Protein Binding and Hepatic Clearance: Re-Examining the Discrimination between Models of Hepatic Clearance with Diazepam in the Isolated Perfused Rat Liver Preparation

Are all measures of liver Kpuu a function of FH, as determined following oral dosing, or have we made a critical error in defining hepatic drug clearance?

Here we present, utilizing universally accepted relationships for hepatic clearance at steady state, that for all models of hepatic elimination the ratio of unbound liver drug concentration to unbound systemic blood concentration, Kpuu, is a function of or related to the hepatic bioavailability for that drug, FH. According to the derivation for the well-stirred model, Kpuu can never exceed unity, can frequently be a function of hepatic blood flow, and is equivalent to the value of FH as determined following oral dosing. For the parallel tube model, Kpuu will not equal FH but will be a function of FH and will also never be a value greater than 1. When hepatic clearance is rate limited by basolateral transporters, Kpuu will be less than 1, and less than FH. We believe that such outcomes are highly unlikely, and that the error arises from a basic assumption concerning hepatic clearance that leads to the mechanistic models of hepatic elimination, the well-stirred, parallel tube and dispersion models. That basic assumption is that the steady-state systemic concentration multiplied by the hepatic systemic clearance is equal to the product of the average unbound liver steady-state concentration and the intrinsic hepatic clearance (Css · CL = CH,u · CLint). Calculations of Kpuu and FH based on present methods of analysis provide a strong argument as to why this universally accepted relationship is not correct. Alternatively, we have shown in recent publications that hepatic clearance may be adequately determined based on Kirchhoff's Laws where no assumption of the above equality concerning hepatic intrinsic clearance is required, and where Kpuu is independent of hepatic extraction ratio and FH.

A Complete Extension of Classical Hepatic Clearance Models Using Fractional Distribution Parameter fd in Physiologically Based Pharmacokinetics

The classical organ clearance models have been proposed to relate the plasma clearance CLp to probable mechanism(s) of hepatic clearance. However, the classical models assume the intrinsic capability of drug elimination (CLu,int) that is physically segregated from the vascular blood but directly acts upon the unbound drug concentration in the blood (fubCavg), and do not handle the transit-time delay between the inlet/outlet concentrations in their closed-form clearance equations. Therefore, we propose unified model structures that can address the internal blood concentration patterns of clearance organs in a more mechanistic/physiological manner, based on the fractional distribution parameter fd operative in PBPK. The basic partial/ordinary differential equations for four classical models are revisited/modified to yield a more complete set of extended clearance models, i.e., the Rattle, Sieve, Tube, and Jar models, which are the counterparts of the dispersion, series-compartment, parallel-tube, and well-stirred models. We demonstrate the feasibility of applying the resulting extended models to isolated perfused rat liver data for 11 compounds and an example dataset for in vitro-in vivo extrapolation of the intrinsic to the systemic clearances. Based on their feasibilities to handle such real data, these models may serve as an improved basis for applying clearance models in the future.

Plasma Protein-Mediated Uptake and Contradictions to the Free Drug Hypothesis: A Critical Review

According to the free drug hypothesis (FDH), only free, unbound drug is available to interact with biological targets. This hypothesis is the fundamental principle that continues to explain the vast majority of all pharmacokinetic and pharmacodynamic processes. Under the FDH, the free drug concentration at the target site is considered the driver of pharmacodynamic activity and pharmacokinetic processes. However, deviations from the FDH are observed in hepatic uptake and clearance predictions, where observed unbound intrinsic hepatic clearance (CL_int,u) is larger than expected. Such deviations are commonly observed when plasma proteins are present and form the basis of the so-called plasma protein-mediated uptake effect (PMUE). This review will discuss the basis of plasma protein binding as it pertains to hepatic clearance based on the FDH, as well as several hypotheses that may explain the underlying mechanisms of PMUE. Notably, some, but not all, potential mechanisms remained aligned with the FDH. Finally, we will outline possible experimental strategies to elucidate PMUE mechanisms. Understanding the mechanisms of PMUE and its potential contribution to clearance underprediction is vital to improving the drug development process.

Evidence of the Need for Modified Well-stirred Model in In Vitro to In Vivo Extrapolation

In vitro to in vivo extrapolation (IVIVE), an approach for hepatic clearance (CL_H) prediction used worldwide, remains controversial due to systematic underprediction. Among the various probable factors, the original assumption of the hepatic mathematical model (i.e., the well-stirred model, WSM) may become problematic, leading to the underestimation of drug CL_H. Having a similar prerequisite that the well-stirred conditions are homogenous with perfectly mixed reactants, but using a different driving concentration, the modified well-stirred model (MWSM) stands apart from the WSM. However, we believe that both models should coexist so that the entire well-stirred scenario can be completely illustrated. Consequently, we collected published data from the literature and employed a logistic regression method to differentiate the optimal timing of use between WSM and MWSM in drug CL_H prediction. Generally, variances adopted in the regression, including partition coefficient (logP), fraction unbound (fu), volumes of distribution at steady-state (Vss), and mean residence time (MRT), corresponded to our assumption when protein-facilitated uptake was considered. Furthermore, a new empirical approach was introduced to allow practical use of the MWSM. The results showed that this model could provide a more precise prediction compared to previous empirical approaches. Therefore, these preliminary results not only delineated a more detailed structure and mechanism of MWSM but also highlighted its necessity and potential.

Effects of Diazepam on Hematological and Histological Parameters in Rats / in Vivo and Unbiased Stereological Investigation

Diazepam-based drugs are widely used today in human treatment. Diazepam may be a primary drug aimed at treating neurological diseases or an associated drug in the treatment of other diseases in the purpose of symptomatic therapy. The sedative effect of diazepam characterizes it as a drug that people usually use on their own and without a doctor’s supervision. Directly, but also through influencing the nervous system, diazepam disrupts proper functioning of all body organs. The purpose of this paper was to examine the effects of diazepam on blood and cytohistological parameters of rats in an in vivo experiment. Mallory-Azan and immunochistochemical staining methods BLX-CX and Survivin tissues of liver, kidney and spleen of rats were used to achieve the set goal. Cytometric analysis of rats detected cells in apoptosis and measurements of stereological parameters were made using a system according to Cavalier’s principle. Results of analysis of hematological and histological parameters indicate a detrimental effect of diazepam on blood parameters, as well as on structure and functioning of the liver, kidneys and spleen of rats. This paper is a foundation for further detailed scientific research with the aim of elucidating all harmful effects that diazepam has on all organs in the body of rats. This data could serve as a starting point for future studies in clinical pharmacology on therapeutic protocols for usage of diazepam-based sedatives.

Precisely adjusting the hepatic clearance of highly extracted drugs using the modified well-stirred model

Hepatic clearance has been widely studied for over 50 yr. Many models have been developed using either theoretical or empirical tests to predict drug metabolism. The well-stirred, parallel-tube, and dispersion metabolic models have been extensively discussed. However, to our knowledge, these models cannot fully describe all relevant scenarios in hepatic clearance. We addressed this issue using the isolated perfused rat liver technique with minor modifications. Diazepam was selected to illustrate different levels of drug plasma-protein binding by changing the added concentration of human serum albumin. The free fractions of diazepam at different albumin concentrations were assayed by rapid equilibrium dialysis. The experimental data provide new insights concerning an accepted formula used to describe hepatic clearance. Regarding drug concentrations passing through the liver, the driving force concentration (C_H,ss) in terms of C_in (influx in the liver) or C_out (efflux from the liver) needs to be carefully considered when determining drug hepatic and intrinsic clearances. The newly established model, termed the modified well-stirred model, which was derived from the original formula, successfully estimated hepatic drug metabolism. Using the modified well-stirred model, a theoretical driving force concentration of diazepam passing through the liver was evaluated. The model was further used to assess the predictability of in vitro to in vivo extrapolation. This study was not intended to refute the existing models, but rather to augment them using experimental data. The results stress the importance of proper calculation of dose when the drug clearance deviates from the prediction of the well-stirred model.

Are There Any Experimental Perfusion Data that Preferentially Support the Dispersion and Parallel-Tube Models over the Well-Stirred Model of Organ Elimination?

In reviewing previously published isolated perfused rat liver studies, we find no experimental data for high-clearance metabolized drugs that reasonably or unambiguously support preference for the dispersion and parallel-tube models versus the well-stirred model of organ elimination when only entering and exiting drug concentrations are available. It is likely that the investigators cited here may have been influenced by: 1) the unphysiologic aspects of the well-stirred model, which may have led them to undervalue the studies that directly test the various hepatic disposition models for high-clearance drugs (for which model differences are the greatest); 2) experimental assumptions made in the last century, which are no longer valid today, related to the predictability of in vivo outcomes from in vitro measures of drug elimination and the influence of albumin in hepatic drug uptake; and 3) a lack of critical review of previously reported experimental studies, resulting in inappropriate interpretation of the available experimental data. The number of papers investigating the theoretical aspects of the dispersion, parallel-tube, and well-stirred models of hepatic elimination greatly outnumber the papers that actually examine the experimental evidence available to substantiate these models. When all experimental studies that measure organ elimination using entering and exiting drug concentrations at steady state are critically reviewed, the simple but unphysiologic well-stirred model is the only model that can describe all trustworthy published available data. SIGNIFICANCE STATEMENT: Although the dispersion model of hepatic elimination more adequately reflects physiologic reality, there are no convincing experimental data that unambiguously favor this model. The well-stirred model can describe all well-designed perfusion studies with high-clearance drugs and nondrug substrates, but the field has not recognized this because of hesitation to accept a nonphysiologic model and flawed attempts to utilize in vitro-in vivo extrapolation approaches.