Physiologically Based Pharmacokinetic Modeling of Drug Disposition in Rat and Human: A Fuzzy Arithmetic Approach

PURPOSE: Probabilistic methods are insufficient for dealing with the vagueness inherent in human judgment of minimal data available during early drug development. We sought to use fuzzy set theory as a basis for quantifying and propagating vague judgment in a physiologically based pharmacokinetic (PBPK) model for diazepam disposition. MATERIALS AND METHODS: First, using diazepam distribution data in rat tissues and fuzzy regression, we estimated fuzzy rat tissue-to-plasma partition coefficients (Kp's). We scaled the coefficients prior to human PBPK modeling. Next, we constructed the fuzzy set of hepatic intrinsic clearance (CLint) by integrating CLint values measured in vitro from human hepatocytes. Finally, we used these parameters, and other physiological and biochemical information, to predict human diazepam disposition. We compared the simulated plasma kinetics with published concentration-time profiles. RESULTS: We successfully identified rat Kp's by fuzzy regression. The predicted rat tissue concentration-time contours enveloped the animal tissue distribution data. For the human PBPK model, the mean in vivo plasma concentrations were contained in the simulated concentration-time envelopes. CONCLUSIONS: We present a novel computational approach for handling information paucity in PBPK models using fuzzy arithmetic. Our methodology can model the vagueness associated with human perception and interpretation of minimal drug discovery data.     

Circulatory transport and capillary-tissue exchange as determinants of the distribution kinetics of inulin and antipyrine in dog

A pharmacokinetic model was developed to estimate physiologically meaningful parameters of distribution kinetics from plasma concentration-time data. The model is based on simultaneously measured disposition curves of drug and vascular marker. Employing residence time distribution theory, a recirculatory model with two subsystems, the pulmonary and systemic circulation, was constructed. In addition to intravascular mixing, the axially distributed model of the systemic circulation accounts for transcapillary transport of solutes, quantified by permeability-surface area product (PS) and diffusional equilibration time. Parameters of ICG, inulin, and antipyrine were estimated from disposition data obtained in awake dogs under control conditions and during an isoproterenol infusion or moderate hypovolemia. Results suggest that distribution kinetics is (1) governed by extravascular diffusion and (2) its dependency on cardiac output decreases with increasing diffusional resistance. Hemorrhage decreased the effective PS of inulin. In conclusion, this novel mechanistic model effectively described both the permeability-limited distribution of inulin into interstitial fluid and the flow-limited distribution of antipyrine into total body water and might be useful for other drugs.     

Comparative adipose tissue kinetics of thiopental, DDE and 2,4,5,2',4',5'-hexachlorobiphenyl in the rat

A comparative study on the fate of thiopental, DDE, and 2,4,5,2',4',5'-hexachlorobiphenyl (6-CB) with emphasis on adipose tissue kinetics was carried out after single i.v. doses to adult male rats. The time course of the concn. in blood, adipose and other tissues were determined for the three compounds for periods up to 40 h, 14 and 28 d, respectively, allowing for mass balances and for calculation of pharmacokinetic parameters. Appreciable amounts of thiopental, DDE and 6-CB appeared in adipose tissues, but the kinetics were profoundly different, the adipose tissue concn. peaking after one hour, 17 h, and five to six weeks, respectively. Thus, although DDE and 6-CB are much more lipophilic than thiopental, they were very much slower in entering adipose tissue. The results indicate that adipose tissue storage of drugs and other xenobiotics cannot be explained as a simple partition phenomenon. Rather, disposition in adipose tissue may be determined by initial binding in other tissues.     

Influence of short-term water deprivation on antipyrine disposition

The effects of acute (96 h) water deprivation on the disposition kinetics of antipyrine and hepatic cytochrome P-450 content were investigated in male rats. The disposition kinetics of antipyrine in rats deprived of water for 96 h was altered significantly: the total body clearance and steady-state volume of distribution decreased by 27.1 and 22.4%, respectively, as compared to control rats. There was no significant change in the disposition rate constant as a result of simultaneous changes in the volume of distribution and clearance. There was a 51.4% decrease in the hepatic cytochrome P-450 content in water-deprived rats. These results suggest that the pharmacokinetic changes observed in acute water deprivation with a model drug, antipyrine, are related to a decrease in total body water and to a reduced amount and/or activity of the hepatic microsomal oxidative enzymes.     

Comparative adipose tissue kinetics of thiopental,DDE and 2,4,5,2′,4′,5′-hexachlorobiphenyl in the rat

1. A comparative study on the fate of thiopental, DDE, and 2,4,5,2′,4′,5′-hexachlorobiphenyl (6-CB) with emphasis on adipose tissue kinetics was carried out after single i.v. doses to adult male rats. The time course of the concn. in blood, adipose and other tissues were determined for the three compounds for periods up to 40 h, 14 and 28 d, respectively, allowing for mass balances and for calculation of pharmacokinetic parameters.

2. Appreciable amounts of thiopental, DDE and 6-CB appeared in adipose tissues, but the kinetics were profoundly different, the adipose tissue concn. peaking after one hour, 17h, and five to six weeks, respectively. Thus, although DDE and 6-CB are much more lipophilic than thiopental, they were very much slower in entering adipose tissue.

3. The results indicate that adipose tissue storage of drugs and other xenobiotics cannot be explained as a simple partition phenomenon. Rather, disposition in adipose tissue may be determined by initial binding in other tissues.     

A semiparametric approach to physiological flow models

By regarding sampled tissues in a physiological model as linear subsystems, the usual advantages of flow models are preserved while mitigating two of their disadvantages, (i) the need for assumptions regarding intratissue kinetics, and (ii) the need to simultaneously fit data from several tissues. To apply the linear systems approach, both arterial blood and (interesting) tissue drug concentrations must be measured. The body is modeled as having an arterial compartment (A) distributing drug to different linear subsystems (tissues), connected in a specific way by blood flow. The response (CA, with dimensions of concentration) of A is measured. Tissues receive input from A (and optionally from other tissues), and send output to the outside or to other parts of the body. The response (CT, total amount of drug in the tissue (T) divided by the volume of T) from the T-th one, for example, of such tissues is also observed. From linear systems theory, CT can be expressed as the convolution of CA with a disposition function, F(t) (with dimensions 1/time). The function F(t) depends on the (unknown) structure of T, but has certain other constant properties: The integral integral infinity0 F(t) dt is the steady state ratio of CT to CA, and the point F(0) is the clearance rate of drug from A to T divided by the volume of T. A formula for the clearance rate of drug from T to outside T can be derived. To estimate F(t) empirically, and thus mitigate disadvantage (i), we suggest that, first, a nonparametric (or parametric) function be fitted to CA data yielding predicted values, CA, and, second, the convolution integral of CA with F(t) be fitted to CT data using a deconvolution method. By so doing, each tissue's data are analyzed separately, thus mitigating disadvantage (ii). A method for system simulation is also proposed. The results of applying the approach to simulated data and to real thiopental data are reported.     

From piecewise to full physiologic pharmacokinetic modeling: Applied to thiopental disposition in the rat

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, C_T(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. Supported in part by Grant RO1-AG04594 from the National Institute of Aging and the Anesthesia/Pharmacology Research Foundation.     

Percutaneous absorption in man: a kinetic approach

A biophysically based kinetic model of chemical absorption via human skin was developed and applied to the penetration kinetics of 12 chemicals: aspirin, benzoic acid, benzyl nicotinate, caffeine, chloramphenicol, colchicine, dinitrochlorobenzene, diethyltoluamide, malathion, methyl nicotinate, nitrobenzene, and salicylic acid. The pharmacokinetic model is linear and includes four first-order rate constants: (1) k1 describes penetrant diffusion through the stratum corneum; (2) k2 relates to further transport across the viable epidermal tissue to the cutaneous blood vessels; (3) k3 is a parameter which delays the partitioning of penetrant at the stratum corneum-viable tissue interface and, in conjunction with k2, reflects the penetrant's relative affinity for the stratum corneum over the viable tissue; and (4) k4 characterizes the elimination rate of chemical from blood to urine. Previously determined diffusion coefficients and molecular weight corrections were used to estimate k1 and k2; k4 values employed were those measured experimentally. Urinary excretion rate data following topical administration were simulated and k3 was estimated for each penetrant by optimizing the fit of the model to the data points. Ratios of k3/k2 should be related to the partition coefficients for the chemicals between stratum corneum and viable tissue and it was shown that these ratios agreed reasonably well with the corresponding octanol-water partition coefficients. This approach may have potential for predicting the general percutaneous absorption kinetics of chemicals based on recognized cutaneous biology and penetrant molecular weight and lipophilicity.     

Tissue distribution of fentanyl and alfentanil in the rat cannot be described by a blood flow limited model

Traditionally, physiological pharmacokinetic models assume that arterial blood flow to tissue is the rate-limiting step in the transfer of drug into tissue parenchyma. When this assumption is made the tissue can be described as a well-stirred single compartment. This study presents the tissue washout concentration curves of the two opioid analgesics fentanyl and alfentanil after simultaneous 1-min iv infusions in the rat and explores the feasibility of characterizing their tissue pharmacokinetics, modeling each of the 12 tissues separately, by means of either a one-compartment model or a unit disposition function. The tissue and blood concentrations of the two opioids were measured by gas-liquid chromatography. The well-stirred one-compartment tissue model could reasonably predict the concentration-time course of fentanyl in the heart, pancreas, testes, muscle, and fat, and of alfentanil in the brain and heart only. In most other tissues, the initial uptake of the opioids was considerably lower than predicted by this model. The unit disposition functions of the opioids in each tissue could be estimated by nonparametric numerical deconvolution, using the arterial concentration times tissue blood flow as the input and measured tissue concentrations as the response function. The observed zero-time intercepts of the unit disposition functions were below the theoretical value of one, and were invariably lower for alfentanil than for fentanyl. These findings can be explained by the existence of diffusion barriers within the tissues and they also indicate that alfentanil is less efficiently extracted by the tissue parenchyma than the more lipophilic compound fentanyl. The individual unit disposition functions obtained for fentanyl and alfentanil in 12 rat tissues provide a starting point for the development of models of intratissue kinetics of these opioids. These submodels can then be assembled into full physiological models of drug disposition.Supported in part by the National Institute on Aging, RO1-AG-4594, the Anesthesia/ Pharmacology Research Foundation, and a travel grant from Janssen Pharma AB (Sweden).     

A Recirculatory Model of the Pulmonary Uptake and Pharmacokinetics of Lidocaine Based on Analysis of Arterial and Mixed Venous Data from Dogs

Pulmonary uptake of basic amine xenobiotics such as lidocaine may influence the onset of drug effect and ameliorate toxicity. To date, pharmacokinetic analysis of pulmonary drug uptake has been only semiquantitative and ill-suited for relating pharmacodynamics to pharmacokinetics or jar estimating the time course of the fraction of drug dose residing in the lung during a single pass. We have developed recirculatory models in an experiment in which lidocaine was injected into the right atrium simultaneously with markers of intravascular space (indocyanine green) and total body water (antipyrine): this was followed by rapid arterial and mixed venous blood sampling. Such models are interpretable physiologically and are capable of characterizing the kinetics of the pulmonary uptake of lidocaine in addition to peripheral tissue distribution and elimination. The apparent pulmonary tissue volume of lidocaine (39 ml/kg) was nearly ninefold greater than that of antipyrine (4.5 ml/kg). The recirculatory model characterized both arterial and mixed venous data, but the latter data were not essential for estimating lidocaine's pulmonary disposition either before or after recirculation of drug was evident.     

Uptake in vitro of lipophilic model compounds into adipose tissue preparations and lipids

In vitro uptake of 11 lipophilic model compounds into rat epididymal adipose tissue slices, adipocytes, triglycerides, and lecithin was studied. Relative uptake at equilibrium into adipose tissue slices increased from 6 to 87% in the following sequence: phenazone, morphine less than pentobarbital less than glutethimide, phenylbutazone less than thiopental, methadone less than chlorpromazine, imipramine. In the presence of albumin a similar sequence was obtained at lower uptake levels, with DDE and 2,4,5,2',4',5'-hexachlorobiphenyl (6-CB) on top with 95% uptake. However, the time to reach equilibrium was unproportionately greater for DDE and 6-CB (16-40 hr) than for other compounds (1-4 hr). A linear positive correlation was found between relative uptake and partition coefficient (octanol/water). Relative uptake was independent of drug concentration. There were no significant differences between uptake values measured with adipose tissue slices, adipocytes, triolein, and a saturated short-chain triglyceride. In contrast, uptake into lecithin was not correlated with the octanol partition coefficient. Thiopental, imipramine, and 6-CB were taken up into lean tissue slices (liver, lung, skin) in excess of their lipid content, suggesting additional binding sites. Release from preloaded adipose tissue slices followed first order kinetics, was accelerated by albumin, and was much slower for 6-CB and DDE than for thiopental and imipramine. The results indicate that uptake of lipophilic xenobiotics in vitro is a partition process between the aqueous medium and the triglyceride of the adipose tissue preparation. In contrast, the extent of adipose tissue storage of drugs in vivo has recently been shown not to correlate with octanol partition coefficients.     

Application of 4-hydroxyantipyrine and acetaminophen O-sulfate as biodistribution promoter.

The effects of 4-hydroxyantipyrine (4-OH), a major metabolite of antipyrine and its sulfate, 4-hydroxyantipyrine O-sulfate (4-S), on the pharmacokinetics of citicoline and thiopental sodium were investigated in rats. The concomitant use of 4-OH increased significantly the tissue-to-plasma concentration ratio (Kp) of citicoline in the brain and liver and that of thiopental sodium in the brain, liver, and heart, while 4-S did not affect them. The permeability clearance of blood-brain barrier (BBB) (Kin) and the total distribution volume (Vdbr) of citicoline were not affected by either 4-OH or 4-S. However, those of thiopental sodium were significantly increased by not only 4-OH but also by 4-S. On the other hand, the plasma concentration of antipyrine was significantly decreased by the intravenous bolus coadministration of N-acetyl-p-aminophenyl O-sulfate (APAPS) at steady-state plasma concentration of antipyrine. A similar reduction was not observed with the intravenous coadministration of acetaminophen (APAP). The Kp value of antipyrine was significantly increased in the brain by the coadministration of APAPS, but was not affected by APAP. The increment in the drug distribution to the brain with the concomitant use of 4-OH (or APAPS) observed in this study is useful information for the application of drug combinations as biodistribution promoters.     

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.     

Constant-rate infusion of nicotine and cotinine. I. A physiological pharmacokinetic analysis of the cotinine disposition, and effects on clearance and distribution in the rat

The tissue partition of cotinine was measured by a GC-MS method following a 6-day constant-rate input of nicotine and cotinine to male rats by means of an osmotic minipump. The tissue-to-blood partition coefficients of cotinine were calculated for adipose (0.08), brain (0.48), heart muscle (0.51), following the cotinine infusion. When nicotine was infused the tissue partitioning of cotinine increased by a factor of 2.3-4.9, depending on the tissue sampled. Another group of animals were killed at timed intervals from 10 min to 30 hr, after having received a single intravenous bolus dose of 0.5 mg cotinine, and the washout of cotinine was traced in blood and tissues. A physiological model was used to simulate the disposition of cotinine. Generally, the model-predicted concentrations were consistent with those found experimentally. The fractional uptake of cotinine into various tissues was simulated. Blood, intestinal, and skeletal muscle tissues embodied more than 70% of the total body load of the drug. Clearance (Cl), volume of distribution (Vd), and the biological half-life (t1/2) were calculated both from the infusion study and by fitting a monoexponential model to the iv blood data of the rat. Significant differences were found in the apparent clearance calculated from the single iv bolus dose compared to the constant rate infusion. The volume of distribution was, however, consistent from both studies. The impact of a change in clearance was also simulated.     

Effects of fasting on biperiden pharmacokinetics in the rat

The effects of fasting on the pharmacokinetics of biperiden in rats were examined. Total clearance of biperiden was greater than 90% ascribable to hepatic clearance and was essentially blood-flow dependent. The number of compartments in the preferred pharmacokinetic model of biperiden changed from three (for normal rats) to two (for fasted rats). The smaller mean residence time (MRT) values found for fasted rats were attributable to decreases in distribution volume. Biperiden showed much higher lipophilicity than haloperidol, thiopental, and hexobarbital, and its tissue-to-plasma partition coefficient in adipose tissue was 20-fold higher than that in muscle. The influence of changes in volumes of adipose tissue and muscle on distribution volume (Vdss/BW) was evaluated from tissue-to-plasma partition coefficients. The value of Vdss/BW was predicted to decrease with decrease of adipose tissue, and to increase with decrease of muscle tissue. These results suggest that the observed decrease of Vdss/BW in fasted rats reflects reduced capacity to trap biperiden in the body, especially in adipose tissue. Possible clinical implications of these results are discussed.     

Physiologically based pharmacokinetic (PBPK) modeling of disposition of epiroprim in humans

The objective of this study was to use in synergy physiologically based and empirical approaches to estimate the drug-specific input parameters of PBPK models of disposition to simulate the plasma concentration-time profile of epiroprim in human. The estimated input parameters were the tissue:plasma partition coefficients (Pt:p) for distribution and the blood clearance (CL) for the in vivo conditions. Epiroprim represents a challenge for such methods, because it shows large interspecies differences in its pharmacokinetic properties. Two approaches were used to predict the human Pt:p values: the tissue composition model (TCM) and the "Arundel approach" based on the volume of distribution at steady state (Vdss) determined in vivo in the rat. CL in human was predicted by (1) conventional allometric scaling of in vivo animal clearances (CAS), (2) physiologically based direct scaling up of in vitro hepatocyte data (DSU), and (3) allometric scaling of animal intrinsic in vivo blood CL normalized by the ratios of animal:human intrinsic clearances determined in vitro with hepatocytes (NAS). The performance of prediction was assessed by comparing separately the above pharmacokinetic parameters (Vdss estimated from the Pt:p values and blood CL) with the corresponding in vivo data obtained from the plasma kinetic profiles. These input parameters were used in PBPK models, and the resulting plasma concentration-time profiles of epiroprim were compared with those observed in rat and human. Previously to the construction of the human PBPK model, a model for the rat was also developed to gain more confidence on the model structure and assumptions. Overall, using the TCM and the NAS for the parameterization of the distribution and clearance, respectively, the PBPK model gave the more accurate predictions of epiroprim's disposition in human. This study represents therefore an attractive approach, which may potentially help the clinical candidate selection.     

Kinetics of propranolol uptake in muscle, skin, and fat of the isolated perfused rat hindlimb.

The tissue distribution kinetics of a highly bound solute, propranolol, was investigated in a heterogeneous organ, the isolated perfused limb, using the impulse-response technique and destructive sampling. The propranolol concentration in muscle, skin, and fat as well as in outflow perfusate was measured up to 30 min after injection. The resulting data were analysed assuming (1) vascular, muscle, skin and fat compartments as well mixed (compartmental model) and (2) using a distributed-in-space model which accounts for the noninstantaneous intravascular mixing and tissue distribution processes but consists only of a vascular and extravascular phase (two-phase model). The compartmental model adequately described propranolol concentration-time data in the three tissue compartments and the outflow concentration-time curve (except of the early mixing phase). In contrast, the two-phase model better described the outflow concentration-time curve but is limited in accounting only for the distribution kinetics in the dominant tissue, the muscle. The two-phase model well described the time course of propranolol concentration in muscle tissue, with parameter estimates similar to those obtained with the compartmental model. The results suggest, first that the uptake kinetics of propranolol into skin and fat cannot be analysed on the basis of outflow data alone and, second that the assumption of well-mixed compartments is a valid approximation from a practical point of view (as, e.g., in physiological based pharmacokinetic modelling). The steady-state distribution volumes of skin and fat were only 16 and 4%, respectively, of that of muscle tissue (16.7 ml), with higher partition coefficient in fat (6.36) than in skin (2.64) and muscle (2.79).     

Residence Time Dispersion as a General Measure of Drug Distribution Kinetics: Estimation and Physiological Interpretation

Purpose To evaluate distribution kinetics of drugs by the relative dispersion of disposition residence time and demonstrate its uses, interpretation and limitations. Materials and Methods The relative dispersion was estimated from drug disposition data of inulin and digoxin fitted by three-exponential functions, and calculated from compartmental parameters published for fentanyl and alfentanil. An interpretation is given in terms of a lumped organs model and the distributional equilibration process in a noneliminating system. Results As a measure of the deviation from mono-exponential disposition (one-compartment behavior), the relative dispersion provides information on the distribution kinetics of drugs, i.e., diffusion-limited distribution or slow tissue binding, without assuming a specific structural model. It also defines the total distribution clearance which has a clear physical meaning. Conclusion The residence time dispersion is a model-independent measure that can be used to characterize the distribution kinetics of drugs and to reveal the influence of disease states. It can be estimated with high precision from drug disposition data.     

Antipyrine kinetics in undernourished diabetics

Summary In developing countries diabetics frequently suffer from varying grades of malnutrition. The combined effect of malnutrition and non-insulin dependent diabetes (NIDDM) on the drug metabolising enzyme system has been evaluated using antipyrine as a protodrug. All the patients were under treatment and their plasma glucose values were within normal limits.The AUC of antipyrine was similar in all the groups. Although none of the kinetic parameters was altered in normal diabetics, the clearance of antipyrine was decreased and its half life was prolonged, with an increase in volume of distribution, in undernourished diabetics compared to undernourished controls. The results indicate that diabetes per se may not influence antipyrine kinetics when the blood glucose is well under control, but in the presence of undernutrition, it significantly alters the disposition of the drug.