A paradigm shift in pharmacokinetic-pharmacodynamic (PKPD) modeling: rule of thumb for estimating free drug level in tissue compared with plasma to guide drug design

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.

Modeling Pharmacokinetic Natural Product-Drug Interactions for Decision-Making: A NaPDI Center Recommended Approach

The popularity of botanical and other purported medicinal natural products (NPs) continues to grow, especially among patients with chronic illnesses and patients managed on complex prescription drug regimens. With few exceptions, the risk of a given NP to precipitate a clinically significant pharmacokinetic NP-drug interaction (NPDI) remains understudied or unknown. Application of static or dynamic mathematical models to predict and/or simulate NPDIs can provide critical information about the potential clinical significance of these complex interactions. However, methods used to conduct such predictions or simulations are highly variable. Additionally, published reports using mathematical models to interrogate NPDIs are not always sufficiently detailed to ensure reproducibility. Consequently, guidelines are needed to inform the conduct and reporting of these modeling efforts. This recommended approach from the Center of Excellence for Natural Product Drug Interaction Research describes a systematic method for using mathematical models to interpret the interaction risk of NPs as precipitants of potential clinically significant pharmacokinetic NPDIs. A framework for developing and applying pharmacokinetic NPDI models is presented with the aim of promoting accuracy, reproducibility, and generalizability in the literature. SIGNIFICANCE STATEMENT: Many natural products (NPs) contain phytoconstituents that can increase or decrease systemic or tissue exposure to, and potentially the efficacy of, a pharmaceutical drug; however, no regulatory agency guidelines exist to assist in predicting the risk of these complex interactions. This recommended approach from a multi-institutional consortium designated by National Institutes of Health as the Center of Excellence for Natural Product Drug Interaction Research provides a framework for modeling pharmacokinetic NP-drug interactions.

Seeking Nonspecific Binding: Assessing the Reliability of Tissue Dilutions for Calculating Fraction Unbound

It has become commonplace (270+ article citations to date) to measure the fraction unbound (FrUn) of drugs in tissue homogenates and diluted plasma and then use a Correction Factor Equation (CFE) to extrapolate to the undiluted state. The CFE is based on assumptions of nonspecific binding with experimental use of very low drug concentrations. There are several possible determinants of apparent nonspecific binding as measured by methods such as equilibrium dialysis: true macromolecule binding and lipid partitioning along with receptor, enzyme, and transporter interactions. Theoretical calculations based on nonlinear protein binding indicate that the CFE will be most reliable to obtain FrUn when added drug concentration is small, binding constants are weak, protein concentrations are relatively high, and tissue dilution is minimal. When lipid partitioning is the sole factor determining apparent tissue binding, the CFE should be perfectly accurate. Use of very low drug concentrations, however, makes it more likely that specific binding to receptors and other targets may occur, and thus FrUn may reflect some binding to such components. Inclusion of trapped blood can clearly cause minor to marked discrepancies from purely tissue binding alone, which can be corrected. Furthermore, assessment of the occurrence of ionization/pH shifts, drug instability, and tissue metabolism may be necessary. Caution is needed in the use and interpretation of results from tissue dilution studies and other assessments of nonspecific binding, particularly for very strongly bound drugs with very small FrUn values and in tissues with metabolic enzymes, receptors, and trapped blood. SIGNIFICANCE STATEMENT: The use of tissue, plasma, and cell preparations to help obtain fraction unbound and tissue-to-plasma partition coefficients in pharmacokinetics has grown commonplace, especially for brain. This report examines theoretical, physiological, and experimental issues that need consideration before trusting such measurements and calculations.

Interpretation of Drug Interaction Using Systemic and Local Tissue Exposure Changes

Systemic exposure of a drug is generally associated with its pharmacodynamic (PD) effect (e.g., efficacy and toxicity). In this regard, the change in area under the plasma concentration-time curve (AUC) of a drug, representing its systemic exposure, has been mainly considered in evaluation of drug-drug interactions (DDIs). Besides the systemic exposure, the drug concentration in the tissues has emerged as a factor to alter the PD effects. In this review, the status of systemic exposure, and/or tissue exposure changes in DDIs, were discussed based on the recent reports dealing with transporters and/or metabolic enzymes mediating DDIs. Particularly, the tissue concentration in the intestine, liver and kidney were referred to as important factors of PK-based DDIs.

Variational Principle of Least Psychomotor Action: Modelling Effects on Action from Disturbances in Psychomotor Work Involving Human, Cyborg, and Robot Workers

Optimal psychomotor work can be expressed in terms of the principle of least psychomotor action (PLPA). Modelling psychomotor action encompasses modelling workers, work, and interactions between them that involve different types of situated entropy. Modelling of psychomotor workers encompasses three types of workers: human, cyborg, and robot. The type of worker and the type of work interact to affect positioning actions, performing actions, and perfecting actions undertaken in psychomotor tasks. There are often disturbances in psychomotor work, for example due to weather conditions, which have a determining influence on what work can be undertaken with least psychomotor action by different types of workers. In this paper, findings are reported from a study focused on the modelling disturbances in psychomotor work. Five contributions are provided. First, a heuristic framework for modelling disturbances and their effects is provided. In addition to PLPA and situated entropy, this framework encompasses Markov processes, the theory of perturbations, and calculus of variations. Second, formulae and ratios are provided for heuristic modelling of effects on internal action (S_int) from disturbances to psychomotor work. Third, formulae and ratios are provided for heuristic modelling of effects on external action (S_e). Fourth, examples are provided of heuristic modelling of disturbances in psychomotor work. Fifth, formulae and examples show how task complexity can be modelled heuristically in terms of microstates across the cyber domain and the physical domain of cyber-physical systems. Overall, the study reported in this paper addresses variational aspects of PLPA.

PKQuest: PBPK modeling of highly lipid soluble and extracellular solutes

One of the primary objectives of physiologically based pharmacokinetics (PBPK) is the prediction of a drug’s pharmacokinetics just from knowledge of its physicochemical structure. Unfortunately, at present, the accuracy of this prediction is limited for most drugs because of uncertainty about the drug’s organ/blood partition coefficient (K). However, there are two classes of solutes which are exceptions to this: 1) the highly lipid soluble (HLS) solutes, and 2) the extracellular (ECS) solutes. Since the HLS drugs (eg, volatile anesthetics, propofol, cannabinol) have lipid/water partition coefficients (P_L/W) of 100 or greater, their K is dominated by the tissue fat fraction and one can accurately predict K just from in vitro measurements of P_L/W along with prior anatomic measurements of the fat fraction of the organs in the PBPK model. Since the ECS drugs, such as most antibiotics, cannot penetrate cells, they are not subject to the intracellular binding that complicates the prediction of K for the weak bases and acids. The ECS K is determined primarily by plasma and interstitial albumin binding and can be predicted from in vitro measurements of plasma albumin binding along with prior measurements of interstitial tissue volume and albumin concentrations. This review provides an in depth discussion of the PBPK modeling of these two drug classes along with many specific clinical examples illustrating the good PBPK predictions possible with just zero (volatile anesthetics) or 1 (the clearance) adjustable parameter. The PBPK analysis uses PKQuest, a freely distributed, general purpose pharmacokinetic program. PKQuest is designed so that application to the HLS and ECS solute classes is especially easy. The user only needs to enter the specific parameters that are required to characterize the drug (eg, P_L/W for HLS or plasma albumin binding for ECS) with all the other PBPK parameters (organ blood flow, fat fraction, extracellular volumes, etc.) are set by default.

Integration of a plasma protein binding factor to the Chemical-Specific Adjustment Factor (CSAF) for facilitating the estimation of uncertainties in interspecies extrapolations when deriving health-based exposure limits for active pharmaceutical ingredients: Investigation of recent drug datasets

The objective was to challenge cross-species extrapolation factors with which to scale animal doses to human by any route for non-carcinogenic endpoints. The conventional hypothesis of the toxicokinetics (TK)-toxicodynamics (TD) relationship was equal toxicity at equal plasma level of the total drug moiety in each species, but this should also follow the free drug assumption, which states that only the unbound drug moiety in plasma may elicit a TD effect in tissue. Therefore, a protein binding factor (PBF) was combined with the Chemical-Specific Adjustment Factor (CSAF) (i.e., CSAF x PBF). The value of PBF of each drug was set equal to the ratio between human and animals of the unbound fraction in plasma (fu_p). Recent drug datasets were investigated. Our results indicate that any CSAF value would be increased or decreased while PBF deviates to the unity, and this required more attention. Accordingly, further testing indicated that the CSAF values set equal to basic allometric uncertainty factors according to the conventional hypothesis (dog∼2, monkey∼3.1, rat∼7, mouse∼12) would increase by including PBF for 30% of the drugs tested that showed a superior fu_p value in human compared to animals. However, default uncertainty factors in the range of 10-100 were less frequently exceeded. Overall, PBF could be combined with any other uncertainty factor to get reliable estimate of CSAF for each bound drug in deriving health-based exposure limits.

Revolutionizing Therapeutic Drug Monitoring with the Use of Interstitial Fluid and Microneedles Technology

While therapeutic drug monitoring (TDM) that uses blood as the biological matrix is the traditional gold standard, this practice may be impossible, impractical, or unethical for some patient populations (e.g., elderly, pediatric, anemic) and those with fragile veins. In the context of finding an alternative biological matrix for TDM, this manuscript will provide a qualitative review on: (1) the principles of TDM; (2) alternative matrices for TDM; (3) current evidence supporting the use of interstitial fluid (ISF) for TDM in clinical models; (4) the use of microneedle technologies, which is potentially minimally invasive and pain-free, for the collection of ISF; and (5) future directions. The current state of knowledge on the use of ISF for TDM in humans is still limited. A thorough literature review indicates that only a few drug classes have been investigated (i.e., anti-infectives, anticonvulsants, and miscellaneous other agents). Studies have successfully demonstrated techniques for ISF extraction from the skin but have failed to demonstrate commercial feasibility of ISF extraction followed by analysis of its content outside the ISF-collecting microneedle device. In contrast, microneedle-integrated biosensors built to extract ISF and perform the biomolecule analysis on-device, with a key feature of not needing to transfer ISF to a separate instrument, have yielded promising results that need to be validated in pre-clinical and clinical studies. The most promising applications for microneedle-integrated biosensors is continuous monitoring of biomolecules from the skin's ISF. Conducting TDM using ISF is at the stage where its clinical utility should be investigated. Based on the advancements described in the current review, the immediate future direction for this area of research is to establish the suitability of using ISF for TDM in human models for drugs that have been found suitable in pre-clinical experiments.

A physiologically based pharmacokinetic model of vitamin D

Despite the plethora of studies discussing the benefits of vitamin D on physiological functioning, few mathematical models of vitamin D predict the response of the body on low-concentration supplementation of vitamin D under sunlight-restricted conditions. This study developed a physiologically based pharmacokinetic (PBPK) model utilizing published human data on the metabolic cascade of orally derived, low-concentration (placebo, 5 μg and 10 μg) supplementation of vitamin D over the course of 28 days in the absence of sunlight. Vitamin D and its metabolites are highly lipophilic and binding assays of these compounds in serum may not account for binding by lipids and additional proteins. To compensate for the additional bound amounts, this study allowed the effective adipose-plasma partition coefficient to vary dynamically with the concentration of each compound in serum utilizing the Hill equation for binding. Through incorporating the optimized parameters with the adipose partition coefficient adaptation to the PBPK model, this study was able to fit serum concentration data for circulating vitamin D at all three supplementation concentrations within confidence intervals of the data. Copyright © 2017 John Wiley & Sons, Ltd.

Modeling Sex Differences in Pharmacokinetics, Pharmacodynamics, and Disease Progression Effects of Naproxen in Rats with Collagen-Induced Arthritis

Naproxen (NPX) is a frequently used nonsteroidal anti-inflammatory drug for rheumatoid arthritis (RA). Lack of quantitative information about the drug exposure-response relationship has resulted in empirical dosage regimens for use of NPX in RA. Few studies to date have included sex as a factor, although RA predominates in women. A pharmacokinetic, pharmacodynamic, and disease progression model described the anti-inflammatory effects of NPX in collagen-induced arthritic (CIA) male and female rats. Three groups of rats were included for each sex: healthy animals, CIA controls, and CIA rats given a single 50-mg/kg dose of NPX intraperitoneally. Paw volumes of healthy rats indicated natural growth, and disease status was measured by paw edema. An innovative minimal physiologically based pharmacokinetic (mPBPK) model incorporating nonlinear albumin binding of NPX in both plasma and interstitial fluid (ISF) was applied. Arthritic rats exhibited lower plasma and ISF albumin concentrations and reduced clearances of unbound drug to explain pharmacokinetic profiles. The unbound ISF NPX concentrations predicted by the mPBPK model were used as the driving force for pharmacological effects of NPX. A logistic growth function accounting for natural paw growth and an indirect response model for paw edema and drug effects (inhibition of k_in) was applied. Female rats showed a higher incidence of CIA, earlier disease onset, and more severe symptoms. NPX had stronger effects in males, owing to higher unbound ISF NPX concentrations and lower IC₅₀ values. The model described the pharmacokinetics, unbound NPX in ISF, time course of anti-inflammatory effects, and sex differences in CIA rats.

Specific Inhibition of the Distribution of Lobeglitazone to the Liver by Atorvastatin in Rats: Evidence for a Rat Organic Anion Transporting Polypeptide 1B2-Mediated Interaction in Hepatic Transport

Cytochrome P450 enzymes and human organic anion transporting polypeptide (OATP) 1B1 are reported to be involved in the pharmacokinetics of lobeglitazone (LB), a new peroxisome proliferator-activated receptor γ agonist. Atorvastatin (ATV), a substrate for CYP3A and human OATP1B1, is likely to be coadministered with LB in patients with the metabolic syndrome. We report herein on a study of potential interactions between LB and ATV in rats. When LB was administered intravenously with ATV, the systemic clearance and volume of distribution at steady state for LB remained unchanged (2.67 ± 0.63 ml/min per kg and 289 ± 20 ml/kg, respectively), compared with that of LB without ATV (2.34 ± 0.37 ml/min per kg and 271 ± 20 ml/kg, respectively). Although the tissue-to-plasma partition coefficient (K_p) of LB was not affected by ATV in most major tissues, the liver K_p for LB was decreased by ATV coadministration. Steady-state liver K_p values for three levels of LB were significantly decreased as a result of ATV coadministration. LB uptake was inhibited by ATV in rat OATP1B2-overexpressing Madin-Darby canine kidney cells and in isolated rat hepatocytes in vitro. After incorporating the kinetic parameters for the in vitro studies into a physiologically based pharmacokinetics model, the characteristics of LB distribution to the liver were consistent with the findings of the in vivo study. It thus appears that the distribution of LB to the liver is mediated by the hepatic uptake of transporters such as rat OATP1B2, and carrier-mediated transport is involved in the liver-specific drug-drug interaction between LB and ATV in vivo.

The Role of Extracellular Binding Proteins in the Cellular Uptake of Drugs: Impact on Quantitative In Vitro-to-In Vivo Extrapolations of Toxicity and Efficacy in Physiologically Based Pharmacokinetic-Pharmacodynamic Research

A critical component in the development of physiologically based pharmacokinetic-pharmacodynamic (PBPK/PD) models for estimating target organ dosimetry in pharmacology and toxicology studies is the understanding of the uptake kinetics and accumulation of drugs and chemicals at the cellular level. Therefore, predicting free drug concentrations in intracellular fluid will contribute to our understanding of concentrations at the site of action in cells in PBPK/PD research. Some investigators believe that uptake of drugs in cells is solely driven by the unbound fraction; conversely, others argue that the protein-bound fraction contributes a significant portion of the total amount delivered to cells. Accordingly, the current literature suggests the existence of a so-called albumin-mediated uptake mechanism(s) for the protein-bound fraction (i.e., extracellular protein-facilitated uptake mechanisms) at least in hepatocytes and cardiac myocytes; however, such mechanism(s) and cells from other organs deserve further exploration. Therefore, the main objective of this present study was to discuss further the implication of potential protein-facilitated uptake mechanism(s) on drug distribution in cells under in vivo conditions. The interplay between the protein-facilitated uptake mechanism(s) and the effects of a pH gradient, metabolism, transport, and permeation limitation potentially occurring in cells was also discussed, as this should violate the basic assumption on similar free drug concentration in cells and plasma. This was made because the published equations used to calculate drug concentrations in cells in a PBPK/PD model did not consider potential protein-facilitated uptake mechanism(s). Consequently, we corrected some published equations for calculating the free drug concentrations in cells compared with plasma in PBPK/PD modeling studies, and we proposed a refined strategy for potentially performing more accurate quantitative in vitro-to-in vivo extrapolations (IVIVEs) of toxicity (efficacy) at the cellular level from data generated in cell assays. Overall, this present study may help to optimize the human dose prediction in preclinical and clinical studies, while prescribing drugs with narrow therapeutic windows that are highly bound to extracellular proteins and/or highly ionized at the physiological pH. This may facilitate building a more accurate safety (efficacy) profile for such drugs.

Physiologically Based Pharmacokinetic (PBPK) Modeling and Simulation Approaches: A Systematic Review of Published Models, Applications, and Model Verification

Modeling and simulation of drug disposition has emerged as an important tool in drug development, clinical study design and regulatory review, and the number of physiologically based pharmacokinetic (PBPK) modeling related publications and regulatory submissions have risen dramatically in recent years. However, the extent of use of PBPK modeling by researchers, and the public availability of models has not been systematically evaluated. This review evaluates PBPK-related publications to 1) identify the common applications of PBPK modeling; 2) determine ways in which models are developed; 3) establish how model quality is assessed; and 4) provide a list of publically available PBPK models for sensitive P450 and transporter substrates as well as selective inhibitors and inducers. PubMed searches were conducted using the terms "PBPK" and "physiologically based pharmacokinetic model" to collect published models. Only papers on PBPK modeling of pharmaceutical agents in humans published in English between 2008 and May 2015 were reviewed. A total of 366 PBPK-related articles met the search criteria, with the number of articles published per year rising steadily. Published models were most commonly used for drug-drug interaction predictions (28%), followed by interindividual variability and general clinical pharmacokinetic predictions (23%), formulation or absorption modeling (12%), and predicting age-related changes in pharmacokinetics and disposition (10%). In total, 106 models of sensitive substrates, inhibitors, and inducers were identified. An in-depth analysis of the model development and verification revealed a lack of consistency in model development and quality assessment practices, demonstrating a need for development of best-practice guidelines.