Real-World Application of a Quantitative Systems Pharmacology (QSP) Model to Predict Potassium Concentrations from Electronic Health Records: A Pilot Case towards Prescribing Monitoring of Spironolactone.

Quantitative systems pharmacology (QSP) models are rarely applied prospectively for decision-making in clinical practice. We therefore aimed to operationalize a QSP model for potas-sium homeostasis to predict potassium trajectories based on spironolactone administrations. For this purpose, we proposed a general workflow that was applied to electronic health records (EHR) from patients treated in a German tertiary care hospital. The workflow steps included model exploration, local and global sensitivity analyses (SA), identifiability analysis (IA) of model parameters, and specification of their inter-individual variability (IIV). Patient covariates, selected parameters, and IIV then defined prior information for the Bayesian a posteriori prediction of individual potassium trajectories of the following day. Following these steps, the successfully operationalized QSP model was interactively explored via a Shiny app. SA and IA yielded five influential and estimable parameters (extracellular fluid volume, hyperaldosteronism, mineral corticoid receptor abundance, potassium intake, sodium intake) for Bayesian prediction. The operationalized model was validated in nine pilot patients and showed satisfactory performance based on the (absolute) average fold error. This provides proof-of-principle for a Prescribing Monitoring of potassium concentrations in a hospital system, which could suggest preemptive clinical measures and therefore potentially avoid dangerous hyperkalemia or hypokalemia.

Beyond the basics: A deep dive into parameter estimation for advanced PBPK and QSP models.

Physiologically-based pharmacokinetic (PBPK) models and quantitative systems pharmacology (QSP) models have contributed to drug development strategies. The parameters of these models are commonly estimated by capturing observed values using the nonlinear least-squares method. Software packages for PBPK and QSP modeling provide a range of parameter estimation algorithms. To choose the most appropriate method, modelers need to understand the basic concept of each approach. This review provides a general introduction to the key points of parameter estimation with a focus on the PBPK and QSP models, and the respective parameter estimation algorithms. The latter part assesses the performance of five parameter estimation algorithms - the quasi-Newton method, Nelder-Mead method, genetic algorithm, particle swarm optimization, and Cluster Gauss-Newton method - using three examples of PBPK and QSP modeling. The assessment revealed that some parameter estimation results were significantly influenced by the initial values. Moreover, the choice of algorithms demonstrating good estimation results heavily depends on factors such as model structure and the parameters to be estimated. To obtain credible parameter estimation results, it is advisable to conduct multiple rounds of parameter estimation under different conditions, employing various estimation algorithms.

A Quantitative Systems Pharmacology Model of the Incretin Hormones GIP and GLP1, Glucagon, Glucose, Insulin, and the Small Molecule DPP-4 Inhibitor, Linagliptin.

In the current study, we established a comprehensive quantitative systems pharmacology (QSP) model using linagliptin as the model drug, where drug disposition, drug intervention on dipeptidyl peptidase-4 (DPP-4), glucose-dependent insulinotropic peptide (GIP), Glucagon-like peptide-1 (GLP-1), glucagon, glucose, and insulin are integrated together with the cross talk and feedback loops incorporated among the whole glycemic control system. In the final linagliptin QSP model, the complicated disposition of linagliptin was characterized by a 2-compartment pharmacokinetic (PK) model with an enterohepatic cycling (EHC) component as well as target-mediated drug disposition (TMDD) processes occurring in both tissues and plasma, and the inhibitory effect of linagliptin on DPP-4 was determined by the linagliptin-DPP-4 complex in the central compartment based on target occupancy principle. The integrated GIP-GLP1-glucagon-glucose-insulin system contains five indirect response models as the "skeleton" structure with 12 feedback loops incorporated within the glucose control system. Our model adequately characterized the substantial nonlinear PK of linagliptin, time course of DPP-4 inhibition, as well as the kinetics of GIP, GLP-1, glucagon, and glucose simultaneously in humans. Our model provided valuable insights on linagliptin pharmacokinetics/pharmacodynamics and complicated glucose homeostasis. Since the glucose regulation modeling framework within the QSP model is "drug-independent", our model can be easily adopted by others to evaluate the effect of other DPP-4 inhibitors on the glucose control system. In addition, our QSP model, which contains more components than other reported glucose regulation models, can potentially be used to evaluate the effect of combination antidiabetic therapy targeting different components of glucose control system.

Using quantitative systems pharmacology modeling to optimize combination therapy of anti-PD-L1 checkpoint inhibitor and T cell engager.

Although immune checkpoint blockade therapies have shown evidence of clinical effectiveness in many types of cancer, the outcome of clinical trials shows that very few patients with colorectal cancer benefit from treatments with checkpoint inhibitors. Bispecific T cell engagers (TCEs) are gaining popularity because they can improve patients' immunological responses by promoting T cell activation. The possibility of combining TCEs with checkpoint inhibitors to increase tumor response and patient survival has been highlighted by preclinical and clinical outcomes. However, identifying predictive biomarkers and optimal dose regimens for individual patients to benefit from combination therapy remains one of the main challenges. In this article, we describe a modular quantitative systems pharmacology (QSP) platform for immuno-oncology that includes specific processes of immune-cancer cell interactions and was created based on published data on colorectal cancer. We generated a virtual patient cohort with the model to conduct in silico virtual clinical trials for combination therapy of a PD-L1 checkpoint inhibitor (atezolizumab) and a bispecific T cell engager (cibisatamab). Using the model calibrated against the clinical trials, we conducted several virtual clinical trials to compare various doses and schedules of administration for two drugs with the goal of therapy optimization. Moreover, we quantified the score of drug synergy for these two drugs to further study the role of the combination therapy.

Quantifying Intratumoral Heterogeneity and Immunoarchitecture Generated In-Silico by a Spatial Quantitative Systems Pharmacology Model.

Spatial heterogeneity is a hallmark of cancer. Tumor heterogeneity can vary with time and location. The tumor microenvironment (TME) encompasses various cell types and their interactions that impart response to therapies. Therefore, a quantitative evaluation of tumor heterogeneity is crucial for the development of effective treatments. Different approaches, such as multiregional sequencing, spatial transcriptomics, analysis of autopsy samples, and longitudinal analysis of biopsy samples, can be used to analyze the intratumoral heterogeneity (ITH) and temporal evolution and to reveal the mechanisms of therapeutic response. However, because of the limitations of these data and the uncertainty associated with the time points of sample collection, having a complete understanding of intratumoral heterogeneity role is challenging. Here, we used a hybrid model that integrates a whole-patient compartmental quantitative-systems-pharmacology (QSP) model with a spatial agent-based model (ABM) describing the TME; we applied four spatial metrics to quantify model-simulated intratumoral heterogeneity and classified the TME immunoarchitecture for representative cases of effective and ineffective anti-PD-1 therapy. The four metrics, adopted from computational digital pathology, included mixing score, average neighbor frequency, Shannon's entropy and area under the curve (AUC) of the G-cross function. A fifth non-spatial metric was used to supplement the analysis, which was the ratio of the number of cancer cells to immune cells. These metrics were utilized to classify the TME as "cold", "compartmentalized" and "mixed", which were related to treatment efficacy. The trends in these metrics for effective and ineffective treatments are in qualitative agreement with the clinical literature, indicating that compartmentalized immunoarchitecture is likely to result in more efficacious treatment outcomes.

Complex PK-PD of an engineered IL-15/IL-15Rα-Fc fusion protein in cynomolgus monkeys: QSP modeling of lymphocyte dynamics.

XmAb24306 is a lymphoproliferative interleukin (IL)-15/IL-15 receptor α (IL-15Rα) Fc-fusion protein currently under clinical investigation as an immunotherapeutic agent for cancer treatment. XmAb24306 contains mutations in IL-15 that attenuate its affinity to the heterodimeric IL-15 receptor ßγ (IL-15R). We observe substantially prolonged pharmacokinetics (PK) (half-life ∼ 2.5 to 4.5 days) in single- and repeat-dose cynomolgus monkey (cyno) studies compared to wild-type IL-15 (half-life ∼ 1 hour), leading to increased exposure and enhanced and durable expansion of NK cells, CD8+ T cells and CD4-CD8- (double negative [DN]) T cells. Drug clearance varied with dose level and time post-dose, and PK exposure decreased upon repeated dosing, which we attribute to increased target-mediated drug disposition (TMDD) resulting from drug-induced lymphocyte expansion (i.e., pharmacodynamic (PD)-enhanced TMDD). We developed a quantitative systems pharmacology (QSP) model to quantify the complex PKPD behaviors due to the interactions of XmAb24306 with multiple cell types (CD8+, CD4+, DN T cells, and NK cells) in the peripheral blood (PB) and lymphoid tissues. The model, which includes nonspecific drug clearance, binding to and TMDD by IL15R differentially expressed on lymphocyte subsets, and resultant lymphocyte margination/migration out of PB, expansion in lymphoid tissues, and redistribution to the blood, successfully describes the systemic PK and lymphocyte kinetics observed in the cyno studies. Results suggest that after 3 doses of every-two-week (Q2W) doses up to 70 days, the relative contributions of each elimination pathway to XmAb24306 clearance are: DN T cells > NK cells > CD8+ T cells > nonspecific clearance > CD4+ T cells. Modeling suggests that observed cellular expansion in blood results from the influx of cells expanded by the drug in lymphoid tissues. The model is used to predict lymphoid tissue expansion and to simulate PK-PD for different dose regimens. Thus, the model provides insight into the mechanisms underlying the observed PK-PD behavior of an engineered cytokine and can serve as a framework for the rapid integration and analysis of data that emerges from ongoing clinical studies in cancer patients as single-agent or given in combination.

Sources of inter-individual variability leading to significant changes in anti-PD-1 and anti-PD-L1 efficacy identified in mouse tumor models using a QSP framework.

While anti-PD-1 and anti-PD-L1 [anti-PD-(L)1] monotherapies are effective treatments for many types of cancer, high variability in patient responses is observed in clinical trials. Understanding the sources of response variability can help prospectively identify potential responsive patient populations. Preclinical data may offer insights to this point and, in combination with modeling, may be predictive of sources of variability and their impact on efficacy. Herein, a quantitative systems pharmacology (QSP) model of anti-PD-(L)1 was developed to account for the known pharmacokinetic properties of anti-PD-(L)1 antibodies, their impact on CD8+ T cell activation and influx into the tumor microenvironment, and subsequent anti-tumor effects in CT26 tumor syngeneic mouse model. The QSP model was sufficient to describe the variability inherent in the anti-tumor responses post anti-PD-(L)1 treatments. Local sensitivity analysis identified tumor cell proliferation rate, PD-1 expression on CD8+ T cells, PD-L1 expression on tumor cells, and the binding affinity of PD-1:PD-L1 as strong influencers of tumor growth. It also suggested that treatment-mediated tumor growth inhibition is sensitive to T cell properties including the CD8+ T cell proliferation half-life, CD8+ T cell half-life, cytotoxic T-lymphocyte (CTL)-mediated tumor cell killing rate, and maximum rate of CD8+ T cell influx into the tumor microenvironment. Each of these parameters alone could not predict anti-PD-(L)1 treatment response but they could shift an individual mouse's treatment response when perturbed. The presented preclinical QSP modeling framework provides a path to incorporate potential sources of response variability in human translation modeling of anti-PD-(L)1.

Chimeric Antigen Receptor T Cell Therapies: A Review of Cellular Kinetic-Pharmacodynamic Modeling Approaches.

Chimeric antigen receptor T cell (CAR-T cell) therapies have shown significant efficacy in CD19+ leukemias and lymphomas. There remain many challenges and questions for improving next-generation CAR-T cell therapies, and mathematical modeling of CAR-T cells may play a role in supporting further development. In this review, we introduce a mathematical modeling taxonomy for a set of relatively simple cellular kinetic-pharmacodynamic models that describe the in vivo dynamics of CAR-T cell and their interactions with cancer cells. We then discuss potential extensions of this model to include target binding, tumor distribution, cytokine-release syndrome, immunophenotype differentiation, and genotypic heterogeneity.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment.

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

Systems pharmacological analysis of mitochondrial cardiotoxicity induced by selected tyrosine kinase inhibitors.

Tyrosine kinase inhibitors (TKIs) are targeted therapies rapidly becoming favored over conventional cytotoxic chemotherapeutics. Our study investigates two FDA approved TKIs, DASATINIB; indicated for IMATINIB-refractory chronic myeloid leukemia, and SORAFENIB; indicated for hepatocellular carcinoma and advanced renal cell carcinoma. Limited but crucial evidence suggests that these agents can have cardiotoxic side effects ranging from hypertension to heart failure. A greater understanding of the underlying mechanisms of this cardiotoxicity are needed as concerns grow and the capacity to anticipate them is lacking. The objective of this study was to explore the mitochondrial-mediated cardiotoxic mechanisms of the two selected TKIs. This was achieved experimentally using immortalized human cardiomyocytes, AC16 cells, to investigate dose- and time-dependent cell killing, along with measurements of temporal changes in key signaling proteins involved in the intrinsic apoptotic and autophagy pathways upon exposure to these agents. Quantitative systems pharmacology (QSP) models were developed to capture the toxicological response in AC16 cells using protein dynamic data. The developed QSP models captured well all the various trends in protein signaling and cellular responses with good precision on the parameter estimates, and were successfully qualified using external data sets. An interplay between the apoptotic and autophagic pathways was identified to play a major role in determining toxicity associated with the investigated TKIs. The established modeling platform showed utility in elucidating the mechanisms of cardiotoxicity of SORAFENIB and DASATINIB. It may be useful for other small molecule targeted therapies demonstrating cardiac toxicities, and may aid in informing alternate dosing strategies to alleviate cardiotoxicity associated with these therapies.

Understanding the Effect of Statins and Patient Adherence in Atherosclerosis via a Quantitative Systems Pharmacology Model Using a Novel, Hybrid, and Multi-Scale Approach.

Background and Objective: Statins are one of the most prescribed drugs to treat atherosclerosis. They inhibit the hepatic HMG-CoA reductase, causing a reduction of circulating cholesterol and LDL levels. Statins have had undeniable success; however, the benefits of statin therapy crystallize only if patients adhere to the prescribed treatment, which is far away from reality since adherence decreases with time with around half of patients discontinue statin therapy within the first year. The objective of this work is to; firstly, demonstrate a formal in-silico methodology based on a hybrid, multiscale mathematical model used to study the effect of statin treatment on atherosclerosis under different patient scenarios, including cases where the influence of medication adherence is examined and secondly, to propose a flexible simulation framework that allows extensions or simplifications, allowing the possibility to design other complex simulation strategies, both interesting features for software development. Methods: Different mathematical modeling paradigms are used to present the relevant dynamic behavior observed in biological/physiological data and clinical trials. A combination of continuous and discrete event models are coupled to simulate the pharmacokinetics (PK) of statins, their pharmacodynamic (PD) effect on lipoproteins levels (e.g., LDL) and relevant inflammatory pathways whilst simultaneously studying the dynamic effect of flow-related variables on atherosclerosis progression. Results: Different scenarios were tested showing the impact of: (1) patient variability: a virtual population shows differences in plaque growth for different individuals could be as high as 100%; (2) statin effect on atherosclerosis: it is shown how a patient with a 1-year statin treatment will reduce his plaque growth by 2-3% in a 2-year period; (3) medical adherence: we show that a patient missing 10% of the total number of doses could increase the plaque growth by ~1% (after 2 years) compared to the same "regular" patient under a 1-year treatment with statins. Conclusions: The results in this paper describe the effect of pharmacological intervention combined with biological/physiological or behavioral factors in atherosclerosis progression and treatment in specific patients. It also provides an exemplar of basic research that can be practically developed into an application software.

Mechanistic Modelling of Drug-Induced Liver Injury: Investigating the Role of Innate Immune Responses.

Drug-induced liver injury (DILI) remains an adverse event of significant concern for drug development and marketed drugs, and the field would benefit from better tools to identify liver liabilities early in development and/or to mitigate potential DILI risk in otherwise promising drugs. DILIsym software takes a quantitative systems toxicology approach to represent DILI in pre-clinical species and in humans for the mechanistic investigation of liver toxicity. In addition to multiple intrinsic mechanisms of hepatocyte toxicity (ie, oxidative stress, bile acid accumulation, mitochondrial dysfunction), DILIsym includes the interaction between hepatocytes and cells of the innate immune response in the amplification of liver injury and in liver regeneration. The representation of innate immune responses, detailed here, consolidates much of the available data on the innate immune response in DILI within a single framework and affords the opportunity to systematically investigate the contribution of the innate response to DILI.

From PK/PD to QSP: Understanding the Dynamic Effect of Cholesterol-Lowering Drugs on Atherosclerosis Progression and Stratified Medicine.

Current computational and mathematical tools are demonstrating the high value of using systems modeling approaches (e.g. Quantitative Systems Pharmacology) to understand the effect of a given compound on the biological and physiological mechanisms related to a specific disease. This review provides a short survey of the evolution of the mathematical approaches used to understand the effect of particular cholesterol-lowering drugs, from pharmaco-kinetic (PK) / pharmaco-dynamic (PD) models, through physiologically base pharmacokinetic models (PBPK) to QSP. These mathematical models introduce more mechanistic information related to the effect of these drugs on atherosclerosis progression and demonstrate how QSP could open new ways for stratified medicine in this field.