Impact of saturable distribution in compartmental PK models: dynamics and practical use

Population pharmacokinetics of imetelstat, a first-in-class oligonucleotide telomerase inhibitor

Imetelstat is a novel, first-in-class, oligonucleotide telomerase inhibitor in development for the treatment of hematologic malignancies including lower-risk myelodysplastic syndromes and myelofibrosis. A nonlinear mixed-effects model was developed to characterize the population pharmacokinetics of imetelstat and identify and quantify covariates that contribute to its pharmacokinetic variability. The model was developed using plasma concentrations from 7 clinical studies including 424 patients with solid tumors or hematologic malignancies who received single-agent imetelstat via intravenous infusion at various dose levels (0.4-11.7 mg/kg) and schedules (every week to every 4 weeks). Covariate analysis included factors related to demographics, disease, laboratory results, renal and hepatic function, and antidrug antibodies. Imetelstat was described by a two-compartment, nonlinear disposition model with saturable binding/distribution and dose- and time-dependent elimination from the central compartment. Theory-based allometric scaling for body weight was included in disposition parameters. The final covariates included sex, time, malignancy, and dose on clearance; malignancy and sex on volume of the central compartment; and malignancy and spleen volume on concentration of target. Clearance in females was modestly lower, resulting in nonclinically relevant increases in predicted exposure relative to males. No effects on imetelstat pharmacokinetics were identified for mild-to-moderate hepatic or renal impairment, age, race, and antidrug antibody status. All model parameters were estimated with adequate precision (relative standard error < 29%). Visual predictive checks confirmed the capacity of the model to describe the data. The analysis supports the imetelstat body-weight-based dosing approach and lack of need for dose individualizations for imetelstat-treated patients.

What should patients do if they miss a dose of medication? A theoretical approach

Medication adherence is a major problem for patients with chronic diseases that require long term pharmacotherapy. Many unanswered questions surround adherence, including how adherence rates translate into treatment efficacy and how missed doses of medication should be handled. To address these questions, we formulate and analyze a mathematical model of the drug concentration in a patient with imperfect adherence. We find exact formulas for drug concentration statistics, including the mean, the coefficient of variation, and the deviation from perfect adherence. We determine how adherence rates translate into drug concentrations, and how this depends on the drug half-life, the dosing interval, and how missed doses are handled. While clinical recommendations require extensive validation and should depend on drug and patient specifics, as a general principle our theory suggests that nonadherence is best mitigated by taking double doses following missed doses if the drug has a long half-life. This conclusion contradicts some existing recommendations that cite long drug half-lives as the reason to avoid a double dose after a missed dose. Furthermore, we show that a patient who takes double doses after missed doses can have at most only slightly more drug in their body than a perfectly adherent patient if the drug half-life is long. We also investigate other ways of handling missed doses, including taking an extra fractional dose following a missed dose. We discuss our results in the context of hypothyroid patients taking levothyroxine.

Clinical Pharmacokinetics and Pharmacodynamics of Immune Checkpoint Inhibitors

Immune checkpoint inhibitors (ICIs) have demonstrated significant clinical impact in improving overall survival of several malignancies associated with poor outcomes; however, only 20–40% of patients will show long-lasting survival. Further clarification of factors related to treatment response can support improvements in clinical outcome and guide the development of novel immune checkpoint therapies. In this article, we have provided an overview of the pharmacokinetic (PK) aspects related to current ICIs, which include target-mediated drug disposition and time-varying drug clearance. In response to the variation in treatment exposure of ICIs and the significant healthcare costs associated with these agents, arguments for both dose individualization and generalization are provided. We address important issues related to the efficacy and safety, the pharmacodynamics (PD), of ICIs, including exposure–response relationships related to clinical outcome. The unique PK and PD aspects of ICIs give rise to issues of confounding and suboptimal surrogate endpoints that complicate interpretation of exposure–response analysis. Biomarkers to identify patients benefiting from treatment with ICIs have been brought forward. However, validated biomarkers to monitor treatment response are currently lacking.

The computation of biomarkers in pharmacokinetics with the aid of singular perturbation methods

In pharmacokinetics, exact solutions to one-compartment models with nonlinear elimination kinetics cannot be found analytically, if dosages are assumed to be administered repetitively through extravascular routes (Tang and Xiao in J Pharmacokinet Pharmacodyn 34(6):807-827, 2007). Hence, for the corresponding impulsed dynamical system, alternative methods need to be developed to find approximate solutions. The primary purpose of this paper is to use the method of matched asymptotic expansions (Holmes Introduction to Perturbation Methods, vol 20. Springer Science & Business Media, Berlin, 2012), a singular perturbation method (Holmes, Introduction to Perturbation Methods, vol 20. Springer Science & Business Media, Berlin, 2012; Keener Principles of Applied Mathematics, Addison-Wesley, Boston, 1988), to obtain approximate solutions. With this method, we are able to rigorously determine conditions under which there is a stable periodic solution of the model equations. Furthermore, typical important biomarkers that enable the design of practical, efficient and safe drug delivery protocols, such as the time the drug concentration reaches the peak and the peak concentrations, are theoretically estimated by the perturbation method we employ.

Impact of mathematical pharmacology on practice and theory: four case studies

Drug-discovery has become a complex discipline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathematics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be transformed into their equilibrium concentration-response (target or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response-time dataset; when what-if? predictions beyond the observational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged. These four examples are typical situations when standard approaches known to the general community of pharmacokineticists prove to be inadequate.