Multiple‐compartment and Non‐compartment Pharmacokinetic Models

Radiopharmaceuticals are considered highly valuable for diagnosis and therapy of several types of cancers. Radiopharmaceuticals currently used for neuroendocrine tumors (NETs) and prostate cancer are applied in a theranostic approach. This approach comprises the use of comparable tumor targeted radiopharmaceuticals for both diagnosis and therapy, which is achieved by using peptides labeled with different radionuclides that determine whether the radiopharmaceutical is used for therapeutic or diagnostic purposes. This theranostic aspect of radionuclide therapies advocates for applying precision medicine to improve these therapies, which can be accomplished by using pharmacometric approaches. Pharmacometric approaches are a proven and often applied mathematical tool to study the absorption, distribution, metabolism and excretion of drugs. Such pharmacokinetic (PK) modelling and simulation applications are regularly used for development and clinical research of nonradioactive drugs. Although these approaches also have a potential benefit in improving the evolving research regarding radiopharmaceuticals, its use for radiopharmaceuticals is surprisingly limited. To evolve theranostic agents towards patient-centered precision medicine, PK modelling and simulation approaches should be regularly applied to radiopharmaceuticals similar to nonradioactive drugs. By applying these pharmacometric approaches, this thesis focused on gaining a better understanding of PK of several theranostic agents. Part I introduced two PK modelling approaches, namely population PK models and physiologically based pharmacokinetic (PBPK) models. The relevance of PK modelling for radiopharmaceuticals and its great potential for the nearby future was underlined, which was the central thread of this thesis. Part II focused on improving the application of theranostic agents in patients with advanced stage NETs (Gallium-68 (68Ga) labeled to DOTATATE or HA-DOTATATE for diagnosis and Lutetium-177 (177Lu) labeled to HA-DOTATATE for therapy). In five chapters, we identified factors that impact biodistribution of several compounds, assessed the effect of different peptide doses on tumor and organ accumulation (to reveal potential receptor saturation), predicted therapeutic uptake based on single time point pre-treatment imaging and quantified a cycle effect (i.e. uptake in tumors reduced over treatment cycles) for [177Lu]Lu-HA-DOTATATE . In Part III, all chapters contributed to improve the use of theranostic agents for prostate cancer (68Ga labeled to the prostate specific membrane antigen (PSMA) ligand for diagnostic imaging and 177Lu labeled to PSMA for therapy). In four chapters, we assessed the effect of peptide amount on tumor accumulation, investigated the effect of folates on [68Ga]Ga-PSMA-11 accumulation, described population PK and identified relatively minor inter-individual variability for [177Lu]Lu-PSMA-617 and developed a PK/PD model for [177Lu]Lu-PSMA-I&T to describe individual biochemical prostate-specific antigen response after therapy. In summary, this thesis described the use of pharmacometric approaches and data analyses to optimize theranostic applications for NETs and prostate cancer. Nuclear imaging data were successfully used to develop and evaluate different PK models of several radiopharmaceuticals. In addition, this thesis pointed out that pharmacometric approaches are a useful approach to answer many remaining questions in nuclear medicine research. Therefore, the time is ripe to start applying pharmacometric approaches to radiopharmaceuticals on a regular basis, similar to its use in drug development and clinical research of nonradioactive drugs.

Obese patients with sepsis or septic shock may have altered vancomycin pharmacokinetics compared with the general population that may result in improper dosing or inadequate drug concentrations. The objective of this study was to characterize vancomycin pharmacokinetics in obese patients with sepsis or septic shock, and to develop a novel pharmacokinetic dosing model based on pharmacokinetic-pharmacodynamic target requirements. Prospective observational pharmacokinetic study. Large quaternary academic medical center. Sixteen obese (body mass index [BMI] 30kg/m2 or higher) adults with sepsis and either a gram-positive bacteremia or requiring vasopressor support (septic shock), who were receiving vancomycin between November 2016 and June 2018, were included. Patients were excluded if they were receiving renal replacement therapy or extracorporeal membrane oxygenation, treatment for central nervous system infections, pregnant, or receiving vancomycin for surgical prophylaxis. Four blood samples per patient were collected following a single dose of vancomycin: one peak serum vancomycin level (within 1-2hrs of infusion completion), two random levels during the dosing interval, and one trough level (within 30-60min of the next dose) were measured. A population pharmacokinetic model was developed to describe vancomycin concentrations over time. Simulations to determine optimal dosing were performed using the pharmacokinetic model with different ranges of creatinine clearance (Clcr ) and different vancomycin daily doses. Median age of the patients was 62years; median BMI was 36.1kg/m2 , Acute Physiology and Chronic Health Evaluation II score was 26, and Sequential Organ Failure Assessment score was 11. Eleven patients (69%) had an acute kidney injury. Median initial vancomycin dose was 15mg/kg; median vancomycin trough concentration was 17mg/L. A one-compartment model best characterized the pharmacokinetics of vancomycin in obese patients with sepsis or septic shock. Volume of distribution was slightly increased in this population (0.8L/kg) compared with the general population (0.7L/kg). Only Clcr effect on drug clearance was found to be significant (decrease in the objective function value by 16.4 points), confirming that it is a strong predictor of vancomycin clearance. To our knowledge, this study provides the first population-based pharmacokinetic model in obese patients with sepsis or septic shock. The nomograms generated from this pharmacokinetic model provide a simplified approach to vancomycin dosing in this patient population.

Therapeutic drug monitoring (TDM) of busulfan (Bu) is well-established in pediatric hematopoietic stem cell transplantation (HSCT), but its use in adults is limited due to a lack of clear recommendations and scarcity of evidence regarding its utility. GSTA1 promoter variants are reported to affect Bu clearance in both adults and pediatric patients. This study aimed to evaluate the value of preemptive genotyping GSTA1 and body composition (obesity) in individualizing Bu dosing in adults, through pharmacokinetic (PK) modeling and simulations. A population pharmacokinetic (PopPK) model was developed and validated with data from 60 adults who underwent HSCT. Simulations assessed different dosing scenarios based on body size metrics and GSTA1 genotypes. Due to the limited number of obese patients in the cohort, the effect of obesity on Bu pharmacokinetics (PK) was evaluated in silico using a physiologically-based pharmacokinetic (PBPK) model and relevant virtual populations from Simcyp software. Patients with at least 1 GSTA1*B haplotype had 17% lower clearance on average. PopPK simulations indicated that adjusting doses based on genotype increased the probability of achieving the target exposure (3.7 to 5.5 mg.h/L) from 53% to 60 % in GSTA1*A homozygous patients, and from 50% to 61% in *B carriers. Still, Approximately 40% of patients would not achieve this therapeutic window without TDM. A 2-sample optimal design was validated for routine model-based Bu first dose AUC0-∞ estimation, and the model was implemented in the Tucuxi user-friendly TDM software. PBPK simulations confirmed body surface area-based doses of 29 to 31 mg/m2/6h as the most appropriate, regardless of obesity status. This study emphasizes the importance of individualized Bu dosing strategies in adults to achieve therapeutic targets. Preemptive genotyping alone may not have a significant clinical impact, and routine TDM may be necessary for optimal transplantation outcomes.

This paper presents a three-dimensional (3D) tumor spheroid chip where the pharmacokinetic (PK) drug elimination model is developed by balanced droplet dispensing. The PK model should reflect the exponential decrease of drug concentration in a body to improve the reliability of cell-based screening assay. The previous cell chips, however, maintain the concentration of anti-cancer agents at constant or discretely decrease the concentration level by manual process. In the present chip where medium droplet dispensers are integrated on a well array, the small droplets of fresh medium and well waste are autonomously replaced each other, the exponential elimination of drug concentration in the well is provided. In the experimental study, we demonstrated that the present chip successfully develops the exponential elimination model using fluorescein isothiocyanate (FITC) and cisplatin. Although the exponential decay of cisplatin in the present chip did not show significant effect biologically due to the current protocol where 3 days of constant concentration pre-treatment is performed, we observed different growth pattern of H358 spheroids depending on peak concentration of 0, 1, 10, and 100 μM. The present chip has potential for analyzing the response of 3D tumor spheroids in the pharmacokinetically relevant drug elimination model for high-reliability spheroid-based drug screening chip.

Understanding the impact of altered hepatic uptake and/or efflux on the hepatobiliary disposition of the imaging agents [99mTc]Mebrofenin (MEB) and [153Gd]Gadobenate dimeglumine (BOPTA) is important for proper estimation of liver function. A multi-compartmental pharmacokinetic (PK) model describing MEB and BOPTA disposition in isolated perfused rat livers (IPRLs) was developed. The PK model was simultaneously fit to MEB and BOPTA concentration-time data in the extracellular space, hepatocytes, bile canaliculi, and sinusoidal efflux in livers from healthy rats, and to BOPTA concentration-time data in rats pretreated with monocrotaline (MCT). The model adequately described MEB and BOPTA disposition in each compartment. The hepatocyte uptake clearance was much higher for MEB (55.3mL/min) than BOPTA (6.67mL/min), whereas the sinusoidal efflux clearance for MEB (0.000831mL/min) was lower than BOPTA (0.0127mL/min). The clearance from hepatocytes to bile (CLbc) for MEB (0.658mL/min) was similar to BOPTA (0.642mL/min) in healthy rat livers. The BOPTA CLbc was reduced in livers from MCT-pretreated rats (0.496mL/min), while the sinusoidal efflux clearancewas increased (0.0644mL/min). A PK model developed to characterize MEB and BOPTA disposition in IPRLs was used to quantify changes in the hepatobiliary disposition of BOPTA caused by MCT pretreatment of rats to induce liver toxicity. This PK model could be applied to simulate changes in the hepatobiliary disposition of these imaging agents in rats in response to altered hepatocyte uptake or efflux associated with disease, toxicity, or drug-drug interactions.

Linking biomarker data to pharmacokinetic (PK) models permits comparison of absorbed dose with a toxicological benchmark, which is an important step to understanding the health implications of pesticide exposure. The purpose of this analysis was to evaluate the feasibility of reconstructing the absorbed dose of two pesticides using PK models developed from biomarker data in a study of occupational application of these compounds. Twenty-four-hour urine samples were collected from farmers 24 h before through 96 h after a typical application of chlorpyrifos or 2,4-D. PK models were used to link the amounts found in urine samples to absorbed dose. Modeled total body dose estimates (in micrograms) were compared to measured dose from time 0–96 h. Despite the complexities surrounding the interpretation of biomonitoring data from a field setting, the models developed as part of this analysis accurately estimated the absorbed dose of 2,4-D and chlorpyrifos when collection of urine samples was largely complete. Over half of the farmers were excluded from modeling due to suspected noncompliance with urine collection or confounding exposure events, which highlights the importance of these issues for designing and interpreting biomonitoring data in future studies. Further evaluation of PK models in scenarios using single void samples is warranted for improving field-based dose assessments.

In vivo bioluminescence imaging (BLI) is a promising tool for monitoring the growth and metastasis of tumors. However, quantitative BLI research based on intravenous (IV) injection is limited, which greatly restricts its further application. To address this problem, we designed a pharmacokinetic (PK) model which is suitable for applying on IV administration of small amounts of D-Luciferin. After three weeks of postimplantation, mkn28-luc xenografted mice were subjected to 40-min dynamic BLI immediately following D-Luciferin intravenous injection on days 1, 3, 5, 7, and 9. Furthermore, the PK model was applied on dynamic BLI data to obtain the sum of kinetic rate constants (SKRC). Results showed that the SKRC values decreased rapidly with the growth of the tumor. There was a statistical difference between the SKRC values measured at different time points, while the time point of luminous intensity peak was unaffected by the growth of the tumor. In short, our results imply that dynamic BLI combined with our PK model can predict tumor growth earlier and with higher sensitivity compared to the conventional method, which is crucial for improving drug evaluation efficacy. In addition, the dynamic BLI may provide a valuable reference for the noninvasive acquiring arterial input function, which may also provide a new application prospect for hybrid PET-optical imaging.

We explore use of "bootstrapping" methods to obtain a measure of reliability of predictions made in part from fits of individual drug level data with a pharmacokinetic (PK) model, and to help clarify parameter identifiability for such models. Simulation studies use four sets (A-D) of drug concentration data obtained following a single oral dose. Each set is fit with a two compartment PK model, and the "bootstrap" is employed to examine the potential predictive variation in estimates of parameter sets. This yields an empirical distribution of plausible steady state (SS) drug concentration predictions that can be used to form a confidence interval for a prediction. A distinct, narrow confidence region in parameter space is identified for subjects A and B. The bootstrapped sets have a relatively large coefficient of variation (CV) (35-90% for A), yet the corresponding SS drug levels are tightly clustered (CVs only 2-9%). The results for C and D are dramatically different. The CVs for both the parameters and predicted drug levels are larger by a factor of 5 and more. The results reveal that the original data for C and D, but not A and B, can be represented by at least two different PK model manifestations, yet only one provides reliable predictions. The insights gained can facilitate making decisions about parameter identifiability. In particular, the results for C and D have important implications for the degree of implicit overparameterization that may exist in the PK model. In cases where the data support only a single model manifestation, the "bootstrap" method provides information needed to form a confidence interval for a prediction.

BackgroundResearchers have long been interested in the potential drug–drug interactions (DDIs) between opioids and benzodiazepines. However, much remains unknown concerning the interactions between these two drug classes. The objective of this work is to study the mechanism underlying the DDIs between opioids and benzodiazepines from the perspective of their pharmacokinetic (PK) interactions. A PK interaction occurs when two drugs are metabolized by the same cytochrome P450 enzymes and is one of the most common reasons for DDIs.MethodsWe quantitatively predicted the DDIs between three opioids (fentanyl, oxycodone and buprenorphine) and four benzodiazepines (alprazolam, diazepam, midazolam and triazolam) using a physiologically based pharmacokinetic (PBPK) modeling approach. A set of PBPK models was first constructed for these common opioids and benzodiazepines using SimCYP software, and the DDIs between them were then explored at various dosages.ResultsOur simulation results suggested there were no PK interactions between normal doses of opioids and benzodiazepines; but weak interactions can be expected with the combination of opioids and overdosed benzodiazepines. Particular attention should be given to the combination of fentanyl and overdosed alprazolam since a PK interaction can be observed between them.ConclusionOur results appear to indicate that pharmacodynamics may play a more important role than PKs in causing DDIs between opioids and benzodiazepines. This study also demonstrated that molecular modeling can be a very useful tool to mitigate the problem of “missing metabolic reaction parameters” in PK modeling and simulation.Electronic supplementary materialThe online version of this article (10.1007/s40268-019-00282-3) contains supplementary material, which is available to authorized users.

Lipophilic persistent environmental chemicals (LPECs) can accumulate in a woman's body and transfer to her developing child across the placenta and via breast milk. To assess health risks associated with developmental exposures to LPECs, we developed a pharmacokinetic (PK) model that quantifies mother-to-offspring transfer of LPECs during pregnancy and lactation and facilitates internal dosimetry calculations for offspring. We parameterized the model for mice, rats, and humans using time-varying functions for body mass and milk consumption rates. The only required substance-specific parameter is the elimination half-life of the LPEC in the animal species of interest. We used the model to estimate whole-body concentrations in mothers and offspring following maternal exposures to hexachlorobenzene (HCB) and 2,2',4,4',5,5'-hexachlorobiphenyl (PCB 153) and compared these with measured concentrations from animal studies. We also compared estimated concentrations for humans to those generated using a previously published human LPEC PK model. Finally, we compared human equivalent doses (HEDs) calculated using our model and an allometric scaling method. Estimated and observed whole-body concentrations of HCB and PCB 153 in offspring followed similar trends and differed by less than 60%. Simulations of human exposure yielded concentration estimates comparable to those generated using the previously published model, with concentrations in offspring differing by less than 12%. HEDs calculated using our PK model were about 2 orders of magnitude lower than those generated using allometric scaling. Our PK model can be used to calculate internal dose metrics for offspring and corresponding HEDs and thus informs assessment of developmental toxicity risks associated with LPECs.

Previously, we performed population pharmacokinetic analysis and indicated age, mycophenolate mofetil (MMF)/mycophenolic acid (MPA) daily dose, and presence of nifedipine in patient therapy as significant predictors of MPA apparent clearance (CL/F) variability. This study aimed to determine the reliability of previously published population pharmacokinetic models derived from similar studies. Furthermore, this study investigated correspondence between chosen population models from the literature. By means of the Monte Carlo simulation method, pharmacokinetic models from different studies are simulated and analysed in the range of standard deviations of measured system parameters as well as the range of observed model parameters taken from the comparison studies. The 1000 numerical simulations were performed for every analysed model in order to calculate the most possible MPA CL/F values according to the expected values from the performed experiment. Fitting our results with other models showed how the presence of nifedipine makes difference in MPA CL/F values. By testing the data from selected studies into our model, a similar range of expected CL/F values was obtained, which may confirm the validity of our model. The results of our population pharmacokinetic study are partially applicable in models by other researchers.

Food can influence drug bioavailability by altering gut physiology and microenvironment. Conventional approaches such as dissolution testing and biopharmaceutics classification system (BCS) often fail to predict food effect on drug bioavailability. To address this, we proposed a mechanistic BCS (mBCS) (Figure 1) based on analysing literature data. The mBCS first classifies drugs based on if their absorption is solubility‐limited (Class I) or permeability‐limited (Class II), which are sub‐grouped based on if the food effect is predictable (IA and IIA) or not predictable (IB, IC, IIB and IIC) using the dissolution testing (Figure 1A). Finally, mBCS allows identifying the mechanisms that lead to unpredictable food‐effect on drug bioavailability. Particularly, out of 288 drugs where the food‐effect data were reported, 105 drugs exhibited negative food effect. Further evaluation suggested that the primary reason for the unpredictable negative food effect is the interplay of intestinal efflux transport and delayed gastric emptying (Figure 1B). For example, amongst all drugs that showed negative food effect, majority (58%) were substrates of GI efflux transporters (e.g., maraviroc, afatinib, furosemide, ixazomib, asciminib, and omadacycline). We thus hypothesized that since gastric emptying time in fed state is higher (>2 h) as compared to the fasting state (15 min), drug co‐administration with food results in decreased concentration gradient across intestinal wall (lumen to blood), which eventually causes desaturation of GI efflux transporters. To test this hypothesis, we developed an mBCS‐guided physiologically based pharmacokinetic (PBPK) model in MATLAB (MathWorks, Natick, MA) by incorporating the regional protein abundance and saturation kinetics (Km and Vmax) of selected drugs (maraviroc, afatinib, and furosemide). The results from maraviroc PBPK modeling are presented below. The model was successful in predicting non‐linear PK within 2‐fold at varied dose ranges (e.g., 0.5, 0.61, 0.88, 1.17, 1.07 and 1.02 folds for 30, 100, 300, 600, 900 and 1200 mg, respectively for maraviroc) in the fasted state. The model successfully captured ~37% reduction in AUC in fed state at lower clinical doses of 100 and 300 mg of maraviroc. Similarly, consistent with the observed clinical data 1, the predicted magnitude of negative food effect was significantly lower (~22 and 18% reduction in AUC) at higher doses of 900 and 1200 mg, respectively. Parameter sensitivity analysis showed that gastric emptying time and kinetic parameters of P‐gp are important mechanisms that regulate non‐linear PK and food effect for maraviroc. Therefore, the proposed mBCS‐guided PBPK modeling approach can be used for prospective prediction of negative food effect, which can also be used to justify clinical trial waiver for the food effect studies.Support or Funding InformationDepartment of Pharmaceutical Sciences, Washington State University, SpokaneMechanistic biopharmaceutics classification system (mBCS) framework (A) and proposed mechanism of interplay between GI efflux and gastric emptying in fasting and fed states for mBCS class‐IIC drugs (B).Figure 1

Diltiazem is a benzothiazepine calcium blocker and widely used in renal transplant patients since it improves the level of tacrolimus or cyclosporine A concentration. Several population pharmacokinetic (PopPK) models had been established for cyclosporine A and tacrolimus but no specific PopPK model was established for diltiazem. The aim of the study is to develop a PopPK model for diltiazem in renal transplant recipients and provide relevant pharmacokinetic parameters of diltiazem for further pharmacokinetic interaction study. Patients received tacrolimus as primary immunosuppressant agent after renal transplant and started administration of diltiazem 90mg twice daily on 5th day. The concentration of diltiazem at 0, 0.5, 1, 2, 8, and 12h was measured by high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). Genotyping for CYP3A4*1G, CYP3A5*3, and MDR1 3435 was conducted by polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). 25 covariates were considered in the stepwise covariate model (SCM) building procedure. One-compartment structural pharmacokinetic model with first-order absorption and elimination was used to describe the pharmacokinetic characteristics of diltiazem. Total bilirubin (TBIL) influenced apparent volume of distribution (V/F) of diltiazem in the forward selection. The absorption rate constant (K a), V/F, and apparent oral clearance (CL/F) of the final population pharmacokinetic (PopPK) model of diltiazem were 1.96/h, 3550 L, and 92.4 L/h, respectively. A PopPK model of diltiazem is established in Chinese renal transplant recipients and it will provide relevant pharmacokinetic parameters of diltiazem for further pharmacokinetic interaction study.

Plasma concentrations of acetaminophen, its glucuronide and sulfate conjugates, and cysteinyl acetaminophen were experimentally determined after oral administrations of 10 mg/kg in humanised-liver mice, control mice, rats, common marmosets, cynomolgus monkeys, and minipigs; the results were compared with reported human pharmacokinetic data. Among the animals tested, only rats predominantly converted acetaminophen to sulfate conjugates, rather than glucuronide conjugates. In contrast, the values of area under the plasma concentration curves of acetaminophen, its glucuronide and sulfate conjugates, and cysteinyl acetaminophen after oral administration of acetaminophen in marmosets and minipigs were consistent with those reported in humans under the present conditions. Physiologically based pharmacokinetic (PBPK) models (consisting of the gut, liver, and central compartments) for acetaminophen and its primary metabolite could reproduce and estimate, respectively, the plasma and hepatic concentrations of acetaminophen in experimental animals and humans after single virtual oral doses. The values of area under the curves of hepatic concentrations of acetaminophen estimated using PBPK models were correlated with the measured levels of cysteinyl acetaminophen (a deactivated metabolite) in plasma fractions in these species. Consequently, using simple PBPK models and plasma data to predict hepatic chemical concentrations after oral doses could be helpful as an indicator of in vivo possible hepatotoxicity of chemicals such as acetaminophen.

Positron Emission Tomography (PET) with pharmacokinetic (PK) modelling is a quantitative molecular imaging technique, however the long data acquisition time is prohibitive in clinical practice. An approach has been proposed to incorporate blood flow information from Arterial Spin Labelling (ASL) Magnetic Resonance Imaging (MRI) into PET PK modelling to reduce the acquisition time. This requires the conversion of cerebral blood flow (CBF) maps, measured by ASL, into the relative tracer delivery parameter (\(R_1\)) used in the PET PK model. This was performed regionally using linear regression between population \(R_1\) and ASL values. In this paper we propose a novel technique to synthesise \(R_1\) maps from ASL data using a database with both \(R_1\) and CBF maps. The local similarity between the candidate ASL image and those in the database is used to weight the propagation of \(R_1\) values to obtain the optimal patient specific \(R_1\) map. Structural MRI data is also included to provide information within common regions of artefact in ASL data. This methodology is compared to the linear regression technique using leave one out analysis on 32 subjects. The proposed method significantly improves regional \(R_1\) estimation (\(p<0.001\)), reducing the error in the pharmacokinetic modelling. Furthermore, it allows this technique to be extended to a voxel level, increasing the clinical utility of the images.