PKPD Model of Interleukin-21 Effects on Thermoregulation in Monkeys—Application and Evaluation of Stochastic Differential Equations

PK/PD modeling of 5-hydroxytryptophan (5-HTP) challenge test with cortisol measurement in serum and saliva

This research was planned to build a Pharmacokinetic/Pharmacodynamic (PK/PD) model of 5‐hydroxytryptophan (5‐HTP) challenge study including a circadian rhythm component of cortisol and to predict serum cortisol based on saliva cortisol. Data from three 5‐HTP challenge studies in healthy volunteers were collected. Serum 5‐HTP, saliva, and serum cortisol were sampled as PK and PD marker. The population PK/PD modeling approach was applied. A baseline model of serum cortisol was built to assess the circadian rhythm before a pharmacodynamic model was used to evaluate the drug effect of the 5‐HTP on cortisol. Finally, linear and power function relationships were tested to predict serum cortisol based on saliva cortisol. The PK of 5‐HTP could be described using a one‐compartment model with a transit compartment. The typical value for clearance was 20.40 L h⁻¹ and showed inter‐study variability. A cosine function was chosen and properly described the circadian rhythm of serum cortisol. A linear approximation model was applied to fit the 5‐HTP PD effect on cortisol data with a slope of 4.16 ng mL⁻¹ h. A power function provided a better description than a linear function to relate the saliva and serum cortisol. In conclusion, a circadian rhythm component was built in the PK/PD model of the 5‐HTP challenge test which could better improve the understanding of the stimulating effect on HPA with cortisol change. After the 5‐HTP challenge, saliva cortisol correlated well with serum cortisol and was predictable by a population PK‐PD model.

Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics

Nonlinear mixed effects (NLME) modeling based on stochastic differential equations (SDEs) have evolved into a promising approach for analysis of PK/PD data. SDE-NLME models go beyond the realm of standard population modeling as they consider stochastic dynamics, thereby introducing a probabilistic perspective on the state variables. This article presents a summary of the main contributions to SDE-NLME models found in the literature. The aims of this work were to develop an exact gradient version of the first-order conditional estimation (FOCE) method for SDE-NLME models and to investigate whether it enabled faster estimation and better gradient precision/accuracy compared to the use of gradients approximated by finite differences. A simulation-estimation study was set up whereby finite difference approximations of the gradients of each level were interchanged with the exact gradients. Following previous work, the uncertainty of the state variables was accounted for using the extended Kalman filter (EKF). The exact gradient FOCE method was implemented in Mathematica 11 and evaluated on SDE versions of three common PK/PD models. When finite difference gradients were replaced by exact gradients at both FOCE levels, relative runtimes improved between 6- and 32-fold, depending on model complexity. Additionally, gradient precision/accuracy was significantly better in the exact gradient case. We conclude that parameter estimation using FOCE with exact gradients can successfully be applied to SDE-NLME models.

Development of a mechanism-based pharmacokinetic/pharmacodynamic model to characterize the thermoregulatory effects of serotonergic drugs in mice

We have shown recently that concurrent harmaline, a monoamine oxidase-A inhibitor (MAOI), potentiates serotonin (5-HT) receptor agonist 5-methoxy-N,N-dimethyltryptamine (5-MeO-DMT)-induced hyperthermia. The objective of this study was to develop an integrated pharmacokinetic/pharmacodynamic (PK/PD) model to characterize and predict the thermoregulatory effects of such serotonergic drugs in mice. Physiological thermoregulation was described by a mechanism-based indirect-response model with adaptive feedback control. Harmaline-induced hypothermia and 5-MeO-DMT–elicited hyperthermia were attributable to the loss of heat through the activation of 5-HT_1A receptor and thermogenesis via the stimulation of 5-HT_2A receptor, respectively. Thus serotonergic 5-MeO-DMT–induced hyperthermia was readily distinguished from handling/injection stress-provoked hyperthermic effects. This PK/PD model was able to simultaneously describe all experimental data including the impact of drug-metabolizing enzyme status on 5-MeO-DMT and harmaline PK properties, and drug- and stress-induced simple hypo/hyperthermic and complex biphasic effects. Furthermore, the modeling results revealed a 4-fold decrease of apparent SC₅₀ value (1.88–0.496 µmol/L) for 5-MeO-DMT when harmaline was co-administered, providing a quantitative assessment for the impact of concurrent MAOI harmaline on 5-MeO-DMT–induced hyperthermia. In addition, the hyperpyrexia caused by toxic dose combinations of harmaline and 5-MeO-DMT were linked to the increased systemic exposure to harmaline rather than 5-MeO-DMT, although the body temperature profiles were mispredicted by the model. The results indicate that current PK/PD model may be used as a new conceptual framework to define the impact of serotonergic agents and stress factors on thermoregulation.

A review on estimation of stochastic differential equations for pharmacokinetic/pharmacodynamic models

This paper is a survey of existing estimation methods for pharmacokinetic/pharmacodynamic (PK/PD) models based on stochastic differential equations (SDEs). Most parametric estimation methods proposed for SDEs require high frequency data and are often poorly suited for PK/PD data which are usually sparse. Moreover, PK/PD experiments generally include not a single individual but a group of subjects, leading to a population estimation approach. This review concentrates on estimation methods which have been applied to PK/PD data, for SDEs observed with and without measurement noise, with a standard or a population approach. Besides, the adopted methodologies highly differ depending on the existence or not of an explicit transition density of the SDE solution.

An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers

Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected “training” data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent “validation” data in melanoma and renal cell carcinoma-challenged mice (R²>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R²>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic.

Among the many potential drugs explored within the scope of cancer immunotherapy are selected cytokines which possess promising immune-boosting properties. Yet, the natural involvement of these proteins in multiple, often contradicting biological processes can complicate their use in the clinic. The cytokine interleukin (IL)-21 is no exception: while its strength as an anticancer agent has been established in several animal studies, response rates in melanoma and renal cell carcinoma patients remain low. To help guide the design of effective IL-21 therapy, we have developed a mathematical model that bridges between the complex biology of IL-21 and its optimal clinical use. Our model integrates data from preclinical studies under diverse IL-21 treatment settings, and was validated by extensive experiments in tumor-bearing mice. Model simulations predicted that beneficial, clinically practical IL-21 therapy should be composed of low-dose schedules, and/or schedules in which several partial doses are administered rather than a single complete dose. These findings were subsequently confirmed in mice with melanoma. Thus, future testing of these strategies in solid cancer patients can be a promising starting point for improving IL-21 therapy. Our model can thus provide a computational platform for rationalizing IL-21 regimens and streamlining its clinical development.

A semi-physiological-based pharmacokinetic/pharmacodynamic model to describe the effects of topotecan on b-lymphocyte lineage cells

PURPOSE

To develop a semi-physiological-based model describing simultaneously the time course of immature and mature B-lymphocytes after topotecan (TPT) administration to tumor-bearing rats.

METHODS

Twenty-four tumor-bearing BDIX male rats received a single 6 mg/kg intra-peritoneal dose of TPT or saline. Mature and immature B-cell levels were measured every two days during three weeks and showed a very different temporal pattern. Both B-cell populations declined rapidly, reaching the nadir at 3-4 days after TPT administration; however, mature cells returned to baseline at day 8, while immature B-cells stayed at nadir until day 9 instead. Data were modeled using the population approach with NONMEM VI.

RESULTS

The model developed maintains the proliferation, maturation and degradation elements of previous published models for myelosuppresion. In order to describe the rapid recovery of mature cells, it includes a peripheral compartment providing a constant supply of mature cells to the bloodstream.

CONCLUSIONS

The major contribution of the model is its new structure and the dynamical consequences, demonstrating an independent behavior between mature and immature B-cells during recovery. The final model could represent a good basis for the optimization of cytotoxic drugs oriented to attain a maximum antitumor efficacy while minimizing hematological toxicity.