Prediction of drug distribution in vivo on the basis of in vitro binding data

Modeling Corticosteroid Pharmacokinetics and Pharmacodynamics, Part I: Determination and Prediction of Dexamethasone and Methylprednisolone Tissue Binding in the Rat

The plasma and tissue binding properties of two corticosteroids, dexamethasone (DEX) and methylprednisolone (MPL), were assessed in the rat in anticipation of developing physiologically based pharmacokinetic and pharmacokinetic/pharmacodynamic models. The tissue-to-plasma partition coefficients (K _P) of DEX and MPL were measured in liver, muscle, and lung in vivo after steady-state infusion and bolus injection in rats. Since K _P is often governed by reversible binding to macromolecules in blood and tissue, an attempt was made to assess K _P values of DEX and MPL by in vitro binding studies using rat tissue homogenates and to compare these estimates to those obtained from in vivo kinetics after dosing. The K _P values of both steroids were also calculated in rat tissues using mechanistic tissue composition-based equations. The plasma binding of DEX and MPL was linear with moderate binding (60.5% and 82.5%) in male and female rats. In vivo estimates of steroid uptake appeared linear across the tested concentrations and K _P was highest in liver and lowest in muscle for both steroids. Assessment of hepatic binding of MPL in vitro was severely affected by drug loss at 37°C in male liver homogenates, whereas DEX was stable in both male and female liver homogenates. With the exception of MPL in liver, in vitro-derived K _P estimates reasonably agreed with in vivo values. The mechanistic equations modestly underpredicted K _P for both drugs. Tissue metabolism, saturable tissue binding, and active uptake are possible factors that can complicate assessments of in vivo tissue binding of steroids when using tissue homogenates. SIGNIFICANCE STATEMENT: Assuming the free hormone hypothesis, the ratio of the unbound drug fraction in plasma and in tissues defines the tissue-to-plasma partition coefficient (K _P), an important parameter in physiologically based pharmacokinetic modeling that determines total drug concentrations within tissues and the steady-state volume of distribution. This study assessed the plasma and tissue binding properties of the synthetic corticosteroids, dexamethasone and methylprednisolone, in rats using ultrafiltration and tissue homogenate techniques. In vitro-in vivo and in silico-in vivo extrapolation of K _P was assessed for both drugs in liver, muscle, and lung. Although the extrapolation was fairly successful across the tissues, in vitro homogenate studies severely underpredicted the K _P of methylprednisolone in liver, partly attributable to the extensive hepatic metabolism.

Application of chemical reaction engineering principles to 'body-on-a-chip' systems

The combination of cell culture models with microscale technology has fostered emergence of in vitro cell-based microphysiological models, also known as organ-on-a-chip systems. Body-on-a-chip systems, which are multi-organ systems on a chip to mimic physiological relations, enable recapitulation of organ-organ interactions and potentially whole-body response to drugs, as well as serve as models of diseases. Chemical reaction engineering principles can be applied to understanding complex reactions inside the cell or human body, which can be treated as a multi-reactor system. These systems use physiologically-based pharmacokinetic (PBPK) models to guide the development of microscale systems of the body where organs or tissues are represented by living cells or tissues, and integrated into body-on-a-chip systems. Here, we provide a brief overview on the concept of chemical reaction engineering and how its principles can be applied to understanding and predicting the behavior of body-on-a-chip systems.

Physiologically based pharmacokinetic models of small molecules and therapeutic antibodies: a mini-review on fundamental concepts and applications

The mechanisms of absorption, distribution, metabolism and elimination of small and large molecule therapeutics differ significantly from one another and can be explored within the framework of a physiologically based pharmacokinetic (PBPK) model. This paper briefly reviews fundamental approaches to PBPK modeling, in which drug kinetics within tissues and organs are explicitly represented using physiologically meaningful parameters. The differences in PBPK models applied to small/large molecule drugs are highlighted, thus elucidating differences in absorption, distribution and elimination properties between these two classes of drugs in a systematic manner. The absorption of small and large molecules differs with respect to their common extravascular routes of delivery (oral versus subcutaneous). The role of the lymphatic system in drug distribution, and the involvement of tissues as sites of elimination (through catabolism and target mediated drug disposition) are unique features of antibody distribution and elimination that differ from small molecules, which are commonly distributed into the tissues but are eliminated primarily by liver metabolism. Fundamental differences exist in the ability to predict human pharmacokinetics based upon preclinical data due to differing mechanisms governing small and large molecule disposition. These differences have influence on the evolving utilization of PBPK modeling in the discovery and development of small and large molecule therapeutics.

Integration of in silico and in vitro platforms for pharmacokinetic-pharmacodynamic modeling

IMPORTANCE OF THE FIELD

Pharmacokinetic-pharmacodynamic (PK-PD) modeling enables quantitative prediction of the dose-response relationship. Recent advances in microscale technology enabled researchers to create in vitro systems that mimic biological systems more closely. Combination of mathematical modeling and microscale technology offers the possibility of faster, cheaper and more accurate prediction of the drug's effect with a reduced need for animal or human subjects.

AREAS COVERED IN THIS REVIEW

This article discusses combining in vitro microscale systems and PK-PD models for improved prediction of drug's efficacy and toxicity. First, we describe the concept of PK-PD modeling and its applications. Different classes of PK-PD models are described. Microscale technology offers an opportunity for building physical systems that mimic PK-PD models. Recent progress in this approach during the last decade is summarized.

WHAT THE READER WILL GAIN

This article is intended to review how microscale technology combined with cell cultures, also known as 'cells-on-a-chip', can confer a novel aspect to current PK-PD modeling. Readers will gain a comprehensive knowledge of PK-PD modeling and 'cells-on-a-chip' technology, with the prospect of how they may be combined for synergistic effect.

TAKE HOME MESSAGE

The combination of microscale technology and PK-PD modeling should contribute to the development of a novel in vitro/in silico platform for more physiologically-realistic drug screening.

Mechanistic Approaches to Volume of Distribution Predictions: Understanding the Processes

PURPOSE

To use recently developed mechanistic equations to predict tissue-to-plasma water partition coefficients (Kpus), apply these predictions to whole body unbound volume of distribution at steady state (Vu(ss)) determinations, and explain the differences in the extent of drug distribution both within and across the various compound classes.

MATERIALS AND METHODS

Vu(ss) values were predicted for 92 structurally diverse compounds in rats and 140 in humans by two approaches. The first approach incorporated Kpu values predicted for 13 tissues whereas the second was restricted to muscle.

RESULTS

The prediction accuracy was good for both approaches in rats and humans, with 64-78% and 82-92% of the predicted Vu(ss) values agreeing with in vivo data to within factors of +/-2 and 3, respectively.

CONCLUSIONS

Generic distribution processes were identified as lipid partitioning and dissolution where the former is higher for lipophilic unionised drugs. In addition, electrostatic interactions with acidic phospholipids can predominate for ionised bases when affinities (reflected by binding to constituents within blood) are high. For acidic drugs albumin binding dominates when plasma protein binding is high. This ability to explain drug distribution and link it to physicochemical properties can help guide the compound selection process.

Physiologically based pharmacokinetic modelling 2: Predicting the tissue distribution of acids, very weak bases, neutrals and zwitterions

A key component of whole body physiologically based pharmacokinetic (WBPBPK) models is the tissue-to-plasma water partition coefficients (Kpu's). The predictability of Kpu values using mechanistically derived equations has been investigated for 7 very weak bases, 20 acids, 4 neutral drugs and 8 zwitterions in rat adipose, bone, brain, gut, heart, kidney, liver, lung, muscle, pancreas, skin, spleen and thymus. These equations incorporate expressions for dissolution in tissue water and, partitioning into neutral lipids and neutral phospholipids. Additionally, associations with acidic phospholipids were incorporated for zwitterions with a highly basic functionality, or extracellular proteins for the other compound classes. The affinity for these cellular constituents was determined from blood cell data or plasma protein binding, respectively. These equations assume drugs are passively distributed and that processes are nonsaturating. Resultant Kpu predictions were more accurate when compared to published equations, with 84% as opposed to 61% of the predicted values agreeing with experimental values to within a factor of 3. This improvement was largely due to the incorporation of distribution processes related to drug ionisation, an issue that is not addressed in earlier equations. Such advancements in parameter prediction will assist WBPBPK modelling, where time, cost and labour requirements greatly deter its application.

Tissue Distribution of Basic Drugs: Accounting for Enantiomeric, Compound and Regional Differences Amongst β-Blocking Drugs in Rat

The purpose of this research was to identify the major factors controlling the distribution of beta-blockers (acebutolol, betaxolol, bisoprolol, metoprolol, oxprenolol, pindolol, propranolol and timolol) in rats, across tissues, compounds and enantiomers. Tissue distribution was assessed at steady state by infusing cassette doses of beta-blockers into the jugular vein via an indwelling catheter at a constant rate. Blood was sampled via an indwelling catheter in the carotid artery, and 12 tissues excised at the end of dose infusion (4 or 8 h). Drug concentrations were quantified using a novel chiral LC-MS method and the tissue-to-plasma (Kp) and tissue-to-plasma water (Kpu) values were calculated for each tissue. Differences between Kp were observed between many enantiomeric pairs, and largely explained by enantiomeric differences in plasma protein binding. Across compounds, Kpu values were generally highest in lung and lowest in adipose, and were higher for the more lipophilic drugs betaxolol and propranolol. For any tissue, Kpu differences between the individual beta-blockers correlated well with the corresponding affinity for blood cells. For all compounds, regional tissue distribution correlated well with tissue acidic phospholipid concentrations, with phosphatidylserine appearing to have the strongest influence. This information may be used as the basis for predicting the tissue distribution of basic drugs.

Physiologically Based Pharmacokinetic Modeling 1: Predicting the Tissue Distribution of Moderate-to-Strong Bases

Tissue-to-plasma water partition coefficients (Kpu's) form an integral part of whole body physiologically based pharmacokinetic (WBPBPK) models. This research aims to improve the predictability of Kpu values for moderate-to-strong bases (pK(a) > or = 7), by developing a mechanistic equation that accommodates the unique electrostatic interactions of such drugs with tissue acidic phospholipids, where the affinity of this interaction is readily estimated from drug blood cell binding data. Additional model constituents are drug partitioning into neutral lipids and neutral phospholipids, and drug dissolution in tissue water. Major assumptions of this equation are that electrostatic interactions predominate, drugs distribute passively, and non-saturating conditions prevail. Resultant Kpu predictions for 28 moderate-to-strong bases were significantly more accurate than published equations with 89%, compared to 45%, of the predictions being within a factor of three of experimental values in rat adipose, bone, gut, heart, kidney, liver, muscle, pancreas, skin, spleen and thymus. Predictions in rat brain and lung were less accurate probably due to the involvement of additional processes not incorporated within the equation. This overall improvement in prediction should facilitate the further application of WBPBPK modeling, where time, cost and labor requirements associated with experimentally determining Kpu's have, to a large extent, deterred its application.

Relationship between exposure and nonspecific binding of thirty-three central nervous system drugs in mice

Unbound fractions in mouse brain and plasma were determined for 31 structurally diverse central nervous system (CNS) drugs and two active metabolites. Three comparisons were made between in vitro binding and in vivo exposure data, namely: 1) mouse brain-to-plasma exposure versus unbound plasma-to-unbound brain fraction ratio (fu(plasma)/fu(brain)), 2) cerebrospinal fluid-to-brain exposure versus unbound brain fraction (fu(brain)), and 3) cerebrospinal fluid-to-plasma exposure versus unbound plasma fraction (fu(plasma)). Unbound fraction data were within 3-fold of in vivo exposure ratios for the majority of the drugs examined (i.e., 22 of 33), indicating a predominately free equilibrium across the blood-brain and blood-CSF barriers. Some degree of distributional impairment at either the blood-CSF or the blood-brain barrier was indicated for 8 of the 11 remaining drugs (i.e., carbamazepine, midazolam, phenytoin, sulpiride, thiopental, risperidone, 9-hydroxyrisperidone, and zolpidem). In several cases, the indicated distributional impairment is consistent with other independent literature reports for these drugs. Through the use of this approach, it appears that most CNS-active agents freely equilibrate across the blood-brain and blood-CSF barriers such that unbound drug concentrations in brain approximate those in the plasma. However, these results also support the intuitive concept that distributional impairment does not necessarily preclude CNS activity.

Prediction of in vivo tissue distribution from in vitro data. 3. Correlation between in vitro and in vivo tissue distribution of a homologous series of nine 5-n-alkyl-5-ethyl barbituric acids

PURPOSE

To evaluate the ability to determine accurate in vivo tissue-to-unbound plasma distribution coefficients (Kpue) from in vitro data.

METHODS

Fresh pieces of fifteen rat tissues/organs were incubated at 37 degrees C with a homologous series of nine barbiturates covering a wide range of lipophilicity (Log P 0.02 to 4.13). Steady-state in vivo Kpue values were estimated from the tissue and plasma concentrations following simultaneous dosing by constant rate i.v. infusion of all nine barbiturates. Drug concentrations in the tissues and media were determined by HPLC with UV or mass spectrometric detection.

RESULTS

The pharmacokinetics of the barbiturate series following constant rate i.v. infusion indicated a range of clearance (0.49 to 30 ml x min(-1) x kg(-1)) and volume of distribution at steady state (0.51 to 1.9 l x kg(-1)) values. Good agreement was observed between the in vitro and in vivo Kpu values, although for the most lipophilic barbiturates the in vitro data underpredicted the in vivo tissue distribution for all tissues.

CONCLUSION

The in vitro system for predicting the extent of in vivo tissue distribution works well for compounds of widely differing lipophilicity, although for the most lipophilic drugs it may result in an underprediction of in vivo values.

Influence of nonspecific brain and plasma binding on CNS exposure: implications for rational drug discovery

Relative plasma, brain and cerebrospinal fluid (CSF) exposures and unbound fractions in plasma and brain were examined for 18 proprietary compounds in rats. The relationship between in vivo brain-to-plasma ratio and in vitro plasma-to-brain unbound fraction (fu) was examined. In addition, plasma fu and brain fu were examined for their relationship to in vivo CSF-to-plasma and CSF-to-brain ratios, respectively. Findings were delineated based on the presence or absence of active efflux. Finally, the same comparisons were examined in FVB vs. MDR 1a/1b knockout mice for a selected P-glycoprotein (Pgp) substrate. For the nine compounds without indications of active efflux, predictive correlations were observed between ratios of brain-to-plasma exposure and plasma-to-brain fu (r(2) = 0.98), CSF-to-brain exposure vs. brain fu (r(2) = 0.72), and CSF-to-plasma exposure vs. plasma fu (r(2) = 0.82). For the nine compounds with indications of active efflux, nonspecific binding data tended to over predict the brain-to-plasma and CSF-to-plasma exposure ratios. Interestingly, CSF-to-brain exposure ratio was consistently under predicted by brain fu for this set. Using a select Pgp substrate, it was demonstrated that the brain-to-plasma exposure ratio was identical to that predicted by plasma-to-brain fu ratio in MDR 1a/1b knockout mice. In FVB mice, plasma-to-brain fu over predicted brain-to-plasma exposure ratio to the same degree as the difference in brain-to-plasma exposure ratio between MDR 1a/1b and FVB mice. Consistent results were obtained in rats, suggesting a similar kinetic behavior between species. These data illustrate how an understanding of relative tissue binding (plasma, brain) can allow for a quantitative examination of active processes that determine CNS exposure. The general applicability of this approach offers advantages over species- and mechanism-specific approaches.

Prediction of adipose tissue: plasma partition coefficients for structurally unrelated drugs

Tissue:plasma (P(t:p)) partition coefficients (PCs) are important parameters describing tissue distribution of drugs. The ultimate goal in early drug discovery is to develop and validate in silico methods for predicting a priori the P(t:p) for each new drug candidate. In this context, tissue composition-based equations have recently been developed and validated for predicting a priori the non-adipose and adipose P(t:p) for neutral organic solvents and pollutants. For ionizable drugs that bind to different degrees to common plasma proteins, only their non-adipose P(t:p) values have been predicted with these equations. The only compound-dependent input parameters for these equations are the lipophilicity parameter, such as olive oil-water PC (K(vo:w)) or n-octanol-water PC (P(o:w)), and/or unbound fraction in plasma (fu(p)) determined under in vitro conditions. Tissue composition-based equations could potentially also be used to predict adipose tissue-plasma PCs (P(at:p)) for ionized drugs. The main objective of the present study was to modify these equations for predicting in vivo P(at:p) (white fat) for 14 structurally unrelated ionized drugs that bind substantially to plasma macromolecules in rats, rabbits, or humans. The second objective was to verify whether K(vo:w) or P(o:w) provides more accurate predictions of in vivo P(at:p) (i.e., to verify whether olive oil or n-octanol is the better surrogate for lipids in adipose tissue). The second objective was supported by comparing in vitro data on P(at:p) with those on olive oil-plasma PC (K(vo:p)) for five drugs. Furthermore, in vivo P(at:p) was not only predicted from K(vo:w) and P(o:w) of the non-ionized species, but also from K*(vo:w) and P*(o:w), taking into account the ionized species in addition. The P(at:p) predicted from K*(vo:w), P*(o:w), and P(o:w) differ from the in vivo P(at:p) by an average factor of 1.17 (SD = 0.44, r = 0.95), 15.0 (SD = 15.7, r = 0.59), and 40.7 (SD = 57.2, r = 0.33), respectively. The in vitro values of K(vo:p) differ from those of P(at:p) by an average factor of 0.86 (SD = 0.16, r = 0.99, n = 5). The results demonstrate that (i) the equation using only data on fu(p) as input and olive oil as lipophilicity surrogate is able to provide accurate predictions of in vivo P(at:p), and (ii) olive oil is a better surrogate of the adipose tissue lipids than n-octanol. The present study is an innovative method for predicting in vivo fat partitioning of drugs in mammals.

A priori prediction of tissue:plasma partition coefficients of drugs to facilitate the use of physiologically-based pharmacokinetic models in drug discovery

The tissue:plasma (P(t:p)) partition coefficients (PCs) are important drug-specific input parameters in physiologically based pharmacokinetic (PBPK) models used to estimate the disposition of drugs in biota. Until now the use of PBPK models in early stages of the drug discovery process was not possible, since the estimation of P(t:p) of new drug candidates by using conventional in vitro and/or in vivo methods is too time and cost intensive. The objectives of the study were (i) to develop and validate two mechanistic equations for predicting a priori the rabbit, rat and mouse P(t:p) of non-adipose and non-excretory tissues (bone, brain, heart, intestine, lung, muscle, skin, spleen) for 65 structurally unrelated drugs and (ii) to evaluate the adequacy of using P(t:p) of muscle as predictors for P(t:p) of other tissues. The first equation predicts P(t:p) at steady state, assuming a homogenous distribution and passive diffusion of drugs in tissues, from a ratio of solubility and macromolecular binding between tissues and plasma. The ratio of solubility was estimated from log vegetable oil:water PCs (K(vo:w)) of drugs and lipid and water levels in tissues and plasma, whereas the ratio of macromolecular binding for drugs was estimated from tissue interstitial fluid-to-plasma concentration ratios of albumin, globulins and lipoproteins. The second equation predicts P(t:p) of drugs residing predominantly in the interstitial space of tissues. Therefore, the fractional volume content of interstitial space in each tissue replaced drug solubilities in the first equation. Following the development of these equations, regression analyses between P(t:p) of muscle and those of the other tissues were examined. The average ratio of predicted-to-experimental P(t:p) values was 1.26 (SD = 1.40, r = 0.90, n = 269), and 85% of the 269 predicted values were within a factor of three of the corresponding literature values obtained under in vivo and in vitro conditions. For predicted and experimental P(t:p), linear relationships (r > 0.9 in most cases) were observed between muscle and other tissues, suggesting that P(t:p) of muscle is a good predictor for the P(t:p) of other tissues. The two previous equations could explain the mechanistic basis of these linear relationships. The practical aim of this study is a worthwhile goal for pharmacokinetic screening of new drug candidates.

Extrapolating in vitro data on drug metabolism to in vivo pharmacokinetics: evaluation of the pharmacokinetic interaction between amitriptyline and fluoxetine

Recently, models have been proposed to extrapolate in vitro data on the influence of inhibitors on drug metabolism to in vivo decrement in drug clearance. Many factors influence drug clearance such as age, gender, habits, diet, environment, liver disease, heredity, and other drugs. In vitro investigation of hepatic cytochrome P450 activity has generally centered on genetic influences and interactions with other drugs. This group of enzymes is involved in many, although not all, drug interactions. The interaction of amitriptyline and fluoxetine is an example. Of the different in vitro paradigms, interaction studies utilizing human liver microsomal preparations have proved to be the most generally applicable for in vitro scaling models. Assuming Michaelis-Menten conditions and applying nonlinear regression, a hybrid inhibition constant (Ki) can be generated that allows classification of the inhibitory potency of an inhibitor toward a specific reaction. This constant is largely independent of the substrate concentration, but in vivo relevance is critically dependent on the inhibitor concentration in the site of metabolic activity, the liver cell cytosol. Many lipophilic drugs are extensively bound to plasma protein but, nonetheless, demonstrate extensive partitioning into liver tissue. This is not compatible with diffusion only of the unbound drug fraction into liver cells. The introduction of a partition factor, based on data from a number of possible sources, provided a reasonable basis for the scaling of in vitro data to in vivo conditions. Many interactions could be reconstructed or predicted with greater accuracy and clinical relevance for interactions such as terfenadine or midazolam and ketoconazole. Even for less marked interactions such as amitriptyline and fluoxetine, this model provides a forecast consistent with the clinically observed range of 22-45% reduction in oral clearance, although this interaction is complicated by the presence of two inhibitors, fluoxetine and norfluoxetine. The concept of in vitro-in vivo scaling is promising and might ultimately yield a fast and more cost-effective screening for drug interactions with reduced human drug exposure and risk.

In vitro approaches to predicting drug interactions in vivo

In vitro metabolic models using human liver microsomes can be applied to quantitative prediction of in vivo drug interactions caused by reversible inhibition of metabolism. One approach utilizes in vitro Ki, values together with in vivo values of inhibitor concentration to forecast in vivo decrements of clearance caused by coadministration of inhibitor. A critical limitation is the lack of a general scheme for assigning intrahepatic exposure of enzyme to inhibitor or substrate based only on plasma concentration; however, the assumption that plasma protein binding necessarily restricts hepatic uptake is not tenable. Other potential limitations include: flow-dependent hepatic clearance, "mechanism-based" chemical inhibition, concurrent induction, or a major contribution of gastrointestinal P450-3A isoforms to presystemic extraction. Nonetheless, the model to date has provided reasonably accurate forecasts of in vivo inhibition of clearance of several substrates (desipramine, terfenadine, triazolam, alprazolam, midazolam) by coadministration of selective serotonin reuptake-inhibitor antidepressants and azole antifungal agents. Such predictive models deserve further evaluation, since they may ultimately yield more cost-effective and expeditious screening for drug interactions, with reduced human drug exposure and risk.

Effect of altered tissue binding on the disposition of barbital in the isolated perfused rat liver: application of the axial dispersion model

To examine the dependence of hepatic dispersion on tissue binding, the distribution kinetics of barbital under varying conditions of barbiturate perfusate concentrations was studied in the isolated perfused rat liver preparation (n = 5). The in situ liver was perfused in a single-pass mode with protein-free Krebs bicarbonate medium (15 mL/min). During steady-state infusion with various barbiturate concentrations (barbital, 1 g/L; butethal, 0.1, 1 g/L), a bolus containing [3H]water (cellular space marker) and [14C]barbital was injected into the portal vein. The recoveries of [3H]water and [14C]barbital were complete. The mean transit time and hence the volume of distribution for barbital in the absence of bulk barbiturate concentration (56 s and 1.24 mL/g) were about 2-fold higher than those for water (29 s and 0.58 mL/g), and they decreased progressively as the perfusate barbiturate concentration increased, indicating a decrease in tissue binding. However, the relative dispersion values (CV2H) of water (0.60) and barbital (0.66) were about the same magnitude and independent of the bulk concentration of barbiturate. The one-compartment dispersion model adequately described the data of barbital with a constant DN (dispersion number) value of 0.35. The results indicate that varying the tissue binding of barbital does not change the magnitude of DN; as such it offers a new experimental approach to examine the hepatic dispersion of solutes with a large distribution volume.

An understanding of flow- and diffusion-limited vs. carrier-mediated hepatic transport: a simulation study

Concentration-dependent changes in the hepatic extraction ratio E and tissue accumulation of drugs were examined in a simulation study, wherein plasma protein binding, flow, and mode of entry were altered. A tubular flow model that described carrier-mediated (influx: Kml = 20 microM, Vmax1 = 1000 nmol min-1; efflux, Km2 = 200 microM, Vmax2 = 250 nmol min-1), flow-limited (influx clearance CLin = efflux clearance CLef = 50 ml min-1), or diffusion-limited (CLin = CLef = 0.1 ml min-1) hepatocytic entry was employed; drug removal was solely via biliary excretion (Km3 = 100 microM, Vmax3 = 1500 nmol min-1). Other parameter space and the combination of carrier-mediated transport and passive diffusion were also explored. Increased plasma protein binding reduced the hepatic extraction of the substrate, and in some instances, constituted the rate-controlling factor, especially at lower input concentrations for which tighter binding existed. Increased flow rate also brought about a reduction in E, affecting E almost inversely when values of E were low (e.g., for the diffusion-limited case or at higher input concentration). Tissue accumulation patterns and the apparent tissue distribution equilibrium ratio, i.e., tissue to plasma unbound concentration ratio Kp, differed among the systems. The behavior of Kp may be used as an identifier for the mode of drug transport: A declining (concave-down) Kp curve or a parabolic Kp that approached unity with input concentration (Cln) is associated with carrier-mediated entry; a rising Kp curve that approaches unity with Cln suggests flow limitation; and a waning concave-up Kp curve of very low magnitude represents diffusion limitation. Since the unbound tissue concentration (Ct) differs from the logarithmic average of the unbound input and output concentrations in plasma (Cu) for carrier-mediated and diffusion-limited systems, excretion parameters may be obtained only upon fitting of the overall excretion rate vs. Ct in the Michaelis-Menten equation; whereas when data are fitted with Cu, the rate-limiting step, influx, or deviations of influx, efflux, and excretion, will be obtained. When Ct equals Cu, as in flow-limited systems, accurate excretion parameters will be provided with the fitting of data against either Ct or Cu.

Prediction of drug distribution in distribution dialysis and in vivo from binding to tissues and blood

Relationships between the binding and the distribution of drugs have been studied in vitro and compared with in vivo data. By use of a standardized technique of distribution dialysis, 10 model drugs were allowed to be distributed among blood and homogenates of seven tissues. The drugs represented a variety of distinct molecules with different lipophilicities, ionization constants, and binding characteristics. The tissue/blood drug concentration ratios were below unity for salicylic acid and phenylbutazone, at about unity for antipyrine (phenazone) and morphine, and above unity for two barbiturates and four basic lipophilic drugs. The binding of the 10 drugs to blood and homogenates of seven tissues was determined by use of conventional equilibrium dialysis and experimental conditions identical to those used in distribution dialysis. From these binding values (free fractions), the theoretical concentration ratios were calculated. There was a good correlation between the calculated values and those determined by distribution dialysis. Thus, the distribution of drugs in the in vitro model of distribution dialysis clearly is the result of binding competition and is predictable from binding values. The correlation between distribution in vitro (or calculated from binding values) and distribution in vivo, on the basis of literature data, indicated a reasonable agreement for antipyrine and the acidic lipophilic drugs used, as well as for the basic lipophilic drugs, with respect to the brain, muscle, and adipose tissue. However, the distribution of the latter drugs in the lungs, liver, and kidneys was grossly underestimated.(ABSTRACT TRUNCATED AT 250 WORDS)

Prediction of the volume of distribution of 7-hydroxycoumarin in man from in vitro and ex vivo data obtained in rat

The essential parameter to estimate the first dose size of a drug in man is the volume of distribution. For a drug that has never been used in man before, estimates of the volume of distribution can only be obtained from animals and in vitro data. The purpose of this study was to compare various approaches presented in the literature for predicting the volume of distribution at steady state (VSS) and the terminal phase volume of distribution (Vd beta) in man. A lipophilic active metabolite of coumarin, 7-hydroxycoumarin (7OHC), was selected for this investigation. This compound is extensively metabolized in both the central and peripheral compartments. Of the six methods evaluated, only an empirical allometric approach yielded a reasonable estimate of VSS. All methods underestimated VSS and none of the applicable methods were able to predict Vd beta. The reason for this discrepancy may be due to the fact that the calculation of VSS in man was done assuming elimination from the central compartment.

Significance of binding to Na,K-ATPase in the tissue distribution of ouabain in guinea pigs

Ouabain binds specifically to Na,K-ATPase on the plasma membrane and therefore serves to measure the tissue concentration of Na,K-ATPase. We examined the role of ouabain binding to Na,K-ATPase in its overall tissue distribution. The tissue-to-plasma concentration ratio (Kp,vivo) was defined in each tissue after intravenous administration of 3H-ouabain in guinea pigs, and specific binding of ouabain to Na,K-ATPase was measured in tissue homogenate to obtain the dissociation constant and binding capacity in each tissue. A predicted tissue-to-plasma concentration ratio (Kp,vitro) was calculated using the obtained binding parameters and the volume of extracellular space in each tissue. The absolute values of Kp,vitro were comparable to those of Kp,vivo, except in brain. Regression analysis showed that the specific binding capacity of Na,K-ATPase in each tissue is the main factor in the tissue variation of Kp,vivo. Therefore, the binding of ouabain to Na,K-ATPase plays a significant role in the tissue distribution of ouabain.

The potential role of lysosomes in tissue distribution of weak bases

The potential importance of lysosomes as a site of accumulation of weak bases in tissues is discussed. A simple mathematical treatment predicts the quantitative significance of lysosomal trapping for monoacidic and diacidic weak bases. The features which are characteristics of lysosomal trapping are discussed, particularly in comparison with active transport and intracellular binding mechanisms. These features include: linear accumulation at low concentrations; nonlinearity at higher concentrations; dependence on structural integrity of tissue; energy dependence and competition with other weak bases. Subcellular distribution studies have previously shown that weak bases accumulate extensively in membranes; however, the dependence of accumulation on the structural integrity of tissue suggests that this is not the only significant mechanism of accumulation. The results of a range of studies of tissue distribution of weak bases are discussed to illustrate that these findings are consistent with accumulation in lung and liver being attributable to a combination of lysosomal trapping and accumulation in membranes whereas, in muscle, accumulation in membranes is the predominant mechanism of accumulation. The possible pharmacokinetic significance of lysosomal trapping of weak bases is also discussed.

Physiologic pharmacokinetic modeling

Although physiologic modeling has not gained the widespread acceptance that was originally projected, it may serve as the basis for future PK/PD modeling approaches. In addition, with more effort applied to developing in vitro and animal-to-human predictions, physiologic modeling may assume a higher position in the pharmacokinetic modeling hierarchy.

Physiological pharmacokinetic models: some aspects of theory, practice and potential

Models are intellectual constructs that pattern selected relationships among the elements of one system to correspond in some way to elements of a second system. In pharmacokinetics, physiological models provide a clearly articulated, rational, explanatory basis for the integration of empirical data; they do this by partitioning the biological system into relevant components (tissues, organs, etc.) and linking them together through the circulatory system. Unlike conventional mammillary compartment models, there is a clear correspondence between model system elements and physiological entities. By virtue of their high degree of physical and biochemical relevance, these models can help provide deep insight into structure, function and mechanism. Pharmacokinetic (and potentially pharmacodynamic) response-time relationships can thus be understood in terms of interconnections and behavior of constituent subsystems. At their worst, these models provide stale or infertile views of reality and thus frustrate and alienate us with the triviality of their insights. At their best, they allow us to understand the accumulation of thought in pharmacokinetics and pharmacodynamics, and help with the integration of data and improvement of experimental design.