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Purpose or ObjectiveDrug concentration–response curves (DRCs) are crucial in pharmacology for assessing the drug effects on biological systems. The widely used sigmoid Emax model, which accounts for response saturation, relies heavily on the effective drug concentration (ED50). This reliance can lead to validation errors and inaccuracies in model fitting. The Emax model cannot generate multiple DRCs, raising concerns about whether the dataset is fully utilized.MethodsThis study formulates an extended Emax (eEmax) model designed to overcome these limitations. The eEmax model generates multiple DRCs from a single dataset by using various estimated α′s∈0,100, while keeping EDα fixed, rather than estimating an ED50 value as in the Emax model.ResultsThis model effectively captures a broader range of concentration–response behavior, including non-sigmoidal patterns, thus providing greater flexibility and accuracy compared to the Emax model. Validation using various drug-response data and PKPD frameworks demonstrates the eEmax model’s improved accuracy and versatility in handling concentration–response data.ConclusionsThe eEmax model provides a robust and flexible method for drug concentration–response analysis, facilitating the generation of multiple DRCs from a single dataset and reducing the possibility of validation errors. This model is particularly valuable for its ease of use and its capability to fully utilize datasets, providing its potential in PKPD modeling and drug discovery.

ABSTRACT Mechanistic PKPD models are now advocated not only by academic and industrial researchers, but also by regulators. A recent development in this area is based on the growing realisation that innovation could be dramatically catalysed by creating synergy at the interface between Systems Biology and PKPD, two disciplines which until now have largely existed in ‘parallel universes’ with a limited track record of impactful collaboration. This has led to the emergence of systems pharmacology. Broadly speaking, this is the quantitative analysis of the dynamic interactions between drug(s) and a biological system to understand the behaviour of the system as a whole, as opposed to the behaviour of its individual constituents; thus, it has become the interface between PKPD and systems biology. It applies the concepts of Systems Engineering, Systems Biology, and PKPD to the study of complex biological systems through iteration between computational and/or mathematical modelling and experimentation. Application of systems pharmacology can now impact across all stages of drug research and development, ranging from very early discovery programs to large-scale Phase 3/4 patient studies, and has the potential to become an integral component of a new ‘enhanced quantitative drug discovery and development’ (EQD3) R&D paradigm.

Abstract Background There is an unmet need for prediction of treatment outcome or patient selection for [177Lu]Lu-PSMA therapy in patients with metastatic castration-resistant prostate cancer (mCRPC). Quantification of the tumor exposure–response relationship is pivotal for further treatment optimization. Therefore, a population pharmacokinetic (PK) model was developed for [177Lu]Lu-PSMA-I&T using SPECT/CT data and, subsequently, related to prostate-specific antigen (PSA) dynamics after therapy in patients with mCRPC using a pharmacokinetic/pharmacodynamic (PKPD) modelling approach. Methods A population PK model was developed using quantitative SPECT/CT data (406 scans) of 76 patients who received multiple cycles [177Lu]Lu-PSMA-I&T (± 7.4 GBq with either two- or six-week interval). The PK model consisted of five compartments; central, salivary glands, kidneys, tumors and combined remaining tissues. Covariates (tumor volume, renal function and cycle number) were tested to explain inter-individual variability on uptake into organs and tumors. The final PK model was expanded with a PD compartment (sequential fitting approach) representing PSA dynamics during and after treatment. To explore the presence of a exposure–response relationship, individually estimated [177Lu]Lu-PSMA-I&T tumor concentrations were related to PSA changes over time. Results The population PK model adequately described observed data in all compartments (based on visual inspection of goodness-of-fit plots) with adequate precision of parameters estimates (< 36.1% relative standard error (RSE)). A significant declining uptake in tumors (k14) during later cycles was identified (uptake decreased to 73%, 50% and 44% in cycle 2, 3 and 4–7, respectively, compared to cycle 1). Tumor growth (defined by PSA increase) was described with an exponential growth rate (0.000408 h−1 (14.2% RSE)). Therapy-induced PSA decrease was related to estimated tumor concentrations (MBq/L) using both a direct and delayed drug effect. The final model adequately captured individual PSA concentrations after treatment (based on goodness-of-fit plots). Simulation based on the final PKPD model showed no evident differences in response for the two different dosing regimens currently used. Conclusions Our population PK model accurately described observed [177Lu]Lu-PSMA-I&T uptake in salivary glands, kidneys and tumors and revealed a clear declining tumor uptake over treatment cycles. The PKPD model adequately captured individual PSA observations and identified population response rates for the two dosing regimens. Hence, a PKPD modelling approach can guide prediction of treatment response and thus identify patients in whom radioligand therapy is likely to fail.

In-vitro to in-vivo correlations (IVIVC), relating in-vitro parameters like IC50 to in-vivo drug exposure in plasma and tumour growth, are widely used in oncology for experimental design and dose decisions. However, they lack a deeper understanding of the underlying mechanisms. Our paper therefore focuses on linking empirical IVIVC relations for small-molecule kinase inhibitors with a semi-mechanistic tumour-growth model. We develop an approach incorporating parameters like the compound’s peak-trough ratio (PTR), Hill coefficient of in-vitro dose-response curves, and xenograft-specific properties. This leads to formulas for determining efficacious doses for tumor stasis under linear pharmacokinetics equivalent to traditional empirical IVIVC relations, but enabling more systematic analysis. Our findings reveal that in-vivo xenograft-specific parameters, specifically the growth rate (g) and decay rate (d), along with the average exposure, are generally more significant determinants of tumor stasis and effective dose than the compound’s peak-trough ratio. However, as the Hill coefficient increases, the dependency of tumor stasis on the PTR becomes more pronounced, indicating that the compound is more influenced by its maximum or trough values rather than the average exposure. Furthermore, we discuss the translation of our method to predict population dose ranges in clinical studies and propose a resistance mechanism that solely relies on specific in-vivo xenograft parameters instead of IC50 exposure coverage. In summary, our study aims to provide a more mechanistic understanding of IVIVC relations, emphasizing the importance of xenograft-specific parameters and PTR on tumor stasis.

Quantitative Systems Pharmacology (QSP) has emerged as a powerful ensemble of approaches aiming at developing integrated mathematical and computational models elucidating the complex interactions between pharmacology, physiology, and disease. As the field grows and matures its applications expand beyond the boundaries of research and development and slowly enter the decision making and regulatory arenas. However, widespread acceptance and eventual adoption of a new modeling approach requires assessment criteria and quantifiable metrics that establish credibility and increase confidence in model predictions. QSP aims to provide an integrated understanding of pathology in the context of therapeutic interventions. Because of its ambitious nature and the fact that QSP emerged in an uncoordinated manner as a result of activities distributed across organizations and academic institutions, high entropy characterizes the tools, methods, and computational methodologies and approaches used. The eventual acceptance of QSP model predictions as supporting material for an application to a regulatory agency will require that two key aspects are considered: (1) increase confidence in the QSP framework, which drives standardization and assessment; and (2) careful articulation of the expectations. Both rely heavily on our ability to rigorously and consistently assess QSP models. In this manuscript, we wish to discuss the meaning and purpose of such an assessment in the context of QSP model development and elaborate on the differentiating features of QSP that render such an endeavor challenging. We argue that QSP establishes a conceptual, integrative framework rather than a specific and well-defined computational methodology. QSP elicits the use of a wide variety of modeling and computational methodologies optimized with respect to specific applications and available data modalities, which exceed the data structures employed by chemometrics and PK/PD models. While the range of options fosters creativity and promises to substantially advance our ability to design pharmaceutical interventions rationally and optimally, our expectations of QSP models need to be clearly articulated and agreed on, with assessment emphasizing the scope of QSP studies rather than the methods used. Nevertheless, QSP should not be considered an independent approach, rather one of many in the broader continuum of computational models.

Rationale: The psychedelic effects of the traditional Amazonian botanical decoction known as ayahuasca are often attributed to agonism at brain serotonin 5-HT 2A receptors by N,N -dimethyltryptamine (DMT). To reduce first pass metabolism of oral DMT, ayahuasca preparations additionally contain reversible monoamine oxidase A (MAO-A) inhibitors, namely β-carboline alkaloids such as harmine. However, there is lacking biochemical evidence to substantiate this pharmacokinetic potentiation of DMT in brain via systemic MAO-A inhibition. Objectives: We measured the pharmacokinetic profile of harmine and/or DMT in rat brain, and tested for pharmacodynamic effects on brain glucose metabolism and DMT occupancy at brain serotonin 5-HT 2A receptors. Methods: We first measured brain concentrations of harmine and DMT after treatment with harmine and/or DMT at low sub-cutaneous doses (1 mg/kg each) or harmine plus DMT at moderate doses (3 mg/kg each). In the same groups of rats, we also measured ex vivo the effects of these treatments on the availability of serotonin 5-HT 2A receptors in frontal cortex. Finally, we explored effects of DMT and/or harmine (1 mg/kg each) on brain glucose metabolism with [ 18 F]FDG-PET. Results: Results confirmed that co-administration of harmine inhibited the formation of the DMT metabolite indole-3-acetic acid (3-IAA) in brain, while correspondingly increasing the cerebral availability of DMT. However, we were unable to detect any significant occupancy by DMT at 5-HT 2A receptors measured ex vivo , despite brain DMT concentrations as high as 11.3 µM. We did not observe significant effects of low dose DMT and/or harmine on cerebral [ 18 F]FDG-PET uptake. Conclusion: These preliminary results call for further experiments to establish the dose-dependent effects of harmine/DMT on serotonin receptor occupancy and cerebral metabolism.

The application of model-informed drug discovery and development (MID3) approaches in the early stages of drug discovery can help determine feasibility of drugging a target, prioritize between targets, or define optimal drug properties for a target product profile (TPP). However, applying MID3 in early discovery can be challenging due to the lack of pharmacokinetic (PK) and pharmacodynamic (PD) data at this stage. Early Feasibility Assessment (EFA) is the application of mechanistic PKPD models, built from first principles, and parameterized by data that is readily available early in drug discovery to make effective dose predictions. This manuscript demonstrates the ability of EFA to make accurate predictions of clinical effective doses for nine approved biotherapeutics and outlines the potential of extending this approach to novel therapeutics to impact early drug discovery decisions.

The administration of therapeutic drugs through dermal routes, such as creams and ointments, has emerged as an increasingly popular alternative to traditional delivery methods, such as tablets and injections. In the context of drug development, it is crucial to identify the optimal doses and delivery routes that ensure successful outcomes. Physiologically based pharmacokinetic (PBPK) models have been proposed to simulate drug delivery and optimize drug formulations, but the calibration of these models is challenging due to the multitude of variables involved and limited experimental data. One significant research gap that this article addresses is the need for more efficient and accurate methods for calibrating PBPK models for dermal drug delivery. This manuscript presents a novel approach and an integrated dermal drug delivery model to address this gap that leverages virtual in vitro release (IVRT) and permeation (IVPT) testing data to optimize mechanistic models. The proposed approach was demonstrated through a study involving Desoximetasone cream and ointment formulations, where the release kinetics and permeation profiles of Desoximetasone were determined experimentally, and a computational model was created to simulate the results. The experimental studies showed that, even though the cumulative permeation of Desoximetasone at the end of the permeation study was comparable, there was a significant difference seen in the lag time in the permeation of Desoximetasone between the cream and ointment. Additionally, there was a significant difference seen in the amount of Desoximetasone permeated through human cadaver skin at early time points when the cream and ointment were compared. The computational model was optimized and validated, suggesting that this approach has the potential to bridge the existing research gap by improving the accuracy and efficiency of drug development processes. The model results show a good fit between the experimental data and model predictions. During the model optimization process, it became evident that there was variability in both the permeability and the partition coefficient within the stratum corneum. This variability had a significant and noteworthy influence on the overall performance of the model, especially when it came to its capacity to differentiate between cream and ointment formulations. Leveraging virtual models significantly aids the comprehension of drug release and permeation, mitigating the demanding data requirements. The use of virtual IVRT and IVPT data can accelerate the calibration of PBPK models, streamline the selection of the appropriate doses, and optimize drug delivery. Moreover, this novel approach could potentially reduce the time and resources involved in drug development, thus making it more cost-effective and efficient.

Treatment response variability across patients is a common phenomenon in clinical practice. For many drugs this inter-individual variability does not require much (if any) individualisation of dosing strategies. However, for some drugs, including chemotherapies and some monoclonal antibody treatments, individualisation of dosages are needed to avoid harmful adverse events. Model-informed precision dosing (MIPD) is an emerging approach to guide the individualisation of dosing regimens of otherwise difficult-to-administer drugs. Several MIPD approaches have been suggested to predict dosing strategies, including regression, reinforcement learning (RL) and pharmacokinetic and pharmacodynamic (PKPD) modelling. A unified framework to study the strengths and limitations of these approaches is missing. We develop a framework to simulate clinical MIPD trials, providing a cost and time efficient way to test different MIPD approaches. Central for our framework is a clinical trial model that emulates the complexities in clinical practice that challenge successful treatment individualisation. We demonstrate this framework using warfarin treatment as a use case and investigate three popular MIPD methods: 1. Neural network regression; 2. Deep RL; and 3. PKPD modelling. We find that the PKPD model individualises warfarin dosing regimens with the highest success rate and the highest efficiency: 75.1% of the individuals display INRs inside the therapeutic range at the end of the simulated trial; and the median time in the therapeutic range (TTR) is 74%. In comparison, the regression model and the deep RL model have success rates of 47.0% and 65.8%, and median TTRs of 45% and 68%. We also find that the MIPD models can attain different degrees of individualisation: the Regression model individualises dosing regimens up to variability explained by covariates; the Deep RL model and the PKPD model individualise dosing regimens accounting also for additional variation using monitoring data. However, the Deep RL model focusses on control of the treatment response, while the PKPD model uses the data also to further the individualisation of predictions.

PBPK models, in particular, provide a mechanistic understanding of drug behavior across species and routes of administration, reducing reliance on animal testing, enhancing translational success, and drug interaction prediction (Jiang et al., 2023;Liao et al., 2024;Ren et al., 2021;Yang et al., 2025). The study by Sanchez et al. on bispecific antibodies exemplifies how mathematical models can predict the impact of binding affinity on trimeric complex formation and patient outcomes Combining mathematical modeling, in vitro data and clinical target expression to support bispecific antibody binding affinity selection: a case example with FAP-4-1BBLSanchez et al.By simulating FAP-4-1BBL’s binding dynamics, researchers identified optimal affinity thresholds that maximize therapeutic benefits across diverse patient populations. The leritrelvir study demonstrated how population pharmacokinetic analyses could optimize dosing regimens and trial designs within compressed timelines Model informed dose regimen optimizing in development of leritrelvir for the treatment of mild or moderate COVID-19Wang et al.By leveraging existing data and predictive modeling, researchers efficiently navigated regulatory requirements and clinical complexities, highlighting PKPD modeling’s role in public health responses. A recent study demonstrated the value of PKPD modeling in optimizing infliximab induction dosing to achieve clinical remission in patients with Crohn’s disease Optimising infliximab induction dosing to achieve clinical remission in Chinese patients with Crohn’s diseaseZhu et al.By leveraging patient-specific data and modeling insights, researchers were able to identify optimal dosing regimens that maximize therapeutic benefits while minimizing adverse effects.