Mathematical modeling in autoimmune diseases: from theory to clinical application.

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

An integrative mechanistic model of thymocyte dynamics.

Background: The thymus plays a central role in shaping human immune function. A mechanistic, quantitative description of immune cell dynamics and thymic output under homeostatic conditions and various patho-physiological scenarios are of particular interest in drug development applications, e.g., in the identification of potential therapeutic targets and selection of lead drug candidates against infectious diseases. Methods: We here developed an integrative mathematical model of thymocyte dynamics in human. It incorporates mechanistic features of thymocyte homeostasis as well as spatial constraints of the thymus and considerations of age-dependent involution. All model parameter estimates were obtained based on published physiological data of thymocyte dynamics and thymus properties in mouse and human. We performed model sensitivity analyses to reveal potential therapeutic targets through an identification of processes critically affecting thymic function; we further explored differences in thymic function across healthy subjects, multiple sclerosis patients, and patients on fingolimod treatment. Results: We found thymic function to be most impacted by the egress, proliferation, differentiation and death rates of those thymocytes which are most differentiated. Model predictions also showed that the clinically observed decrease in relapse risk with age, in multiple sclerosis patients who would have discontinued fingolimod therapy, can be explained mechanistically by decreased thymic output with age. Moreover, we quantified the effects of fingolimod treatment duration on thymic output. Conclusions: In summary, the proposed model accurately describes, in mechanistic terms, thymic output as a function of age. It may be further used to perform predictive simulations of clinically relevant scenarios which combine specific patho-physiological conditions and pharmacological interventions of interest.

Optimization of the MACE endpoint composition to increase power in studies of lipid-lowering therapies-a model-based meta-analysis.

Aims: To develop a model-informed methodology for the optimization of the Major Adverse Cardiac Events (MACE) composite endpoint, based on a model-based meta-analysis across anti-hypercholesterolemia trials of statin and anti-PCSK9 drugs. Methods and results: Mixed-effects meta-regression modeling of stand-alone MACE outcomes was performed, with therapy type, population demographics, baseline and change over time in lipid biomarkers as predictors. Randomized clinical trials up to June 28, 2022, of either statins or anti-PCSK9 therapies were identified through a systematic review process in PubMed and ClinicalTrials.gov databases. In total, 54 studies (270,471 patients) were collected, reporting 15 different single cardiovascular events. Treatment-mediated decrease in low density lipoprotein cholesterol, baseline levels of remnant and high-density lipoprotein cholesterol as well as non-lipid population characteristics and type of therapy were identified as significant covariates for 10 of the 15 outcomes. The required sample size per composite 3- and 4-point MACE endpoint was calculated based on the estimated treatment effects in a population and frequencies of the incorporated events in the control group, trial duration, and uncertainty in model parameters. Conclusion: A quantitative tool was developed and used to benchmark different compositions of 3- and 4-point MACE for statins and anti-PCSK9 therapies, based on the minimum population size required to achieve statistical significance in relative risk reduction, following meta-regression modeling of the single MACE components. The approach we developed may be applied towards the optimization of the design of future trials in dyslipidemia disorders as well as in other therapeutic areas.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics.

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early-phase studies and patient-reported outcomes as well as event risks or rates in late-phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non-small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness-of-fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed-effects models and software tools in an integrative and exhaustive manner.

Evaluation of Combination Strategies for the A2AR Inhibitor AZD4635 Across Tumor Microenvironment Conditions via a Systems Pharmacology Model.

Background: Adenosine receptor type 2 (A2AR) inhibitor, AZD4635, has been shown to reduce immunosuppressive adenosine effects within the tumor microenvironment (TME) and to enhance the efficacy of checkpoint inhibitors across various syngeneic models. This study aims at investigating anti-tumor activity of AZD4635 alone and in combination with an anti-PD-L1-specific antibody (anti-PD-L1 mAb) across various TME conditions and at identifying, via mathematical quantitative modeling, a therapeutic combination strategy to further improve treatment efficacy. Methods: The model is represented by a set of ordinary differential equations capturing: 1) antigen-dependent T cell migration into the tumor, with subsequent proliferation and differentiation into effector T cells (Teff), leading to tumor cell lysis; 2) downregulation of processes mediated by A2AR or PD-L1, as well as other immunosuppressive mechanisms; 3) A2AR and PD-L1 inhibition by, respectively, AZD4635 and anti-PD-L1 mAb. Tumor size dynamics data from CT26, MC38, and MCA205 syngeneic mice treated with vehicle, anti-PD-L1 mAb, AZD4635, or their combination were used to inform model parameters. Between-animal and between-study variabilities (BAV, BSV) in treatment efficacy were quantified using a non-linear mixed-effects methodology. Results: The model reproduced individual and cohort trends in tumor size dynamics for all considered treatment regimens and experiments. BSV and BAV were explained by variability in T cell-to-immunosuppressive cell (ISC) ratio; BSV was additionally driven by differences in intratumoral adenosine content across the syngeneic models. Model sensitivity analysis and model-based preclinical study simulations revealed therapeutic options enabling a potential increase in AZD4635-driven efficacy; e.g., adoptive cell transfer or treatments affecting adenosine-independent immunosuppressive pathways. Conclusions: The proposed integrative modeling framework quantitatively characterized the mechanistic activity of AZD4635 and its potential added efficacy in therapy combinations, across various immune conditions prevailing in the TME. Such a model may enable further investigations, via simulations, of mechanisms of tumor resistance to treatment and of AZD4635 combination optimization strategies.

Longitudinal FEV1 and Exacerbation Risk in COPD: Quantifying the Association Using Joint Modelling.

BACKGROUND: Lung function, measured as forced expiratory volume in one second (FEV1), and exacerbations are two endpoints evaluated in chronic obstructive pulmonary disease (COPD) clinical trials. Joint analysis of these endpoints could potentially increase statistical power and enable assessment of efficacy in shorter and smaller clinical trials. OBJECTIVE: To evaluate joint modelling as a tool for analyzing treatment effects in COPD clinical trials by quantifying the association between longitudinal improvements in FEV1 and exacerbation risk reduction. METHODS: A joint model of longitudinal FEV1 and exacerbation risk was developed based on patient-level data from a Phase III clinical study in moderate-to-severe COPD (1740 patients), evaluating efficacy of fixed-dose combinations of a long-acting bronchodilator, formoterol, and an inhaled corticosteroid, budesonide. Two additional studies (1604 and 1042 patients) were used for external model validation and parameter re-estimation. RESULTS: A significant (p<0.0001) association between FEV1 and exacerbation risk was estimated, with an approximate 10% reduction in exacerbation risk per 100 mL improvement in FEV1, consistent across trials and treatment arms. The risk reduction associated with improvements in FEV1 was relatively small compared to the overall exacerbation risk reduction for treatment arms including budesonide (10-15% per 160 µg budesonide). High baseline breathlessness score and previous history of exacerbations also influenced the risk of exacerbation. CONCLUSION: Joint modelling can be used to co-analyze longitudinal FEV1 and exacerbation data in COPD clinical trials. The association between the endpoints was consistent and appeared unrelated to treatment mechanism, suggesting that improved lung function is indicative of an exacerbation risk reduction. The risk reduction associated with improved FEV1 was, however, generally small and no major impact on exacerbation trial design can be expected based on FEV1 alone. Further exploration with other longitudinal endpoints should be considered to further evaluate the use of joint modelling in analyzing COPD clinical trials.

Longitudinal Tumor Size and Neutrophil-to-Lymphocyte Ratio Are Prognostic Biomarkers for Overall Survival in Patients With Advanced Non-Small Cell Lung Cancer Treated With Durvalumab.

Therapy optimization remains an important challenge in the treatment of advanced non-small cell lung cancer (NSCLC). We investigated tumor size (sum of the longest diameters (SLD) of target lesions) and neutrophil-to-lymphocyte ratio (NLR) as longitudinal biomarkers for survival prediction. Data sets from 335 patients with NSCLC from study NCT02087423 and 202 patients with NSCLC from study NCT01693562 of durvalumab were used for model qualification and validation, respectively. Nonlinear Bayesian joint models were designed to assess the impact of longitudinal measurements of SLD and NLR on patient subgrouping (by Response Evaluation Criteria in Solid Tumors 1.1 criteria at 3 months after therapy start), long-term survival, and precision of survival predictions. Various validation scenarios were investigated. We determined a more distinct patient subgrouping and a substantial increase in the precision of survival estimates after the incorporation of longitudinal measurements. The highest performance was achieved using a multivariate SLD and NLR model, which enabled predictions of NSCLC clinical outcomes.

Dose dependence of treatment-related adverse events for immune checkpoint inhibitor therapies: a model-based meta-analysis.

Programmed cell death-1 (PD-1) and/or cytotoxic T lymphocyte-associated antigen 4 (CTLA-4) immune checkpoint inhibitor (ICI) treatments are associated with adverse events (AEs), which may be dependent on ICI dose. Applying a model-based meta-analysis to evaluate safety data from published clinical trials from 2005 to 2018, we analyzed the dose/exposure dependence of ICI treatment-related AE (trAE) and immune-mediated AE (imAE) rates. Unlike with PD-1 inhibitor monotherapy, CTLA-4 inhibitor monotherapy exhibited a dose/exposure dependence on most AE types evaluated. Furthermore, combination therapy with PD-1 inhibitor significantly strengthened the dependence of trAE and imAE rates on CTLA-4 inhibitor dose/exposure.

Quantification of Scheduling Impact on Safety and Efficacy Outcomes of Brain Metastasis Radio- and Immuno-Therapies: A Systematic Review and Meta-Analysis.

Objectives: The goal of this quantitative research was to evaluate the impact of various factors (e.g., scheduling or radiotherapy (RT) type) on outcomes for RT vs. RT in combination with immune checkpoint inhibitors (ICI), in the treatment of brain metastases, via a meta-analysis. Methods: Clinical studies with at least one ICI+RT treatment combination arm with brain metastasis patients were identified via a systematic literature search. Data on 1-year overall survival (OS), 1-year local control (LC) and radionecrosis rate (RNR) were extracted; for combination studies which included an RT monotherapy arm, odds ratios (OR) for the aforementioned endpoints were additionally calculated and analyzed. Mixed-effects meta-analysis models were tested to evaluate impact on outcome, for different factors such as combination treatment scheduling and the type of ICI or RT used. Results: 40 studies representing a total of 4,359 patients were identified. Higher 1-year OS was observed in ICI and RT combination vs. RT alone, with corresponding incidence rates of 59% [95% CI: 54-63%] vs. 32% [95% CI: 25-39%] (P < 0.001). Concurrent ICI and RT treatment was associated with significantly higher 1-year OS vs. sequential combinations: 68% [95% CI: 60-75%] vs. 54% [95% CI: 47-61%]. No statistically significant differences were observed in 1-year LC and RNR, when comparing combinations vs. RT monotherapies, with 1-year LC rates of 68% [95% CI: 40-90%] vs. 72% [95% CI: 63-80%] (P = 0.73) and RNR rates of 6% [95% CI: 2-13%] vs. 9% [95% CI: 5-14%] (P = 0.37). Conclusions: A comprehensive, study-level meta-analysis of brain metastasis disease treatments suggest that combinations of RT and ICI result in higher OS, yet comparable neurotoxicity profiles vs. RT alone, with a superiority of concurrent vs. sequential combination regimens. A similar meta-analysis using patient-level data from past trials, as well as future prospective randomized trials would help confirming these findings.

Renal Effects of Dapagliflozin in People with and without Diabetes with Moderate or Severe Renal Dysfunction: Prospective Modeling of an Ongoing Clinical Trial.

Sodium glucose cotransporter 2 inhibitors (SGLT2i) reduce cardiovascular events and onset and progression of renal disease by mechanisms that remain incompletely understood but may include clearance of interstitial congestion and reduced glomerular hydrostatic pressure. The ongoing DAPASALT mechanistic clinical study will evaluate natriuretic, diuretic, plasma/extracellular volume, and blood pressure responses to dapagliflozin in people with type 2 diabetes with normal or impaired renal function (D-PRF and D-IRF, respectively) and in normoglycemic individuals with renal impairment (N-IRF). In this study, a mathematical model of renal physiology, pathophysiology, and pharmacology was used to prospectively predict changes in sodium excretion, blood and interstitial fluid volume (IFV), blood pressure, glomerular filtration rate, and albuminuria in DAPASALT. After validating the model with previous diabetic nephropathy trials, virtual patients were matched to DAPASALT inclusion/exclusion criteria, and the DAPASALT protocol was simulated. Predicted changes in glycosuria, blood pressure, glomerular filtration rate, and albuminuria were consistent with other recent studies in similar populations. Predicted albuminuria reductions were 46% in D-PRF, 34.8% in D-IRF, and 14.2% in N-IRF. The model predicts a similarly large IFV reduction between D-PRF and D-IRF and less, but still substantial, IFV reduction in N-IRF, even though glycosuria is attenuated in groups with impaired renal function. When DAPASALT results become available, comparison with these simulations will provide a basis for evaluating how well we understand the cardiorenal mechanism(s) of SGLT2i. Meanwhile, these simulations link dapagliflozin's renal mechanisms to changes in IFV and renal biomarkers, suggesting that these benefits may extend to those with impaired renal function and individuals without diabetes. SIGNIFICANCE STATEMENT: Mechanisms of SGLT2 inhibitors' cardiorenal benefits remain incompletely understood. We used a mathematical model of renal physiology/pharmacology to prospectively predict responses to dapagliflozin in the ongoing DAPASALT study. Key predictions include similarly large interstitial fluid volume (IFV) reductions between subjects with normal and impaired renal function and less, but still substantial, IFV reduction in those without diabetes, even though glycosuria is attenuated in these groups. Comparing prospective simulations and study results will assess how well we understand the cardiorenal mechanism(s) of SGLT2 inhibitors.

A Physiology-Based Model of Bile Acid Distribution and Metabolism Under Healthy and Pathologic Conditions in Human Beings.

BACKGROUND & AIMS: Disturbances of the enterohepatic circulation of bile acids (BAs) are seen in a number of clinically important conditions, including metabolic disorders, hepatic impairment, diarrhea, and gallstone disease. To facilitate the exploration of underlying pathogenic mechanisms, we developed a mathematical model built on quantitative physiological observations across different organs. METHODS: The model consists of a set of kinetic equations describing the syntheses of cholic, chenodeoxycholic, and deoxycholic acids, as well as time-related changes of their respective free and conjugated forms in the systemic circulation, the hepatoportal region, and the gastrointestinal tract. The core structure of the model was adapted from previous modeling research and updated based on recent mechanistic insights, including farnesoid X receptor-mediated autoregulation of BA synthesis and selective transport mechanisms. The model was calibrated against existing data on BA distribution and feedback regulation. RESULTS: According to model-based predictions, changes in intestinal motility, BA absorption, and biotransformation rates affected BA composition and distribution differently, as follows: (1) inhibition of transintestinal BA flux (eg, in patients with BA malabsorption) or acceleration of intestinal motility, followed by farnesoid X receptor down-regulation, was associated with colonic BA accumulation; (2) in contrast, modulation of the colonic absorption process was predicted to not affect the BA pool significantly; and (3) activation of ileal deconjugation (eg, in patents with small intestinal bacterial overgrowth) was associated with an increase in the BA pool, owing to higher ileal permeability of unconjugated BA species. CONCLUSIONS: This model will be useful in further studying how BA enterohepatic circulation modulation may be exploited for therapeutic benefits.

Differentiating the Sodium-Glucose Cotransporter 1 Inhibition Capacity of Canagliflozin vs. Dapagliflozin and Empagliflozin Using Quantitative Systems Pharmacology Modeling.

The aim of this research was to differentiate dapagliflozin, empagliflozin, and canagliflozin based on their capacity to inhibit sodium-glucose cotransporter (SGLT) 1 and 2 in patients with type 2 diabetes using a previously developed quantitative systems pharmacology model of renal glucose filtration, reabsorption, and excretion. The analysis was based on pooled, mean study-level data on 24-hour urinary glucose excretion, average daily plasma glucose, and estimated glomerular filtration rate collected from phase I and II clinical trials of SGLT2 inhibitors. Variations in filtered glucose across clinical studies were shown to drive the apparent differences in the glucosuria dose-response relationships among the gliflozins. A normalized dose-response analysis demonstrated similarity of dapagliflozin and empagliflozin, but not canagliflozin. At approved doses, SGLT1 inhibition by canagliflozin but not dapagliflozin or empagliflozin contributed to ~ 10% of daily urinary glucose excretion.

Comparison of the urinary glucose excretion contributions of SGLT2 and SGLT1: A quantitative systems pharmacology analysis in healthy individuals and patients with type 2 diabetes treated with SGLT2 inhibitors.

AIM: To develop a quantitative drug-disease systems model to investigate the paradox that sodium-glucose co-transporter (SGLT)2 is responsible for >80% of proximal tubule glucose reabsorption, yet SGLT2 inhibitor treatment results in only 30% to 50% less reabsorption in patients with type 2 diabetes mellitus (T2DM). MATERIALS AND METHODS: A physiologically based four-compartment model of renal glucose filtration, reabsorption and excretion via SGLT1 and SGLT2 was developed as a system of ordinary differential equations using R/IQRtools. SGLT2 inhibitor pharmacokinetics and pharmacodynamics were estimated from published concentration-time profiles in plasma and urine and from urinary glucose excretion (UGE) in healthy people and people with T2DM. RESULTS: The final model showed that higher renal glucose reabsorption in people with T2DM versus healthy people was associated with 54% and 28% greater transporter capacity for SGLT1 and SGLT2, respectively. Additionally, the analysis showed that UGE is highly dependent on mean plasma glucose and estimated glomerular filtration rate (eGFR) and that their consideration is critical for interpreting clinical UGE findings. CONCLUSIONS: Quantitative drug-disease system modelling revealed mechanistic differences in renal glucose reabsorption and UGE between healthy people and those with T2DM, and clearly showed that SGLT2 inhibition significantly increased glucose available to SGLT1 downstream in the tubule. Importantly, we found that the findings of lower than expected UGE with SGLT2 inhibition are explained by the shift to SGLT1, which recovered additional glucose (~30% of total).

Comparative quantitative systems pharmacology modeling of anti-PCSK9 therapeutic modalities in hypercholesterolemia.

Since the discovery of proprotein convertase subtilisin/kexin type 9 (PCSK9) as an attractive target in the treatment of hypercholesterolemia, multiple anti-PCSK9 therapeutic modalities have been pursued in drug development. The objective of this research is to set the stage for the quantitative benchmarking of two anti-PCSK9 pharmacological modality classes, monoclonal antibodies (mAbs) and small interfering RNA (siRNA). To this end, we developed an integrative mathematical model of lipoprotein homeostasis describing the dynamic interplay between PCSK9, LDL-cholesterol (LDL-C), VLDL-cholesterol, HDL-cholesterol (HDL-C), apoB, lipoprotein a [Lp(a)], and triglycerides (TGs). We demonstrate that LDL-C decreased proportionally to PCSK9 reduction for both mAb and siRNA modalities. At marketed doses, however, treatment with mAbs resulted in an additional ∼20% LDL-C reduction compared with siRNA. We further used the model as an evaluation tool and determined that no quantitative differences were observed in HDL-C, Lp(a), TG, or apoB responses, suggesting that the disruption of PCSK9 synthesis would provide no additional effects on lipoprotein-related biomarkers in the patient segment investigated. Predictive model simulations further indicate that siRNA therapies may reach reductions in LDL-C levels comparable to those achieved with mAbs if the current threshold of 80% PCSK9 inhibition via siRNA could be overcome.

Role of T Cell-To-Dendritic Cell Chemoattraction in T Cell Priming Initiation in the Lymph Node: An Agent-Based Modeling Study.

The adaptive immune response is initiated in lymph nodes by contact between antigen-bearing dendritic cells (DCs) and antigen-specific T cells. A selected number of naïve T cells that recognize a specific antigen may proliferate into expanded clones, differentiate, and acquire an effector phenotype. Despite growing experimental knowledge, certain mechanistic aspects of T cell behavior in lymph nodes remain poorly understood. Computational modeling approaches may help in addressing such gaps. Here we introduce an agent-based model describing T cell movements and their interactions with DCs, leading to activation and expansion of cognate T cell clones, in a two-dimensional representation of the lymph node paracortex. The primary objective was to test the putative role of T cell chemotaxis toward DCs, and quantitatively assess the impact of chemotaxis with respect to T cell priming efficacy. Firstly, we evaluated whether chemotaxis of naïve T cells toward a nearest DC may accelerate the scanning process, by quantifying, through simulations, the number of unique T cell-DC contact events. We demonstrate that, in the presence of naïve T cell-to-DC chemoattraction, a higher total number of contacts occurs, as compared to a T cell random walk scenario. However, the forming swarm of naïve T cells, as these cells get attracted to the neighborhood of a DC, may then physically restrict access of additional T cells to the DC, leading to an actual decrease in the cumulative number of unique contacts between naïve T cells and DCs. Secondly, we investigated the potential role of chemotaxis in maintaining cognate T cell clone expansion. The time course of cognate T cells number in the system was used as a quantitative characteristic of the expansion. Model-based simulations indicate that inclusion of chemotaxis, which is selective for already activated (but not naïve) antigen-specific T cells, may strongly accelerate the time of immune response occurrence, which subsequently increases the overall amplitude of the T cell clone expansion process.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology.

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

Quantitative Systems Pharmacology: An Exemplar Model-Building Workflow With Applications in Cardiovascular, Metabolic, and Oncology Drug Development.

Quantitative systems pharmacology (QSP), a mechanistically oriented form of drug and disease modeling, seeks to address a diverse set of problems in the discovery and development of therapies. These problems bring a considerable amount of variability and uncertainty inherent in the nonclinical and clinical data. Likewise, the available modeling techniques and related software tools are manifold. Appropriately, the development, qualification, application, and impact of QSP models have been similarly varied. In this review, we describe the progressive maturation of a QSP modeling workflow: a necessary step for the efficient, reproducible development and qualification of QSP models, which themselves are highly iterative and evolutive. Furthermore, we describe three applications of QSP to impact drug development; one supporting new indications for an approved antidiabetic clinical asset through mechanistic hypothesis generation, one highlighting efficacy and safety differentiation within the sodium-glucose cotransporter-2 inhibitor drug class, and one enabling rational selection of immuno-oncology drug combinations.

Resistance models to EGFR inhibition and chemotherapy in non-small cell lung cancer via analysis of tumour size dynamics.

PURPOSE: Imaging time-series data routinely collected in clinical trials are predominantly explored for covariates as covariates for survival analysis to support decision-making in oncology drug development. The key objective of this study was to assess if insights regarding two relapse resistance modes, de-novo (treatment selects out a pre-existing resistant clone) or acquired (resistant clone develops during treatment), could be inferred from such data. METHODS: Individual lesion size time-series data were collected from ten Phase III study arms where patients were treated with either first-generation EGFR inhibitors (erlotinib or gefitinib) or chemotherapy (paclitaxel/carboplatin combination or docetaxel). The data for each arm of each study were analysed via a competing models framework to determine which of the two mathematical models of resistance, de-novo or acquired, best-described the data. RESULTS: Within the first-line setting (treatment naive patients), we found that the de-novo model best-described the gefitinib data, whereas, for paclitaxel/carboplatin, the acquired model was preferred. In patients pre-treated with paclitaxel/carboplatin, the acquired model was again preferred for docetaxel (chemotherapy), but for patients receiving gefitinib or erlotinib, both the acquired and de-novo models described the tumour size dynamics equally well. Furthermore, in all studies where a single model was preferred, we found a degree of correlation in the dynamics of lesions within a patient, suggesting that there is a degree of homogeneity in pharmacological response. CONCLUSIONS: This analysis highlights that tumour size dynamics differ between different treatments and across lines of treatment. The analysis further suggests that these differences could be a manifestation of differing resistance mechanisms.

Erratum: Publisher Correction: Mathematical model of hemodynamic mechanisms and consequences of glomerular hypertension in diabetic mice.

[This corrects the article DOI: 10.1038/s41540-018-0077-9.].

Mathematical model of hemodynamic mechanisms and consequences of glomerular hypertension in diabetic mice.

Many preclinically promising therapies for diabetic kidney disease fail to provide efficacy in humans, reflecting limited quantitative translational understanding between rodent models and human disease. To quantitatively bridge interspecies differences, we adapted a mathematical model of renal function from human to mice, and incorporated adaptive and pathological mechanisms of diabetes and nephrectomy to describe experimentally observed changes in glomerular filtration rate (GFR) and proteinuria in db/db and db/db UNX (uninephrectomy) mouse models. Changing a small number of parameters, the model reproduced interspecies differences in renal function. Accounting for glucose and Na+ reabsorption through sodium glucose cotransporter 2 (SGLT2), increasing blood glucose and Na+ intake from normal to db/db levels mathematically reproduced glomerular hyperfiltration observed experimentally in db/db mice. This resulted from increased proximal tubule sodium reabsorption, which elevated glomerular capillary hydrostatic pressure (P gc) in order to restore sodium balance through increased GFR. Incorporating adaptive and injurious effects of elevated P gc, we showed that preglomerular arteriole hypertrophy allowed more direct transmission of pressure to the glomerulus with a smaller mean arterial pressure rise; Glomerular hypertrophy allowed a higher GFR for a given P gc; and P gc-driven glomerulosclerosis and nephron loss reduced GFR over time, while further increasing P gc and causing moderate proteinuria, in agreement with experimental data. UNX imposed on diabetes increased P gc further, causing faster GFR decline and extensive proteinuria, also in agreement with experimental data. The model provides a mechanistic explanation for hyperfiltration and proteinuria progression that will facilitate translation of efficacy for novel therapies from mouse models to human.