs depends on several variables at the same time and therefore will be dominated by an attractor of a dimension greater than zero. The pharmacokinetic behavior is likely to be dominated by a zero dimensional point attractor so that it is highly predictable. Pharmacokinetics is discussed from a dynamical systems point of view, whereby the transport of drugs in the tissues and organs is considered a stochastic process characterized by density functions of transit times and blood flows. In the body, the tissues and organs are arranged in parallel, in series, and in a feedback-loop fashion. Consequently, the single-pass transport of drugs through the body is again a stochastic process characterized by the density function of total body transit times, the cardiac output, and the total body extraction. The drug molecules, however, may pass through the body several times before ultimately leaving the system by metabolism or excretion. As a result, the body may be regarded as a positive feedback system with the pulmonary circulation (and its tissues) as the forward transfer function and the systemic circulation (with all its tissues) as the feedback transfer function. Consequently, the total body transport function (closed loop) is again a stochastic process characterized by a density function of total body residence times. The relationship between the body transit time distribution and the body residence distribution is determined by the feedback-loop arrangement, the cardiac output, and the extraction ratio which can easily be written in the Laplace domain. The pharmacokinetic parameters logically follow from the systems approach. They are the cardiac output, the mean transit time, the extraction ratio, the clearance, the volume of distribution in steady state, the mean residence time, and the average number of recirculations. The dynamic systems approach in pharmacokinetics has been illustrated with some examples notably with caffeine.

Negative power functions of time in pharmacokinetics and their implications

When a clearance curve in pharmacokinetic studies--and in tracer kinetics in general--is well fitted by a sum of negative exponentials of time, in very many cases the data would also be well fitted over much or all of the same period by a function of time consisting mainly of a negative power or by a gamma function. There are also instances where two such power functions can be observed in the same clearance curve. Examples are given from numerous reanalyses of published results. These facts have not been explained, except as being fortuitous, by any existing theory or model based on two or more homogeneous compartments. Theoretical and practical implications are outlined and some general recipes are put forward with a view to replacing multicompartmental analysis.

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.

Use of gamma distributed residence times in pharmacokinetics

Using a nonclassical statistically based pharmacokinetic concept, a theory is presented which can be applied to the analysis of concentration-time data fitted by power functions of time C = At-ae-bt, which is shown to be equivalent to the assumption of gamma distributed residence times of drugs. The shape and scale parameters a and b, respectively, are interpreted physiologically in terms of a recirculatory model. It is shown how the shape parameter a, which is only dependent on the coefficient of variation of residence times, is affected by the processes of drug distribution and elimination. The time course of the blood concentration following multiple doses and continuous infusion is predicted for gamma-like drug disposition curves. The assumption of gamma distributed disposition residence times is theoretically based on a random walk model of circulatory drug transport, and the conditions are investigated under which gamma curves can be empirically fitted to oral concentration-time data. The parameters of concentration-time profiles following solid dosage forms, for example, are explained by the means and coefficients of variation of the disposition residence time and dissolution time distribution, respectively. The advantages of this concept compared to the conventional method of fitting sums of exponentials to the data are described.