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Erythropoietin (EPO) and thrombopoietin (TPO) have long been known to promote erythropoiesis and megakaryopoiesis, respectively. However, the fate-changing role of EPO and TPO on megakaryocyte-erythroid progenitors (MEPs) to develop along the erythroid versus megakaryocyte lineage remains unclear. We have previously shown that EPO may have a fate-changing role because EPO treatment could induce progenitor cells depletion and result in EPO resistance. Therefore, we hypothesize that a combination of romiplostim, a TPO receptor agonist that could stimulate the expansion of progenitors, with EPO can treat EPO resistance. Using rats with anemia due to chronic kidney disease, we demonstrated that romiplostim synergized with EPO to promote red blood cells production whereas EPO inhibited platelet production in a dose-dependent manner to reduce the risk of thrombosis. Corroborating findings from in vivo, in vitro experiments demonstrated that romiplostim expanded hematopoietic stem cells and stimulated megakaryopoiesis whereas EPO drove the progenitors toward an erythroid fate. We further developed a novel pharmacokinetic-pharmacodynamic model to quantify the effects of EPO and romiplostim on megakaryopoiesis and erythropoiesis simultaneously. The modeling results demonstrated that EPO increased the differentiation rate of MEPs into burst-forming unit-erythroid cells up to 22-fold, indicating that the slight increase of MEPs induced by romiplostim could be further amplified and recruited by EPO to promote erythropoiesis. The data herein support that romiplostim in combination with EPO can treat EPO resistance. SIGNIFICANCE STATEMENT: This study clarified that erythropoietin (EPO) drives the fate of megakaryocyte-erythroid progenitors (MEPs) toward the erythroid lineage, thus reducing their megakaryocyte (MK) lineage commitment, whereas romiplostim, a thrombopoietin receptor agonist, stimulates megakaryopoiesis through the MK-committed progenitor and MEP bifurcation pathways simultaneously. These findings support an innovative combination of romiplostim and EPO to treat EPO-resistant anemia because the combination therapy further promotes erythropoiesis compared to EPO monotherapy and inhibits platelet production compared to romiplostim monotherapy.

Indomethacin is used commonly in preterm neonates for the prevention of intracranial hemorrhage and closure of an abnormally open cardiac vessel. Due to biomedical advances, the infants who receive this drug in the neonatal intensive care unit setting have become younger, smaller, and less mature (more preterm) at the time of treatment. To develop a pharmacokinetics (PK) model to aid future dosing, we designed a prospective cohort study to characterize indomethacin PK in a dynamically changing patient population. A population PK base model was created using NONMEM, and a covariate model was developed in a primary development cohort and subsequently was tested for accuracy in a validation cohort. Postnatal age was a significant covariate for hepatic clearance (CL

Recombinant human erythropoietin (rHuEPO) is effective in managing chronic kidney disease and chemotherapy-induced anemia. However, hyporesponsiveness to rHuEPO treatment was reported in about 10% of the patients. A decreased response in rats receiving a single or multiple doses of rHuEPO was also observed. In this study, we aimed to develop a quantitative systems pharmacology (QSP) model to examine hyporesponsiveness to rHuEPO in rats. Pharmacokinetic (PK) and pharmacodynamic (PD) data after a single intravenous dose of rHuEPO (100 IU/kg) was obtained from a previous study (Yan et al. in Pharm Res, 30:1026-1036, 2013) including rHuEPO plasma concentrations, erythroid precursors counts in femur bone marrow and spleen, reticulocytes (RETs), red blood cells (RBCs), and hemoglobin (HGB) in circulation. Parameter values were obtained from literature or calibrated with experimental data. Global sensitivity analysis and model-based simulations were performed to assess parameter sensitivity and hyporesponsiveness. The final QSP model adequately characterizes time courses of rHuEPO PK and nine PD endpoints in both control and treatment groups simultaneously. The model indicates that negative feedback regulation, neocytolysis, and depletion of erythroid precursors are major factors leading to hyporesponsiveness to rHuEPO treatment in rats.

Population pharmacokinetic/pharmacodynamic (PK/PD) analysis was performed for extensive data for differing dosage forms and routes for dexamethasone (DEX) and betamethasone (BET) in 48 healthy nonpregnant Indian women in a partial and complex cross-over design. Single doses of 6 mg dexamethasone phosphate (DEX-P), betamethasone phosphate (BET-P), or 1:1 mixture of betamethasone phosphate and acetate (BET-PA) were administered orally (PO) or intramuscularly (IM) where each woman enrolled in a two-period cross-over study. Plasma concentrations collected over 96 h were described with a two-compartment model with differing PO and IM first-order absorption inputs. Overall, BET exhibited slower clearance, similar volume of distribution, faster absorption, and longer persistence than DEX with BET acetate producing extremely slow absorption but full bioavailability of BET. Six biomarkers were assessed over a 24-h baseline period with four showing circadian rhythms with complex baselines. These baselines and the strong responses seen after drug dosing were fitted with various indirect response models using the Laplace estimation methods in NONMEM 7.4. Both the PK and six biomarker responses were well-described with modest variability likely due to the homogeneous ages, weights, and ethnicities of the women. The drugs either inhibited or stimulated the influx processes with some models requiring joint inclusion of drug effects on circadian cortisol suppression. The biomarkers and order of sensitivity (lowest IC50/SC50 to highest) were: cortisol, T-helper cells, basophils, glucose, neutrophils, and T-cytotoxic cells. DEX sensitivities were generally greater than BET with corresponding mean ratios for these biomarkers of 2.86, 1.27, 1.72, 1.27, 2.69, and 1.06. Overall, the longer PK (e.g. half-life) of BET, but lesser PD activity (e.g. higher IC50), produces single-dose response profiles that appear quite similar, except for the extended effects from BET-PA. This comprehensive population modeling effort provides the first detailed comparison of the PK profiles and six biomarker responses of five commonly used dosage forms of DEX and BET in healthy women.

Population analysis of pharmacokinetic data for five differing dosage forms and routes for dexamethasone and betamethasone in 48 healthy nonpregnant Indian women was performed that accounted for a partial and complex cross-over design. Single doses of 6 mg dexamethasone phosphate (DEX-P), betamethasone phosphate (BET-P), or 1:1 mixture of betamethasone phosphate and acetate (BET-PA) were administered orally (PO) or intramuscularly (IM). Plasma concentrations collected for two periods over 96 h were described with a two-compartment model with differing PO and IM first-order absorption inputs. Clearances and volumes were divided by the IM bioavailability $${F}_{IM}$$ F IM . The homogeneous ages, body weights, and ethnicity of the women obviated covariate analysis. Parameter estimates were obtained by the Laplace estimation method implemented in NONMEM 7.4. Typical values for dexamethasone were clearance ($${CL/F}_{IM})$$ C L / F IM ) of 9.29 L/h, steady-state volume ($${{V}_{ss}/F}_{IM})$$ V ss / F IM ) of 56.4 L, IM absorption constant $$\left({k}_{aIM}\right)$$ k aIM of 0.460 1/h and oral absorption constant ($${k}_{aPO})$$ k aPO ) of 0.936 1/h. Betamethasone parameters were CL/FIM of 5.95 L/h, $${Vss/F}_{IM}$$ V s s / F IM of 72.4 L, $${k}_{aIM}$$ k aIM of 0.971 1/h, and $${k}_{aPO}$$ k aPO of 1.21 1/h. The PO to IM F values were close to 1.0 for both drugs. The terminal half-lives averaged about 7.5 h for DEX, 17 h for BET, and 78 h for BET from BET-PA with the latter reflecting very slow release of BET from the acetate ester. Overall, BET exhibited slower clearance, larger volume of distribution, faster absorption, and longer persistence than DEX. These data may be useful in considering exposures when substituting one form of corticosteroid for another.

Serum creatinine (sCr) is a commonly measured biomarker to estimate glomerular filtration rate (GFR) and therefore widely used as a covariate in population pharmacokinetic models of renally excreted drugs. In neonates, sCr dynamically changes during the first few weeks after birth. Missing covariates are a common problem in pharmacokinetic modeling of neonates due to the limited availability of blood sampling in number and volume. The objective of this work is to develop a parsimonious population model describing time courses of sCr in neonates with the intent to be incorporated into pharmacokinetic models of various drugs where sCr values are sparse or missing. The data for model development consisted of sCr measurements in 1080 newborns with a gestational age of 24–42 weeks. The model is based on a pharmacokinetic model of sCr that involves GFR, backflow of creatinine from the renal tubules, and urinary flow. Gestational age is the only covariate explaining between-subject variability of sCr. The model adequately describes distinct features of the sCr time course such as a peak and decline to a plateau. For a neonate with a GA of 35 weeks, the typical value of sCr at birth was 0.584 mg/dL, the peak (0.794 mg/dL) occurred 2.3 days after birth, to reach a plateau of 0.255 mg/dL approximately after 24.7 days. Model simulations reveal that in neonates with a similar postnatal age, sCr decreases with increasing GA. In summary, our model is designed to be a part of full random effects pharmacokinetic models where sCr is a significant covariate.

Serum creatinine (sCr) is a commonly measured biomarker to estimate glomerular filtration rate (GFR) and therefore widely used as a covariate in population pharmacokinetic models of renally excreted drugs. In neonates, sCr dynamically changes during the first few weeks after birth. Missing covariates are a common problem in pharmacokinetic modeling of neonates due to the limited availability of blood sampling in number and volume. The objective of this work is to develop a parsimonious population model describing time courses of sCr in neonates with the intent to be incorporated into pharmacokinetic models of various drugs where sCr values are sparse or missing. The data for model development consisted of sCr measurements in 1080 newborns with a gestational age of 24-42 weeks. The model is based on a pharmacokinetic model of sCr that involves GFR, backflow of creatinine from the renal tubules, and urinary flow. Gestational age is the only covariate explaining between-subject variability of sCr. The model adequately describes distinct features of the sCr time course such as a peak and decline to a plateau. For a neonate with a GA of 35 weeks, the typical value of sCr at birth was 0.584 mg/dL, the peak (0.794 mg/dL) occurred 2.3 days after birth, to reach a plateau of 0.255 mg/dL approximately after 24.7 days. Model simulations reveal that in neonates with a similar postnatal age, sCr decreases with increasing GA. In summary, our model is designed to be a part of full random effects pharmacokinetic models where sCr is a significant covariate.

Delay differential equations (DDEs) are commonly used in pharmacometric models to describe delays present in pharmacokinetic and pharmacodynamic data analysis. Several DDE solvers have been implemented in NONMEM 7.5 for the first time. Two of them are based on algorithms already applied elsewhere, while others are extensions of existing ordinary differential equations (ODEs) solvers. The purpose of this tutorial is to introduce basic concepts underlying DDE based models and to show how they can be developed using NONMEM. The examples include previously published DDE models such as logistic growth, tumor growth inhibition, indirect response with precursor pool, rheumatoid arthritis, and erythropoiesis-stimulating agents. We evaluated the accuracy of NONMEM DDE solvers, their ability to handle stiff problems, and their performance in parameter estimation using both first-order conditional estimation (FOCE) and the expectation–maximization (EM) method. NONMEM control streams and excerpts from datasets are provided for all discussed examples. All DDE solvers provide accurate and precise solutions with the number of significant digits controlled by the error tolerance parameters. For estimation of population parameters, the EM method is more stable than FOCE regardless of the DDE solver. published

In many models of pharmacodynamic systems with delays, a delay of an input is introduced by means of the convolution with the gamma distribution. An approximation of the convolution integral of bound functions based on a system of ordinary differential equations that utilizes properties of the binomial series has been introduced. The approximation converges uniformly on every compact time interval and an estimate of the approximation error has been found $$O\left( {\frac{1}{{N^{\nu } }}} \right)$$ where $$N$$ is the number of differential equations and $$\nu$$ is the shape parameter of the gamma distribution. The accuracy of approximation has been tested on a set of input functions for which the convolution is known explicitly. For tested functions, $$N \ge 20$$ has resulted in an accurate approximation, if $$\nu \ge 1$$ . However, if $$\nu < 1$$ the error of approximation decreases slowly with increasing $$N$$ , and $$N > 100$$ might be necessary to achieve acceptable accuracy. Finally, the approximation was applied to estimate parameters for the distributed delay model of chemotherapy-induced myelosuppression from previously published WBC count data in rats treated with 5-fluorouracil.

The ability to control dosage regimens of erythropoiesis‐stimulating agents (ESAs) to maintain a desired hemoglobin (HGB) target is still elusive. We utilized a Bayesian approach and informative priors to characterize HGB profiles, using simulated drug concentrations, in patients with end‐stage renal disease receiving maintenance doses of epoetin alfa. We also demonstrated an adaptive Bayesian method, applied to individual patients, to improve the accuracy of HGB predictions over time. The results showed that sparse HGB data from daily clinical practice were characterized successfully. The adaptive Bayesian method effectively improved the accuracy of HGB predictions by updating the individual model with new data accounting for within‐subject changes over time. The Bayesian approach presented leverages existing knowledge of the model parameters and has a potential utility in clinical practice to individualize dosage regimens of epoetin alfa and ESAs to achieve target HGB. Further studies are warranted to develop an application for practical use.

Shortened red blood cell (RBC) lifespan is one of the major factors contributing to anemia in end-stage renal disease (ESRD) patients and should be taken into account in anemia management protocols. In this study, we aimed to estimate RBC lifespan and the source of between-subject variability in ESRD patients. The resulting individual parameters (empirical Bayes estimates) were used to predict hemoglobin concentrations 2 weeks in advance. The reticulocyte-based estimation of RBC lifespan (REBEL) and the population modeling of RBC count data were used. A total of 120 blood samples collected biweekly over 10 weeks in 24 patients receiving maintenance doses of recombinant human erythropoietin (rHuEPO) subcutaneously were included in this analysis. Typical RBC lifespan was estimated to be 63.3 days. RBC lifespan was found to increase with erythroferrone, a recently identified hormone participating in iron metabolism. Approximately, a 10% increase in plasma erythroferrone was associated with a 5% increase in RBC lifespan. In addition, RBC lifespan was 18.7% shorter in females compared with males. Out of 24 subjects, 16 had hemoglobin concentrations predicted within 95% prediction intervals. The median absolute prediction error was 15.9% (interquartile range, 9.5 to 24.7%). We demonstrated that REBEL coupled with the population modeling technique can be used effectively to estimate RBC lifespan. Then, individual parameters can be used to predict future hemoglobin concentrations in ESRD patients.

The distributed delay model has been introduced that replaces the transit compartments in the classic model of chemotherapy-induced myelosuppression with a convolution integral. The maturation of granulocyte precursors in the bone marrow is described by the gamma probability density function with the shape parameter (ν). If ν is a positive integer, the distributed delay model coincides with the classic model with ν transit compartments. The purpose of this work was to evaluate performance of the distributed delay model with particular focus on model deterministic identifiability in the presence of the shape parameter. The classic model served as a reference for comparison. Previously published white blood cell (WBC) count data in rats receiving bolus doses of 5-fluorouracil were fitted by both models. The negative two log-likelihood objective function (-2LL) and running times were used as major markers of performance. Local sensitivity analysis was done to evaluate the impact of ν on the pharmacodynamics response WBC. The ν estimate was 1.46 with 16.1% CV% compared to ν = 3 for the classic model. The difference of 6.78 in - 2LL between classic model and the distributed delay model implied that the latter performed significantly better than former according to the log-likelihood ratio test (P = 0.009), although the overall performance was modestly better. The running times were 1 s and 66.2 min, respectively. The long running time of the distributed delay model was attributed to computationally intensive evaluation of the convolution integral. The sensitivity analysis revealed that ν strongly influences the WBC response by controlling cell proliferation and elimination of WBCs from the circulation. In conclusion, the distributed delay model was deterministically identifiable from typical cytotoxic data. Its performance was modestly better than the classic model with significantly longer running time.

Dexmedetomidine (DEX) is a fairly new alfa2-agonist which has been increasingly used in recent years for analgosedation, mostly because it offers a unique ability of providing both moderate level of sedation and analgesia without respiratory depression. Despite of many papers published, there are still only a few concerning the PK of the drug given as long-term infusion in ICU patients. The aim of this work was to characterize the population pharmacokinetics of dexmedetomidine and to investigate the potential benefits of individualization of drug dosing based on patient characteristics in the heterogeneous group of medical and surgical patients staying in intensive care unit. This study was performed in the group of 17 males and 10 females patients with a median age of 59.5 years and median body weight of 75 kg. Blood samples for dexmedetomidine assay were collected from arterial catheter, during and after discontinuation of a standard infusion, that ranged from 24 to 102 h. The following covariates were examined to influence dexmedetomidine PK: age, sex, body weight, patients’ health status described by Sequential Organ Failure Assessment Score (SOFA), inotropes usage, and infusion duration. The dexmedetomidine PK was best described by a two-compartment model. The typical values of PK parameters were estimated as 27 L for the volume of the central compartment, 87.6 L for the volume of the peripheral compartment, 38.5 L/h (9.2 mL/min/kg for a 70 kg patient) for systemic clearance and 46.4 L/h for the distribution clearance. Those values are consistent with literature findings. We were unable to show any significant relationship between collected covariates and dexmedetomidine PK. This study does not provide sufficient evidence to support the individualization of dexmedetomidine dosing based on age, sex, body weight, SOFA, and infusion duration. Electronic supplementary material The online version of this article (10.1007/s10928-017-9564-7) contains supplementary material, which is available to authorized users.

Age-structured cell population model was introduced to describe cell survival. The impact of the environment on the cell population is represented by drug plasma concentration. A key model variable is the hazard of cell removal that is a subject to the environment effect. The model is capable of describing cohort and random labeling cell survival data. In addition, it accounts for cell loss due to labeling of cell sample, but it lacks ability to describe the effect of label elution on the survival data. The model was applied to red blood cell (RBC) survival data in two groups of Wistar rats obtained by two techniques: cohort labeling using 14C-glycine (N = 4) and random labeling using biotin (N = 8). The Weibull probability density function was selected for the RBC lifespan distribution. The data were simultaneously fitted by the mixed effects model implemented in Monolix 4.3.3. The estimated typical values of RBC lifespan and age were 53.7 and 27.8 days, respectively. A noticeable effect of biotinylation on RBC survival was observed that resulted in a significant difference between the means of individual RBC lifespan for two groups. The model provides a mechanistic framework flexible enough to account for various experimental designs to generate the cell survival data. Despite model qualification using animal data, the model has the same potential to be applied to cell survival data analysis in humans.

This study aimed to develop a method for implementing dose correction in a Michaelis-Menten (M-M) approximation of a target-mediated drug disposition (TMDD) model with multiple intravenous (IV) bolus administrations. We derived the formula of a correction factor (Fcorr) for each dose in a multiple IV bolus dosing regimens for M-M model. Fcorr depends on the residual free drug amount prior IV bolus dosing event and dose amount. We conducted a stochastic simulation and estimation (SSE) exercise based on therapeutic antibody PK parameters to evaluate the effect of Fcorr on parameter estimation. Previously published clinical PK data of recombinant human erythropoietin (rHuEPO) from four clinical trials in healthy subjects receiving multiple IV bolus doses were analyzed by both M-M model with and without dose correction (MMC and MMNC) as well as the rapid-binding/quasi-steady-state (RB/QSS) TMDD models. Our results showed that MMNC introduced bias to fixed-effect parameter estimates and overestimated random-effect variables. Compared with MMC, MMNC was not able to adequately characterize the nonlinearity in the PK data of antibody and rHuEPO. The MMC-based simulation demonstrated that thricely weekly 10 IU/kg rHuEPO dosing regimen yielded Fcorr = 0.5. This result suggested that the lower-than-expected exposure for rHuEPO at low dose is due to target binding. An M-M approximation of the TMDD model should include a dose correction to avoid model misfitting and potential bias in the estimated PK parameters.

Body weight is the primary covariate in pharmacokinetics of many drugs and dramatically changes during the first weeks of life of neonates. The objective of this study is to determine if missing body weights in preterm and term neonates affect estimates of model parameters and which methods can be used to improve performance of a population pharmacokinetic model of paracetamol. Data for our analysis were obtained from previously published studies on the pharmacokinetics of intravenous paracetamol in neonates. We adopted a population model of body weight change in neonates to implement three previously introduced methods of handling missing covariates based on data imputation, likelihood function modification, and full random effects modeling. All models were implemented in NONMEM 7.4, and population parameters were estimated using the FOCE method. Our major finding was that missing body weights minimally affect population estimates of pharmacokinetic parameters but do affect the covariate relationship parameters, particularly the one describing dependence of clearance on body weight. None of the tested methods changed estimates of between-subject variability nor impacted the predictive performance of the model. Our analysis shows that a modeling approach towards handling missing covariates allows borrowing information gathered in various studies as long as they target the same population. This approach is particularly useful for handling time-dependent missing covariates. ispartof: AAPS JOURNAL vol:21 issue:4 ispartof: location:United States status: published

Hepcidin (H25) is a hormone peptide synthesized by the liver that binds to ferroportin and blocks iron export. In this study, H25 was inhibited by administration of single and multiple doses of an anti-H25 monoclonal antibody Ab 12B9m in cynomolgus monkeys. The objective of this analysis was to develop a pharmacodynamic model describing the role of H25 in regulating iron homeostasis and the impact of hepcidin inhibition by Ab 12B9m. Total serum H25 and Ab 12B9m were determined in each animal. Corresponding measurements of serum iron and hemoglobin (Hb) were obtained. The PD model consisted of iron pools in serum (FeS), reticuloendothelial macrophages (FeM), hemoglobin (FeHb), and liver (FeL). The iron was assumed to be transported between the FeS, FeHb, and FeM unidirectionally at rates k S, k Hb, and k M. H25 serum concentrations were described by the previously developed PK model with the parameters fixed at their estimates. The serum iron and Hb data were fitted simultaneously. The corresponding estimates of the rate constants were k S/Fe0 = 0.113 h−1, k M = 0.00191 h−1, and k Hb = 0.00817 h−1. The model-based IC50 value for the H25 inhibitory effect on ferroportin activity was 0.398 nM. The PD model predicted a negligible effect of Ab 12B9m on Hb levels for the tested doses. The presented PD model adequately described the serum iron time courses following single and multiple doses of Ab 12B9m. Ab 12B9m-induced inhibition of H25 resulted in a temporal increase in serum and liver iron and a decrease in the iron stored in reticuloendothelial macrophages.

Rhythmicity in baseline responses over a 24-h period for an indirect pharmacological effect R(t) can arise from either a periodic time-dependent input rate $$ k_{in} \left( t \right) $$ or a periodic time-dependent loss constant $$ k_{out} \left( t \right) $$ . If either $$ k_{in} \left( t \right) $$ or $$ k_{out} \left( t \right) $$ follows some nonstationary biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. Indirect response models assuming time-dependent input rates $$ \left[ {k_{in} \left( t \right)} \right] $$ have been utilized to capture drug effects on various physiological responses such as hormone suppression, immune cell trafficking, and gene expression in tissues. This paradigm was extended to consider responses with circadian-controlled loss $$ \left[ {k_{out} \left( t \right)} \right] $$ mechanisms. Theoretical equations describing this model are presented and simulations were performed to examine expected response behaviors. The model was able to capture the chronobiology and pharmacodynamics of applicable drug responses, including the uricosuric effects of lesinurad in humans, suppression of the beta amyloid (Aβ) peptide by a gamma-secretase inhibitor in mouse brain, and the modulation of extracellular dopamine by a dopamine transporter inhibitor in rat brain. This type of model has a mechanistic basis and shows utility for capturing drug responses displaying nonstationary baselines controlled by removal mechanism(s).

Erythropoiesis-stimulating agents (eg, epoetin alfa) are the primary treatment for anemia in patients with end-stage renal disease. Hemoglobin variability in and out of a narrow target range is common and associated with higher morbidity and mortality risk. More robust erythropoiesis-stimulating agent response metrics are needed to define optimal dosing and their association with clinical outcomes. In this cross-sectional, single-center, retrospective study, 49 patients with end-stage renal disease on hemodialysis were followed over 12 months. To quantify hemoglobin deviations outside the target range (10-12 g/dL), the area under the curve of hemoglobin versus time over a 12-month period (AUC-HGB) was calculated using the trapezoidal rule. Patients were categorized into 4 responder groups based on AUC-HGB quartiles. Comparative analyses of demographic and clinical characteristics between responder groups were performed. Correlations between AUC-HGB, erythropoietin resistance index, and time within therapeutic range were calculated. There were no significant differences in laboratory and dialysis parameters between responder groups except hemoglobin concentration and epoetin alfa dose. There was a negative correlation between AUC-HGB and time within therapeutic range (r = -.92; P < .001) and hemoglobin concentration (r = -.85; P < .01), indicating internal validity of the metric. There was a positive correlation between AUC-HGB and erythropoietin resistance index (r = .70; P < .001) indicating external validity. The poor response group received a higher median epoetin alfa dose (160 U/kg/week) compared to the excellent response group (68.8 U/kg/week; P < .001) with a similar number of dose changes between the groups. AUC-HGB is a valid marker of epoetin alfa response and should be considered in future analyses of larger populations.

The purpose of this report is to apply multi-scale modeling using the theory of physiologically structured populations (PSP) to develop a mathematical model for antimicrobial resistance based on a heterogeneous distribution of receptors and affinities among bacterial cells. The theory has been tested on data obtained from an in vitro static time-kill infection model analyzing the pharmacodynamics of polymyxin B against Gram-negative bacteria. The drug binding parameter KD (dissociation equilibrium constant) is assumed to vary between the bacterial cells. The PSP model describes the time course of the density distribution of KD upon exposure to cytotoxic drug concentrations. The drug increases the hazard of cell death as a function of receptor occupancy. The initial distribution of KD is described by the Weibull function. Time-kill data were used for model qualification. In vitro static time-kill experiments to evaluate the rate and extent of killing due to polymyxin B against two Klebsiella pneumoniae clinical isolates with differing susceptibilities to polymyxin B were performed over 48 h. The time-kill kinetics data of bacterial load cfu (colony forming units)/mL was used for model qualification. The resistant bacterial population is determined by the balance between growth rate and hazard of cell death controlled by polymyxin B concentrations. There exists a critical KD value below which cells continue to grow. Estimates of shape parameters for distributions of KD yielded unimodal distributions with the modes at 0 nM and the right tails containing approximately 25% of the bacteria. Our findings support a hypothesis that resistance of Klebsiella pneumoniae to polymyxin B can be at least partially attributed to a drug-induced selection of a subpopulation due to heterogeneity of polymyxin B receptor binding in the bacterial population.

We aimed to develop a cell-level pharmacodynamics-mediated drug disposition (PDMDD) model to analyze in vivo systems where the PD response to a drug has an appreciable effect on the pharmacokinetics (PK). An existing cellular level model of PD stimulation was combined with the standard target-mediated drug disposition (TMDD) model and the resulting model structure was parametrically identifiable from typical in vivo PK and PD data. The PD model of the cell population was controlled by the production rate k in and elimination rate k out which could be stimulated or inhibited by the number of bound receptors on a single cell. Simulations were performed to assess the impact of single and repeated dosing on the total drug clearance. The clinical utility of the cell-level PDMDD model was demonstrated by fitting published data on the stimulatory effects of filgrastim on absolute neutrophil counts in healthy subjects. We postulated repeated dosing as a means of detecting and quantifying PDMDD as a single dose might not be sufficient to elicit the cellular response capable of altering the receptor pool to visibly affect drug disposition. In the absence of any PD effect, the model reduces down to the standard TMDD model. The applications of this model can be readily extended to include chemotherapy-induced cytopenias affecting clearance of endogenous hematopoietic growth factors, different monoclonal antibodies and immunogenicity effects on PK.

Based on the paradigm of mechanistic modeling, three types of pharmacodynamic models are introduced: direct effect, indirect response, and signal transduction. The underlying pharmacological and biological assumptions about the model structures and operations are provided along with examples of their applications. A brief historical perspective is introduced for each model class. Mathematical equations defining the model are presented and explored to link model parameters with model characteristics such as the shape of the response curve. The impact of dose on the time courses of pharmacodynamic responses is evaluated for large doses and exemplified with computer simulations. A common theme is the extent of delay between drug pharmacokinetics and response. When relevant, alternative parameterizations and parameter identifiability are discussed. Only the simplest forms of models are provided with some guidelines on how to build more complex models based on a systems pharmacology approach.

The purpose of this work is to review basic pharmacodynamic (PD) models describing drug effects on cell populations and expand them to age-structured models using the theory of physiologically structured populations. The plasma drug concentrations are interpreted as the environment affecting the cell production and mortality rates. An explicit solution to model equations provides the age density distribution that serves to establish a relationship between the cell lifespan distribution and the hazard of cell removal. Given the lifespan distributions, the age distributions for most commonly applied PD models of cell responses including basic cell turnover, transit compartments, and basic lifespan models have been derived both for the baseline conditions and drug treatment. The steady-state age distribution for basic indirect response models is exponential, and it is uniform for the basic lifespan model. As an example of more complex cell population, the age distribution of human red blood cells has been simulated based on a recent model of red blood cell survival. The age distribution for cells in the transit compartment model is the sum of the gamma functions. Means and variances of age distributions for all discussed models were calculated. A brief discussion of numerical challenges and possible future model developments is presented.

A mechanistic model describing the effects of chemotherapy and radiation on platelet counts and endogenous thrombopoietin (eTPO) in mice was developed. Thrombocytopenia was induced in mice by injection of carboplatin followed by the whole body irradiation on days 0, 28, and 56, with platelet and eTPO samples collected over 84 days. The pharmacodynamic model consisted of a series of aging compartments representing proliferating megakaryocyte precursors, megakaryocytes, and platelets with possible eTPO clearance through internalization. The cytotoxic effects of treatment were described by the kinetics of the effect (K-PD) model, and stimulation of platelet production by eTPO was considered to be driven by receptor occupancy. The proposed PD model adequately described the platelet counts and eTPO concentrations in mice by accounting for nadirs and peaks of platelet count, and rebounds in eTPO time course profiles. The estimates of model parameters were in good agreement with their physiological values reported in literature for mice with platelet lifespan of 4.3 days and 185 cMpl receptors per platelet. The predicted duration of the treatment effect was 0.82 h (approximately 5 carboplatin half-lives in mice). The data was not informative about the eTPO stimulatory effect as the nominal precursor production rate was sufficient to account for platelet response to treatment. The model quantified the inverse relationship between eTPO levels and platelet counts and offered an explanation of the tolerance effect observed in the eTPO data. The simulated rebound in free receptors levels correlated with rebounds in eTPO levels. The model suggests that the duration of the toxic effects is determined by the turnover of the proliferating cells in the bone marrow. This indicates that the lifespan of the target cells (megakaryocyte precursors, megakaryocytes and platelets) is a key determinant in the duration of both drug exposure and toxicity due to treatment. The model can be extended to account for pharmacokinetics of exogenous drugs and be applied to analysis of human data.

Mammalian erythropoiesis is a conserved process tightly controlled by the hypoxia-inducible factor (HIF1) pathway. In this study, a small molecule inhibitor (PHI-1) of prolyl-hydroxylase-2 (PHD2) enzyme involved in regulating HIF1α levels was orally administered to male BALB/c mice at 10 and 30 mg/kg. A systems pharmacology model was developed based on the measured PHI-1 plasma exposures, kidney HIF1α, kidney erythropoietin (EPO) mRNA, plasma EPO, reticulocyte counts, red blood cells, and hemoglobin levels. The model fit resulted in the estimation of drug potency (IC50: 1.7μM), and systems parameters such as EPO mRNA turnover (kdeg_EPOmRNA: 0.43 hr-1) and mean lifespan of reticulocytes (Tr: 81 hours). The model correctly described the observed 30–40-fold increase in kidney HIF1α protein, ∼1,000 fold increase in EPO mRNA and 2–3-fold increase in the reticulocytes at 30 mg/kg. This study presents the first parsimonious systems model of erythropoiesis to quantitatively describe the in vivo effects of PHD2 inhibition. CPT Pharmacometrics Syst. Pharmacol. (2015) 4, 106–115; doi:10.1002/psp4.12; published online on 11 February 2015.