Journal of Pharmacokinetics and Pharmacodynamics最新文献

{"title":"Comparing heavy-tailed residual error models for outlier handling in population PK modeling.","authors":"Yiming Cheng, Yan Li","doi":"10.1007/s10928-026-10047-6","DOIUrl":"10.1007/s10928-026-10047-6","url":null,"abstract":"<p><strong>Background: </strong>Reliable population pharmacokinetic (PopPK) estimation is often compromised by outliers under Gaussian error models. While post hoc filtering using conditional weighted residuals (CWRES) is common, this approach is often insensitive due to model \"masking\" from variance inflation.</p><p><strong>Methods: </strong>We implemented a one-compartment model in Monolix using a custom likelihood workaround to benchmark four distributions: Normal, Laplace, Generalized Error Distribution (GED), and Student's t. We assessed CWRES sensitivity under extreme contamination and compared estimation performance using theoretical tail-behavior analysis, controlled simulation studies spanning multiple contamination severities, and a real-world caffeine PK case study with influential terminal-phase deviations.</p><p><strong>Results: </strong>Simulations revealed that CWRES-based diagnostics are unreliable; extreme outliers frequently produced |CWRES| < 6 because the Normal model inflated residual variance, masking the contamination. Exponential-tail models (Laplace, GED) improved robustness for moderate outliers but failed under extreme deviations due to insufficiently heavy tails. Conversely, the Student's t model, utilizing power-law tail behavior, maintained stable and minimally biased structural parameter estimates across the contamination settings examined. These patterns were confirmed in the caffeine case study.</p><p><strong>Conclusions: </strong>Reliance on CWRES-driven residual screening alone is methodologically fragile. Among the models evaluated, exponential-tail distributions are insufficient for extreme outliers, whereas the Student's t distribution provided the most consistent stability across the contamination settings examined here and showed the most robust overall performance among the residual-error models evaluated when influential outliers were present.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148264685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pediatric oral cavity physiologically based pharmacokinetic model to predict pharmacokinetics of mucoadhesive atropine gel to treat sialorrhea.","authors":"Madison Parrot, Nancy Murphy, Joseph E Rower, Christopher A Reilly, Danielle Green, Ariel Tarrell, Kevin Watt, Venkata Yellepeddi","doi":"10.1007/s10928-026-10039-6","DOIUrl":"10.1007/s10928-026-10039-6","url":null,"abstract":"<p><p>Sialorrhea significantly impairs quality of life in children with neurodisabilities, including cerebral palsy, yet safe and effective pharmacologic treatment options remain limited. Although atropine is widely used for sialorrhea, it is most commonly used off-label as ophthalmic drops administered intraorally, an approach constrained by poor mucosal retention, frequent dosing, medication-error risk, and systemic anticholinergic adverse effects. To address these limitations, we developed a novel mucoadhesive atropine oral gel (0.01% weight/weight (w/w)) to enhance intraoral residence time and support controlled local and systemic exposure. The pharmacokinetics and safety of the atropine gel were evaluated in a Phase I clinical trial in healthy adults, which informed the development and validation of a physiologically based pharmacokinetic (PBPK) model incorporating a mechanistic oral cavity framework. The oral cavity PBPK model accounts for salivary flow, mucosal absorption, swallowing, and saliva-tissue exchange across six compartments, enabling predictions of local and systemic exposure and evaluation of formulation-relevant determinants of intraoral absorption. Pediatric PBPK simulations were scaled from the adult model using Population Estimates for Age-Related Physiology™ (PEAR Physiology™) to support model-informed dose selection. Simulations identified a minimum pediatric dose range of 0.25 mg/kg once or twice daily, with twice-daily dosing to maintain plasma concentrations within the established minimum effective and maximum tolerated concentration range. Collectively, this work demonstrates the utility of PBPK modeling as a translational tool to integrate formulation attributes, oral cavity physiology, and pediatric dose selection, and supports the clinical advancement of mucoadhesive atropine gel as a safer alternative to off-label intraoral atropine eye drops.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148163397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exposure-safety analyses of talazoparib in combination with enzalutamide in patients with metastatic castration-resistant prostate cancer (mCRPC) in the TALAPRO-2 trial.","authors":"Yibo Wang, Mark Hadigol, Victor Ruberio Lincha, Justin Hoffman, Arun A Azad, Neeraj Agarwal, Nobuaki Matsubara, Fabian Zohren, Liza DeAnnuntis, Diane D Wang","doi":"10.1007/s10928-026-10038-7","DOIUrl":"10.1007/s10928-026-10038-7","url":null,"abstract":"<p><p>The TALAPRO-2 trial (NCT03395197) showed that the addition of talazoparib, a potent PARP inhibitor, to enzalutamide significantly improved radiographic progression-free survival in patients with mCRPC. Due to adverse events (AEs), approximately 62% of patients experienced dose interruption and 53% of patients experienced dose reduction of talazoparib in TALAPRO-2 trial. Hematologic AEs such as anemia, thrombocytopenia, and neutropenia were the most common AEs leading to dose interruptions or reductions. We investigated the relationship between talazoparib exposure as well as baseline patients/disease characteristics and Grade ≥ 3 anemia, thrombocytopenia, and neutropenia using graphical examination and Cox proportional hazard models. The results indicated that higher talazoparib exposure, C_{avg, t}, was associated with a higher risk of Grade ≥ 3 anemia, thrombocytopenia, and neutropenia. Additionally, among the other baseline factors, we observed that higher risk of all tested safety endpoints was associated with lower baseline hemoglobin. In addition, higher risk of anemia was associated with lower baseline body weight and higher baseline lactate dehydrogenase. Higher risk of neutropenia was associated with lower baseline absolute neutrophil count and lower baseline body weight. These findings support the proposed dose modification algorithm as an effective approach for management of AEs.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13236835/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148163395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Personalized prophylactic therapy optimization in hemophilia A using a hybrid PK-PD-TTE model and deep RL.","authors":"Mahdi Rabbani, S Ehsan Razavi, Masoud Goharimanesh, S Ehsan Razavi","doi":"10.1007/s10928-026-10041-y","DOIUrl":"10.1007/s10928-026-10041-y","url":null,"abstract":"<p><p>Hemophilia A is a genetic bleeding disorder caused by a deficiency or absence of Factor VIII, leading to recurrent and spontaneous hemorrhages. Standard treatment typically involves regular prophylactic infusions of clotting factors to prevent bleeding episodes. However, individual variations in treatment response and reliance solely on plasma Factor VIII levels provide an imprecise assessment of bleeding risk. This study presents an intelligent dose-control system utilizing Deep Reinforcement Learning (DRL) integrated with a hybrid Pharmacokinetic-Pharmacodynamic Time-to-Event (PK-PD-TTE) environment. Within this framework, the control policy is learned using a Deep Q‑Network (DQN), enabling the agent to adapt treatment decisions through interaction with the simulated physiological environment. Unlike conventional methods, this framework allows the agent to observe continuous physiological states via Endogenous Thrombin Potential (ETP) and learn optimal dosing policies through trial-and-error. The proposed DQN agent was benchmarked against standard prophylaxis, a Fuzzy Logic controller, and a Bayesian Adaptive Model-Informed Precision Dosing (MIPD) strategy. Simulation results from a virtual cohort (N = 200) demonstrate that the DQN agent achieves a safety profile comparable to Bayesian MIPD while significantly improving factor utilization efficiency. Notably, in patients with low bleeding‑risk phenotypes, the DRL‑based approach achieved a similar bleeding rate to MIPD while reducing annual factor VIII consumption by approximately 39% relative to MIPD and by up to 70% compared to the reference prophylaxis protocol adopted as the simulation baseline. These findings suggest that incorporating reinforcement learning with mechanistic PD feedback can act as a powerful complementary layer to established clinical protocols, facilitating personalized and cost-effective hemophilia management.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148163416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-objective optimization in population pharmacokinetic model selection and optimization: application of NSGA-II in pyDarwin.","authors":"Xinnong Li, Mark Sale, James Craig, Keith Nieforth, Alex Mazur, Robert R Bies","doi":"10.1007/s10928-026-10036-9","DOIUrl":"10.1007/s10928-026-10036-9","url":null,"abstract":"<p><p>The selection of a \"good\" model usually involves a combination of objective and subjective criteria. Although many aspects of model quality can be expressed numerically, certain desirable characteristics remain difficult-or even impossible-to quantify precisely. Multi-objective optimization (MOO) provides a systematic way to handle this challenge by explicitly incorporating and balancing both objective (measurable) and subjective (judgment-based) considerations when choosing among candidate solutions. The generated Pareto front represents a set of non-dominated models where no single solution can be improved in one objective without sacrificing the performance in another objective. Using the non-dominated sorting genetic algorithm II (NSGA-II), an implementation of MOO, we simultaneously considered objective function value and number of estimated parameters as competing criteria. Concentration measurements of 17-DMAG, quetiapine, clozapine and ziprasidone were applied to build population pharmacokinetic models through traditional stepwise search, machine learning based single-objective hybrid genetic algorithm (SOHGA) and MOO. Local downhill search with MOO was also assessed in this study. While both objectives improved, models with lower objective function value generally contained more estimated parameters. The number of non-dominated solutions for DMAG, ziprasidone, clozapine, and quetiapine was 17, 9, 9, and 13, respectively. The optimal model selected by SOHGA appeared on the Pareto front for DMAG, ziprasidone and clozapine datasets. Overall, MOO provides objective transparency to the cost of tradeoffs between competing model objectives, allowing researchers to better contextualize subjective criteria (e.g., biological plausibility, improvements in diagnostic plots) when aligning model selection with clinical context.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13179877/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147960035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A missed synthesis from the 1930s: Teorell, Mayneord, and the origins of physiological PK-TGI modelling.","authors":"Hitesh B Mistry","doi":"10.1007/s10928-026-10032-z","DOIUrl":"10.1007/s10928-026-10032-z","url":null,"abstract":"<p><p>The historical origins of mechanistic pharmacokinetic–tumour growth inhibition (PK–TGI) modelling are usually located in the later twentieth century. However, many of the essential ideas were already present in the 1930s, although not brought together in a single formal framework. In 1937, Torsten Teorell published a physiological theory of drug absorption, distribution, and elimination based on transport across biological boundaries and exchange between anatomical spaces. Five years earlier, W. V. Mayneord showed that the growth of Jensen’s rat sarcoma was more naturally described on a linear dimension than on tumour volume and explained this behaviour mechanistically by assuming proliferation within a thin outer rim surrounding a necrotic core. Read together, these papers contain the key ingredients of a physiological PK–TGI model: Teorell provides the concentration–time function, C(t), and Mayneord provides a growth law expressed on tumour radius, dR/dt = g. The missing link is an effect term coupling exposure to inhibition of radial growth. In its simplest form, this yields dR/dt = g - ψ(C). This article is not intended as an exhaustive review. Rather, it argues that the 1930s should be recognised as a formative period in mechanistic biomedicine in which the conceptual foundations of physiological PK–TGI modelling were already available in print. Selected later examples are used only to show that, even when tumour growth is recast in exponential, Gompertzian, reaction-diffusion, agent-based, or modern semi-mechanistic PK–TGI language, the field repeatedly returns to the same central point: for a solid tumour, net growth is governed by the behaviour of a viable outer region rather than by the bulk alone.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147959993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive PK/PD model optimization: a comparative analysis of bounded optimization methods for individual BIS prediction.","authors":"Zheyan Tu, Sean Jeffries, Eric Pelletier, Oliver Cafferty, Joshua Morse, Avinash Sinha, Thomas Hemmerling","doi":"10.1007/s10928-026-10033-y","DOIUrl":"10.1007/s10928-026-10033-y","url":null,"abstract":"<p><p>This study investigates the feasibility of adaptive optimization in pharmacokinetic/pharmacodynamic (PK/PD) models for predicting individual Bispectral Index (BIS) values during sedation and anesthesia by refining established models—specifically the Schnider, Marsh, Schuttler, Eleveld model for propofol and Minto model for remifentanil — using bounded optimization techniques. We adapt these population-based models through cumulative intraoperative BIS data to derive an effective set of PK/PD parameters for improved patient-specific BIS prediction. Comparative analyses using datasets from sedation and general anesthesia demonstrate that wider parameter bounding constraints improve model performance, as shown by higher Pearson correlations, and lower prediction errors, while maintaining computational efficiency. Our experiment results showed that Sequential Least Squares Quadratic Programming (SLSQP) and Least Squares methods excel in accuracy and computational efficiency, having the highest Pearson correlation of 0.56 and lowest root mean square error of 10.3. Real-time updates to PK/PD models using continuous BIS data may improve patient-specific BIS prediction during sedation and general anesthesia. These findings support the feasibility of adaptive calibration of population PK/PD models as a component of future model-based anesthetic management. Individualized dosing strategies could support closed-loop anesthesia systems and advance personalized medicine in perioperative care.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147960017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of a novel rabeprazole modified release formulation to reduce the dosing frequency: A trial and triumph with physiologically based biopharmaceutics modeling.","authors":"Harika Maddukuri, Rajkumar Boddu, Sangmesh Mallikarjun Chaudhari, Anup Avijit Choudhury, Veena Kambam, Sohel Mohammed Khan, Venkat Ramana Naidu, Sanjay Kumar Singh, Anuj Kumar Saini, Sivacharan Kollipara","doi":"10.1007/s10928-026-10035-w","DOIUrl":"10.1007/s10928-026-10035-w","url":null,"abstract":"<p><p>Advanced in silico tools, such as physiologically based biopharmaceutics models (PBBM) and physiologically based pharmacokinetic models (PBPK), play a pivotal role in model-informed formulation development (MIFD). In the present study, these methodologies were utilized in the development of a novel rabeprazole modified-release (MR) formulation for improved patient compliance by reducing the dosing frequency relative to existing delayed-release (DR) formulation. A MR formulation containing combination of delayed release and pulsatile release components was designed based on the hypothetical dissolution targets. A PBBM was first established using literature-derived clinical data and used to simulate the performance of formulations with varied dissolution profiles. Initial MR formulation prototypes (once a day) were evaluated in pilot-1 bioequivalence (BE) study against reference formulation (twice a day) but results indicated infra bioequivalence outcome. After pilot-1 study, the formulation and the dissolution method were optimized and then model was refined to predict the pilot 1 outcomes. The validated model was then employed to select suitable pilot-2 prototypes and to prospectively predict their BE outcomes under fasted and fed conditions. The predicted BE ratios were in good agreement with the observed pilot-2 study results. Therefore, the same model was used to make prospective predictions with increased subjects to understand the in vivo performance of pivotal test formulation and lead to the successful bioequivalence outcome, product commercialization, ultimately aiding in increased patient compliance. This work highlights the value of a model-informed strategy in accelerating formulation optimization, reducing development timelines and costs, and strengthening decision-making within pharmaceutical development programs.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147959984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tracer kinetic modeling of a 14 kDa anti-CD8 PET tracer (2C8v144) for in vivo estimation of CD8 expression in tissue and blood, binding affinity, and total body receptor occupancy.","authors":"Ruediger E Port, C Andrew Boswell, Annie Ogasawara, Herman Gill, Jan Marik, Alice F Tarantal, Eric Berg, Simon P Williams, Gregory Z Ferl","doi":"10.1007/s10928-026-10029-8","DOIUrl":"10.1007/s10928-026-10029-8","url":null,"abstract":"<p><p>We are developing a 14.3 kDa anti-CD8 VHH tracer, [[Formula: see text]F]-2C8v144 (binding tracer, B), along with a nonbinding control tracer, [[Formula: see text]F]-2C8v145 (C), in order to track CD8+ (“cytotoxic”) T cells in malignant tumors during immunotherapy by Positron Emission Tomography (PET). Arterial blood concentrations of C and B were monitored in three rhesus monkeys upon i.v. injection of mass doses/kg varying approximately 5–fold for both tracers. Plasma concentrations, calculated from individual hematocrit measurements assuming no cellular uptake, were analyzed by mixed–effects compartmental modeling, by assuming the parameters of non-specific distribution and elimination (estimated based on the PET-based arterial blood concentrations) to be the same for B as for C. C exhibited linear three–compartment kinetics with a mean residence time of 26 min. Nonlinear kinetics of B suggesting saturable, reversible binding outside of circulating blood were described by an average association rate constant, [Formula: see text], and an equilibrium dissociation constant, [Formula: see text]. Binding in blood to circulating CD8+ cells was described by a different association rate constant, [Formula: see text], and the same [Formula: see text]. The total body content of CD8 receptors was estimated at 1.7 nmol/kg body weight, with 2.7% of the total present in blood. The estimate of [Formula: see text], 0.0097/(min·nM), was > 50–fold lower than [Formula: see text] determined in vitro by Surface Plasmon Resonance (SPR, 0.50/(min·nM), yet the estimated [Formula: see text], 0.23 nM, was similar to the SPR estimate (0.13 nM) suggesting that the model informs about affinity. The model also yields predicted total body receptor occupancies and plasma concentrations of unbound B, i.e. the arterial input function needed for analyzing tracer kinetics in malignant tumors.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 3","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13503381/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147774662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A structure-preserving hybrid learning framework for compartmental pharmacokinetic models.","authors":"Hanan Al Lawati, Mohamed Al-Lawatia","doi":"10.1007/s10928-026-10031-0","DOIUrl":"10.1007/s10928-026-10031-0","url":null,"abstract":"<p><p>Pharmacokinetic (PK) models are widely used in drug development and dose planning, but they often face a trade-off between interpretability and flexibility. Traditional physiology-based PK models are transparent but may be too simple to capture complex or nonlinear behavior, while AI models are more flexible but can violate basic physical constraints such as nonnegativity or mass balance. In this work, we propose a constrained hybrid AI-PK approach in which small AI components are embedded within the PK equations as bounded corrections to mechanistic rates. The correction network is constructed to be internally conservative across compartments and to act as a controlled perturbation of the base model. We provide a simple mathematical analysis showing that this design preserves key qualitative properties, including boundedness and, under suitable conditions, positivity and stability. Numerical experiments on simulated and reported PK datasets show that the constrained hybrid model improves prediction accuracy and yields more stable extrapolation than both purely mechanistic and unconstrained hybrid models, while respecting the underlying physical structure.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":"53 3","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147645810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}