Interpretation of transit compartments pharmacodynamic models as lifespan based indirect response models

Kinetic modelling of sterol transport between plasma membrane and endo-lysosomes based on quantitative fluorescence and X-ray imaging data

Niemann Pick type C1 and C2 (NPC1 and NPC2) are two sterol-binding proteins which, together, orchestrate cholesterol transport through late endosomes and lysosomes (LE/LYSs). NPC2 can facilitate sterol exchange between model membranes severalfold, but how this is connected to its function in cells is poorly understood. Using fluorescent analogs of cholesterol and quantitative fluorescence microscopy, we have recently measured the transport kinetics of sterol between plasma membrane (PM), recycling endosomes (REs) and LE/LYSs in control and NPC2 deficient fibroblasts. Here, we use kinetic modeling of this data to determine rate constants for sterol transport between intracellular compartments. Our model predicts that sterol is trapped in intraluminal vesicles (ILVs) of LE/LYSs in the absence of NPC2, causing delayed sterol export from LE/LYSs in NPC2 deficient fibroblasts. Using soft X-ray tomography, we confirm, that LE/LYSs of NPC2 deficient cells but not of control cells contain enlarged, carbon-rich intraluminal vesicular structures, supporting our model prediction of lipid accumulation in ILVs. By including sterol export via exocytosis of ILVs as exosomes and by release of vesicles-ectosomes-from the PM, we can reconcile measured sterol efflux kinetics and show that both pathways can be reciprocally regulated by the intraluminal sterol transfer activity of NPC2 inside LE/LYSs. Our results thereby connect the in vitro function of NPC2 as sterol transfer protein between membranes with its in vivo function.

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Extended transit compartment model to describe tumor delay using Coxian distribution

The measured response of cell population is often delayed relative to drug injection, and individuals in a population have a specific age distribution. Common approaches for describing the delay are to apply transit compartment models (TCMs). This model reflects that all damaged cells caused by drugs suffer transition processes, resulting in death. In this study, we present an extended TCM using Coxian distribution, one of the phase-type distributions. The cell population attacked by a drug is described via age-structured models. The mortality rate of the damaged cells is expressed by a convolution of drug rate and age density. Then applying to Erlang and Coxian distribution, we derive Erlang TCM, representing the existing model, and Coxian TCMs, reflecting sudden death at all ages. From published data of drug and tumor, delays are compared after parameter estimations in both models. We investigate the dynamical changes according to the number of the compartments. Model robustness and equilibrium analysis are also performed for model validation. Coxian TCM is an extended model considering a realistic case and captures more diverse delays.

Delay differential equations based models in NONMEM

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.

Quantitative Systems Pharmacology Modeling of PBMC-Humanized Mouse to Facilitate Preclinical Immuno-oncology Drug Development

Progress in immunotherapy has resulted in explosively increased new therapeutic interventions and they have shown promising results in the treatment of cancer. Animal testing is performed to provide preliminary efficacy and safety data for drugs under development prior to clinical trials. However, translational challenges remain for preclinical studies such as study design and the relevance of animal models to humans. Hence, only a small fraction of cancer patients showed response. The explosion of drug candidates and therapies makes preclinical assessment of every plausible option impossible, but it can be easily tested using Quantitative System Pharmacology (QSP) models. Here, we developed a QSP model for humanized mice. Tumor growth dynamics, T cell dynamics, cytokine release, immune checkpoint expression, and drug administration were modeled and calibrated using experimental data. Tumor growth inhibition data were used for model validation. Pharmacokinetics of T cell engager (TCE), tumor growth profile, T cell expansion in the blood and infiltration into tumor, T cell dissemination from primary tumor, cytokine release profile, and expression of additional PD-L1 induced by IFN-γ were modeled and calibrated using a variety of experimental data and showed good consistency. Mouse-specific response to T cell engager monotherapy also showed the key features of in vivo efficacy of TCE. This novel QSP model, designed for human peripheral blood mononuclear cells (PBMC) engrafted xenograft mice, incorporating the most critical components of the mouse model with key cancer and immune cells, can become an integral part of preclinical drug development.

Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.

A Modeling Framework to Characterize Cytokine Release upon T-Cell-Engaging Bispecific Antibody Treatment: Methodology and Opportunities

T‐cell–engaging bispecific antibodies (T‐BsAbs) are an important class of antibody therapeutics in immuno‐oncology. T‐BsAbs simultaneously bind to CD3 on T cells and a tumor‐associated antigen on tumor cells, activate T cells, and redirect T cells’ cytotoxicity against tumor cells. Cytokine release syndrome (CRS), a common dose‐limiting adverse event for T‐BsAbs, is associated with T‐cell activation. A “priming” dose strategy (i.e., a lower initial dose followed by a higher maintenance dose) has been implemented in the clinic to mitigate CRS and to achieve efficacious doses with T‐BsAbs. So far, the selection of the optimal priming dosing regimen is largely empirical. A “fit‐for‐purpose” semimechanistic pharmacokinetic/pharmacodynamic model was developed to characterize the cytokine release profiles upon T‐BsAb treatment, including the priming effect observed with repeated dosing. This model can be utilized to simulate cytokine profiles following various dosing regimens and may assist the design of clinical dosing strategies for T‐BsAbs programs.

A Population Pharmacokinetic-Pharmacodynamic Model of Pegfilgrastim

Neutropenia and febrile neutropenia (FN) are serious side effects of cytotoxic chemotherapy which may be alleviated with the administration of recombinant granulocyte colony-stimulating factor (GCSF) derivatives, such as pegfilgrastim (PG) which increases absolute neutrophil count (ANC). In this work, a population pharmacokinetic-pharmacodynamic (PKPD) model was developed based on data obtained from healthy volunteers receiving multiple administrations of PG. The developed model was a bidirectional PKPD model, where PG stimulated the proliferation, maturation, and margination of neutrophils and where circulating neutrophils in turn increased the elimination of PG. Simulations from the developed model show disproportionate changes in response with changes in dose. A dose increase of 10% from the 6 mg therapeutic dose taken as a reference leads to area under the curve (AUC) increases of ~50 and ~5% for PK and PD, respectively. A full random effects covariate model showed that little of the parameter variability could be explained by sex, age, body size, and race. As a consequence, little of the secondary parameter variability (C_max and AUC of PG and ANC) could be explained by these covariates.

Dipeptidyl Peptidase 1 Inhibitor AZD7986 Induces a Sustained, Exposure-Dependent Reduction in Neutrophil Elastase Activity in Healthy Subjects

Neutrophil serine proteases (NSPs), such as neutrophil elastase (NE), are activated by dipeptidyl peptidase 1 (DPP1) during neutrophil maturation. High NSP levels can be detrimental, particularly in lung tissue, and inhibition of NSPs is therefore an interesting therapeutic opportunity in multiple lung diseases, including chronic obstructive pulmonary disease (COPD) and bronchiectasis. We conducted a randomized, placebo‐controlled, first‐in‐human study to assess the safety, tolerability, pharmacokinetics, and pharmacodynamics of single and multiple oral doses of the DPP1 inhibitor AZD7986 in healthy subjects. Pharmacokinetic and pharmacodynamic data were analyzed using nonlinear mixed effects modeling and showed that AZD7986 inhibits whole blood NE activity in an exposure‐dependent, indirect manner—consistent with in vitro and preclinical predictions. Several dose‐dependent, possibly DPP1‐related, nonserious skin findings were observed, but these were not considered to prevent further clinical development. Overall, the study results provided confidence to progress AZD7986 to phase II and supported selection of a clinically relevant dose.

Population Pharmacokinetics and Pharmacodynamics of Benralizumab in Healthy Volunteers and Patients With Asthma

Benralizumab is a humanized, afucosylated, anti‐interleukin‐5 receptor α, immunoglobulin G (IgG) ₁ κ monoclonal antibody. We developed a population pharmacokinetic (PK)/pharmacodynamic (PD) model for benralizumab by analyzing PK and blood eosinophil count data from two healthy volunteer studies (N = 48) and four studies in patients with asthma (N = 152). Benralizumab PK was dose‐proportional and adequately described by a two‐compartment model with first‐order elimination from the central compartment and first‐order absorption from the subcutaneous dosing site. The estimated systemic clearance and volume of distribution were typical for human IgG. Body weight and high‐titer antidrug antibodies were identified as relevant covariates influencing the PK of benralizumab. Depletion of blood eosinophil counts was depicted by a modified transit model in which benralizumab induced depletion of eosinophils in each age compartment. Stochastic simulations supported an every‐8‐week dosing schedule of benralizumab for a phase IIb study in patients with uncontrolled asthma.

Models for the red blood cell lifespan

The lifespan of red blood cells (RBCs) plays an important role in the study and interpretation of various clinical conditions. Yet, confusion about the meanings of fundamental terms related to cell survival and their quantification still exists in the literature. To address these issues, we started from a compartmental model of RBC populations based on an arbitrary full lifespan distribution, carefully defined the residual lifespan, current age, and excess lifespan of the RBC population, and then derived the distributions of these parameters. For a set of residual survival data from biotin-labeled RBCs, we fit models based on Weibull, gamma, and lognormal distributions, using nonlinear mixed effects modeling and parametric bootstrapping. From the estimated Weibull, gamma, and lognormal parameters we computed the respective population mean full lifespans (95 % confidence interval): 115.60 (109.17-121.66), 116.71 (110.81-122.51), and 116.79 (111.23-122.75) days together with the standard deviations of the full lifespans: 24.77 (20.82-28.81), 24.30 (20.53-28.33), and 24.19 (20.43-27.73). We then estimated the 95th percentiles of the lifespan distributions (a surrogate for the maximum lifespan): 153.95 (150.02-158.36), 159.51 (155.09-164.00), and 160.40 (156.00-165.58) days, the mean current ages (or the mean residual lifespans): 60.45 (58.18-62.85), 60.82 (58.77-63.33), and 57.26 (54.33-60.61) days, and the residual half-lives: 57.97 (54.96-60.90), 58.36 (55.45-61.26), and 58.40 (55.62-61.37) days, for the Weibull, gamma, and lognormal models respectively. Corresponding estimates were obtained for the individual subjects. The three models provide equally excellent goodness-of-fit, reliable estimation, and physiologically plausible values of the directly interpretable RBC survival parameters.

Platelet Dynamics in Peritoneal Carcinomatosis Patients Treated with Cytoreductive Surgery and Hyperthermic Intraperitoneal Oxaliplatin

The aim of the study was to characterize the platelet count (PLT) dynamics in peritoneal carcinomatosis patients treated with cytoreductive surgery (CRS) and hyperthermic intraperitoneal oxaliplatin (HIO). Data from patients treated with CRS alone (N = 18) or CRS and HIO (N = 62) were used to estimate the baseline platelet count (PLT0), rate constants for platelet maturation (k tr ) and platelet random destruction (k s ), feedback on progenitor cell proliferation (γ), and the drug-specific model parameters (α, β). Plasma oxaliplatin concentrations, C p , reduced the proliferation rate of progenitor cells (k prol) according to a power function α × C p (β) . The surgery effect on k prol and k s was explored. The typical values (between subject variability) of the PLT0, k tr , k s , γ, α, and β were estimated to be 237 × 10(9) cells/L (32.9%), 7.09 × 10(-3) h(-1) (47.1%), 8.86 × 10(-3) h(-1) (80.0%), 0.621, 0.88 L/mg (56.9%), and 2.63. Surgery induced a maximal 2.09-fold increase in k prol that was attenuated with a half-life of 8.42 days. Splenectomy decreased k s by 47.5%. Age, sex, body surface area, sex, total proteins, and HIO carrier solution did not impact the model parameters. The model developed suggests that, following CRS and HIO, thrombocytopenia and thrombocytosis were reversible and short-lasting; the severity of the thrombocytopenia and thrombocytosis was inversely correlated, with splenectomized patients having thrombocytopenia of lower severity and thrombocytosis of higher severity; and the HIO dose and treatment duration determine the severity and duration of the thrombocytopenia. Higher HIO dose or longer treatment duration could be used without substantially increasing the risk of major hematological toxicity.

Pharmacodynamic models of age-structured cell populations

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.

Assessment of hemoglobin responsiveness to epoetin alfa in patients on hemodialysis using a population pharmacokinetic pharmacodynamic model

A population pharmacokinetic pharmacodynamic (PK/PD) model describing the effect of epoetin alfa on hemoglobin (Hb) response in hemodialysis patients was developed. Epoetin alfa pharmacokinetics was described using a linear 2-compartment model. PK parameter estimates were similar to previously reported values. A maturation-structured cytokinetic model consisting of 5 compartments linked in a catenary fashion by first-order cell transfer rates following a zero-order input process described the Hb time course. The PD model described 2 subpopulations, one whose Hb response reflected epoetin alfa dosing and a second whose response was unrelated to epoetin alfa dosing. Parameter estimates from the PK/PD model were physiologically reasonable and consistent with published reports. Numerical and visual predictive checks using data from 2 studies were performed. The PK and PD of epoetin alfa were well described by the model.

Simplification of complex physiologically based pharmacokinetic models of monoclonal antibodies

Monoclonal antibodies (mAbs) exhibit biexponential profiles in plasma that are commonly described with a standard two-compartment model with elimination from the central compartment. These models adequately describe mAb plasma PK. However, these models ignore elimination from the peripheral compartment. This may lead to underestimation of the volume of distribution of the peripheral compartment and thus over-predicts concentration in the peripheral compartment. We developed a simple and physiologically relevant model that incorporates information on binding and dissociation rates between mAb and FcRn receptor, mAb uptake, reflection, and catabolic degradation. We employed a previously published PBPK model and, with assumptions regarding rates of processes controlling mAb disposition, reduced the complex PBPK model to a simpler circular model with central, peripheral, and lymph compartments specifying elimination from both central and peripheral. We successfully applied the model to describe the PK of an investigational mAb. Our model presents an improvement over standard two-compartmental models in predicting whole-body average tissue concentrations while adequately describing plasma PK with minimal complexity and physiologically more meaningful parameters.

Clinical population pharmacokinetics and toxicodynamics of linezolid

Thrombocytopenia is a common side effect of linezolid, an oxazolidinone antibiotic often used to treat multidrug-resistant Gram-positive bacterial infections. Various risk factors have been suggested, including linezolid dose and duration of therapy, baseline platelet counts, and renal dysfunction; still, the mechanisms behind this potentially treatment-limiting toxicity are largely unknown. A clinical study was conducted to investigate the relationship between linezolid pharmacokinetics and toxicodynamics and inform strategies to prevent and manage linezolid-associated toxicity. Forty-one patients received 42 separate treatment courses of linezolid (600 mg every 12 h). A new mechanism-based, population pharmacokinetic/toxicodynamic model was developed to describe the time course of plasma linezolid concentrations and platelets. A linezolid concentration of 8.06 mg/liter (101% between-patient variability) inhibited the synthesis of platelet precursor cells by 50%. Simulations predicted treatment durations of 5 and 7 days to carry a substantially lower risk than 10- to 28-day therapy for platelet nadirs of <100 ×10(9)/liter. The risk for toxicity did not differ noticeably between 14 and 28 days of therapy and was significantly higher for patients with lower baseline platelet counts. Due to the increased risk of toxicity after longer durations of linezolid therapy and large between-patient variability, close monitoring of patients for development of toxicity is important. Dose individualization based on plasma linezolid concentration profiles and platelet counts should be considered to minimize linezolid-associated thrombocytopenia. Overall, oxazolidinone therapy over 5 to 7 days even at relatively high doses was predicted to be as safe as 10-day therapy of 600 mg linezolid every 12 h.

Romiplostim dose-response in patients with myelodysplastic syndromes

AIM

To characterize the romiplostim dose-response in subjects with low or intermediate-1 risk myelodysplastic syndromes (MDS) receiving subcutaneous romiplostim.

METHODS

Data from 44 MDS subjects receiving subcutaneous romiplostim (dose range 300-1500 μg week(-1) ) were used to develop a pharmacodynamic model consisting of a romiplostim-sensitive progenitor cell compartment linked to the peripheral blood compartment through four transit compartments representing the maturation in the bone marrow from megakaryocytes to platelets. A kinetics of drug effect model was used to quantify the stimulatory effect of romiplostim on the proliferation of sensitive progenitor cells and pharmacodynamics-mediated disposition was modelled by assuming the kinetics of drug effect constant (kDE ) to be proportional to the change in platelet count relative to baseline.

RESULTS

The estimated values (between subject variability) for baseline platelet count, mean transit time, and kDE were 24 × 10(9) l(-1) (47%), 9.6 days (44%) and 0.28 days(-1) , respectively. MDS subjects had a shorter platelet lifespan (42 h) than healthy subjects (257 h). Romiplostim effect was described for responders (78%) and non-responders (22%). The average weekly stimulatory effect of romiplostim on the production rate of sensitive progenitor cells at baseline was 269% per 100 μg week(-1) for responders. Body weight, age, gender and race were not statistically related to romiplostim pharmacodynamic parameters. Visual predictive checks confirmed the model adequacy.

CONCLUSION

The time course of platelet counts in MDS subjects receiving subcutaneous administration of escalating doses of romiplostim was characterized and showed a linear dose-response for romiplostim responders to increase the platelet counts.

Solution and implementation of distributed lifespan models

We consider a population where every individual has a unique lifespan. After expiring of its lifespan the individual has to leave the population. A realistic approach to describe these lifespans is by a continuous distribution. Such distributed lifespan models (DLSMs) were introduced earlier in the indirect response context and consist of the mathematical convolution operator to describe the rate of change. Therefore, DLSMs could not directly be implemented in standard PKPD software. In this work we present the solution representation of DLSMs with and without a precursor population and an implementation strategy for DLSMs in ADAPT , NONMEM and MATLAB . We fit hemoglobin measurements from literature and investigate computational properties.

A mathematical model of the effect of immunogenicity on therapeutic protein pharmacokinetics

A mathematical pharmacokinetic/anti-drug-antibody (PK/ADA) model was constructed for quantitatively assessing immunogenicity for therapeutic proteins. The model is inspired by traditional pharmacokinetic/pharmacodynamic (PK/PD) models, and is based on the observed impact of ADA on protein drug clearance. The hypothesis for this work is that altered drug PK contains information about the extent and timing of ADA generation. By fitting drug PK profiles while accounting for ADA-mediated drug clearance, the model provides an approach to characterize ADA generation during the study, including the maximum ADA response, sensitivity of ADA response to drug dose level, affinity maturation rate, time lag to observe an ADA response, and the elimination rate for ADA-drug complex. The model also provides a mean to estimate putative concentration-time profiles for ADA, ADA-drug complex, and ADA binding affinity-time profile. When simulating ADA responses to various drug dose levels, bell-shaped dose-response curves were generated. The model contains simultaneous quantitative modeling and provides estimation of the characteristics of therapeutic protein drug PK and ADA responses in vivo. With further experimental validation, the model may be applied to the simulation of ADA response to therapeutic protein drugs in silico, or be applied in subsequent PK/PD models.

A semi-physiological model of amyloid-β biosynthesis and clearance in human cerebrospinal fluid: a tool for alzheimer's disease research and drug development

Stable isotope labeling kinetics (SILK) was successfully applied to quantify endogenous amyloid-β (Aβ) metabolism in human cerebrospinal fluid (CSF). A semi-physiological model describing Aβ biosynthesis and degradation in human CSF and the impact of the γ-secretase inhibitor semagacestat should be developed and validated based on digitized data from three published SILK studies. Aβ biosynthesis was adequately characterized by six transit compartments. At each transition step, a first-order degradation process was implemented. A two-compartment model best described semagacestat CSF concentration-time profiles. Semagacestat concentrations were linked to the Aβ production by an inhibitory Emax model. For model validation, three individual Aβ profiles from literature were successfully predicted. Model application demonstrated a 35% decreased Aβ elimination rate constant in Alzheimer's disease (AD) patients. Study design optimization revealed that SILK studies could be conducted with significant less sampling points compared to the standard protocol without losing information about the Aβ metabolism, if analyzed by the presented model. In conclusion, the analysis outlined the advantages and opportunities of integrating all available data and knowledge into a semi-physiological model. The model can serve as valuable tool for researchers and clinicians interested in the pathology of AD as well as in the development of new therapeutics for AD.

Pharmacokinetic and pharmacodynamic modeling of romiplostim in animals

PURPOSE

Romiplostim is a novel thrombopoiesis-stimulating peptibody that targets the thrombopoietin c-Mpl receptor, resulting in increased platelet production. The pharmacodynamic-mediated disposition (PDMDD) and its stimulatory effect on platelet production in Sprague-Dawley rats, rhesus monkeys, and cynomolgus monkeys following IV bolus and SC administration at various dose levels were determined.

METHODS

The pharmacokinetic (PK) profile was described by a PDMDD model that accounts for romiplostim binding to the c-Mpl receptor. The PD model contained a series of aging compartments for precursor cells in bone marrow and platelets. The stimulatory function was described by an on-and-off function operating on the fractional receptor occupancy (RO). The threshold effect, RO(thr), and K(D) parameters were determinants of drug potency, whereas S(max) reflected drug efficacy.

RESULTS

The model implicated that receptor-mediated clearance was negligible. RO(thr) estimated occupancies were 0.288, 0.385, 0.771 for rats, rhesus, and cynomolgus monkeys, respectively. The analogous estimated values of K(D) were 4.05, 2320, and 429 ng/mL, implying that romiplostim was much more potent in rats, which was confirmed by a dose-response (ratio of peak platelet count to baseline) relationship.

CONCLUSIONS

The model adequately described romiplostim serum concentrations and platelet counts in rats, rhesus monkeys, and cynomolgus monkeys, and quantified linear clearance, PDMDD, and potency of romiplostim.

Pharmacokinetic and pharmacodynamic comparability study of moxetumomab pasudotox, an immunotoxin targeting CD22, in cynomolgus monkeys

Moxetumomab pasudotox is an immunotoxin currently being investigated in patients for the treatment of CD22-expressing B-cell malignancies. A single-cycle pharmacokinetic (PK)-pharmacodynamic (PD) study was conducted in cynomolgus monkeys for PK comparability assessment and population PK-PD modeling after major manufacturing process and site changes. Primates were randomized by body weight and baseline CD22 lymphocyte counts to receive intravenous administrations of 1 mg/kg moxetumomab pasudotox (n = 12/group) on Days 1, 3, and 5. PK and B-lymphocyte count data were modeled using a population approach. The 90% confidence intervals of the geometric mean ratios of PK exposure were within the 80%-125% range. The B lymphocytes were depleted to a similar extent, and the immunogenicity incidences were similar across the two groups. The B-cell depletion was described by a novel lifespan model in which moxetumomab pasudotox induced random destruction of B cells in each aging compartment. The endogenous de novo influx from bone marrow was subject to a negative feedback mechanism. The estimated B cell apparent lifespan was 51 days. Covariate analysis confirmed that the manufacturing change had no impact on PK or PD of moxetumomab pasudotox. Results from this study supported continued clinical investigation of moxetumomab pasudotox using the new material.

Modeling of red blood cell life-spans in hematologically normal populations

Despite the impact of red blood cell (RBC) Life-spans in some disease areas such as diabetes or anemia of chronic kidney disease, there is no consensus on how to quantitatively best describe the process. Several models have been proposed to explain the elimination process of RBCs: random destruction process, homogeneous life-span model, or a series of 4-transit compartment model. The aim of this work was to explore the different models that have been proposed in literature, and modifications to those. The impact of choosing the right model on future outcomes prediction--in the above mentioned areas--was also investigated. Both data from indirect (clinical data) and direct life-span measurement (biotin-labeled data) methods were analyzed using non-linear mixed effects models. Analysis showed that: (1) predictions from non-steady state data will depend on the RBC model chosen; (2) the transit compartment model, which considers variation in life-span in the RBC population, better describes RBC survival data than the random destruction or homogenous life-span models; and (3) the additional incorporation of random destruction patterns, although improving the description of the RBC survival data, does not appear to provide a marked improvement when describing clinical data.

Implementation of dose superimposition to introduce multiple doses for a mathematical absorption model (transit compartment model)

A mathematical absorption model (e.g. transit compartment model) is useful to describe complex absorption process. However, in such a model, an assumption has to be made to introduce multiple doses that a prior dose has been absorbed nearly completely when the next dose is administered. This is because the drug input cannot be determined from drug depot compartment through integration of the differential equation system and has to be analytically calculated. We propose a method of dose superimposition to introduce multiple doses; thereby eliminating the assumption. The code for implementing the dose superimposition in WinNonlin and NONMEM was provided. For implementation in NONMEM, we discussed a special case (SC) and a general case (GC). In a SC, dose superimposition was implemented solely using NM-TRAN abbreviated code and the maximum number of the doses that can be administered for any subject must be pre-defined. In a GC, a user-supplied function (FUNCA) in FORTRAN code was defined to perform dose superimposition to remove the restriction that the maximum number of doses must be pre-defined.

Lifespan based indirect response models

In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.

Multi-response model for rheumatoid arthritis based on delay differential equations in collagen-induced arthritic mice treated with an anti-GM-CSF antibody

Collagen-induced arthritis (CIA) in mice is an experimental model for rheumatoid arthritis, a human chronic inflammatory destructive disease. The therapeutic effect of neutralizing the cytokine granulocyte-macrophage colony-stimulating factor (GM-CSF) by an antibody was examined in the mouse disease in a view of deriving a pharmacokinetic/pharmacodynamic (PKPD) model. In CIA mice the development of disease is measured by a total arthritic score (TAS) and an ankylosis score (AKS). We present a multi-response PKPD model which describes the time course of the unperturbed and perturbed TAS and AKS. The antibody acts directly on GM-CSF by binding to it. Therefore, a compartment for the cytokine GM-CSF is an essential component of the mathematical model. This compartment drives the disease development in the PKPD model. Different known properties of arthritis development in the CIA model are included in the PKPD model. Firstly, the inflammation, driven by GM-CSF, dominates at the beginning of the disease and decreases after some time. Secondly, a destructive (ankylosis) part evolves in the TAS that is delayed in time. In order to model these two properties a delay differential equation was used. The PKPD model was applied to different experiments with doses ranging from 0.1 to 100 mg/kg. The influence of the drug was modeled by a non-linear approach. The final mathematical model consists of three differential equations representing the compartments for GM-CSF, inflammation and destruction. Our mathematical model described well all available dosing schedules by a simultaneous fit. We also present an equivalent and easy reformulation as ordinary differential equation which grants the use of standard PKPD software.

Romiplostim dose response in patients with immune thrombocytopenia

A pharmacodynamic model was developed for platelet counts in 52 patients with immune thrombocytopenia (ITP) receiving subcutaneous romiplostim in 3 phase I/II studies (dose range, 0.2-10 µg/kg). The model consisted of a drug-sensitive progenitor cell compartment linked to a peripheral blood compartment through 4 transition compartments. The baseline platelet count, mean transit time, and kinetics of drug effect constant were 11.1 × 10(9)/L, 170 hours, and 0.6 day(-1), respectively. The ITP patients had a shorter platelet life span and lower progenitor cell production rates than healthy volunteers. Romiplostim response was described for 2 subpopulations. The romiplostim stimulatory effect in ITP patients was 351%/100 µg/wk and 12%/100 µg/wk in 68% and 32% of patients, respectively. Visual and numerical predictive checks suggested accurate prediction of platelet time course and durable response rate in ITP patients. Model-based simulations confirmed the effectiveness of dose reduction to prevent platelet counts >400 × 10(9)/L.

Population pharmacokinetic and pharmacodynamic model-based comparability assessment of a recombinant human Epoetin Alfa and the Biosimilar HX575

The aim of this study was to develop an integrated pharmacokinetic and pharmacodynamic (PK/PD) model and assess the comparability between epoetin alfa HEXAL/Binocrit (HX575) and a comparator epoetin alfa by a model-based approach. PK/PD data-including serum drug concentrations, reticulocyte counts, red blood cells, and hemoglobin levels-were obtained from 2 clinical studies. In sum, 149 healthy men received multiple intravenous or subcutaneous doses of HX575 (100 IU/kg) and the comparator 3 times a week for 4 weeks. A population model based on pharmacodynamics-mediated drug disposition and cell maturation processes was used to characterize the PK/PD data for the 2 drugs. Simulations showed that due to target amount changes, total clearance may increase up to 2.4-fold as compared with the baseline. Further simulations suggested that once-weekly and thrice-weekly subcutaneous dosing regimens would result in similar efficacy. The findings from the model-based analysis were consistent with previous results using the standard noncompartmental approach demonstrating PK/PD comparability between HX575 and comparator. However, due to complexity of the PK/PD model, control of random effects was not straightforward. Whereas population PK/PD model-based analyses are suited for studying complex biological systems, such models have their limitations (statistical), and their comparability results should be interpreted carefully.

Comparative performance of cell life span and cell transit models for describing erythropoietic drug effects

Prolonged time delay in response to drug action is a common feature of hematological responses to pharmacotherapy such as erythropoiesis. The objective of this study was to compare the performance of two competing modeling approaches for delayed drug effects, mechanistic cell life span models, and semi-mechanistic cell transit models. The comparison was performed with an experimental dataset from multiple dose administrations of an erythropoietin mimetic to Cynomolgus monkeys. Comparative performance measures include visual predictive checks, goodness-of-fit plots, model estimation time, estimation status, and estimation error. The analysis revealed that both models resulted in a similarly good description of the erythropoietic drug effect, with precision and bias of the model-based predictions of red blood cell counts of less than 11%. The cell transit model needed slightly longer time to converge compared to the cell life span model. The system and drug effect parameters were similar in both models indicating that the models can be interchangeably used to describe the current data. Thus, model selection would be dependent on the purpose of the modeling exercise, the available data, and the time allocated for model development.