C-Reactive Protein as an Early Predictor of Efficacy in Advanced Non-Small-Cell Lung Cancer Patients: A Tumor Dynamics-Biomarker Modeling Framework.

In oncology, longitudinal biomarkers reflecting the patient's status and disease evolution can offer reliable predictions of the patient's response to treatment and prognosis. By leveraging clinical data in patients with advanced non-small-cell lung cancer receiving first-line chemotherapy, we aimed to develop a framework combining anticancer drug exposure, tumor dynamics (RECIST criteria), and C-reactive protein (CRP) concentrations, using nonlinear mixed-effects models, to evaluate and quantify by means of parametric time-to-event models the significance of early longitudinal predictors of progression-free survival (PFS) and overall survival (OS). Tumor dynamics was characterized by a tumor size (TS) model accounting for anticancer drug exposure and development of drug resistance. CRP concentrations over time were characterized by a turnover model. An x-fold change in TS from baseline linearly affected CRP production. CRP concentration at treatment cycle 3 (day 42) and the difference between CRP concentration at treatment cycles 3 and 2 were the strongest predictors of PFS and OS. Measuring longitudinal CRP allows for the monitoring of inflammatory levels and, along with its reduction across treatment cycles, presents a promising prognostic marker. This framework could be applied to other treatment modalities such as immunotherapies or targeted therapies allowing the timely identification of patients at risk of early progression and/or short survival to spare them unnecessary toxicities and provide alternative treatment decisions.

A prognostic baseline blood biomarker and tumor growth kinetics integrated model in paclitaxel/platinum treated advanced non-small cell lung cancer patients.

Paclitaxel/platinum chemotherapy, the backbone of standard first-line treatment of advanced non-small cell lung cancer (NSCLC), exhibits high interpatient variability in treatment response and high toxicity burden. Baseline blood biomarker concentrations and tumor size (sum of diameters) at week 8 relative to baseline (RS8) are widely investigated prognostic factors. However, joint analysis of data on demographic/clinical characteristics, blood biomarker levels, and chemotherapy exposure-driven early tumor response for improved prediction of overall survival (OS) is clinically not established. We developed a Weibull time-to-event model to predict OS, leveraging data from 365 patients receiving paclitaxel/platinum combination chemotherapy once every three weeks for ≤six cycles. A developed tumor growth inhibition model, combining linear tumor growth and first-order paclitaxel area under the concentration-time curve-induced tumor decay, was used to derive individual RS8. The median model-derived RS8 in all patients was a 20.0% tumor size reduction (range from -78% to +15%). Whereas baseline carcinoembryonic antigen, cytokeratin fragments, and thyroid stimulating hormone levels were not significantly associated with OS in a subset of 221 patients, and lactate dehydrogenase, interleukin-6 and neutrophil-to-lymphocyte ratio levels were significant only in univariate analyses (p value < 0.05); C-reactive protein (CRP) in combination with RS8 most significantly affected OS (p value < 0.01). Compared to the median population OS of 11.3 months, OS was 128% longer at the 5th percentile levels of both covariates and 60% shorter at their 95th percentiles levels. The combined paclitaxel exposure-driven RS8 and baseline blood CRP concentrations enables early individual prognostic predictions for different paclitaxel dosing regimens, forming the basis for treatment decision and optimizing paclitaxel/platinum-based advanced NSCLC chemotherapy.

A continued learning approach for model-informed precision dosing: Updating models in clinical practice.

Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.

Physiology-based toxicokinetic modelling of aluminium in rat and man.

A sufficient quantitative understanding of aluminium (Al) toxicokinetics (TK) in man is still lacking, although highly desirable for risk assessment of Al exposure. Baseline exposure and the risk of contamination severely limit the feasibility of TK studies administering the naturally occurring isotope 27Al, both in animals and man. These limitations are absent in studies with 26Al as a tracer, but tissue data are limited to animal studies. A TK model capable of inter-species translation to make valid predictions of Al levels in humans-especially in toxicological relevant tissues like bone and brain-is urgently needed. Here, we present: (i) a curated dataset which comprises all eligible studies with single doses of 26Al tracer administered as citrate or chloride salts orally and/or intravenously to rats and humans, including ultra-long-term kinetic profiles for plasma, blood, liver, spleen, muscle, bone, brain, kidney, and urine up to 150 weeks; and (ii) the development of a physiology-based (PB) model for Al TK after intravenous and oral administration of aqueous Al citrate and Al chloride solutions in rats and humans. Based on the comprehensive curated 26Al dataset, we estimated substance-dependent parameters within a non-linear mixed-effect modelling context. The model fitted the heterogeneous 26Al data very well and was successfully validated against datasets in rats and humans. The presented PBTK model for Al, based on the most extensive and diverse dataset of Al exposure to date, constitutes a major advancement in the field, thereby paving the way towards a more quantitative risk assessment in humans.

Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses.

The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. Although covariate selection criteria have been studied extensively, the choice of the functional relationship between covariates and parameters, however, has received much less attention. Often, a simple particular class of covariate-to-parameter relationships (linear, exponential, etc.) is chosen ad hoc or based on domain knowledge, and a statistical evaluation is limited to the comparison of a small number of such classes. Goodness-of-fit testing against a nonparametric alternative provides a more rigorous approach to covariate model evaluation, but no such test has been proposed so far. In this manuscript, we derive and evaluate nonparametric goodness-of-fit tests for parametric covariate models, the null hypothesis, against a kernelized Tikhonov regularized alternative, transferring concepts from statistical learning to the pharmacological setting. The approach is evaluated in a simulation study on the estimation of the age-dependent maturation effect on the clearance of a monoclonal antibody. Scenarios of varying data sparsity and residual error are considered. The goodness-of-fit test correctly identified misspecified parametric models with high power for relevant scenarios. The case study provides proof-of-concept of the feasibility of the proposed approach, which is envisioned to be beneficial for applications that lack well-founded covariate models.

Reinforcement learning and Bayesian data assimilation for model-informed precision dosing in oncology.

Model-informed precision dosing (MIPD) using therapeutic drug/biomarker monitoring offers the opportunity to significantly improve the efficacy and safety of drug therapies. Current strategies comprise model-informed dosing tables or are based on maximum a posteriori estimates. These approaches, however, lack a quantification of uncertainty and/or consider only part of the available patient-specific information. We propose three novel approaches for MIPD using Bayesian data assimilation (DA) and/or reinforcement learning (RL) to control neutropenia, the major dose-limiting side effect in anticancer chemotherapy. These approaches have the potential to substantially reduce the incidence of life-threatening grade 4 and subtherapeutic grade 0 neutropenia compared with existing approaches. We further show that RL allows to gain further insights by identifying patient factors that drive dose decisions. Due to its flexibility, the proposed combined DA-RL approach can easily be extended to integrate multiple end points or patient-reported outcomes, thereby promising important benefits for future personalized therapies.

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs.

The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.

Time-to-Event Analysis of Paclitaxel-Associated Peripheral Neuropathy in Advanced Non-Small-Cell Lung Cancer Highlighting Key Influential Treatment/Patient Factors.

Paclitaxel-associated peripheral neuropathy (PN), a major dose-limiting toxicity, significantly impacts patients' quality of life/treatment outcome. Evaluation of risk factors often ignores time of PN onset, precluding the impact of time-dependent factors, e.g., drug exposure, needed to comprehensively characterize PN. We employed parametric time-to-event (TTE) analysis to describe the time course of risk of first occurrence of clinically relevant PN grades ≥2 (PN2+, n = 105, common terminology criteria v4.0) and associated patient/treatment characteristics, leveraging data from 365 patients (1454 cycles) receiving paclitaxel every 3 weeks (plus carboplatin AUC = 6 or cisplatin 80 mg/m2) for ≤6 cycles. Paclitaxel was intravenously administered (3 hours) as standard 200-mg/m2 doses (n = 182) or as pharmacokinetic-guided dosing (n = 183). A cycle-varying hazard TTE model linking surge in hazard of PN2+ to paclitaxel administration [PN2+ proportions (i.e., cases per 1000 patients), 1st day, cycle 1: 4.87 of 1000; cycle 6: 7.36 of 1000] and linear decline across cycle (last day, cycle 1: 1.64 of 1000; cycle 6: 2.48 of 1000) adequately characterized the time-varying hazard of PN2+. From joint covariate evaluation, PN2+ proportions (1st day, cycle 1) increased by 1.00 per 1000 with 5-µmol·h/l higher paclitaxel exposure per cycle (AUC between the start and end of a cycle, most relevant covariate), 0.429 per 1000 with 5-year higher age, 1.31 per 1000 (smokers vs. nonsmokers), and decreased by 0.670 per 1000 (females vs. males). Compared to 200 mg/m2 dosing every 3 weeks, model-predicted cumulative risk of PN2+ was significantly higher (42%) with 80 mg/m2 weekly dosing but reduced by 11% with 175 mg/m2 dosing every 3 weeks. The established TTE modeling framework enables quantification and comparison of patient's cumulative risks of PN2+ for different clinically relevant paclitaxel dosing schedules, sparing patients PN2+ to improve paclitaxel therapy. SIGNIFICANCE STATEMENT: Characterization of risk factors of paclitaxel-associated peripheral neuropathy (PN) typically involves time-independent comparison of PN odds in patient subpopulations, concealing the impact of time-dependent factors, e.g., changing paclitaxel exposure, required to comprehensively characterize PN. We developed a parametric time-to-event model describing the time course in risk of clinically relevant paclitaxel-associated PN, identifying the highest risk in older male smokers with higher paclitaxel area under the plasma concentration-time curve between the start and end of a cycle. The developed framework enabled quantification of patient's risk of PN for clinically relevant paclitaxel dosing schedules, facilitating future dosing decisions.

Pharmacokinetic/Pharmacodynamic Evaluation of Hydrocortisone Therapy in Pediatric Patients with Congenital Adrenal Hyperplasia.

OBJECTIVES: Patients with congenital adrenal hyperplasia (CAH) require lifelong replacement therapy with glucocorticoids. Optimizing hydrocortisone therapy is challenging, since there are no established cortisol concentration targets other than the cortisol circadian rhythm profile. 17-hydroxyprogesterone (17-OHP) concentrations are elevated in these patients and commonly used to monitor therapy. This study aimed to characterize the pharmacokinetics/pharmacodynamics (PK/PD) of cortisol using 17-OHP as a biomarker in pediatric patients with CAH and to assess different hydrocortisone dosing regimens. METHODS: Cortisol and 17-OHP concentrations from 30 CAH patients (7-17 years of age) receiving standard hydrocortisone replacement therapy (5-20 mg) twice (n = 17) or 3 times (n = 13) daily were used to develop a PK/PD model. Sequentially, simulated cortisol concentrations for clinically relevant 3- and 4-times daily dosing regimens were compared with cortisol and 17-OHP target ranges and to concentrations in healthy children. RESULTS: Cortisol concentration-time profiles were accurately described by a 2-compartment model with first-order absorption and expected high bioavailability (82.6%). A time-delayed model with cortisol-mediated inhibition of 17-OHP synthesis accurately described 17-OHP concentrations. The cortisol concentration inhibiting 50% of 17-OHP synthesis was 48.6 nmol/L. A 4-times-daily dosing better attained the target ranges and mimicked the cortisol concentrations throughout the 24-hour period than 3-times-daily. CONCLUSIONS: A PK/PD model following hydrocortisone administration has been established. An improved dosing regimen of 38% at 06:00, 22% at 12:00, 17% at 18:00, and 22% at 24:00 of the daily hydrocortisone dose was suggested. The 4-times-daily dosing regimen was superior, avoiding subtherapeutic cortisol concentrations and better resembling the circadian rhythm of cortisol.

Bayesian Data Assimilation to Support Informed Decision Making in Individualized Chemotherapy.

An essential component of therapeutic drug/biomarker monitoring (TDM) is to combine patient data with prior knowledge for model-based predictions of therapy outcomes. Current Bayesian forecasting tools typically rely only on the most probable model parameters (maximum a posteriori (MAP) estimate). This MAP-based approach, however, does neither necessarily predict the most probable outcome nor does it quantify the risks of treatment inefficacy or toxicity. Bayesian data assimilation (DA) methods overcome these limitations by providing a comprehensive uncertainty quantification. We compare DA methods with MAP-based approaches and show how probabilistic statements about key markers related to chemotherapy-induced neutropenia can be leveraged for more informative decision support in individualized chemotherapy. Sequential Bayesian DA proved to be most computationally efficient for handling interoccasion variability and integrating TDM data. For new digital monitoring devices enabling more frequent data collection, these features will be of critical importance to improve patient care decisions in various therapeutic areas.

The circadian rhythm of corticosteroid-binding globulin has little impact on cortisol exposure after hydrocortisone dosing.

CONTEXT: Optimization of hydrocortisone replacement therapy is important to prevent under- and over dosing. Hydrocortisone pharmacokinetics is complex as circulating cortisol is protein bound mainly to corticosteroid-binding globulin (CBG) that has a circadian rhythm. OBJECTIVE: A detailed analysis of the CBG circadian rhythm and its impact on cortisol exposure after hydrocortisone administration. DESIGN AND METHODS: CBG was measured over 24 hours in 14 healthy individuals and, employing a modelling and simulation approach using a semi-mechanistic hydrocortisone pharmacokinetic model, we evaluated the impact on cortisol exposure (area under concentration-time curve and maximum concentration of total cortisol) of hydrocortisone administration at different clock times and of the changing CBG concentrations. RESULTS: The circadian rhythm of CBG was well described with two cosine terms added to the baseline of CBG: baseline CBG was 21.8 µg/mL and interindividual variability 11.9%; the amplitude for the 24 and 12 hours cosine functions were relatively small (24 hours: 5.53%, 12 hours: 2.87%) and highest and lowest CBG were measured at 18:00 and 02:00, respectively. In simulations, the lowest cortisol exposure was observed after administration of hydrocortisone at 23:00-02:00, whereas the highest was observed at 15:00-18:00. The differences between the highest and lowest exposure were minor (≤12.2%), also regarding the free cortisol concentration and free fraction (≤11.7%). CONCLUSIONS: Corticosteroid-binding globulin has a circadian rhythm but the difference in cortisol exposure is ≤12.2% between times of highest and lowest CBG concentrations; therefore, hydrocortisone dose adjustment based on time of dosing to adjust for the CBG concentrations is unlikely to be of clinical benefit.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Predicting Cortisol Exposure from Paediatric Hydrocortisone Formulation Using a Semi-Mechanistic Pharmacokinetic Model Established in Healthy Adults.

BACKGROUND AND OBJECTIVE: Optimisation of hydrocortisone replacement therapy in children is challenging as there is currently no licensed formulation and dose in Europe for children under 6 years of age. In addition, hydrocortisone has non-linear pharmacokinetics caused by saturable plasma protein binding. A paediatric hydrocortisone formulation, Infacort® oral hydrocortisone granules with taste masking, has therefore been developed. The objective of this study was to establish a population pharmacokinetic model based on studies in healthy adult volunteers to predict hydrocortisone exposure in paediatric patients with adrenal insufficiency. METHODS: Cortisol and binding protein concentrations were evaluated in the absence and presence of dexamethasone in healthy volunteers (n = 30). Dexamethasone was used to suppress endogenous cortisol concentrations prior to and after single doses of 0.5, 2, 5 and 10 mg of Infacort® or 20 mg of Infacort®/hydrocortisone tablet/hydrocortisone intravenously. A plasma protein binding model was established using unbound and total cortisol concentrations, and sequentially integrated into the pharmacokinetic model. RESULTS: Both specific (non-linear) and non-specific (linear) protein binding were included in the cortisol binding model. A two-compartment disposition model with saturable absorption and constant endogenous cortisol baseline (Baseline cort,15.5 nmol/L) described the data accurately. The predicted cortisol exposure for a given dose varied considerably within a small body weight range in individuals weighing <20 kg. CONCLUSIONS: Our semi-mechanistic population pharmacokinetic model for hydrocortisone captures the complex pharmacokinetics of hydrocortisone in a simplified but comprehensive framework. The predicted cortisol exposure indicated the importance of defining an accurate hydrocortisone dose to mimic physiological concentrations for neonates and infants weighing <20 kg. EudraCT number: 2013-000260-28, 2013-000259-42.

Role of renal function in risk assessment of target non-attainment after standard dosing of meropenem in critically ill patients: a prospective observational study.

BACKGROUND: Severe bacterial infections remain a major challenge in intensive care units because of their high prevalence and mortality. Adequate antibiotic exposure has been associated with clinical success in critically ill patients. The objective of this study was to investigate the target attainment of standard meropenem dosing in a heterogeneous critically ill population, to quantify the impact of the full renal function spectrum on meropenem exposure and target attainment, and ultimately to translate the findings into a tool for practical application. METHODS: A prospective observational single-centre study was performed with critically ill patients with severe infections receiving standard dosing of meropenem. Serial blood samples were drawn over 4 study days to determine meropenem serum concentrations. Renal function was assessed by creatinine clearance according to the Cockcroft and Gault equation (CLCRCG). Variability in meropenem serum concentrations was quantified at the middle and end of each monitored dosing interval. The attainment of two pharmacokinetic/pharmacodynamic targets (100%T>MIC, 50%T>4×MIC) was evaluated for minimum inhibitory concentration (MIC) values of 2 mg/L and 8 mg/L and standard meropenem dosing (1000 mg, 30-minute infusion, every 8 h). Furthermore, we assessed the impact of CLCRCG on meropenem concentrations and target attainment and developed a tool for risk assessment of target non-attainment. RESULTS: Large inter- and intra-patient variability in meropenem concentrations was observed in the critically ill population (n = 48). Attainment of the target 100%T>MIC was merely 48.4% and 20.6%, given MIC values of 2 mg/L and 8 mg/L, respectively, and similar for the target 50%T>4×MIC. A hyperbolic relationship between CLCRCG (25-255 ml/minute) and meropenem serum concentrations at the end of the dosing interval (C8h) was derived. For infections with pathogens of MIC 2 mg/L, mild renal impairment up to augmented renal function was identified as a risk factor for target non-attainment (for MIC 8 mg/L, additionally, moderate renal impairment). CONCLUSIONS: The investigated standard meropenem dosing regimen appeared to result in insufficient meropenem exposure in a considerable fraction of critically ill patients. An easy- and free-to-use tool (the MeroRisk Calculator) for assessing the risk of target non-attainment for a given renal function and MIC value was developed. TRIAL REGISTRATION: Clinicaltrials.gov, NCT01793012 . Registered on 24 January 2013.

Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes.

BACKGROUND: Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/ ß-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/ ß-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells. RESULTS: Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/ ß-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength. CONCLUSIONS: Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter- and intracellular processes, such as Dkk feedback, diffusion and Wnt/ ß-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.

Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision.

BACKGROUND: Evolution of metastatic melanoma (MM) under B-RAF inhibitors (BRAFi) is unpredictable, but anticipation is crucial for therapeutic decision. Kinetics changes in metastatic growth are driven by molecular and immune events, and thus we hypothesized that they convey relevant information for decision making. PATIENTS AND METHODS: We used a retrospective cohort of 37 MM patients treated by BRAFi only with at least 2 close CT-scans available before BRAFi, as a model to study kinetics of metastatic growth before, under and after BRAFi. All metastases (mets) were individually measured at each CT-scan. From these measurements, different measures of growth kinetics of each met and total tumor volume were computed at different time points. A historical cohort permitted to build a reference model for the expected spontaneous disease kinetics without BRAFi. All variables were included in Cox and multistate regression models for survival, to select best candidates for predicting overall survival. RESULTS: Before starting BRAFi, fast kinetics and moreover a wide range of kinetics (fast and slow growing mets in a same patient) were pejorative markers. At the first assessment after BRAFi introduction, high heterogeneity of kinetics predicted short survival, and added independent information over RECIST progression in multivariate analysis. Metastatic growth rates after BRAFi discontinuation was usually not faster than before BRAFi introduction, but they were often more heterogeneous than before. CONCLUSIONS: Monitoring kinetics of different mets before and under BRAFi by repeated CT-scan provides information for predictive mathematical modelling. Disease kinetics deserves more interest.

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.

Parameter non-identifiability of the Gyllenberg-Webb ODE model.

An ODE model introduced by Gyllenberg and Webb (Growth Develop Aging 53:25-33, 1989) describes tumour growth in terms of the dynamics between proliferating and quiescent cell states. The passage from one state to another and vice versa is modelled by two functions r0 and ri depending on the total tumour size. As these functions do not represent any observable quantities, they have to be identified from the observations. In this paper we show that there is an infinite number of pairs (r0, ri) corresponding to the same solution of the ODE system and the functions (r0, ri) will be classified in terms of this equivalence. Surprisingly, the technique used for this classification permits a uniqueness proof of the solution of the ODE model in a non-Lipschitz case. The reasoning can be widened to a more general setting including an extension of the Gyllenberg-Webb model with a nonlinear birth rate. The relevance of this result is discussed in a preclinical application scenario.