Structural identifiability and sensitivity.

Ordinary differential equation models often contain a large number of parameters that must be determined from measurements by estimation procedure. For an estimation to be successful there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not structurally identifiable with the given set of inputs and outputs. The local identifiability of linear and nonlinear models was investigated by an approach based on the rank of the sensitivity matrix of model output with respect to parameters. Associated with multiple random drawn of parameters used as nominal values, the approach reinforces conclusions regarding the local identifiability of models. The numerical implementation for obtaining the sensitivity matrix without any approximation, the extension of the approach to multi-output context and the detection of unidentifiable parameters were also discussed. Based on elementary examples, we showed that (1°) addition of nonlinear elements switches an unidentifiable model to identifiable; (2°) in the presence of nonlinear elements in the model, structural and parametric identifiability are connected issues; and (3°) addition of outputs or/and new inputs improve identifiability conditions. Since the model is the basic tool to obtain information from a set of measurements, its identifiability must be systematically checked.

A reaction limited in vivo dissolution model for the study of drug absorption: Towards a new paradigm for the biopharmaceutic classification of drugs.

The aim of this work is to develop a gastrointestinal (GI) drug absorption model based on a reaction limited model of dissolution and consider its impact on the biopharmaceutic classification of drugs. Estimates for the fraction of dose absorbed as a function of dose, solubility, reaction/dissolution rate constant and the stoichiometry of drug-GI fluids reaction/dissolution were derived by numerical solution of the model equations. The undissolved drug dose and the reaction/dissolution rate constant drive the dissolution rate and determine the extent of absorption when high-constant drug permeability throughout the gastrointestinal tract is assumed. Dose is an important element of drug-GI fluids reaction/dissolution while solubility exclusively acts as an upper limit for drug concentrations in the lumen. The 3D plots of fraction of dose absorbed as a function of dose and reaction/dissolution rate constant for highly soluble and low soluble drugs for different "stoichiometries" (0.7, 1.0, 2.0) of the drug-reaction/dissolution with the GI fluids revealed that high extent of absorption was found assuming high drug- reaction/dissolution rate constant and high drug solubility. The model equations were used to simulate in vivo supersaturation and precipitation phenomena. The model developed provides the theoretical basis for the interpretation of the extent of drug's absorption on the basis of the parameters associated with the drug-GI fluids reaction/dissolution. A new paradigm emerges for the biopharmaceutic classification of drugs, namely, a model independent biopharmaceutic classification scheme of four drug categories based on either the fulfillment or not of the current dissolution criteria and the high or low % drug metabolism.

Revisiting dosing regimen using PK/PD modeling: the MODEL1 phase I/II trial of docetaxel plus epirubicin in metastatic breast cancer patients.

The MODEL1 trial is the first model-driven phase I/II dose-escalation study of densified docetaxel plus epirubicin administration in metastatic breast cancer patients, a regimen previously known to induce unacceptable life-threatening toxicities. The primary objective was to determine the maximum tolerated dose of this densified regimen. Study of the efficacy was a secondary objective. Her2-negative, hormone-resistant metastatic breast cancer patients were treated with escalating doses of docetaxel plus epirubicin every 2 weeks for six cycles with granulocyte colony stimulating factor support. A total of 16 patients were treated with total doses ranging from 85 to 110 mg of docetaxel plus epirubicin per cycle. Dose escalation was controlled by a non-hematological toxicity model. Dose densification was guided by a model of neutrophil kinetics, able to optimize docetaxel plus epirubicin dosing with respect to pre-defined acceptable levels of hematological toxicity while ensuring maximal efficacy. The densified treatment was safe since hematological toxicity was much lower compared to previous findings, and other adverse events were consistent with those observed with this regimen. The maximal tolerated dose was 100 mg given every 2 weeks. The response rate was 45 %; median progression-free survival was 10.4 months, whereas 54.6 months of median overall survival was achieved. The optimized docetaxel plus epirubicin dosing regimen led to fewer toxicities associated with higher efficacy as compared with standard or empirical densified dosing. This study suggests that model-driven dosage adjustment can lead to improved efficacy-toxicity balance in patients with cancer when several anticancer drugs are combined.

Revisiting Dosing Regimen Using Pharmacokinetic/Pharmacodynamic Mathematical Modeling: Densification and Intensification of Combination Cancer Therapy.

Controlling effects of drugs administered in combination is particularly challenging with a densified regimen because of life-threatening hematological toxicities. We have developed a mathematical model to optimize drug dosing regimens and to redesign the dose intensification-dose escalation process, using densified cycles of combined anticancer drugs. A generic mathematical model was developed to describe the main components of the real process, including pharmacokinetics, safety and efficacy pharmacodynamics, and non-hematological toxicity risk. This model allowed for computing the distribution of the total drug amount of each drug in combination, for each escalation dose level, in order to minimize the average tumor mass for each cycle. This was achieved while complying with absolute neutrophil count clinical constraints and without exceeding a fixed risk of non-hematological dose-limiting toxicity. The innovative part of this work was the development of densifying and intensifying designs in a unified procedure. This model enabled us to determine the appropriate regimen in a pilot phase I/II study in metastatic breast patients for a 2-week-cycle treatment of docetaxel plus epirubicin doublet, and to propose a new dose-ranging process. In addition to the present application, this method can be further used to achieve optimization of any combination therapy, thus improving the efficacy versus toxicity balance of such a regimen.

Model-based assessment of erlotinib effect in vitro measured by real-time cell analysis.

Real time cell analysis (RTCA) is an impedance-based technology which tracks various living cell characteristics over time, such as their number, morphology or adhesion to the extra cellular matrix. However, there is no consensus about how RTCA data should be used to quantitatively evaluate pharmacodynamic parameters which describe drug efficacy or toxicity. The purpose of this work was to determine how RTCA data can be analyzed with mathematical modeling to explore and quantify drug effect in vitro. The pharmacokinetic-pharmacodynamic erlotinib concentration profile predicted by the model and its effect on the human epidermoïd carcinoma cell line A431 in vitro was measured through RTCA output, designated as cell index. A population approach was used to estimate model parameter values, considering a plate well as the statistical unit. The model related the cell index to the number of cells by means of a proportionality factor. Cell growth was described by an exponential model. A delay between erlotinib pharmacokinetics and cell killing was described by a transit compartment model, and the effect potency, by an E max function of erlotinib concentration. The modeling analysis performed on RTCA data distinguished drug effects in vitro on cell number from other effects likely to modify the relationship between cell index and cell number. It also revealed a time-dependent decrease of erlotinib concentration over time, described by a mono-exponential pharmacokinetic model with nonspecific binding.

Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice.

Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading during the earliest stages of cancer.

Biodistribution, tumor uptake and efficacy of 5-FU-loaded liposomes: why size matters.

PURPOSE: We have investigated the impact of particle size on the biodistribution, tumor uptake and antiproliferative efficacy of 5-FU-loaded liposomes. METHODS: Three different batches of pegylated liposomes varying in size (i.e., 70, 120 and 250 nm respectively) were tested. The active compounds encapsulated were an equimolar mix of 5-FU, 2'-deoxyinosine and folinic acid. Liposomes were subsequently tested on the human breast cancer model MDA231 cells, a model previously found to be resistant to 5-FU. In vitro, antiproliferative efficacy and microscopy studies of liposomes uptake were carried out. In vivo, comparative biodistribution and efficacy studies were performed in tumor-bearing mice. RESULTS: Difference in size did not change in vitro antiproliferative activity. Fluorescence-Microscopy studies showed that liposomes were mainly uptaken by tumor cells through a direct internalization process, regardless of their size. Biodistribution profiles in tumor-bearing mice revealed higher accumulation of small liposomes in tumors throughout time as compared with normal and large liposomes (p < 0.05). Additionally, we observed that the bigger were the tumors, the more vascularised they were and the greater was the difference in accumulation between small and large liposomes. Consequently, in vivo efficacy studies showed at study conclusion that a 68% reduction in tumor size was achieved with small liposomes (p < 0.05), whereas larger liposomes failed to reduce significantly tumor growth. Similarly, at study conclusion a trend towards higher survival-rate in animals treated with smaller liposomes was observed. CONCLUSION: This study suggests that particle size is critical to achieve higher selectivity and efficacy in experimental oncology, including in resistant tumors.

Physiologically based pharmacokinetic modeling of CYP3A4 induction by rifampicin in human: influence of time between substrate and inducer administration.

The induction of cytochrome P450 enzymes (CYPs) is an important source of drug-drug interaction (DDI) and can result in pronounced changes in pharmacokinetics (PK). Rifampicin (RIF) is a potent inducer of CYP3A4 and also acts as a competitive inhibitor which can partially mask the induction. The objective of this study was to determine a clinical DDI study design for RIF resulting in maximum CYP3A4 induction. A physiologically based pharmacokinetic (PBPK) model was developed to project the dynamics and magnitude of CYP3A4 induction in vivo from in vitro data generated with primary human hepatocytes. The interaction model included both inductive and inhibitory effects of RIF on CYP3A4 in gut and liver and accounting for the observed RIF auto-induction. The model has been verified for 4 CYP3A4 substrates: midazolam, triazolam, alfentanil and nifedipine using plasma concentration data from 20 clinical study designs with intravenous (n=7) and oral (n=13) administrations. Finally, the influence of the time between RIF and substrate administration was explored for the interaction between midazolam and RIF. The model integrating in vitro induction parameters correctly predicted intravenous induction but underestimated oral induction with 30% of simulated concentrations more than 2-fold higher than of observed data. The use of a 1.6-fold higher value for the maximum induction effect (Emax) improved significantly the accuracy and precision of oral induction with 82% of simulated concentrations and all predicted PK parameters within 2-fold of observed data. Our simulations suggested that a concomitant administration of RIF and midazolam resulted in significant competitive inhibition limited to intestinal enzyme. Accordingly, a maximum induction effect could be achieved with a RIF pretreatment of 600 mg/day during 5 days and a substrate administration at least 2 h after the last RIF dose. A period of 2 weeks after RIF removal was found sufficient to allow return to baseline levels of enzyme.

In vitro and in vivo evaluation of lipofufol, a new triple stealth liposomal formulation of modulated 5-fu: impact on efficacy and toxicity.

PURPOSE: Drug resistance and severe toxicities are limitations when handling 5-FU. We have developed a triple liposomal formulation of 5-FU combined to 2'-deoxyinosine and folinic acid to improve its efficacy-toxicity balance. METHODS: Stealth liposomes were obtained using the thin-film method. Antiproliferative activity was tested on human colorectal and breast cancer models using sensitive (HT29) and resistant (SW620, LS174t, MDA231) cell lines. In vivo, pharmacokinetics, biodistribution and safety studies were performed in rodents. Finally, efficacy was evaluated using two tumor-bearing mice models (LS174 and MDA231) with response and survival as main endpoints. RESULTS: LipoFufol is a 120-nm pegylated liposome, displaying 20-30% encapsulation rates. In vitro, antiproliferative activities were higher than 5-FU, and matched that of FolFox combination in colorectal models, but not in breast. Drug monitoring showed an optimized pharmacokinetics profile with reduced clearance and prolonged half-life. Liposome accumulation in tumors was shown by fluorescence-based biodistribution studies. Beside, milder neutropenia was observed when giving LipoFufol to animals with transient partial DPD-deficiency, as compared with standard 5-FU. In LS174t-bearing mice, higher response and 55% longer survival were achieved with Lipofufol, as compared with 5-FU. CONCLUSION: The issues of drug-resistance and drug-related toxicity can be both addressed using a stealth liposomal formulation of modulated 5-FU.

100% human monoclonal antibodies in oncology: hype or breakthrough?

Targeted therapies have dramatically modified treatment strategies in oncology since the early 2000's, especially for treating digestive cancers. These new biotherapies such as anti-VEGF (bevacizumab) or anti-EGFR (cetuximab) monoclonal antibodies have given oncologists new opportunities to use innovative treatment schedules or combinations with cytotoxics. Consequently, significant improvements in response rates, with trends to longer progression-free survival and/or overall survival have been achieved in patients with metastatic colorectal cancer (mCRC). Panitumumab is a novel, 100% human, anti-EGFR1 (HER1) antibody that has been approved in late 2007 for use as monotherapy in mCRC patients resistant to standard chemotherapy, provided that their tumor express EGFR and display wild-type K-Ras status. Panitumumab has been recently further approved in combination with chemotherapy in mCRC patients. However, owing to the fact that its mechanism of action for targeting EGFR is similar to that of chimeric cetuximab, picturing the specificities in pharmacological and pharmacokinetic properties of this 100% human antibody could help the oncologists to better define their strategies at the bedside.