Predicting efficacy assessment of combined treatment of radiotherapy and nivolumab for NSCLC patients through virtual clinical trials using QSP modeling.

Non-Small Cell Lung Cancer (NSCLC) remains one of the main causes of cancer death worldwide. In the urge of finding an effective approach to treat cancer, enormous therapeutic targets and treatment combinations are explored in clinical studies, which are not only costly, suffer from a shortage of participants, but also unable to explore all prospective therapeutic solutions. Within the evolving therapeutic landscape, the combined use of radiotherapy (RT) and checkpoint inhibitors (ICIs) emerged as a promising avenue. Exploiting the power of quantitative system pharmacology (QSP), we undertook a study to anticipate the therapeutic outcomes of these interventions, aiming to address the limitations of clinical trials. After enhancing a pre-existing QSP platform and accurately replicating clinical data outcomes, we conducted an in-depth study, examining different treatment protocols with nivolumab and RT, both as monotherapy and in combination, by assessing their efficacy through clinical endpoints, namely time to progression (TTP) and duration of response (DOR). As result, the synergy of combined protocols showcased enhanced TTP and extended DOR, suggesting dual advantages of extended response and slowed disease progression with certain combined regimens. Through the lens of QSP modeling, our findings highlight the potential to fine-tune combination therapies for NSCLC, thereby providing pivotal insights for tailoring patient-centric therapeutic interventions.

Dynamical behavior-based approach for the evaluation of treatment efficacy: The case of immuno-oncology.

Sophistication of mathematical models in the pharmacological context reflects the progress being made in understanding physiological, pharmacological, and disease relationships. This progress has illustrated once more the need for advanced quantitative tools able to efficiently extract information from these models. While dynamical systems theory has a long history in the analysis of systems biology models, as emphasized under the dynamical disease concept by Mackey and Glass [Science 197, 287-289 (1977)], its adoption in pharmacometrics is only at the beginning [Chae, Transl. Clin. Pharmacol. 28, 109 (2020)]. Using a quantitative systems pharmacology model of tumor immune dynamics as a case study [Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], we here adopt a dynamical systems analysis to describe, in an exhaustive way, six different statuses that refer to the response of the system to therapy, in the presence or absence of a tumor-free attractor. To evaluate the therapy success, we introduce the concept of TBA, related to the Time to enter the tumor-free Basin of Attraction, and corresponding to the earliest time at which the therapy can be stopped without jeopardizing its efficacy. TBA can determine the optimal time to stop drug administration and consequently quantify the reduction in drug exposure.

Understanding the Mechanisms and Treatment of Heart Failure: Quantitative Systems Pharmacology Models with a Focus on SGLT2 Inhibitors and Sex-Specific Differences.

Heart failure (HF), which is a major clinical and public health challenge, commonly develops when the myocardial muscle is unable to pump an adequate amount of blood at typical cardiac pressures to fulfill the body's metabolic needs, and compensatory mechanisms are compromised or fail to adjust. Treatments consist of targeting the maladaptive response of the neurohormonal system, thereby decreasing symptoms by relieving congestion. Sodium-glucose co-transporter 2 (SGLT2) inhibitors, which are a recent antihyperglycemic drug, have been found to significantly improve HF complications and mortality. They act through many pleiotropic effects, and show better improvements compared to others existing pharmacological therapies. Mathematical modeling is a tool used to describe the pathophysiological processes of the disease, quantify clinically relevant outcomes in response to therapies, and provide a predictive framework to improve therapeutic scheduling and strategies. In this review, we describe the pathophysiology of HF, its treatment, and how an integrated mathematical model of the cardiorenal system was built to capture body fluid and solute homeostasis. We also provide insights into sex-specific differences between males and females, thereby encouraging the development of more effective sex-based therapies in the case of heart failure.

An exploratory analysis of the performance of methylphenidate regimens based on a PKPD model of dopamine and norepinephrine transporter occupancy.

Methylphenidate (MPH) is a psychostimulant which inhibits the uptake of dopamine and norepinephrine transporters, DAT and NET, and is mostly used to treat Attention Deficit/Hyperactivity Disorder. The current dose optimization is done through titration, a cumbersome approach for patients. To assess the therapeutic performance of MPH regimens, we introduce an in silico framework composed of (i) a population pharmacokinetic model of MPH, (ii) a pharmacodynamic (PD) model of DAT and NET occupancy, (iii) a therapeutic box delimited by time and DAT occupancy, and (iv) a performance score computation. DAT occupancy data was digitized (n = 152) and described with Emax models. NET occupancy was described with a KPD model. We used this integrative framework to simulate the performance of extended-release (18-99 mg) and tid MPH regimens (25-40 mg). Early blood samples of MPH seem to lead to higher DAT occupancy, consistent with an acute tolerance observed in clinical rating scales. An Emax model with a time-dependent tolerance was fitted to available data to assess the observed clockwise hysteresis. Peak performance is observed at 63 mg. While our analysis does not deny the existence of an acute tolerance, data precision in terms of formulation and sampling times does not allow a definite confirmation of this phenomenon. This work justifies the need for a more systematic collection of DAT and NET occupancy data to further investigate the presence of acute tolerance and assess the impact of low MPH doses on its efficacy.

Critical assessment of the revised guidelines for vancomycin therapeutic drug monitoring.

BACKGROUND: The revised vancomycin guidelines recommend replacing trough-only with trough or peak/trough Bayesian and first-order equations monitoring, citing their better AUC predictions and poor AUC-trough R2. Yet, evidence suggesting good AUC-trough correlation has been overlooked, and the optimality of peak/trough samples has been doubted. The guidelines recommend Bayesian programs implement richly-sampled PopPK priors despite their scarcity. Therefore, whether complex Bayesian and sample-demanding first-order equations can bring significant advantages to the practice over simple trough-only monitoring is worth weighing. OBJECTIVES: The primary aim is to compare the predictive performance of the AUC monitoring methods. Then, we investigate the impact of not adhering to trough sampling on the Bayesian-based predictions. Moreover, we report the nature of PopPK priors used in Bayesian programs to assess the applicability of the guideline recommendations. METHODS: We calculated the predictive performance of the monitoring methods using a standard PopPK modeling and simulation approach. We thoroughly explored the prior PK models implemented in Bayesian programs. RESULTS: Predictive performances of the monitoring methods were comparable at steady-state relative to the number of samples. Contrary to the recommendation, Bayesian trough monitoring did not result in better predictive performances compared to using random levels. Very few programs implemented richly-sampled priors. CONCLUSION: All the monitoring methods can be, relatively, reliable at steady-state, if properly implemented. Although only Bayesian-based monitoring can be used pre-steady-state, its predictive performance can be modest. Trough-only monitoring is the simplest approach. Constraints regarding trough sampling times could be relaxed. The scarcity of richly-sampled Bayesian priors questions the applicability of the revised guidelines recommendation.

A mechanistic model of ADHD as resulting from dopamine phasic/tonic imbalance during reinforcement learning.

Attention deficit hyperactivity disorder (ADHD) is the most common neurodevelopmental disorder in children. Although the involvement of dopamine in this disorder seems to be established, the nature of dopaminergic dysfunction remains controversial. The purpose of this study was to test whether the key response characteristics of ADHD could be simulated by a mechanistic model that combines a decrease in tonic dopaminergic activity with an increase in phasic responses in cortical-striatal loops during learning reinforcement. To this end, we combined a dynamic model of dopamine with a neurocomputational model of the basal ganglia with multiple action channels. We also included a dynamic model of tonic and phasic dopamine release and control, and a learning procedure driven by tonic and phasic dopamine levels. In the model, the dopamine imbalance is the result of impaired presynaptic regulation of dopamine at the terminal level. Using this model, virtual individuals from a dopamine imbalance group and a control group were trained to associate four stimuli with four actions with fully informative reinforcement feedback. In a second phase, they were tested without feedback. Subjects in the dopamine imbalance group showed poorer performance with more variable reaction times due to the presence of fast and very slow responses, difficulty in choosing between stimuli even when they were of high intensity, and greater sensitivity to noise. Learning history was also significantly more variable in the dopamine imbalance group, explaining 75% of the variability in reaction time using quadratic regression. The response profile of the virtual subjects varied as a function of the learning history variability index to produce increasingly severe impairment, beginning with an increase in response variability alone, then accumulating a decrease in performance and finally a learning deficit. Although ADHD is certainly a heterogeneous disorder, these results suggest that typical features of ADHD can be explained by a phasic/tonic imbalance in dopaminergic activity alone.

Phasic Dopamine Changes and Hebbian Mechanisms during Probabilistic Reversal Learning in Striatal Circuits: A Computational Study.

Cognitive flexibility is essential to modify our behavior in a non-stationary environment and is often explored by reversal learning tasks. The basal ganglia (BG) dopaminergic system, under a top-down control of the pre-frontal cortex, is known to be involved in flexible action selection through reinforcement learning. However, how adaptive dopamine changes regulate this process and learning mechanisms for training the striatal synapses remain open questions. The current study uses a neurocomputational model of the BG, based on dopamine-dependent direct (Go) and indirect (NoGo) pathways, to investigate reinforcement learning in a probabilistic environment through a task that associates different stimuli to different actions. Here, we investigated: the efficacy of several versions of the Hebb rule, based on covariance between pre- and post-synaptic neurons, as well as the required control in phasic dopamine changes crucial to achieving a proper reversal learning. Furthermore, an original mechanism for modulating the phasic dopamine changes is proposed, assuming that the expected reward probability is coded by the activity of the winner Go neuron before a reward/punishment takes place. Simulations show that this original formulation for an automatic phasic dopamine control allows the achievement of a good flexible reversal even in difficult conditions. The current outcomes may contribute to understanding the mechanisms for active control of dopamine changes during flexible behavior. In perspective, it may be applied in neuropsychiatric or neurological disorders, such as Parkinson's or schizophrenia, in which reinforcement learning is impaired.

Trapezoid bioequivalence: A rational bioavailability evaluation approach on account of the pharmaceutical-driven balance of population average and variability.

Among the current approaches for the analysis of bioequivalence, the average bioequivalence (ABE) is limited only to the mean bioavailability, whereas the population bioequivalence (PBE) criterion aggregates both mean and variance in a general comparison formula. However, a rational bioequivalence criterion capable of judging specific drug considerations is always still preferred. As an alternative approach, we introduce an aggregate criterion, namely, the trapezoid bioequivalence (TBE), which includes the consideration of both mean and variance of the bioavailability and adapted weighting of a drug's therapeutic properties. We first applied our method to specific simulated scenarios to compare the strengths and weaknesses of current bioequivalence approaches and demonstrate the improvements brought by TBE. As well, the impact of sample size and variability on ABE, PBE, and TBE are assessed using a population pharmacokinetic model of methylphenidate. Our results indicate that TBE inherits the advantages of both ABE and PBE while greatly reducing their inadequacies. Through simulations with population pharmacokinetic models of specific scenarios, we confirm that (1) TBE does not encounter the overly permissiveness issue of PBE, (2) TBE respects the hierarchy to ABE (TBE => ABE), and (3) TBE assesses bioequivalence with a restriction on σ T 2 - σ R 2 without an increase to type 2 errors. The clinically inspired simulations demonstrate TBE's superiority in a realistic context and its potential usefulness in practice. Moreover, the parameter choice in TBE may be adapted according to the specific context of a drug's pharmacological and pharmacodynamic properties.

Pharmacokinetic equations versus Bayesian guided vancomycin monitoring: Pharmacokinetic model and model-informed precision dosing trial simulations.

The recently released revised vancomycin consensus guideline endorsed area under the concentration-time curve (AUC) guided monitoring. Means to AUC-guided monitoring include pharmacokinetic (PK) equations and Bayesian software programs, with the latter approach being preferable. We aimed to evaluate the predictive performance of these two methods when monitoring using troughs or peaks and troughs at varying single or mixed dosing intervals (DIs), and evaluate the significance of satisfying underlying assumptions of steady-state and model transferability. Methods included developing a vancomycin population PK model and conducting model-informed precision dosing clinical trial simulations. A one-compartment PK model with linear elimination, exponential between-subject variability, and mixed (additive and proportional) residual error model resulted in the best model fit. Conducted simulations demonstrated that Bayesian-guided AUC can, potentially, outperform that of equation-based AUC predictions depending on the quality of model diagnostics and met assumptions. Ideally, Bayesian-guided AUC predictive performance using a trough from the first DI was equivalent to that of PK equations using two measurements (peak and trough) from the fifth DI. Model transferability diagnostics can guide the selection of Bayesian priors but are not strong indicators of predictive performance. Mixed versus single fourth and/or fifth DI sampling seems indifferent. This study illustrated cases associated with the most reliable AUC predictions and showed that only proper Bayesian-guided monitoring is always faster and more reliable than equations-guided monitoring in pre-steady-state DIs in the absence of a loading dose. This supports rapid Bayesian monitoring using data as sparse and early as a trough at the first DI.

An Update on Population Pharmacokinetic Analyses of Vancomycin, Part II: In Pediatric Patients.

Vancomycin is widely used in pediatric patients, however, large inter- and intraindividual variability are observed in vancomycin pharmacokinetics, affecting proper therapeutic monitoring. This review aimed at providing a comprehensive synthesis of the population pharmacokinetic models of vancomycin in pediatric patients and identifying potential factors responsible for the variability observed in various subpopulations. We conducted a literature search of the PubMed and EMBASE databases to obtain population pharmacokinetic studies for vancomycin published between January 2011 and January 2020, which resulted in a total of 33 studies. Vancomycin pharmacokinetics were generally characterized using a one-compartment model (n = 27), while a two-compartment model was used in six studies. The median (interquartile range) of the typical vancomycin clearance (CL) and the total volume of distribution adjusted to the median or mean body weight of the respective study was 0.103 L/h/kg (0.071-0.125) and 0.64 L/kg (0.59-1.03), respectively. Median weight-adjusted CL between different child age groups, such as infants and adolescents, did not appear to vary significantly, although the sample size for many age groups was very small. Examples of the conditions with relatively abnormal vancomycin pharmacokinetic values include renal insufficiency, sepsis, hematological and solid malignancy, and hypothermia treatment. Factors influencing pediatric vancomycin pharmacokinetics after adjusting for size and maturation include various renal function descriptors and some case-specific variables such as dialysate flow rate, ultrafiltrate output, and hypothermia. This review was able to document possible variables explaining the high variability observed in certain subpopulations and contrast vancomycin pharmacokinetics in different pediatric subpopulations.

A Quantitative Systems Pharmacology Framework for Optimal Doxorubicin Granulocyte Colony-Stimulating Factor Regimens in Triple-Negative Breast Cancer.

INTRODUCTION: To mitigate the risk of neutropenia during chemotherapy treatment of triple-negative breast cancer, prophylactic and supportive therapy with granulocyte colony-stimulating factor (G-CSF) is administered concomitant to chemotherapy. The proper timing of combined chemotherapy and G-CSF is crucial for treatment outcomes. METHODS: Leveraging our established mathematical model of neutrophil production by G-CSF, we developed quantitative systems pharmacology (QSP) framework to investigate how modulating chemotherapy dose frequency and intensity can maximize antitumour effects. To establish schedules that best control tumour size while minimizing neutropenia, we combined Gompertzian tumour growth with pharmacokinetic/pharmacodynamic models of doxorubicin and G-CSF, and our QSP model of neutrophil production. RESULTS: We optimized a range of chemotherapeutic cycle lengths and dose sizes to establish regimens that simultaneously reduced tumour burden while minimizing neutropenia. Our results suggest that cytotoxic chemotherapy with doxorubicin 45 mg/m2 every 14 days provides effective control of tumour growth while mitigating neutropenic risks. CONCLUSION: This work suggests future avenues for optimal regimens of chemotherapy with prophylactic G-CSF support. Importantly, the algorithmic approach that we developed can aid in balancing the anticancer and the neutropenic effects of both drugs, and therefore contributes to rational considerations in clinical decision-making in triple-negative breast cancer.

Introduction to Focus Issue: Dynamical disease: A translational approach.

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

Dynamical systems analysis as an additional tool to inform treatment outcomes: The case study of a quantitative systems pharmacology model of immuno-oncology.

Quantitative systems pharmacology (QSP) proved to be a powerful tool to elucidate the underlying pathophysiological complexity that is intensified by the biological variability and overlapped by the level of sophistication of drug dosing regimens. Therapies combining immunotherapy with more traditional therapeutic approaches, including chemotherapy and radiation, are increasingly being used. These combinations are purposed to amplify the immune response against the tumor cells and modulate the suppressive tumor microenvironment (TME). In order to get the best performance from these combinatorial approaches and derive rational regimen strategies, a better understanding of the interaction of the tumor with the host immune system is needed. The objective of the current work is to provide new insights into the dynamics of immune-mediated TME and immune-oncology treatment. As a case study, we will use a recent QSP model by Kosinsky et al. [J. Immunother. Cancer 6, 17 (2018)] that aimed to reproduce the dynamics of interaction between tumor and immune system upon administration of radiation therapy and immunotherapy. Adopting a dynamical systems approach, we here investigate the qualitative behavior of the representative components of this QSP model around its key parameters. The ability of T cells to infiltrate tumor tissue, originally identified as responsible for individual therapeutic inter-variability [Y. Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], is shown here to be a saddle-node bifurcation point for which the dynamical system oscillates between two states: tumor-free or maximum tumor volume. By performing a bifurcation analysis of the physiological system, we identified equilibrium points and assessed their nature. We then used the traditional concept of basin of attraction to assess the performance of therapy. We showed that considering the therapy as input to the dynamical system translates into the changes of the trajectory shapes of the solutions when approaching equilibrium points and thus providing information on the issue of therapy.

Population Pharmacokinetics of Candesartan in Patients with Chronic Heart Failure.

Heart failure (HF) causes pathological changes in multiple organs, thus affecting the pharmacokinetics (PK) of drugs. The aim of this study was to investigate the PK of candesartan in patients with HF while examining significant covariates and their related impact on estimated clearance using a population PK (Pop-PK) modeling approach. Data from a prospective, multicenter study were used. Modeling and simulations were conducted using Nonlinear Mixed-Effects Modeling (NONMEM) and R software. A total of 281 white patients were included to develop the Pop-PK model. The final model developed for apparent oral clearance (CL/F) included weight, estimated glomerular filtration rate (eGFR), and diabetes, which partly explained its interindividual variability. The mean CL/F value estimated was 7.6 L/h (1.7-22.6 L/h). Simulations revealed that an important decrease in CL/F (> 25%) is obtained with the combination of the factors retained in the final model. Considering these factors, a more individualized approach of candesartan dosing should be investigated in patients with HF.

An integrative model of Parkinson's disease treatment including levodopa pharmacokinetics, dopamine kinetics, basal ganglia neurotransmission and motor action throughout disease progression.

Levodopa is considered the gold standard treatment of Parkinson's disease. Although very effective in alleviating symptoms at their onset, its chronic use with the progressive neuronal denervation in the basal ganglia leads to a decrease in levodopa's effect duration and to the appearance of motor complications. This evolution challenges the establishment of optimal regimens to manage the symptoms as the disease progresses. Based on up-to-date pathophysiological and pharmacological knowledge, we developed an integrative model for Parkinson's disease to evaluate motor function in response to levodopa treatment as the disease progresses. We combined a pharmacokinetic model of levodopa to a model of dopamine's kinetics and a neurocomputational model of basal ganglia. The parameter values were either measured directly or estimated from human and animal data. The concentrations and behaviors predicted by our model were compared to available information and data. Using this model, we were able to predict levodopa plasma concentration, its related dopamine concentration in the brain and the response performance of a motor task for different stages of disease.

Nonlinear pharmacodynamics of levodopa through Parkinson's disease progression.

The effect of levodopa in alleviating the symptoms of Parkinson's disease is altered in a highly nonlinear manner as the disease progresses. This can be attributed to different compensation mechanisms taking place in the basal ganglia where the dopaminergic neurons are progressively lost. This alteration in the effect of levodopa complicates the optimization of a drug regimen. The present work aims at investigating the nonlinear dynamics of Parkinson's disease and its therapy through mechanistic mathematical modeling. Using a holistic approach, a pharmacokinetic model of levodopa was combined to a dopamine dynamics and a neurocomputational model of basal ganglia. The influence of neuronal death on these different mechanisms was also integrated. Using this model, we were able to investigate the nonlinear relationships between the levodopa plasma concentration, the dopamine brain concentration, and a response to a motor task. Variations in dopamine concentrations in the brain for different levodopa doses were also studied. Finally, we investigated the narrowing of a levodopa therapeutic index with the progression of the disease as a result of these nonlinearities. In conclusion, various consequences of nonlinear dynamics in Parkinson's disease treatment were studied by developing an integrative model. This model paves the way toward individualization of a dosing regimen. Using sensor based information, the parameters of the model could be fitted to individual data to propose optimal individual regimens.

A non-linear deterministic model of action selection in the basal ganglia to simulate motor fluctuations in Parkinson's disease.

Motor fluctuations and dyskinesias are severe complications of Parkinson's disease (PD), especially evident at its advanced stage, under long-term levodopa therapy. Despite their strong clinical prevalence, the neural origin of these motor symptoms is still a subject of intense debate. In this work, a non-linear deterministic neurocomputational model of the basal ganglia (BG), inspired by biology, is used to provide more insights into possible neural mechanisms at the basis of motor complications in PD. In particular, the model is used to simulate the finger tapping task. The model describes the main neural pathways involved in the BG to select actions [the direct or Go, the indirect or NoGo, and the hyperdirect pathways via the action of the sub-thalamic nucleus (STN)]. A sensitivity analysis is performed on some crucial model parameters (the dopamine level, the strength of the STN mechanism, and the strength of competition among different actions in the motor cortex) at different levels of synapses, reflecting major or minor motor training. Depending on model parameters, results show that the model can reproduce a variety of clinically relevant motor patterns, including normokinesia, bradykinesia, several attempts before movement, freezing, repetition, and also irregular fluctuations. Motor symptoms are, especially, evident at low or high dopamine levels, with excessive strength of the STN and with weak competition among alternative actions. Moreover, these symptoms worsen if the synapses are subject to insufficient learning. The model may help improve the comprehension of motor complications in PD and, ultimately, may contribute to the treatment design.

An Update on Population Pharmacokinetic Analyses of Vancomycin, Part I: In Adults.

Despite the wide clinical use of vancomycin, controversy remains regarding its optimal dosage regimens. This can be attributed to the large between- and within-subject variability in the pharmacokinetics of vancomycin. This review aimed at providing a synthesis of population pharmacokinetic models of vancomycin in adults, determining the most reported pharmacokinetic models, and identifying various sources of variability in different special subpopulations to better inform vancomycin dosing. We searched PubMed and EMBASE for population pharmacokinetic studies of vancomycin published from January 2011 to May 2019. Inspection of the relevant lists of references was conducted, as well. This search resulted in a total of 30 eligible studies, which were included. One-, two-, and three-compartments models were reported to best describe vancomycin population pharmacokinetics in 13, 14, and 3 studies, respectively. Three-compartment models were implemented in three studies to account for an additional cerebrospinal fluid compartment. The most common predictors were creatinine clearance and bodyweight, in 20 and 13 studies, respectively. Estimated values of vancomycin clearance and total volume of distribution varied widely from 0.334 to 8.75 L/h (0.0054-0.1279 L/h/kg) and from 7.12 to 501.8 L (0.097-6.97 L/kg), respectively. Almost all studies implemented an exponential interindividual variability model, and the highest variability on clearance was 99.2%. In conclusion, this review highlights the wide ranges and the high variability of estimated population pharmacokinetic parameters. This information can help guide dosing in different subpopulations. Yet, additional analyses with pooled subpopulations might be needed to confirm the necessity of modified dosage regimens.

Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration.

In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis-Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve ([Formula: see text]) at steady state is higher compared to that at the single dose ([Formula: see text]). Moreover, by splitting the dose and dosing interval into halves, we have revealed that it can result in a significant decrease in the steady-state average concentration. These model-based findings, which contrast with the current knowledge for linear PK, confirm the necessity to revisit drugs exhibiting nonlinear PK and to suggest a rational way of using mathematical analysis for the dosing regimen design.

A Quantitative Comparison Approach for Methylphenidate Drug Regimens in Attention-Deficit/Hyperactivity Disorder Treatment.

OBJECTIVE: Different methylphenidate (MPH) formulations, immediate release (IR) or extended release (ER), have been developed to treat Attention-Deficit/Hyperactivity Disorder (ADHD). A better use of these formulations, with a proper choice of their timing, dosage, and combination, can help to attain optimal therapeutic effect while maintaining a good quality of life. In this study, we aim at presenting a quantitative comparison approach to help identify drug regimens that provide best therapeutic performances and respect patients' specific needs. METHODS: Using pharmacokinetic (PK) models of various MPH formulations constructed with data in hand and a formerly developed performance metric for MPH regimens, we proposed a statistical integral strategy for regimen comparison, which comprises a sequential, a relative, and a probability-over-threshold method. The first is hierarchical in nature and sequentially compares the regimen performance, the total daily dose, and the administration frequency. The second compares two regimens by quantifying their similarity. The third computes the probability of an incremental regimen performance over a specified threshold. The first two comparison approaches are used for naive patients, whereas the third one is for patients under treatment. RESULTS: PK models of one compartment effectively describe both the IR and ER data. Applied to three frequent MPH clinical situations, the three-methods strategy is able to distinguish the regimens proposed for each. A combined regimen of IR and ER taken at the same time performs better than a single ER dose. CONCLUSION: The proposed statistical strategy is able to differentiate ADHD regimens in various clinically relevant situations, and adapt the use of MPH drugs to a patient's daily routine. Since it does not compare fixed doses and formulations but rather any MPH regimen, our approach generalizes the current context of bioequivalence study and provides an accessible computational tool for objectively selecting MPH regimens.