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.

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.

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.

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.

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.

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.

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.

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.

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.

Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis-Menten elimination: the case of single dose.

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis-Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.

Transit and lifespan in neutrophil production: implications for drug intervention.

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino's extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. An extension to the Quartino model is provided by considering a general number of transit compartments and introducing an extra parameter that allows for the decoupling of the maturation time from the production rate of cells. An overview of the well established linear chain technique, used to reformulate transit compartment models with constant transit rates as distributed delay differential equations (DDEs), is then given. A state-dependent time rescaling of the Quartino model is performed to apply the linear chain technique and rewrite the Quartino model as a distributed DDE, yielding a discrete DDE model in a certain parameter limit. Next, stability and bifurcation analyses are undertaken in an effort to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension models incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment. This misspecification can have far reaching consequences on the development of future models of myelosuppression in PK/PD.

Modelling the dose-response relationship: the fair share of pharmacokinetic and pharmacodynamic information.

AIMS: The aim of this paper is to investigate the role of drug concentration samplings in the modelling of the dose-response relationship. METHODS: Using an initial PK/PD model, a reference dataset was simulated. PK and PD samples were extracted to create reduced datasets. PK/PD and K-PD models were fitted to theses reduced datasets. Post hoc estimates from both types of models were compared to the initial PK/PD model and performance was assessed. RESULTS: K-PD models were largely biased when the drug has a nonlinear elimination. PK/PD models with 1 PK and 2 PD samples were superior to K-PD models with 3 PD samples. PK/PD models with 1 or 2 PK samples and 3 PD samples proved to be superior to K-PD models with 4 PD samples. CONCLUSIONS: K-PD models should not be used when the drug has nonlinear elimination. K-PD models should not replace PK/PD modelling but are an alternative approach if the PD information is large enough.

Steady-state volume of distribution of two-compartment models with simultaneous linear and saturated elimination.

The model-independent estimation of physiological steady-state volume of distribution ([Formula: see text]), often referred to non-compartmental analysis (NCA), is historically based on the linear compartment model structure with central elimination. However the NCA-based steady-state volume of distribution ([Formula: see text]) cannot be generalized to more complex models. In the current paper, two-compartment models with simultaneous first-order and Michaelis-Menten elimination are considered. In particular, two indistinguishable models [Formula: see text] and [Formula: see text], both having central Michaelis-Menten elimination, while first-order elimination exclusively either from central or peripheral compartment, are studied. The model-based expressions of the steady-state volumes of distribution [Formula: see text] and their relationships to NCA-based [Formula: see text] are derived. The impact of non-linearity and peripheral elimination is explicitly delineated in the formulas. Being concerned with model identifiability and indistinguishability issues, an interval estimate of [Formula: see text] is suggested.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia.

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy. In response, granulocyte colony-stimulating factor (G-CSF) is co-administered during chemotherapy to stimulate neutrophil production, increase neutrophil counts, and hopefully avoid neutropenia. Its clinical use is, however, largely dictated by trial and error processes. Based on up-to-date knowledge and rational considerations, we develop a physiologically realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate with pharmacokinetic and pharmacodynamic (PKPD) models of a chemotherapeutic agent and an exogenous form of G-CSF (recombinant human G-CSF, or rhG-CSF). In this work, model parameters represent the average values for a general patient and are extracted from the literature or estimated from available data. The dose effect predicted by the model is confirmed through previously published data. Using our model, we were able to determine clinically relevant dosing regimens that advantageously reduce the number of rhG-CSF administrations compared to original studies while significantly improving the neutropenia status. More particularly, we determine that it could be beneficial to delay the first administration of rhG-CSF to day seven post-chemotherapy and reduce the number of administrations from ten to three or four for a patient undergoing 14-day periodic chemotherapy.

Limited sampling strategies for estimating intravenous and oral cyclosporine area under the curve in pediatric hematopoietic stem cell transplantation.

BACKGROUND: The optimal monitoring strategy for cyclosporine (CsA) in pediatric hematopoietic stem cell transplantation (HSCT) patients remains unclear. Although there is a growing interest in the use of the area under the concentration-time curve (AUC), measurement of AUC in clinical settings is often impractical. The objective of this study was to identify and validate limited sampling strategies (LSSs) for the prediction of CsA AUC after intravenous (IV) and oral (PO) administration in this population. METHODS: Sixty-eight pediatric patients who underwent HSCT and received CsA were investigated. Twelve-hour pharmacokinetic profiles (n = 138) performed per standard of care were collected. Weighted multiple linear regression was used to investigate all possible LSSs consisting of 4 or less concentration-time points. Their predictive performance was evaluated by leave one out cross validation and external validation by measuring the root mean squared relative error (RMSE%) and the 95th percentile of the absolute relative error (AE%). Values less than 20% were considered clinically acceptable. RESULTS: Nine LSSs (4 IV and 5 PO) convenient for clinical application proved to have clinically acceptable performance. Notably, LSS based on C0, C2, and C4 was found to be accurate for estimation of CsA exposure after both IV and PO administration with the 95th percentile of AE% of 19.7% and 17.5%, respectively. CONCLUSIONS: LSSs using 3 or 4 concentration-time points obtained within 4 hours postdose provide a convenient and reliable method to estimate CsA exposure in this population. These LSSs may facilitate future research aiming at better defining the relationship between AUC and clinical outcomes.

Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics.

The current study aims to provide the closed form solutions of one-compartment open models exhibiting simultaneous linear and nonlinear Michaelis-Menten elimination kinetics for single- and multiple-dose intravenous bolus administrations. It can be shown that the elimination half-time ([Formula: see text]) has a dose-dependent property and is upper-bounded by [Formula: see text] of the first-order elimination model. We further analytically distinguish the dominant role of different elimination pathways in terms of model parameters. Moreover, for the case of multiple-dose intravenous bolus administration, the existence and local stability of the periodic solution at steady state are established. The closed form solutions of the models are obtained through a newly introduced function motivated by the Lambert W function.

Population pharmacokinetic and pharmacodynamic analysis of tesamorelin in HIV-infected patients and healthy subjects.

The objective of this analysis was to characterize the time course of selected pharmacodynamic (PD) markers of tesamorelin: growth hormone (GH) and insulin-like growth factor (IGF-1) concentrations in HIV-infected patients and healthy volunteers. A total of 41 subjects in Phase I trials receiving subcutaneous daily doses of 1 or 2 mg of tesamorelin during 14 consecutive days were included in this analysis. A previous pharmacokinetic (PK) model of tesamorelin was used as the input function for the PD model of GH. Tesamorelin was hypothesized to stimulate the secretion of GH in an "episodic" manner, i.e., for a finite duration of time. The resulting PK/PD model of GH was used to describe the time course of IGF-1. The effect of age, body weight, body mass index, sex, race, and health status on the model parameters was evaluated. The model was qualified using predictive checks and non-parametric bootstrap. Within the range of the values evaluated no covariates were significantly associated with GH or IGF-1 model parameters. Model evaluation procedures indicated accurate prediction of the selected pharmacodynamic markers. The time course of GH and IGF-1 concentrations following multiple doses of tesamorelin were well predicted by the sequential PK/PD model developed using Phase I data.

Impact of sampling time deviations on the prediction of the area under the curve using regression limited sampling strategies.

The regression limited sampling strategy approach (R-LSS), which is based on a small number of blood samples drawn at selected time points, has been used as an alternative method for the estimation of the area under the concentration-time curve (AUC). However, deviations from planned sampling times may affect the performance of R-LSS, influencing related therapeutic decisions and outcomes. The aim of this study was to investigate the impact of different sampling time deviation (STD) scenarios on the estimation of AUC by the R-LSS using a simulation approach. Three types of scenarios were considered going from the simplest case of fixed deviations, to random deviations and then to a more realistic case where deviations of mixed nature can occur. In addition, the sensitivity of the R-LSS to STD in each involved sampling point was evaluated. A significant impact of STD on the performance of R-LSS was demonstrated. The tolerance of R-LSS to STD was found to depend not only on the number of sampling points but more importantly on the duration of the sampling process. Sensitivity analysis showed that sampling points at which rapid concentration changes occur were relatively more critical for AUC prediction by R-LSS. As a practical approach, nomograms were proposed, where the expected predictive performance of R-LSS was provided as a function of STD information. The investigation of STD impact on the predictive performance of R-LSS is a critical element and should be routinely performed to guide R-LSS selection and use.