Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty.

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.

Making pharmacokinetics useful

Measurement of Therapeutic Agents in Blood

In this paper, compartmental pharmacokinetic models are built to predict the concentration of toxic phytochemical in the gastrointestinal tract and blood following oral intake by an individual vertebrate herbivore. The existing single and multiple dose pharmacokinetic models are extended by inclusion of impulsive differential equations which account for an excretion factor whereby unchanged toxins are excreted in the feces due to gastrointestinal mobility. An index α is defined to measure the fraction of bioavailability attributed to the excretion factor of gastrointestinal motility. Sensitivity analysis was conducted and suggests, for any toxin, the bioavailability index α depends mostly on absorption rate of toxin from gastrointestinal tract into the blood, frequency of elimination due to gastrointestinal motility, and the frequency of toxin intake, under the model assumptions.

Reports characterizing the pharmacokinetics of inhaled fluticasone propionate (FP) using compartmental approaches have suggested that the absorption of FP into the systemic circulation is rapid with a half-life of approximately 10 min. We believe that this is a classical case of misassignment of the pharmacokinetic parameter estimates, a problem often encountered while modeling pharmacokinetic data. The objective of this study was to illustrate and analyze this problem using actual blood level data of FP obtained in 14 healthy subjects. Serum concentration-time data of FP were obtained from a double-blind, randomized study involving single and multiple twice-daily inhalations of 500 microg via a dry powder device, Diskus. The profiles were fitted using one- and two-compartment pharmacokinetic models with first order absorption. Various permutations of the resulting exponential rate constants were analyzed to determine the combination that was most consistent with the underlying physical process. The two-compartment body model with first order absorption gave excellent fits for the observed FP concentrations after both single and multiple dosing. Even though peak levels were reached relatively early (30 - 90 min) after inhalation, the combination that most appropriately described the underlying process was alpha > Ka > beta, i.e. slow absorption, rapid distribution and slower elimination kinetics. The absorption, distribution and elimination half-lives resulted to be 3.8 h, 9.9 min and 13.6 h, respectively, consistent with the high lipophilicity and sustained dissolution characteristics observed in vitro. Analysis of FP pharmacokinetics after inhalation represents a classical case of potential misassignment of the exponential rate constants, which if ignored, could lead to erroneous interpretations regarding the underlying process. The study also elucidates the pitfall of using t(max) to calculate absorption rate.

Exemestane (Aromasin) is an irreversible aromatase inactivator used for the treatment of postmenopausal women with advanced breast cancer. The objective of this study was to evaluate the effect of formulation comparing a sugar-coated tablet (SCT) with a suspension and food on the pharmacokinetics (PK) and pharmacodynamics (PD) with respect to plasma estrone sulphate (E1S) concentrations of exemestane, using a PK/PD approach. This was an open, three-period, randomized, crossover study. Twelve healthy postmenopausal women received single oral doses of 25 mg exemestane as a SCT after fasting or food and as a suspension after fasting. Exemestane and E1S concentrations were determined before and up to 14 days after drug administration. Population analysis was performed in two steps: (i) a compartmental PK model was selected incorporating the effect of food and formulation; (ii) conditional on the PK model, a PD model was developed employing indirect response models. Model selection was performed using standard statistical tests. Validation and assessment of the predictive capability of the selected model was performed using real test data sets obtained from the literature. A three-compartment model with first-order elimination rate best described exemestane disposition (k12 0.454, k21 0.158, k13 0.174, k31 0.016 and k 0.738 h(-1)). Absorption was described by a mono-exponential function [ka 2.3 (SCT after fasting), 1.1 (SCT after food) and 7.6 h(-1) (suspension); lag time 0.2 h]. The PD model assumed that E1S plasma concentrations are determined by a zero-order synthesis rate (6.5 pg ml(-1) h(-1)) and a first-order elimination constant (0.032 h(-1)). Exemestane inhibited E1S synthesis with a C50 value of 22.1 pg ml(-1). The mean population estimates were used to simulate the administration of different doses of the drug (0.5, 1, 2.5, 5 and 25 mg day(-1)). The model predictions were in agreement with historical data. Exemestane absorption is influenced by the formulation of the drug and by food, but its disposition is independent of both. PK differences do no translate into clinically important differences in the PD. The PK/PD model developed was able to predict successfully the response to different doses and administration schedules with respect to oestrogen suppression.

In pharmacokinetics, compartment models often play an important role in the description of the concentration of the drug in the blood over time after its administration to an individual. Statistical inference in these models can be conducted based on a linear approximation with respect to the parameter related to pharmacokinetic indices, in the same way that the usual nonlinear regression models are dealt with. Therefore, it is necessary to assess the degree of nonlinearity in a compartment model and to evaluate its effect on the linear approximation. The relative curvature measure that enables us to assess the intrinsic and parameter-effects (PE) nonlinearity can be used, but in practice it has not been applied to compartment models in pharmacokinetics. One reason may be that the relative curvature measure cannot be directly applied to blood drug concentration data that exhibit heteroscedasticity. Therefore, the relative curvature measure including the heteroscedastic variance function was utilized to assess the nonlinearity in the compartment models, and in particular, the influences of some of the reparameterizations that are empirically used in fitting the compartment models were examined. Several examples showed that the reparameterized compartment model had less PE nonlinearity than the original compartment model, but that several reparameterizations could increase the PE nonlinearity. In addition, by means of a simulation experiment with heteroscedastic blood drug concentration data, the accuracy, and precision of the relative curvature measure with the heteroscedastic variance function were evaluated and compared with those of the original relative curvature measure. The results showed that the relative curvature measure with the variance function was not affected by heteroscedastic blood drug concentration data and could be utilized for the assessment of the nonlinearity in compartment models.

A Linear Pharmacokinetic Model Predicts Usefulness of N‐Methyl‐2‐Pyrrolidone (NMP) in Plasma or Urine as a Biomarker for Biological Monitoring for NMP Exposure: Xiaofei E, et al. Department of Hygiene, Akita University School of Medicine—N‐methyl‐2‐pyrrolidone (NMP: C5H9NO:CAS number 872‐50‐4) is an increasingly used solvent due to the lack of ozone depleting activity. The aim of this study is to construct a simple pharmacokinetic model for NMP. In factory A, four workers who were exposed to NMP at 0.09‐0.69 ppm for 12 h by time weighted average (TWA) were followed up for an entire workweek. Their NMP concentrations in plasma and urine were monitored during the observation period. Five volunteers were exposed to NMP during the observation of workers in the factory A for eight hours. NMP kinetics in plasma and urine were monitored for 2 d after exposure. Concentrations of NMP in plasma and urine as standardized by creatinine concentrations were used to construct a one compartment pharmacokinetic model. The model successfully simulated the kinetics in four workers and five volunteers. In the next step, the model was applied to eight workers in another factory: they were exposed to NMP for 12 h at 0.04 to 0.59 ppm by TWA. The model could successfully predict kinetics of NMP levels in plasma and urine at the end of work. The model was then applied to experimental exposure cases in the literature. The model successfully predicted the concentrations of NMP in plasma and urine at the exposure intensity level of 12 ppm x 8 h. These results imply that metabolic saturation does not occur up to the exposure intensity of 12 ppm x 8 h and demonstrate the usefulness of determinations of NMP in plasma and urine for biological monitoring.

To prepare a suspension form of diclofenac and compare the influence of the injected form (suspension versus solution) on the intravitreal pharmacokinetics of diclofenac in Dutch belted pigmented rabbits. Diclofenac acid was prepared and characterized in a suspension formulation. Rabbit eyes were injected with either diclofenac sodium solution (0.3 mg) or diclofenac acid suspension (10 mg) prepared in 0.1 mL balanced salt solution. Rabbits were killed at regular time intervals, the eyes enucleated, and drug content quantified in the vitreous humor and retina-choroid tissue by high-performance liquid chromatography. Pharmacokinetic models were developed for both the dosage forms, and simulations were performed for different doses. Diclofenac acid with an approximate 5-mum particle size exhibited 3.5-fold lower solubility in vitreous humor, when compared with its sodium salt. The estimated settling velocity of the suspension in the vitreous humor was 3 cm/h. After diclofenac sodium salt solution injection, drug levels declined rapidly with no drug levels detectable after 24 hours in the vitreous humor and 4 hours in the RC. Throughout the assessed time course, drug levels were higher in the vitreous. However, sustained, high drug levels were observed in both the vitreous humor and the retina-choroid even on day 21 after diclofenac acid suspension injection, with retina-choroid drug levels being higher beginning at 0.25 hour. The elimination half-life of diclofenac suspension was 24 and 18 days in vitreous and retina-choroid, respectively, compared to 2.9 and 0.9 hours observed with diclofenac sodium. The pharmacokinetic models developed indicated a slow-release distribution or depot compartment for the diclofenac acid suspension in the posterior segment. Simulations indicated the inability of a 10-mg dose of diclofenac sodium solution to sustain drug levels in the vitreous beyond 11 days. By choosing a less soluble form of a drug such as diclofenac acid, vitreous elimination half-life can be prolonged up to 24 days, potentially resulting in therapeutic levels in the posterior segment tissues for a few months. Higher detectable drug levels in the retina-choroid suggest rapid settling and persistent retention of suspension in retina-choroid tissue.

To develop and test a time-efficient, free-breathing, whole heart T2 mapping technique at 3.0T. ECG-triggered three-dimensional (3D) images were acquired with different T2 preparations at 3.0T during free breathing. Respiratory motion was corrected with a navigator-guided motion correction framework at near perfect efficiency. Image intensities were fit to a monoexponential function to derive myocardial T2 maps. The proposed 3D, free breathing, motion-corrected (3D-FB-MoCo) approach was studied in ex vivo canine hearts and kidneys, healthy volunteers, and canine subjects with acute myocardial infarction (AMI). Ex vivo T2 values from proposed 3D T2 -prep gradient echo were not different from two-dimensional (2D) spin echo (P = 0.7) and T2 -prep balanced steady-state free precession (bSSFP) (P = 0.7). In healthy volunteers, compared with 3D-FB-MoCo and breath-held 2D T2 -prep bSSFP (2D-BH), non-motion-corrected (3D-FB-Non-MoCo) myocardial T2 was longer, had a larger coefficient of variation (COV), and had a lower image quality (IQ) score (T2 = 40.3 ms, COV = 38%, and IQ = 2.3; all P < 0.05). Conversely, the mean and COV and IQ of 3D-FB-MoCo (T2 = 37.7 ms, COV = 17%, and IQ = 3.5) and 2D-BH (T2 = 38.0 ms, COV = 15%, and IQ = 3.8) were not different (P = 0.99, P = 0.74, and P = 0.14, respectively). In AMI, T2 values and edema volumes from 3D-FB-MoCo and 2D-BH were closely correlated (R(2) = 0.88 and 0.96, respectively). The proposed whole heart T2 mapping approach can be performed within 5 min with similar accuracy to that of the 2D-BH T2 mapping approach.

&lt;div&gt;Abstract&lt;p&gt;&lt;b&gt;Purpose:&lt;/b&gt; To elucidate the mechanistic basis for efficacy of intrathecal rituximab. We evaluated complement activation as well as the pharmacokinetics of intraventricular rituximab in patients who participated in two phase 1 multicenter studies.&lt;/p&gt;&lt;p&gt;&lt;b&gt;Experimental Design:&lt;/b&gt; We evaluated complement activation as a candidate mediator of rituximab within the central nervous system (CNS). Complement C3 and C5b-9 were quantified by ELISA in serial cerebrospinal fluid (CSF) specimens after intraventricular rituximab administration. We determined rituximab concentration profiles in CSF and serum. A population three- compartment pharmacokinetic model was built to describe the disposition of rituximab following intraventricular administration. The model was derived from results of the first trial and validated with results of the second trial.&lt;/p&gt;&lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; Complement C3 and C5b-9 were reproducibly activated in CSF after intraventricular rituximab. Ectopic expression of C3 mRNA and protein within CNS lymphoma lesions was localized to myeloid cells. Constitutive high C3 activation at baseline was associated with adverse prognosis. A pharmacokinetic model was built, which contains three distinct compartments, to describe the distribution of rituximab within the neuroaxis after intraventricular administration.&lt;/p&gt;&lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; We provide the first evidence of C3 activation within the neuroaxis with intraventricular immunotherapy and suggest that complement may contribute to immunotherapeutic responses of rituximab in CNS lymphoma. Penetration of rituximab into neural tissue is supported by this pharmacokinetic model and may contribute to efficacy. These findings have general implications for intraventricular immunotherapy. Our data highlight potential innovations to improve efficacy of intraventricular immunotherapy both via modulation of the innate immune response as well as innovations in drug delivery. &lt;i&gt;Clin Cancer Res; 20(4); 1029–41. ©2013 AACR&lt;/i&gt;.&lt;/p&gt;&lt;/div&gt;

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.

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.

Vancomycin is the drug of choice for methicillin-resistant Staphylococcus aureus (MRSA) infection and shows time-dependent bacterial killing. The current study evaluated the pharmacokinetics (PK) and pharmacodynamics (PD) of vancomycin and explored its optimal dosing regimens by modeling and simulation. Pharmacokinetics study was performed for 20 patients who were treated with vancomycin intravenously, 1000mg, every 12h, and blood for PK was randomly drawn within prespecified time windows. PD study was in vitro time-kill experiment for vancomycin against 20 MRSA strains independent of the PK study, where bacterial titre was measured at 0, 2, 4, 8, 24h after the beginning of vancomycin exposure at 0, 1, 2, 4, 8, 16, 32× minimum inhibitory concentrations. PK and PD models were built from each data set, and simulation for MRSA titre changes over time in human body was performed for various vancomycin dosing regimens using NONMEM(®) . Vancomycin followed a two-compartment PK model, and creatinine clearance was the significant covariate affecting the clearance of vancomycin. PD model described the in vitro time-kill data well. The PK/PD model predicted clear dose-response relationships of vancomycin. The therapeutic dosing regimens of vancomycin, suggested by the simulation studies, showed good agreement with the current clinical practice guidance, which indicates that this PK/PD modeling and simulation approach could prove useful for identifying optimal dosing regimens of other antibiotics and expediting novel antibiotic development. Using PD model from in vitro time-kill study and human PK model from phase 1 study, we could predict whether the drug is going to be efficacious or obtain insight into the optimal dosing regimens for a novel antibiotic agent in the early phases of drug development process.

Based on the problems experimentally working scientists have if they want to fit theoretical curves or models (e.g. Bateman curves of compartment models in pharmacokinetics) to data which are nonlinear and can not be treated by usual regression techniques, we developed an interactive APL program called FITTEN in order to carry out nonlinear regressions. Emphasis has been placed on easy practicability, also for users with minor computing experience. Batch processing for high and interactive processing for low amounts of CPU was combined by the usage of several APL libraries. The mode of operation of FITTEN, the possibility to control the search and the output is demonstrated by an example.