Constrained numerical deconvolution using orthogonal polynomials.

In this article, we present an enhanced version of Cutler's deconvolution method to address the limitations of the original algorithm in estimating realistic input and output parameters. Cutler's method, based on orthogonal polynomials, suffers from unconstrained solutions, leading to the lack of realism in the deconvolved signals in some applications. Our proposed approach incorporates constraints using a ridge factor and Lagrangian multipliers in an iterative fashion, maintaining Cutler's iterative projection-based nature. This extension avoids the need for external optimization solvers, making it particularly suitable for applications requiring constraints on inputs and outputs. We demonstrate the effectiveness of the proposed method through two practical applications: the estimation of COVID-19 curves and the study of mavoglurant, an experimental drug. Our results show that the extended method presents a sum of squared residuals in the same order of magnitude of that of the original Cutler's method and other widely known unconstrained deconvolution techniques, but obtains instead physically plausible solutions, correcting the errors introduced by the alternative methods considered, as illustrated in our case studies.

Whole body physiologically based modelling of ß-blockers in the rat: events in tissues and plasma following an i.v. bolus dose.

BACKGROUND AND PURPOSE: Whole body physiologically based pharmacokinetic (PBPK) models have been increasingly applied in drug development to describe kinetic events of therapeutic agents in animals and humans. The advantage of such modelling is the ability to incorporate vast amounts of physiological information, such as organ blood flow and volume, to ensure that the model is as close to reality as possible. EXPERIMENTAL APPROACH: Previous PBPK model development of enantiomers of a series of seven racemic ß-blockers, namely, acebutolol, betaxolol, bisoprolol, metoprolol, oxprenolol, pindolol and propranolol, together with S-timolol in rat was based on tissue and blood concentration data at steady state. Compounds were administered in several cassettes with the composition mix and blood and tissue sampling times determined using a D-optimal design. KEY RESULTS: Closed-loop PBPK models were developed initially based on the application of open loop forcing function models to individual tissues and compounds. For the majority of compounds and tissues, distribution kinetics was adequately characterized by perfusion rate-limited models. For some compounds in the testes and gut, a permeability rate-limited distribution model was required to best fit the data. Parameter estimates of the tissue-to-blood partition coefficient through fitting of individual enantiomers and of racemic pair were generally in agreement and also concur with those from previous steady-state experiments. CONCLUSIONS AND IMPLICATIONS: PBPK modelling is a very powerful tool to aid drug discovery and development of therapeutic agents in animals and humans. However, careful consideration of the assumptions made during the modelling exercise is essential.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients.

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

Population Pharmacokinetics of Selumetinib and Its Metabolite N-desmethyl-selumetinib in Adult Patients With Advanced Solid Tumors and Children With Low-Grade Gliomas.

Selumetinib (AZD6244, ARRY-142886), a mitogen activated protein kinases (MEK1 and 2) inhibitor, has been granted orphan drug designation for differentiated thyroid cancer. The primary aim of this analysis was to characterize the population pharmacokinetics of selumetinib and its active metabolite N-desmethyl-selumetinib in patients with cancer. Concentration-time data from adult and pediatric clinical trials were pooled to develop a population pharmacokinetic model using a sequential approach where selumetinib and N-desmethyl-selumetinib data were modeled separately. A sequential zero- and first-order absorption with lag time with a two-compartment model for selumetinib and a two-compartment model for N-desmethyl-selumetinib best described the concentration-time data. Intrapatient variability in absorption was higher than interpatient variability. The apparent drug clearance (CL/F) from the central compartment was 13.5 L/hr (RSE 4.9%). Significant covariates for CL/F were age, alanine aminotransferase, and body surface area. This study confirms that flat dosing is appropriate in adults, whereas body-surface area based dosing should be used in pediatric patients.

Why has model-informed precision dosing not yet become common clinical reality? lessons from the past and a roadmap for the future.

Patient groups prone to polypharmacy and special subpopulations are susceptible to suboptimal treatment. Refined dosing in special populations is imperative to improve therapeutic response and/or lowering the risk of toxicity. Model-informed precision dosing (MIPD) may improve treatment outcomes by achieving the optimal dose for an individual patient. There is, however, relatively little published evidence of large-scale utility and impact of MIPD, where it is often implemented as local collaborative efforts between academia and healthcare. This article highlights some successful applications of bringing MIPD to clinical care and proposes strategies for wider integration in healthcare. Considerations are brought up herein that will need addressing to see MIPD become "widespread clinical practice," among those, wider interdisciplinary collaborations and the necessity for further evidence-based efficacy and cost-benefit analysis of MIPD in healthcare. The implications of MIPD on regulatory policies and pharmaceutical development are also discussed as part of the roadmap.

Identification of the effect of multiple polymorphisms on the pharmacokinetics of simvastatin and simvastatin acid using a population-modeling approach.

The aim of this work was to develop a joint population pharmacokinetic model for simvastatin (SV) and its active metabolite, simvastatin acid (SVA), that incorporates the effects of multiple genetic polymorphisms and clinical/demographic characteristics. SV/SVA plasma concentrations, demographic/clinical data, and genotypes for 18 genetic variants were collected from 74 individuals (three clinical trials) and analyzed using a nonlinear mixed-effects modeling approach. The structural model that best described the data included a two- and a one-compartment disposition model for SV and SVA, respectively. Age, weight, Japanese ethnicity, and seven genetic polymorphisms-rs4149056 (SLCO1B1), rs776746 (CYP3A5), rs12422149 (SLCO2B1), rs2231142 (ABCG2), rs4148162 (ABCG2), rs4253728 (PPARA), and rs35599367 (CYP3A4)-were identified as significantly affecting model parameters. The developed model was used to assess combinations of these covariates, highlighting specific risk factors associated with altered SV/SVA pharmacokinetics, and consequently myopathy cases that cannot be solely attributed to the rs4149056 CC genotype.

Oral biopharmaceutics tools - time for a new initiative - an introduction to the IMI project OrBiTo.

OrBiTo is a new European project within the IMI programme in the area of oral biopharmaceutics tools that includes world leading scientists from nine European universities, one regulatory agency, one non-profit research organization, four SMEs together with scientists from twelve pharmaceutical companies. The OrBiTo project will address key gaps in our knowledge of gastrointestinal (GI) drug absorption and deliver a framework for rational application of predictive biopharmaceutics tools for oral drug delivery. This will be achieved through novel prospective investigations to define new methodologies as well as refinement of existing tools. Extensive validation of novel and existing biopharmaceutics tools will be performed using active pharmaceutical ingredient (API), formulations and supporting datasets from industry partners. A combination of high quality in vitro or in silico characterizations of API and formulations will be integrated into physiologically based in silico biopharmaceutics models capturing the full complexity of GI drug absorption. This approach gives an unparalleled opportunity to initiate a transformational change in industrial research and development to achieve model-based pharmaceutical product development in accordance with the Quality by Design concept. Benefits include an accelerated and more efficient drug candidate selection, formulation development process, particularly for challenging projects such as low solubility molecules (BCS II and IV), enhanced and modified-release formulations, as well as allowing optimization of clinical product performance for patient benefit. In addition, the tools emerging from OrBiTo are expected to significantly reduce demand for animal experiments in the future as well as reducing the number of human bioequivalence studies required to bridge formulations after manufacturing or composition changes.

Modeling and simulation in clinical pharmacology and dose finding.

The breakout session 2 of the European Medicines Agency/European Federation of Pharmaceutical Industries and Associations Modeling and Simulation (M&S) workshop focused on two topics: when and how M&S should be used and would be accepted by the authorities for the dose-regimen selection; and when and how M&S can be applied to register a dosing regimen without the need for a specific study. Each topic was introduced by an industry and regulatory perspective, followed by case examples for illustration (Table 1).CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e29; doi:10.1038/psp.2013.5; advance online publication 27 February 2013.

Population pharmacokinetic/pharmacodynamic models for duloxetine in the treatment of diabetic peripheral neuropathic pain.

BACKGROUND: Duloxetine is a selective serotonin and norepinephrine reuptake inhibitor approved for the treatment of diabetic peripheral neuropathic pain (DPNP). The current analyses aimed to identify and evaluate the effect of any significant covariates on DPNP treatment response, via the development of a continuous descriptive Pharmacokinetics/Pharmacodynamics (PK/PD) model for pain score reduction and a proportional odds PK/PD model describing the proportion of patients achieving pain relief. METHODS: A total of 1139 patients received placebo, 20, 60 or 120 mg duloxetine daily for 12 weeks. The primary efficacy measure was 24-h pain scores collected on the 11-point categorical numerical rating scale averaged over a week. PK/PD models were fitted using non-linear mixed-effects models. RESULTS: Baseline pain severity was found to be an important factor in both PK/PD models. Larger drops in pain scores were observed for patients with more severe pain. The proportional odds PK/PD model used an a priori definition for adequate pain relief, which was a decrease in two points from baseline. Simulations showed that approximately 70% of patients in the highest dose groups would obtain pain relief at week 12, although placebo response was relatively high at 40%. The proportion of patients who obtained pain relief was slightly lower in those with mild pain compared to those with more severe pain. CONCLUSIONS: Patients with more severe pain at study entry had larger treatment responses and were more likely to achieve clinically meaningful pain relief with similar amounts of drug, compared to patients with milder pain.

Population pharmacokinetic analysis of ropivacaine and its metabolite 2',6'-pipecoloxylidide from pooled data in neonates, infants, and children.

BACKGROUND: The aim was to characterize ropivacaine and 2',6'-pipecoloxylidide (PPX) pharmacokinetics and factors affecting them in paediatric anaesthesia. METHODS: Population pharmacokinetics of ropivacaine and its active metabolite PPX were estimated after single and continuous ropivacaine blocks in 192 patients aged 0-12 yr from six pooled published studies. Unbound and total ropivacaine and PPX plasma concentration and PPX urinary excretion data were used for non-linear mixed-effects modelling by NONMEM. Covariates included age, body weight, gender, ethnic origin, ASA, site and method of administration, and total dose. RESULTS: One-compartment first-order pharmacokinetic models incorporating linear binding of ropivacaine and PPX to α(1)-acid glycoprotein were used. After accounting for the effect of body weight, clearance of unbound ropivacaine and PPX reached 41% and 89% of their mature values, respectively, at the age of 6 months. Ropivacaine half-life decreased with age from 13 h in the newborn to 3 h beyond 1 yr. PPX half-life differed from 19 h in the newborn to 8-11 h between 1 and 12 months to 17 h after 1 yr. Simulations indicate that for a single caudal block, the recommended dose could be increased by a factor of 2.9 (0-1 month group) and 6.3 (1-12 yr group) before the unbound plasma concentrations would cross the threshold for systemic toxicity. Corresponding factors for continuous epidural infusion are 1.8 and 4.9. CONCLUSIONS: Ropivacaine and PPX unbound clearance depends on body weight and age. The results support approved dose recommendations of ropivacaine for the paediatric population.

Phase I pharmacokinetic and pharmacodynamic study of the bioreductive drug RH1.

BACKGROUND: This trial describes a first-in-man evaluation of RH1, a novel bioreductive drug activated by DT-diaphorase (DTD), an enzyme overexpressed in many tumours. PATIENTS AND METHODS: A dose-escalation phase I trial of RH1 was carried out. The primary objective was to establish the maximum tolerated dose (MTD) of RH1. Secondary objectives were assessment of toxicity, pharmacokinetic determination of RH1 and pharmacodynamic assessment of drug effect through measurement of DNA cross linking in peripheral blood mononuclear cells (PBMCs) and tumour, DTD activity in tumour and NAD(P)H:quinone oxidoreductase 1 (NQO1) polymorphism status. RESULTS: Eighteen patients of World Health Organization performance status of zero to one with advanced refractory solid malignancies were enrolled. MTD was 1430 µg/m(2)/day with reversible bone marrow suppression being dose limiting. Plasma pharmacokinetic analysis showed RH1 is rapidly cleared from blood (t(1/2) = 12.3 min), with AUC increasing proportionately with dose. The comet-X assay demonstrated dose-related increases in DNA cross linking in PBMCs. DNA cross linking was demonstrated in tumours, even with low levels of DTD. Only one patient was homozygous for NQO1 polymorphism precluding any conclusion of its effect. CONCLUSIONS: RH1 was well tolerated with predictable and manageable toxicity. The MTD of 1430 µg/m(2)/day is the dose recommended for phase II trials. The biomarkers of DNA cross linking, DTD activity and NQO1 status have been validated and clinically developed.

Corticosteroid-binding globulin regulates cortisol pharmacokinetics.

OBJECTIVE: Corticosteroid-binding globulin (CBG) is the principal carrier for cortisol in the circulation. Variations in CBG-binding capacity are predicted to alter total serum cortisol disposition, but free serum cortisol is believed to be unaffected. Unbound cortisol pharmacokinetics (PK) have not been studied in the context of CBG changes. We aimed to assess the regulation of cortisol PK by CBG. DESIGN AND SUBJECTS: Women on oestrogens [oral contraceptive pill, (OCP)], patients homozygous for a nonfunctioning CBG variant (CBG null) and healthy controls (HV) were studied before and after IV and oral administration of hydrocortisone 20 mg. MEASUREMENTS: PK parameters were studied for total serum cortisol (SerF), free serum cortisol (FreeF) and cortisone (FreeE), and salivary cortisol (SalF) and cortisone (SalE): area under the curve (AUC), clearance (CL), half-life and volume of distribution (V(d)). RESULTS: Following IV hydrocortisone, AUC and half-life of SerF were significantly higher in the OCP group and lower in the CBG null. SerF CL and V(d) were significantly lower in the OCP group and increased in the CBG null, compared to HV. PK parameters for FreeF and the salivary biomarkers were not different between the CBG null and HV, although OCP patients still had higher AUC compared to HV and prolonged half-life. These findings were confirmed following oral hydrocortisone, but concentration-time profiles were highly heterogeneous and SalF interpretation was problematic because of oral contamination. CONCLUSIONS: We have demonstrated that CBG has a distinct effect on cortisol PK. When CBG binding is disrupted, FreeF retains normal PK characteristics, although CBG null patients lack a CBG-bound pool of readily releasable cortisol. Women on oestrogens may have altered free serum cortisol kinetics and thus may be potentially overexposed to glucocorticoids.

Proper lumping in systems biology models.

An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system's states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-B signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-B signalling pathways and were found to be in agreement, in terms of the identified key species for the system's kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.

Design of population pharmacokinetic experiments using prior information.

A population pharmacokinetic study design is a group of elementary designs each composed of a set of sampling times to be performed in a number of subjects in the design. Design factors such as the number of elementary designs, proportion of subjects in each elementary design, number of samples per subject, and sampling times in the subjects need to be carefully balanced in the design of a study. An optimally designed population pharmacokinetic study will give the best combination of these design factors and involves application of statistical experimental design principles to non-linear population pharmacokinetic models. Information from previous experiments, the literature, and experience in the form of model and parameter estimates are used to design a future study by optimization of a design criterion within some constraints. This work provides a brief background of approaches to the designs of a population pharmacokinetic experiment and a review of optimal design methodologies that have been developed for designing population pharmacokinetic experiments. Computer application programs and software that have been developed together with options available in them are also reviewed.

Optimal sampling strategies for early pharmacodynamic measures in tuberculosis.

OBJECTIVES: To evaluate whether methodological optimization of serial sputum colony counting (SSCC) studies, a potentially important component in the drug development process for tuberculosis, could significantly improve their power. METHODS: Simulations were carried out using a model derived from a large SSCC dataset. Variance inflation factors (VIFs) were calculated for model parameters, focusing on the elimination rate constant likely to reflect 'sterilizing' activity and sampling schemes were optimized relative to a scheme of daily sampling during the initial phase of therapy. Corresponding sample sizes required for SSCC studies using different schemes were also computed. RESULTS: Published sampling schemes lacked efficiency with respect to the 'sterilizing' phase. Pragmatic optimized schemes yielding greatest precision were achieved using eleven sampling points around a skeleton of 0, 2, 7, 14 and 56 days. The standard error of the 'sterilizing' rate constant was reduced more than 4-fold, and sample size for realistic treatment effects was effectively halved. Even schemes with a restricted duration of sampling to avoid high proportions of missing data and those with fewer sampling points still achieved significant gains in precision. Sensitivity analysis suggested that such schemes should continue to perform well over the immediately foreseeable range of improvements in therapy. CONCLUSIONS: Methodological improvements in the design of SSCC studies could make them a powerful tool in Phase II development of anti-tuberculosis agents.

Population dynamics of untreated Plasmodium falciparum malaria within the adult human host during the expansion phase of the infection.

A retrospective analysis was performed of parasite count data recorded from the first 7 days of blood or mosquito transmitted Plasmodium falciparum infections given for the treatment of neurosyphilis in the USA before 1963. The objective of this study was to characterize initial growth dynamics before host defences have significant effects on the infecting parasite population. Of the 328 patients' data available for analysis, 83 were excluded because they had received anti-malarial treatment during the first 7 days of the patent infection. Nonlinear mixed effects modelling was performed to estimate the parameters of interest; 'parasite multiplication rate per 48 h' (PMR), and length of the parasite life-cycle (periodicity). The parasitaemia versus time profiles showed great variability between patients. The mean population estimate of 'PMR' was approximately 8, and was highly dependent on the P. falciparum 'strain'. PMR also varied significantly between patients with a 90% prediction interval varying from 5.5 to 12.3-fold. Both intrinsic parasite multiplication rate (an intrinsic virulence determinant), and host susceptibility and defence contribute to expansion of the parasite biomass and thus disease severity in falciparum malaria.

How can we do pharmacokinetic studies in the tropics?

Information regarding the pharmacokinetic (PK) and pharmacodynamic (PD) properties of a drug provides the basis for optimizing dosing. PK-PD information should be obtained from patients representative of the overall target population, but in many tropical hospitals or health care facilities it may be medically hazardous or logistically difficult for an ill patient or a young child to be sampled repeatedly. Traditional methods used to determine the pharmacokinetic properties of a drug require analysis of a large number of blood samples per subject. However, using modern statistical methods, sparse datasets (i.e. with assay results from only a few, or as little as one blood sample per subject) can now be analysed by a method termed 'the population approach'. Modern assay techniques can often be adapted to small blood volumes allowing finger prick blood samples to be taken. One of the major aims of the population approach is to distinguish and characterize patient and disease contributors to inter-individual variance in drug pharmacokinetics. The purpose of this paper is to explain the basis of the population approach, to highlight its advantages compared to traditional methods of analysis, and to review the application of the population approach to data from field studies of antimalarial drugs. The design of population pharmacokinetic studies is also discussed briefly. The principles discussed in the paper are also applicable to pharmacodynamic data.

Modeling and stimulation for clinical trial design involving a categorical response: a phase II case study with naratriptan.

PURPOSE: The overall aim of the present study was to investigate retrospectively the feasibility and utility of model-based clinical trial simulation as applied to the clinical development of naratriptan with effect measured on a categorical scale. METHODS: A PK-PD model for naratriptan was developed by using information gathered from previous naratriptan and sumatriptan preclinical and clinical trials. The phase IIa naratriptan data were used to check the PK-PD model in its ability to describe future data. A further PK-PD model was developed by using the phase IIa naratriptan data, and a phase IIb trial was designed by simulation with the use of Matlab. The design resulting from clinical trial simulation was compared with that derived by using D-optimal design. RESULTS: The PK-PD model showed reasonable agreement with the data observed in the phase IIa naratriptan clinical trial. Clinical trial simulation resulted in a design with four or five arms at 0 mg, 2.5 and/or 5 mg, 10 mg, and 20 mg, PD measurements to be taken at 0, 2, and 4 or 6 h and at least 150 patients per arm. A sub-D-optimal design resulted in two dosing arms at 0 and 10 mg and PD measurements to be taken at 1 and 2 h. CONCLUSIONS: Clinical trial simulation is a useful tool for the quantitative assessment of the influence of the controllable factors and is the only tool for the quantitative assessment of the uncontrollable factors on the power of a clinical trial.