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We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters., (Copyright © 2020. Published by Elsevier Ltd.)

Stability analysis, often overlooked in pharmacometrics, is essential to explore dynamical systems. The model developed by Friberg et al. 1 to describe drug-induced hematotoxicity is widely used to support decisions across drug development, and parameter values are often identified from observed blood counts. We use stability analysis to study the parametric dependence of stable and unstable solutions of several Friberg-type models and highlight the risks associated with system instability in the context of nonlinear mixed effects modeling. We emphasize the consequences of unstable solutions on prediction performance by demonstrating nonbiological system behaviors in a real case study of drug-induced thrombocytopenia. Ultimately, we provide simple criteria for identifying parameters associated with stable solutions of Friberg-type models. For instance, in the original Friberg model, we find that stability depends only on the parameter that governs the feedback from peripheral cells to progenitors and provide the exact range of values that results in stable solutions., (© 2020 AstraZeneca. CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals LLC on behalf of the American Society for Clinical Pharmacology and Therapeutics.)

Introduction: Osimertinib has shown promising activity in patients with leptomeningeal metastases (LMs) of EGFR-positive NSCLC at 160 mg once daily (qd) (BLOOM; NCT02228369). We report LM activity with osimertinib (80 mg qd) in a retrospective analysis of studies across the AURA program (AURA extension, AURA2, AURA17, and AURA3)., Methods: Patients with EGFR T790M-positive advanced NSCLC and progression after previous EGFR-tyrosine kinase inhibitor therapy received osimertinib (80 mg qd). Patients with central nervous system (CNS) metastases (including LMs) were eligible if the lesions were neurologically asymptomatic and stable. Patients with evidence of LMs at the study entry were retrospectively included for the analysis; brain scans were assessed for radiologic LM response by neuroradiologically blinded, independent central review per the modified Response Assessment in Neuro-Oncology LM criteria. LM objective response rate, duration of response, progression-free survival, and overall survival were assessed. A longitudinal analysis was performed to investigate the relationship between changes from the baseline in non-CNS tumor sizes and LM responses at each visit of patients in AURA LM and BLOOM studies., Results: For the 22 patients included in the analysis, LM objective response rate was 55% (95% confidence interval [CI]: 32-76). Median LM duration of response was not reached (95% CI: 2.8-not calculable [NC]). Median LM progression-free survival and overall survival were 11.1 months (95% CI: 4.6-NC) and 18.8 months (95% CI: 6.3-NC), respectively. The longitudinal analysis revealed similar non-CNS and LM responses between the patients in AURA LM and BLOOM programs., Conclusions: Patients with EGFR T790M-positive NSCLC and radiologically detected LM obtained clinical benefit from osimertinib (80 mg qd)., (Copyright © 2020 International Association for the Study of Lung Cancer. Published by Elsevier Inc. All rights reserved.)

Haematological toxicity associated with cancer therapeutics is monitored by changes in blood cell count, and their primary effect is on proliferative progenitors in the bone marrow. Using observations in rat bone marrow and blood, we characterize a mathematical model that comprises cell proliferation and differentiation of the full haematopoietic phylogeny, with interacting feedback loops between lineages in homeostasis as well as following carboplatin exposure. We accurately predicted the temporal dynamics of several mature cell types related to carboplatin-induced bone marrow toxicity and identified novel insights into haematopoiesis. Our model confirms a significant degree of plasticity within bone marrow cells, with the number and type of both early progenitors and circulating cells affecting cell balance, via feedback mechanisms, through fate decisions of the multipotent progenitors. We also demonstrated cross-species translation of our predictions to patients, applying the same core model structure and considering differences in drug-dependent and physiology-dependent parameters., (© 2019 Astrazeneca CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of the American Society for Clinical Pharmacology and Therapeutics.)

Pancreatic ductal adenocarcinoma (PDAC) is among the deadliest cancers, and overall survival rates have barely improved over the past five decades. The antimetabolite gemcitabine remains part of the standard of care but shows very limited antitumor efficacy. Ataxia telangiectasia and Rad3-related protein (ATR), the apical kinase of the intra-S-phase DNA damage response, plays a central role in safeguarding cells from replication stress and can therefore limit the efficacy of antimetabolite drug therapies. We investigated the ability of the ATR inhibitor, AZD6738, to prevent the gemcitabine-induced intra-S-phase checkpoint activation and evaluated the antitumor potential of this combination in vitro and in vivo In PDAC cell lines, AZD6738 inhibited gemcitabine-induced Chk1 activation, prevented cell-cycle arrest, and restrained RRM2 accumulation, leading to the strong induction of replication stress markers only with the combination. Moreover, synergistic growth inhibition was identified in a panel of 5 mouse and 7 human PDAC cell lines using both Bliss Independence and Loewe models. In clonogenic assays, the combination abrogated survival at concentrations for which single agents had minor effects. In vivo , AZD6738 in combination with gemcitabine was well tolerated and induced tumor regression in a subcutaneous allograft model of a Kras G12D ; Trp53 R172H ; Pdx-Cre (KPC) mouse cancer cell line, significantly extending survival. Remarkably, the combination also induced regression of a subgroup of KPC autochthonous tumors, which generally do not respond well to conventional chemotherapy. Altogether, our data suggest that AZD6738 in combination with gemcitabine merits evaluation in a clinical trial in patients with PDAC. Mol Cancer Ther; 17(8); 1670-82. ©2018 AACR ., (©2018 American Association for Cancer Research.)

Purpose: Approximately one-third of patients with non-small cell lung cancer (NSCLC) harboring tumors with EGFR-tyrosine kinase inhibitor (TKI)-sensitizing mutations (EGFRm) experience disease progression during treatment due to brain metastases. Despite anecdotal reports of EGFR-TKIs providing benefit in some patients with EGFRm NSCLC brain metastases, there is a clinical need for novel EGFR-TKIs with improved efficacy against brain lesions., Experimental Design: We performed preclinical assessments of brain penetration and activity of osimertinib (AZD9291), an oral, potent, irreversible EGFR-TKI selective for EGFRm and T790M resistance mutations, and other EGFR-TKIs in various animal models of EGFR-mutant NSCLC brain metastases. We also present case reports of previously treated patients with EGFRm-advanced NSCLC and brain metastases who received osimertinib in the phase I/II AURA study (NCT01802632)., Results: Osimertinib demonstrated greater penetration of the mouse blood-brain barrier than gefitinib, rociletinib (CO-1686), or afatinib, and at clinically relevant doses induced sustained tumor regression in an EGFRm PC9 mouse brain metastases model; rociletinib did not achieve tumor regression. Under positron emission tomography micro-dosing conditions, [ 11 C]osimertinib showed markedly greater exposure in the cynomolgus monkey brain than [ 11 C]rociletinib and [ 11 C]gefitinib. Early clinical evidence of osimertinib activity in previously treated patients with EGFRm-advanced NSCLC and brain metastases is also reported., Conclusions: Osimertinib may represent a clinically significant treatment option for patients with EGFRm NSCLC and brain metastases. Further investigation of osimertinib in this patient population is ongoing. Clin Cancer Res; 22(20); 5130-40. ©2016 AACR., (©2016 American Association for Cancer Research.)

Osimertinib (AZD9291) is a potent, selective, irreversible inhibitor of EGFR-sensitizing (exon 19 and L858R) and T790M-resistant mutation. In vivo, in the mouse, it is metabolized to an active des-methyl metabolite, AZ5104. To understand the therapeutic potential in patients, this study aimed to assess the relationship between osimertinib pharmacokinetics, the pharmacokinetics of the active metabolite, the pharmacodynamics of phosphorylated EGFR reduction, and efficacy in mouse xenograft models of EGFR-driven cancers, including two NSCLC lines. Osimertinib was dosed in xenografted models of EGFR-driven cancers. In one set of experiments, changes in phosphorylated EGFR were measured to confirm target engagement. In a second set of efficacy studies, the resulting changes in tumor volume over time after repeat dosing of osimertinib were observed. To account for the contributions of both molecules, a mathematical modeling approach was taken to integrate the resulting datasets. The model was able to describe the pharmacokinetics, pharmacodynamics, and efficacy in A431, PC9, and NCI-H1975 xenografts, with the differences in sensitivity described by the varying potency against wild-type, sensitizing, and T790M-mutant EGFR and the phosphorylated EGFR reduction required to reduce tumor volume. It was inferred that recovery of pEGFR is slower after chronic dosing due to reduced resynthesis. It was predicted and further demonstrated that although inhibition is irreversible, the resynthesis of EGFR is such that infrequent intermittent dosing is not as efficacious as once daily dosing. Mol Cancer Ther; 15(10); 2378-87. ©2016 AACR., (©2016 American Association for Cancer Research.)

mTOR is an atypical serine threonine kinase involved in regulating major cellular functions, such as nutrients sensing, growth, and proliferation. mTOR is part of the multiprotein complexes mTORC1 and mTORC2, which have been shown to play critical yet functionally distinct roles in the regulation of cellular processes. Current clinical mTOR inhibitors only inhibit the mTORC1 complex and are derivatives of the macrolide rapamycin (rapalogs). Encouraging effects have been observed with rapalogs in estrogen receptor-positive (ER(+)) breast cancer patients in combination with endocrine therapy, such as aromatase inhibitors. AZD2014 is a small-molecule ATP competitive inhibitor of mTOR that inhibits both mTORC1 and mTORC2 complexes and has a greater inhibitory function against mTORC1 than the clinically approved rapalogs. Here, we demonstrate that AZD2014 has broad antiproliferative effects across multiple cell lines, including ER(+) breast models with acquired resistance to hormonal therapy and cell lines with acquired resistance to rapalogs. In vivo, AZD2014 induces dose-dependent tumor growth inhibition in several xenograft and primary explant models. The antitumor activity of AZD2014 is associated with modulation of both mTORC1 and mTORC2 substrates, consistent with its mechanism of action. In combination with fulvestrant, AZD2014 induces tumor regressions when dosed continuously or using intermittent dosing schedules. The ability to dose AZD2014 intermittently, together with its ability to block signaling from both mTORC1 and mTORC2 complexes, makes this compound an ideal candidate for combining with endocrine therapies in the clinic. AZD2014 is currently in phase II clinical trials., (©2015 American Association for Cancer Research.)

It is challenging to evaluate how tumour pathophysiology influences nanomedicine therapeutic effect; however, this is a key question in drug delivery. An advanced analytical method was developed to quantify the spatial distribution of drug-induced effect in tumours with varied stromal morphologies. The analysis utilises standard immunohistochemistry images and quantifies the frequency of positive staining as a function of distance from the stroma. Two stromal morphologies - Estuary and Tumour Island - were classified in 28 tumours from a lung cancer explant model in mice treated with liposomal doxorubicin. Analysis demonstrated that Estuary-like tumours presented a highly convoluted tumour-stroma interface, with most tumour cells in close proximity to vessels; these tumours were 8.8-fold more responsive to liposomal doxorubicin than were Tumour Island-like tumours, which were nearly unresponsive to liposomal doxorubicin. SDARS analysis allows the relative treatment effect to be assessed in tumours individually, and enables investigation of nanomedicine delivery in complex tumour pathophysiologies., From the Clinical Editor: Advances in nanotechnology have brought about many novel treatment modalities for cancer. Nonetheless, there is no standard evaluation technique for tumor cells' drug response. The authors here utilized patient-derived tumour xenograft (PDTX) models to have a more translatable pre-clinical evaluation platform for nanomedicine drugs. They then used advanced imaging acquisition technique to analyze tumor stromal morphology, which they named Spatial Distribution of Apoptosis Relative to Stroma (SDARS). The findings would have significant clinical impact as it would help predict the eventual clinical drug response., (Copyright © 2015 Elsevier Inc. All rights reserved.)

One of the major sources of information on physiological and pathophysiological effects in pre-clinical oncology studies is the xenografted tumour animal model. However, measurement of tumour volume over time potentially masks a range of biological changes that the xenograft is undergoing. In this paper a mechanistic model of tumour growth in xenografts is presented that can be used to investigate the mode of drug action with respect to phenotypic changes. The model encapsulates key histological biomarkers and spatial constraints. The unknown model parameters are first shown to be uniquely identifiable from the proposed experimental studies, and then estimated from the resulting data using the anti-cancer agent docetaxel., (Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.)

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available., (Copyright © 2013. Published by Elsevier Ireland Ltd.)

Introduction: Preclinical assessment of the heart rate corrected QT interval (QTc) is an important component of the cardiovascular safety evaluation in drug discovery. Here we aimed to quantify the translational relationship between QTc prolongation and shortening in the conscious telemetered dog and humans by a retrospective pharmacokinetic-pharmacodynamic (PKPD) analysis., Methods: QTc effects of 2 proprietary compounds and 2 reference drugs (moxifloxacin and dofetilide) were quantified in conscious dogs and healthy volunteers via a linear and Emax pharmacokinetic-pharmacodynamic models. The translational relationship was quantified by correlating the QTc response from dog and human at matching free drug concentrations., Results: A consistent translational relationship was found at low delta-QTc intervals indicating that a QTc change of 2.5-8 ms in dog would correspond to a 10 ms change in human., Discussion: The translational relationship developed here can be used to predict the QTc liability in human using preclinical dog data. It could therefore help protect the health of human volunteers, for example by appropriate clinical study design and dose selection, as well as improve future decision-making and help reduce compound attrition due to changes in QT interval., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Model-based drug discovery (MBDDx) aims to build and continuously improve the quantitative understanding of the relation between drug exposure (target engagement) efficacy and safety, to support target validation; to define compound property criteria for lead optimization and safety margins; to set the starting dose; and to predict human dose and scheduling for clinical candidates alone, or in combination with other medicines. AstraZeneca has systematically implemented MBDDx within all drug discovery programs, with a focused investment to build a preclinical modeling and simulation capability and an in vivo information platform and architecture, the implementation, impact and learning of which are discussed here., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

Insulin Sensitivity is an important parameter for the management of Diabetes. It can be derived for a particular patient using data derived from some glucose challenge tests using measured glucose and insulin levels at various times. Whilst a useful approach, deriving insulin sensitivities to inform insulin dosing in other settings such as Intensive Care Units can be more challenging - especially as insulin levels have to be assayed in a laboratory, not at the bedside. This paper investigates an approach to measure insulin sensitivity from glucose levels only. Estimates of mean and between individual parameter variances are used to derive conditional estimates of insulin sensitivity. The method is demonstrated to perform reasonably well, with conditional estimates comparing well with estimates derived from insulin data as well., (Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.)

Structural identifiability should be considered when developing mathematical models. A globally or at least locally identifiable model has to be obtained in order to have some chance of obtaining unique parameter estimates when real data are available. An indicator of structural unidentifiability may be that some unknown parameter estimates are found to be not well determined from parameter estimation of a model. An example is discussed in this paper to illustrate the procedures involved when such situations arise. Problems with parameter estimation were observed for a PKPD model for an α1A/1L-adrenoceptor partial agonist developed for the treatment of stress urinary incontinence The regulation of the side effects of the increased peripheral resistance, induced by the constriction of the blood vessels, was modelled by adapting a previous cardiovascular nonlinear PKPD model proposed by Franchetau and co-workers. Structural identifiability analysis confirmed that the model was unidentifiable. The model was then reparameterised (parameter list reduction) to obtain a globally identifiable model. Simulation studies confirm the superiority of the reduced parameterisation with respect to parameter estimation. The simulation study also confirms the models behave indistinguishably with respect to the input-output behaviour. The example demonstrates the importance of recognising an unidentifiable model and illustrates step by step identifiability analysis, reparameterisation and validation of reparameterised model against the original model., (Copyright © 2012 Elsevier B.V. All rights reserved.)

An implementation of the Expectation-Maximisation (EM) algorithm in ACSLXTREME (AEGIS Technologies) for the analyses of population pharmacokinetic-pharmacodynamic (PKPD) data is demonstrated. The parameter estimation results are compared with those from NONMEM (Globomax) using the first order conditional estimate method. The estimates are comparable and it is concluded that the EM algorithm is a useful technique in population pharmacokinetic-pharmacodynamic modelling. The implementation also demonstrates the ease with which parameter estimation algorithms for population data can be implemented in simulation software packages.

The deterministic identifiability of models is only normally considered if a problem becomes apparent in the parameter identification stage of data analysis. If no problem is perceived then the analysis will continue. However, although the problem does not become apparent, the implications of ambiguities in what is inferred from the data should be considered. This paper reviews some fundamentals with respect to model indistinguishability and parameter identifiability.

One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.