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Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183–93. ©2017 AACR.

Bioluminescence of GI-ME-N-Luc+ cells

Legends of Figures S1-4

Additional double-tumors models fits and residuals analysis

Combining radiotherapy with immune checkpoint blockade may offer considerable therapeutic impact if the immunosuppressive nature of the tumor microenvironment (TME) can be relieved. In this study, we used mathematical models, which can illustrate the potential synergism between immune checkpoint inhibitors and radiotherapy. A discrete-time pharmacodynamic model of the combination of radiotherapy with inhibitors of the PD1–PDL1 axis and/or the CTLA4 pathway is described. This mathematical framework describes how a growing tumor first elicits and then inhibits an antitumor immune response. This antitumor immune response is described by a primary and a secondary (or memory) response. The primary immune response appears first and is inhibited by the PD1–PDL1 axis, whereas the secondary immune response happens next and is inhibited by the CTLA4 pathway. The effects of irradiation are described by a modified version of the linear-quadratic model. This modeling offers an explanation for the reported biphasic relationship between the size of a tumor and its immunogenicity, as measured by the abscopal effect (an off-target immune response). Furthermore, it explains why discontinuing immunotherapy may result in either tumor recurrence or a durably sustained response. Finally, it describes how synchronizing immunotherapy and radiotherapy can produce synergies. The ability of the model to forecast pharmacodynamic endpoints was validated retrospectively by checking that it could describe data from experimental studies, which investigated the combination of radiotherapy with immune checkpoint inhibitors. In summary, a model such as this could be further used as a simulation tool to facilitate decision making about optimal scheduling of immunotherapy with radiotherapy and perhaps other types of anticancer therapies. Cancer Res; 76(17); 4931–40. ©2016 AACR.

Figure S1: plot of all tumor volumes for double and single (control) tumor groups

Table S1: models equations. Table S2: goodness-of-fit metrics of these three single tumor growth models. Table S3: parameter values and identifiability of the Gompertz, power law and ``proliferation inhibition" model for the single tumor growth fits

Single tumor model fits (exponential, Gompertz and power law) and delay analysis

Metronomic chemotherapy is usually associated with better tolerance than conventional chemotherapy, and encouraging response rates have been reported in various settings. However, clinical development of metronomic chemotherapy has been hampered by a number of limitations, including the vagueness of its definition and the resulting empiricism in protocol design. In this study, we developed a pharmacokinetic/pharmacodynamic mathematical model that identifies in silico the most effective administration schedule for gemcitabine monotherapy. This model is based upon four biological assumptions regarding the mechanisms of action of metronomic chemotherapy, resulting in a set of 6 minimally parameterized differential equations. Simulations identified daily 0.5–1 mg/kg gemcitabine as an optimal protocol to maximize antitumor efficacy. Both metronomic protocols (0.5 and 1 mg/kg/day for 28 days) were evaluated in chemoresistant neuroblastoma-bearing mice and compared with the standard MTD protocol (100 mg/kg once a week for 4 weeks). Systemic exposure to gemcitabine was 14 times lower in the metronomic groups compared with the standard group. Despite this, metronomic gemcitabine significantly inhibited tumor angiogenesis and reduced tumor perfusion and inflammation in vivo, while standard gemcitabine did not. Furthermore, metronomic gemcitabine yielded a 40%–50% decrease in tumor mass at the end of treatment as compared with control mice (P = 0.002; ANOVA on ranks with Dunn test), while standard gemcitabine failed to significantly reduce tumor growth. Stable disease was maintained in the metronomic groups for up to 2 months after treatment completion (67%–72% reduction in tumor growth at study conclusion, P < 0.001; ANOVA on ranks with Dunn test). Collectively, our results confirmed the superiority of metronomic protocols in chemoresistant tumors in vivo. Cancer Res; 77(17); 4723–33. ©2017 AACR.

This file provides some details on the mathematical models and their properties.

Description of additional methods and procedures used in the study.

Supplementary Movie 1: Primary tumor (PT) was assumed to be detected when reaching the size of 4.32 cm in diameter. Post-diagnosis PT growth and development of metastases in the case of no surgical intervention are indicated as dashed line in the left plot and white bars in the histogram on the right, respectively.

Supplementary Movie 2: Primary tumor (PT) was assumed to be detected when reaching the size of 4.32 cm in diameter. Post-diagnosis PT growth and development of metastases in the case of no surgical intervention are indicated as dashed line in the left plot and white bars in the histogram on the right, respectively.

Rapid improvements in the detection and tracking of early-stage tumor progression aim to guide decisions regarding cancer treatments as well as predict metastatic recurrence in patients following surgery. Mathematical models may have the potential to further assist in estimating metastatic risk, particularly when paired with in vivo tumor data that faithfully represent all stages of disease progression. Herein, we describe mathematical analysis that uses data from mouse models of spontaneous metastasis developing after surgical removal of orthotopically implanted primary tumors. Both presurgical (primary tumor) growth and postsurgical (metastatic) growth were quantified using bioluminescence and were then used to generate a mathematical formalism based on general laws of the disease (i.e., dissemination and growth). The model was able to fit and predict pre/postsurgical data at the level of the individual as well as the population. Our approach also enabled retrospective analysis of clinical data describing the probability of metastatic relapse as a function of primary tumor size. In these data-based models, interindividual variability was quantified by a key parameter of intrinsic metastatic potential. Critically, our analysis identified a highly nonlinear relationship between primary tumor size and postsurgical survival, suggesting possible threshold limits for the utility of tumor size as a predictor of metastatic recurrence. These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential and may guide optimal timing of treatments in neoadjuvant (presurgical) and adjuvant (postsurgical) settings to maximize patient benefit. Cancer Res; 76(3); 535–47. ©2015 AACR.

In vitro fit and direct statistical analysis of the xenograft breast data (S1); Population fit of the tumor growth data that were measured by BL, under the Gomp-Exp model and initial volume Vi fixed by the conversion rule inferred from the correlation between volume and BL (S2); Population fits of the breast xenograft data under different growth theories (S3); Population fits of the kidney isograft data under different growth theories (S4); Second kidney data set used for fitting the data (S5); Individual fits of primary tumor and metastatic burden kinetics Breast animal model (S6); Individual fits of primary tumor and metastatic burden kinetics. Kidney animal model (S7); Link between experimental and model survival (S8); Surgery benefit on survival and metastatic burden reduction as a function of resection size, for varying values of metastatic potential (S9); Population fits of the ortho-surgical metastasis animal models for a dissemination coefficient d(Vp) = ??Vyp and various values of y (S10); Population fits of the ortho-surgical metastasis animal models for various values of the signal-to-cell ratio V0 (S11).

Supplementary Figure 1. In vitro fit and direct statistical analysis of the xenograft breast data. Supplementary Figure 2. Population fit of the tumor growth data. Supplementary Figure 3. Population fits of the breast xenograft data under different growth theories. Supplementary Figure 4. Population fits of the kidney isograft data under different growth theories. Supplementary Figure 5. Second kidney data set used for fitting the data (resection time = 23 days). Supplementary Figure 6. Individual fits of primary tumor and metastatic burden kinetics. Supplementary Figure 7. Individual fits of primary tumor and metastatic burden kinetics. Supplementary Figure 8. Link between experimental and model survival. Supplementary Figure 9: Surgery benefit on survival and metastatic burden reduction as a function of resection size, for varying values of metastatic potential. Supplementary Figure 10. Population fits of the ortho-surgical metastasis animal models. Supplementary Figure 11. Population fits of the ortho-surgical metastasis animal models.

A phase Ia/Ib trial of metronomic oral vinorelbine (MOV) driven by a mathematical model was performed in heavily pretreated metastatic Non-Small Cell Lung Cancer or Pleural Mesothelioma patients. Disease Control Rate, progression free survival, toxicity and PK/PD were the main endpoints.Best MOV scheduling was selected using a simplified phenomenological, semi-mechanistic model with a total weekly dose of 150-mg vinorelbine. Computation of individual PK parameters was performed using population approach.The mathematical model proposed the following metronomic schedule for a 150-mg weekly dose of vinorelbine: 60 mg D1, 30 mg D2, 60 mg D4. A total of 37 heavily pre-treated patients (30 evaluable) were enrolled. Grade III/IV neutropenia was observed in 30% patients. Median PFS was 11 weeks. Disease Control Rate was 73% (i.e.; 13% partial response and 60% stable disease). A large variability in drug exposure (AUCMOV was characterized by important variability in drug exposure among patients. However, and despite being all heavily pre-treated, 73% of disease control rate and 11 weeks PFS were achieved with manageable toxicities. PK/PD relationships yielded conflicting results depending on the initial tumor burden and BSA, suggesting that patients should be carefully selected prior to be scheduled for metronomic regimen. Possible role NLR could play as a predictive marker suggests immunomodulating features with MOV.

International audience; PurposeThe aim of the present study was to characterize the pharmacokinetics of irinotecan and its four main metabolites (SN-38, SN-38G, APC and NPC) in metastatic colorectal cancer patients treated with FOLFIRI and FOLFIRINOX regimens and to quantify and explain the inter-individual pharmacokinetic variability in this context.MethodsA multicenter study including 109 metastatic colorectal cancer patients treated with FOLFIRI or FOLFIRINOX regimen, associated or not with a monoclonal antibody, was conducted. Concentrations of irinotecan and its four main metabolites were measured in 506 blood samples during the first cycle of treatment. Collected data were analyzed using the population approach. First, fixed and random effects models were selected using statistical and graphical methods; second, the impact of covariates on pharmacokinetic parameters was evaluated to explain the inter-individual variability in pharmacokinetic parameters.ResultsA seven-compartment model best described the pharmacokinetics of irinotecan and its four main metabolites. First-order rates were assigned to distribution, elimination, and metabolism processes, except for the transformation of irinotecan to NPC which was nonlinear. Addition of a direct conversion of NPC into SN-38 significantly improved the model. Co-administration of oxaliplatin significantly modified the distribution of SN-38.ConclusionTo our knowledge, the present model is the first to allow a simultaneous description of irinotecan pharmacokinetics and of its four main metabolites. Moreover, a direct conversion of NPC into SN-38 had never been described before in a population pharmacokinetic model of irinotecan. The model will be useful to develop pharmacokinetic-pharmacodynamic models relating SN-38 concentrations to efficacy and digestive toxicities.

Highlights • Common long-term memory defects after pediatric brain tumor affect school achievement • The hippocampi, the cerebellum and cerebellar-cortical networks play a role in several memory systems. • This study will provide long-term neuropsychological data about four different memory systems. • We will investigate the correlations between neuropsychological, neuroimaging and radiotherapy dose data. • Imaging will be structural (3DT1), microstructural (DTI), functional (rs-fMRI), vascular (ASL) and metabolic (spectroscopy)., Background Posterior fossa tumors represent two thirds of brain tumors in children. Although progress in treatment has improved survival rates over the past few years, long-term memory impairments in survivors are frequent and have an impact on academic achievement. The hippocampi, cerebellum and cerebellar-cortical networks play a role in several memory systems. They are affected not only by the location of the tumor itself and its surgical removal, but also by the supratentorial effects of complementary treatments, particularly radiotherapy. The IMPALA study will investigate the impact of irradiation doses on brain structures involved in memory, especially the hippocampi and cerebellum. Methods/design In this single-center prospective behavioral and neuro-imaging study, 90 participants will be enrolled in three groups. The first two groups will include patients who underwent surgery for a posterior fossa brain tumor in childhood, who are considered to be cured, and who completed treatment at least 5 years earlier, either with radiotherapy (aggressive brain tumor; Group 1) or without (low-grade brain tumor; Group 2). Group 3 will include control participants matched with Group 1 for age, sex, and handedness. All participants will perform an extensive battery of neuropsychological tests, including an assessment of the main memory systems, and undergo multimodal 3 T MRI. The irradiation dose to the different brain structures involved in memory will be collected from the initial radiotherapy dosimetry. Discussion This study will provide long-term neuropsychological data about four different memory systems (working memory, episodic memory, semantic memory, and procedural memory) and the cognitive functions (attention, language, executive functions) that can interfere with them, in order to better characterize memory deficits among the survivors of brain tumors. We will investigate the correlations between neuropsychological and neuroimaging data on the structural (3DT1), microstructural (DTI), functional (rs-fMRI), vascular (ASL) and metabolic (spectroscopy) impact of the tumor and irradiation dose. This study will thus inform the setting of dose constraints to spare regions linked to the development of cognitive and memory functions. Trial registration ClinicalTrials.gov: NCT04324450, registered March 27, 2020, updated January 25th, 2021. Retrospectively registered, https://www.clinicaltrials.gov/ct2/show/NCT04324450.

International audience; The heat shock protein 27 (Hsp27) has emerged as a principal factor of the castration-resistant prostate cancer (CRPC) progression. Also, an antisense oligonucleotide (ASO) against Hsp27 (OGX-427 or apatorsen) has been assessed in different clinical trials. Here, we illustrate that Hsp27 highly regulates the expression of the human DEAD-box protein 5 (DDX5), and we define DDX5 as a novel therapeutic target for CRPC treatment. DDX5 overexpression is strongly correlated with aggressive tumor features, notably with CRPC. DDX5 downregulation using a specific ASO-based inhibitor that acts on DDX5 mRNAs inhibits cell proliferation in preclinical models, and it particularly restores the treatment sensitivity of CRPC. Interestingly, through the identification and analysis of DDX5 protein interaction networks, we have identified some specific functions of DDX5 in CRPC that could contribute actively to tumor progression and therapeutic resistance. We first present the interactions of DDX5 and the Ku70/80 heterodimer and the transcription factor IIH, thereby uncovering DDX5 roles in different DNA repair pathways. Collectively, our study highlights critical functions of DDX5 contributing to CRPC progression and provides preclinical proof of concept that a combination of ASO-directed DDX5 inhibition with a DNA damage-inducing therapy can serve as a highly potential novel strategy to treat CRPC.

BackgroundImmune checkpoint inhibitors (ICIs) are now a therapeutic standard in advanced non-small cell lung cancer (NSCLC), but strong predictive markers for ICIs efficacy are still lacking. We evaluated machine learning models built on simple clinical and biological data to individually predict response to ICIs.MethodsPatients with metastatic NSCLC who received ICI in second line or later were included. We collected clinical and hematological data and studied the association of this data with disease control rate (DCR), progression free survival (PFS) and overall survival (OS). Multiple machine learning (ML) algorithms were assessed for their ability to predict response.ResultsOverall, 298 patients were enrolled. The overall response rate and DCR were 15.3 % and 53%, respectively. Median PFS and OS were 3.3 and 11.4 months, respectively. In multivariable analysis, DCR was significantly associated with performance status (PS) and hemoglobin level (OR 0.58, pConclusionCombination of simple clinical and biological data could accurately predict disease control rate at the individual level.Highlights-Machine learning applied to a large set of NSCLC patients could predict efficacy of immunotherapy with a 69% accuracy using simple routine data-Hemoglobin levels and performance status were the strongest predictors and significantly associated with DCR, PFS and OS-Neutrophils-to-lymphocyte ratio was also associated with outcome-Benchmark of 8 machine learning models

International audience; Background: The presence of neutrophils in the lung was identified as a factor associated with CLAD but requires invasive smples. The aim of this study was to assess the kinetics of peripheral blood neutrophils after lung transplantation as early predictor of CLAD. Methods: We retrospectively included all recipients transplanted in our center between 2009 and 2014. Kinetics of blood neutrophils were evaluated to predict early CLAD by mathematical modeling using unadjusted and adjusted analyses.Results: 103 patients were included, 80 in the stable group and 23 in the CLAD group. Bacterial infections at 1 year were associated with CLAD occurrence. Neutrophils demonstrated a high increase postoperatively and then a progressive decrease until normal range. Recipients with CLAD had higher neutrophil counts (mixed effect coefficient beta over 3 years = + 1.36 G/L, 95% Confidence Interval [0.99-1.92], p < .001). A coefficient of celerity (S for speed) was calculated to model the kinetics of return to the norm before CLAD occurrence. After adjustment, lower values of S (slower decrease of neutrophils) were associated with CLAD (Odds Ratio = 0.26, 95% Confidence Interval [0.08-0.66], p = .01).Conclusion: A slower return to the normal range of blood neutrophils was early associated with CLAD occurrence.

International audience; The amount of 'big' data generated in clinical oncology, whether from molecular, imaging, pharmacological or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically-based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging or electronic health records), pharmacometrics, quantitative systems pharmacology, tumor size kinetics, and metastasis modeling. Focus is set on studies with high potential of clinical translation, as well as applied to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: 'mechanistic learning'.

Introduction Malgre la place grandissante des inhibiteurs de check-point immunitaire (ICIs) dans le cancer bronchique non a petites cellules (CBNPC), le taux de reponse a ce type de traitement est faible et il existe un risque non negligeable de toxicites specifiques. Aussi, determiner des facteurs predictifs de reponse a l’immunotherapie est essentielle et pouvoir le faire a partir de donnees facilement accessibles au clinicien serait une aide precieuse. L’objectif de cette etude a ete de developper, grâce a l’intelligence artificielle (IA), un outil d’aide a la selection des patients qui pourraient tirer beneficie d’un traitement par ICIs, et ce a partir de caracteristiques cliniques et biologiques simples. Methodes Il s’agit d’une etude de cohorte observationnelle, retrospective de patients souffrant de CBNPC, ayant recu au moins un cycle d’ICI entre avril 2013 et novembre 2017. Les variables etudiees etaient les caracteristiques demographiques, cliniques, hematologiques, therapeutiques et evolutives. Les donnees clinicobiologiques ont ete correlees associees au taux de reponse objective (TRO) et au taux de controle de la maladie (TCM) par regression logistique, et a la survie (survie sans progression [SSP] et survie globale [SG]) par modele de Cox. Resultats Parmi les 350 patients inclus dans cette cohorte, l’âge median etait de 62 ans, 66 % etaient des hommes. 26 % avaient un performance status (PS) ≥ 2. Le TRO etait de 16 %, le TCM etait de 53 %, la SSP mediane etait de 3 mois et la SG mediane etait de 13,7 mois. En analyse multivariee, le PS ≥ 2 et l’IMC etaient significativement correles au TRO (respectivement odds ratio [OR] 0,078, p = 0,002 et 1,09, p = 0,001). Pour le TCM, il avait une correlation significative avec le PS ≥ 2, l’hemoglobine et le rapport neutrophiles/lymphocytes (NLR) (respectivement OR a 0,32, p Conclusion Grâce a l’IA, la combinaison de caracteristiques cliniques et hematologiques basiques pourrait conduire a une prediction de l’efficacite des ICIs a l’echelle individuelle, et ainsi integrer le processus de decision therapeutique a l’heure de la medecine de precision. L’algorithme developpe ici necessitera neanmoins une validation dans une cohorte independante de patients.

FOLFIRINOX regimen is commonly used in colorectal and more recently pancreatic cancer. However, FOLFIRINOX induces significant and dose-limiting toxic effects leading to empirical dose reduction and sometimes treatment discontinuation. Model-based FOLFIRINOX regimen optimization might help improving patients’ outcome. As a first step, the current review aims at bringing together all published population pharmacokinetics models for FOLFIRINOX anticancer drugs. A literature search was conducted in the PubMed database from inception to February 2018, using the following terms: population pharmacokinetic(s), irinotecan, oxaliplatin, fluorouracil, FOLFIRI, FOLFOX, FOLFIRINOX. Only articles displaying nonlinear mixed effect models were included. Study description, pharmacokinetic parameter values and influential covariates are reported. For each model, the typical pharmacokinetic profile was simulated for the standard FOLFIRINOX protocol. The FOLFIRINOX compounds have been studied only separately so far. A total of six articles were retained for 5-fluorouracil, 6 for oxaliplatin and 5 for irinotecan (also including metabolites). Either one- or two-compartment models have been described for 5-fluorouracil, while two- or three-compartment models were reported for oxaliplatin and irinotecan pharmacokinetics. Non-linear elimination was sometimes reported for 5-fluorouracil. Sex and body size were found as influential covariates for all molecules in some publications. Despite some differences in model structures and parameter values, the simulated profiles and subsequent exposure were consistent between studies. The current review allows for a global understanding of FOLFIRINOX pharmacokinetics, and will provide a basis for further development of pharmacokinetics–pharmacodynamics–toxicity models for model-driven FOLFIRINOX protocol optimization to reach the best benefit-to-risk ratio.

// Fabrice Barlesi 1, 2 , Diane-Charlotte Imbs 2 , Pascale Tomasini 1 , Laurent Greillier 1 , Melissa Galloux 1 , Albane Testot-Ferry 1 , Melanie Garcia 3 , Xavier Elharrar 1 , Annick Pelletier 1 , Nicolas Andre 2, 4 , Celine Mascaux 1 , Bruno Lacarelle 2, 3 , Raouf El Cheikh 2 , Raphael Serre 2 , Joseph Ciccolini 2, 3 and Dominique Barbolosi 2 1 Aix Marseille University, APHM, Marseille Early Phases Cancer Trials Center CLIP, Marseille, France 2 Aix Marseille University, SMARTc Unit, INSERM U911, Marseille, France 3 Aix Marseille University, APHM, Department of Pharmacology, Marseille, France 4 Aix Marseille University, APHM, Department of Pediatric Hematology and Oncology, Marseille, France Correspondence to: Fabrice Barlesi, email: fabrice.barlesi@ap-hm.fr Keywords: lung cancer, mesothelioma, mathematical modeling, vinorelbine, metronomic Received: March 24, 2017 Accepted: April 19, 2017 Published: May 02, 2017 ABSTRACT Introduction: Using mathematical modelling allows to select a treatment’s regimen across infinite possibilities. Here, we report the phase I assessment of a new schedule for metronomic vinorelbine in treating refractory advanced NSCLC and mesothelioma patients. Results: Overall, 13 patients were screened and 12 were treated (50% male, median age: 68yrs), including 9 NSCLC patients. All patients received at least one week (3 doses) of treatment. At data cut-off, the median length of treatment was 6.5 weeks (1–32+). All the patients presented with at least one adverse event (AE) and six patients with a severe AE (SAE). One partial response and 5 stable diseases were observed. The median OS was 6.4 months (95% CI, 4.8 to 12 months). The median and mean vinorelbine’s AUC were 122 ng/ml*h and 159 ng/ml*h, respectively, with the higher plasmatic vinorelbine exposure associated with the best ORR (difference of AUC comparison between responders and non-responders, p-value 0.017). Materials and Methods: The mathematical modelling determined the administration of vinorelbine, 60 mg on Day 1, 30 mg on Day 2 and 60 mg on Day 4 weekly until progression, as the best schedule. Advanced NSCLC or mesothelioma patients progressing after standard treatment were eligible for the trial. NCT02555007. Conclusions: Responses with acceptable safety profile were observed in heavily pretreated NSCLC and mesothelioma patients using oral vinorelbine at this metronomic dosage based on a mathematic modeling. This study demonstrates the feasibility of this new type of approach, as mathematical modeling may help to rationally decide the better regimen to be clinically tested across infinite possibilities.

Background: Small-cell lung cancer (SCLC) represents one of the most aggressive forms of lung cancer. Despite the fair sensitivity of SCLC to chemotherapy and radiotherapy, the current standard treatment regimens have modest survival rates and are associated with potential life-threatening adverse events. Therefore, research into new optimised regimens that increase drug efficacy while respecting toxicity constraints is of primary importance. Methods: A PK/PD model for the combination of cisplatin and etoposide to treat extensive-stage SCLC patients was generated. The model takes into consideration both the efficacy of the drugs and their haematological toxicity. Using optimisation techniques, the model can be used to propose new regimens. Results: Three new regimens with varying timing for combining cisplatin and etoposide have been generated that respect haematological toxicity constraints and achieve better or similar tumour regression. The proposed regimens are: (1) Protocol OP1: etoposide 80 mg m−2 over 1 h D1, followed by a long infusion 12 h later (over 3 days) of 160 mg m−2 plus cisplatin 80 mg m−2 over 1 h D1, D1–D1 21 days; (2) Protocol OP2: etoposide 80 mg m−2 over 1 h D1, followed by a long infusion 12 h later (over 4 days) of 300 mg m−2 plus cisplatin 100 mg m−2 over 1 h D1, D1–D1 21 days; and (3) Protocol OP3: etoposide 40 mg m−2 over 1 h, followed by a long infusion 6 h later (3 days) of 105 mg m−2 plus cisplatin 50 mg m−2 over 1 h, D1–D1 14 days. Conclusions: Mathematical modelling can help optimise the design of new cisplatin plus etoposide regimens for managing extensive-stage SCLC patients.

International audience

Brain metastases (BMs) are associated with poor prognosis in non-small cell lung cancer (NSCLC), but are only visible when large enough. Therapeutic decisions such as whole brain radiation therapy would benefit from patient-specific predictions of radiologically undetectable BMs. Here, we propose a mathematical modeling approach and use it to analyze clinical data of BM from NSCLC.Primary tumor growth was best described by a gompertzian model for the pre-diagnosis history, followed by a tumor growth inhibition model during treatment. Growth parameters were estimated only from the size at diagnosis and histology, but predicted plausible individual estimates of the tumor age (2.1-5.3 years). Multiple metastatic models were assessed from fitting either literature data of BM probability (n = 183 patients) or longitudinal measurements of visible BMs in two patients. Among the tested models, the one featuring dormancy was best able to describe the data. It predicted latency phases of 4.4 - 5.7 months and onset of BMs 14 - 19 months before diagnosis. This quantitative model paves the way for a computational tool of potential help during therapeutic management.

Introduction: Based on a mathematical model of trabectedin-induced neutropenia, we assessed the predictive value of absolute neutrophil count (ANC) on progression-free survival (PFS) in an independent validation cohort of patients treated with trabectedin. Methods: We collected data from 87 patients in two expert centers who received at least two cycles of trabectedin for soft tissue sarcomas (STS) treatment. Correlations between ANC, patients&rsquo, characteristics, and survival were assessed, and a multivariate model including tumor grade, performance status, ANC, and hemoglobin level was developed. Results: Therapeutic ANC &ge, 7.5 G/L level was associated with shorter PFS: 3.22 months (95% confidence interval (CI), 1.57&ndash, 4.87) in patients with ANC &ge, 7.5 G/L vs. 5.78 months (95% CI, 3.95&ndash, 7.61) in patients with ANC &lt, 7.5 G/L (p = 0.009). Age, primary localization, lung metastases, dose reduction, hemoglobin, and albumin rates were also associated with PFS. In multivariate analysis, ANC &ge, 7.5 G/L was independently associated with poor PFS and overall survival. Conclusion: We validated increased pre-therapeutic ANC as a predictive factor of short PFS in patients starting trabectedin for STS. ANC appears to have an impact on survival rates and may be used as a decision-making tool for personalizing second-line strategies in patients with metastatic STS.

Background In FDG-PET, SUV images are hampered by large potential biases. Our aim was to develop an alternative method (ParaPET) to generate 3D kinetic parametric FDG-PET images easy to perform in clinical oncology. Methods The key points of our method are the use of a new error model of PET measurement extracted from a late dynamic PET acquisition of 15 min, centered over the lesion and an image-derived input function (IDIF). The 15-min acquisition is reconstructed to obtain five images of FDG mean activity concentration and images of its variance to model errors of PET measurement. Our approach is carried out on each voxel to derive 3D kinetic parameter images. ParaPET was evaluated and compared to Patlak analysis as a reference. Hunter and Barbolosi methods (Barbolosi-Bl: with blood samples or Barbolosi-Im: with IDIF) were also investigated and compared to Patlak. Our evaluation was carried on K i index, the net influx rate and its maximum value in the lesion (K i,max). Results This parameter was obtained from 41 non-small cell lung cancer lesions associated with 4 to 5 blood samples per patient, required for the Patlak analysis. Compare to Patlak, the median relative difference and associated range (median; [min;max]) in K i,max estimates were not statistically significant (Wilcoxon test) for ParaPET (− 3.0%; [− 31.9%; 47.3%]; p = 0.08) but statistically significant for Barbolosi-Bl (− 8.0%; [− 30.8%; 53.7%]; p = 0.001), Barbolosi-Im (− 7.9%; [− 38.4%; 30.6%]; p = 0.007) or Hunter (32.8%; [− 14.6%; 132.2%]; p

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.

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.

International audience; Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition and proliferation inhibition) have been proposed but precise determinants of the phenomenon remain poorly understood. Here we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, p

// Raphael Serre 1 , Fabrice Barlesi 2 , Xavier Muracciole 3 and Dominique Barbolosi 1 1 Simulation & Modelling Adaptive Response for Therapeutics in Cancer (SMARTc), Center for Research on Cancer of Marseille, CRCM Inserm UMR1068, CNRS UMR7258, Aix Marseille Universite U105, Institut Paoli Calmettes, Marseille, France 2 Multidisciplinary Oncology & Therapeutic Innovations Department, Assistance Publique-Hopitaux Marseille, Marseille, France 3 Department of Radiotherapy, Oncology, CHU La Timone, Assistance Publique-Hopitaux de Marseille, Marseille, France Correspondence to: Raphael Serre, email: raphael.serre@inserm.fr Keywords: immunotherapy; radiotherapy; combination; fractionation; linear-quadratic model Received: May 02, 2018 Accepted: June 19, 2018 Published: August 07, 2018 ABSTRACT Objectives: Concomitant radiotherapy with immune checkpoint blockade could be synergistic. Out-of-field effects could improve survival by slowing or blocking metastatic spreading. However, not much is known about the optimal size per fraction and inter-fraction time in that new context. Methods: The new concept of Immunologically Effective Dose (IED) is proposed: it models an intrinsic immunogenicity of radiotherapy schedules, i.e. the fraction of immunogenicity that results from the choice of the dosing regimen. The IED is defined as the single dose, given in infinitely low dose rate, that produces the same amount of abscopal response as the radiation schedule being considered. The IED uses the classic parameters of the BED formula and adds two parameters for immunogenicity that describe the local availability of immune effectors within the tumor micro-environment. Fundamentally, the IED adds a time dimension in the BED formula and describes an intrinsic immunogenicity level for radiotherapy. Results: The IED is positively related to the intensity of the out-of-field, radiotherapy-mediated, immune effects described in some preclinical data. Examples of numerical simulations are given for various schedules. A web-based calculator is freely available. Conclusions: Out-of-field effects of radiotherapy with immune checkpoint blockers might be better predicted and eventually, radiotherapy schedules with better local and systemic immunogenicity could be proposed. Advances in knowledge: A model for the intrinsic level of immunogenicity of radiotherapy schedules, referred to as the Immunologically Effective Dose (IED), that is independent of the type of immunotherapy.

Entdeckungsprozesse im Mathematikunterricht sind sehr komplex. Andererseits zeigt die Geschichte, dass die Motivation zur Einfuhrung neuer Konzepte oftmals einem konkreten (physikalischem, biologischem . . . ) Problem entsprang. Die Erfindung neuer Werkzeuge beruht auf heuristischen Uberlegungen, die ihre genaue Begrundung manchmal erst nach Jahren breiter Anwendung finden. Paradoxerweise werden die historischen Entwicklungen, die zur Entstehung neuer Theorien fuhrten, durch unsere Lehrmethoden ausgeloscht. Dies geschieht zu Gunsten kondensierter Darstellungen, die den Ursprung und die Entwicklung der Ideen ausblenden und eine strenge Theoriebildung zum Nachteil der Anwendungen begunstigen. In diesem Artikel schlagen wir vor, zu einer Lehrmethode zuruckzukehren, die einer naturlicheren Chronologie folgt. Diese wird durch eine konkrete Problematik begrundet und bezieht das heuristische Schlussfolgern ein. Daraus folgt ein funffacher Nutzen: Wiederherstellung des notwendigen Bezugs zwischen der Forschungs- und Lehrtatigkeit, der quasi verschwunden ist; Wiederhervorhebung des Erlernens der wissenschaftlichen Vorgehensweise; den untersuchten mathematischen Objekten einen Sinn geben; Aufzeigen des Interesses der Mathematik in einem multidisziplinaren Kontext; und schlieslich die spezifische Funktionsweise der Mathematik zu verstehen, die darin besteht, einen strengen Gesamtrahmen zu erstellen, um die eingefuhrten Konzepte zu begrunden. Unser Vorschlag wird durch die Resultate unserer dreijahrigen Erfahrungen illustriert, wahrend derer wir diese Ideen im Rahmen des Programms Hippocampus“ erfolgreich umsetzen konnten. Dieses Programm wurde in etwa 15 verschiedenen franzosischen Gymnasien und Colleges durchgefuhrt, deren Schuler aus unterschiedlichen sozialen Schichten stammten.

Objectifs Developpement de ParaPET, une nouvelle methode d’obtention d’images TEP parametriques de la fixation du FDG et comparaison avec les methodes de Hunter et Barbolosi, en utilisant l’analyse de Patlak comme reference, chez des patients atteints d’un cancer bronchique (CBNPC). Methodes ParaPET est basee sur l’estimation de l’activite du FDG dans le compartiment sanguin a partir d’images TEP dynamiques, integrant un modele d’erreur de mesures et permettant la caracterisation de parametres cinetiques a l’echelle du voxel. Afin de valider notre methode, deux acquisitions TEP/TDM sont necessaires. La premiere de 30 minutes centree sur le cœur est realisee simultanement a l’injection du FDG. Elle permet de determiner la fonction d’entree arterielle (AIF) requise pour l’analyse de Patlak. La seconde de 15 minutes, centree sur la lesion, commence 80 minutes post-injection. Elle est associee a cinq prelevements sanguins realises toutes les 3 minutes. Ces informations permettent la mise en œuvre des methodes de Patlak, Hunter et Barbolosi. L’AIF tardive fournit l’activite moyenne du FDG presente dans le compartiment sanguin et sa variabilite, necessaires pour le modele d’erreur de mesures de ParaPET. Un ensemble d’images parametriques de la tumeur est genere a l’issue de ParaPET. Deux parametres cinetiques ont ete etudies : Ki, le debit net entrant de FDG et sa valeur maximale Ki-max au sein de la lesion. Resultats La faisabilite a ete evaluee sur sept lesions presentes chez trois patients inclus dans l’essai clinique ParaPET ( NCT02821936 ). Notre approche presente la meilleure correlation avec Patlak ( r 2 = 0,998), comparee aux autres methodes etudiees ( r 2 = 0,805, r 2 = 0,968 et r 2 = 0,989, respectivement pour Hunter, Barbolosi avec ou sans prelevements). Les erreurs moyennes (± SD) dans l’estimation de Ki-max sont de 31,5 % ± 21,1 % pour Hunter, −7,0 % ± 10,0 % et 4,5 % ± 5,0 %, respectivement pour Barbolosi avec ou sans prelevements, et 3,4 % ± 3,6 % pour ParaPET. Conclusion ParaPET presente la meilleure correlation comparee a Patlak pour l’estimation du Ki au sein de la tumeur et est une alternative non invasive aux methodes de quantification basees sur de multiples prelevements sanguins. Elle permet la caracterisation de parametres cinetiques a l’echelle du voxel, afin de creer une cartographie de l’heterogeneite des lesions. L’etude ParaPET a ete financee par le centre Henri-Becquerel (Rouen) et le Canceropole PACA.

Metronomic chemotherapy is usually associated with better tolerance than conventional chemotherapy, and encouraging response rates have been reported in various settings. However, clinical development of metronomic chemotherapy has been hampered by a number of limitations, including the vagueness of its definition and the resulting empiricism in protocol design. In this study, we developed a pharmacokinetic/pharmacodynamic mathematical model that identifies in silico the most effective administration schedule for gemcitabine monotherapy. This model is based upon four biological assumptions regarding the mechanisms of action of metronomic chemotherapy, resulting in a set of 6 minimally parameterized differential equations. Simulations identified daily 0.5–1 mg/kg gemcitabine as an optimal protocol to maximize antitumor efficacy. Both metronomic protocols (0.5 and 1 mg/kg/day for 28 days) were evaluated in chemoresistant neuroblastoma-bearing mice and compared with the standard MTD protocol (100 mg/kg once a week for 4 weeks). Systemic exposure to gemcitabine was 14 times lower in the metronomic groups compared with the standard group. Despite this, metronomic gemcitabine significantly inhibited tumor angiogenesis and reduced tumor perfusion and inflammation in vivo, while standard gemcitabine did not. Furthermore, metronomic gemcitabine yielded a 40%–50% decrease in tumor mass at the end of treatment as compared with control mice (P = 0.002; ANOVA on ranks with Dunn test), while standard gemcitabine failed to significantly reduce tumor growth. Stable disease was maintained in the metronomic groups for up to 2 months after treatment completion (67%–72% reduction in tumor growth at study conclusion, P < 0.001; ANOVA on ranks with Dunn test). Collectively, our results confirmed the superiority of metronomic protocols in chemoresistant tumors in vivo. Cancer Res; 77(17); 4723–33. ©2017 AACR.

Background Metronomic oral vinorelbine is effective in metastatic NSCLC and malignant pleural mesothelioma, but all the studies published thus far were based upon a variety of empirical and possibly suboptimal schedules, with inconsistent results. Mathematical modelling showed by simulation that a new metronomic protocol could lead to a better safety and efficacy profile. Design This phase Ia/Ib trial was designed to confirm safety (phase Ia) and evaluate efficacy (phase Ib) of a new metronomic oral vinorelbine schedule. Patients with metastatic NSCLC or malignant pleural mesothelioma in whom standard treatments failed and who exhibited ECOG performance status 0–2 and adequate organ function will be eligible. Our mathematical PK-PD model suggested an alternative weekly D1, D2 and D4 schedule (named Vinorelbine Theoretical Protocol) with a respective dose of 60, 30 and 60 mg. Trial recruitment will be two-staged, as 12 patients are planned to participate in phase Ia to confirm safety and consolidate the calibration of the model parameters. Depending on the phase Ia results and after a favourable decision from a consultative committee, the extension phase (phase Ib) will be an efficacy study including 20 patients who will receive the Optimal Vinorelbine Theoretical Protocol. The primary endpoint is the tolerance (assessed by CTC v4.0) for the phase Ia and the objective response according to RECIST 1.1 for phase Ib. An ancillary study on circulating angiogenesis biomarkers will be a subproject of the trial. Discussion This ongoing trial is the first to prospectively test a mathematically optimized schedule in metronomic chemotherapy. As such, this trial can be considered as a proof-of-concept study demonstrating the feasibility to run a computational-driven protocol to ensure an optimal efficacy/toxicity balance in patients with cancer. Trial registration EudraCT N°: 2015-000138-31

e20505 Background: A phase I/II trial (NCT02555007) of oral metronomic Vinorelbine derived from a mathematical model was performed in heavily pretreated metastatic Non-Small Cell Lung Cancer or Pleural Mesothelioma patients. Progression free survival, toxicity and PK/PD endpoints were the main objectives. Methods: Metronomic scheduling was selected using a simplified phenomenological model to identify the best continuous scheduling and dosing of oral vinorelbine with a total dose of 150 mg QW. Patients were monitored on a weekly basis, efficacy was evaluated by CT scans (RECIST). Toxicity was monitored using standard CTCAE criteria. Total tumor size (TTS) was the sum of diamaters of all lesions. Computation of individual PK parameters was done with Monolix software using population approach. Results: The PK/PD model proposed the following schedule: 60 mg D1, 30 mg D2, 60 mg D4. A total of 36 patients (30 evaluable) were enrolled (22M, 13F, 24 NSCLC, 11 mesothelium, median age 69.5, range 33-85.2). Patients were all heavily pre-treated (median 3 lines, range 1-9). Grade 3+ Neutropenia was observed in 30% patients. Median PFS was 11 weeks (range: 6-16.9). Best responses included 4 PR (13%) and 18 SD (60%). Baseline total tumor size was associated with reduced PFS (HR: 1.09, p = 0.026). A large variability in drug exposure (AUC 53 %, range 26 – 501 ng.h/ml) and PK parameters (Cl 82 %, range 45-605 l/h) was observed among patients. Exposure was not associated with efficacy, apart in patients with larger TTS (i.e., > 70 mm) who seemed to have longer PFS (125 days VS. 40 days, p = 0.057). Vinorelbine exposure tended to be associated with higher risk for grade 2+ neutropenia, especially in patients with BSA < 1.8 m² (60% VS. 25.5%, p = 0.055). A non-significant trend towards baseline NLR and PFS was observed (i.e., NLR < 4: 80 days, NLR > 4: 60 days, p = 0.077). Conclusions: Metronomic vinorelbine was characterized by huge variability in drug exposure among patients. However and despite being all heavily pre-treated, 60% of stable disease and 13% of PR were achieved in these patients. Plasma exposure yielded conflicting results depending on the initial tumor burden, suggesting that patients should be carefully selected prior to be scheduled for metronomic regimen. Possible role NLR could play as a predictive marker is intriguing and should be confirmed in larger cohort.

Bevacizumab is the first-in-class antiangiogenic drug and is almost always administrated in combination with cytotoxics. Reports have shown that bevacizumab could induce a transient phase of vascular normalization, thus ensuring a better drug delivery when cytotoxics administration is adjuvant. However, determining the best sequence remains challenging. We have developed a mathematical model describing the impact of antiangiogenics on tumor vasculature. A 3.4 days gap between bevacizumab and paclitaxel was first proposed by our model. To test its relevance, 84 mice were orthotopically xenografted with human MDA-231Luc+ refractory breast cancer cells. Two sets of experiments were performed, based upon different bevacizumab dosing (10 or 20 mg/kg) and inter-cycle intervals (7 or 10 days), comprising several combinations with paclitaxel. Results showed that scheduling bevacizumab 3 days before paclitaxel improved antitumor efficacy (48% reduction in tumor size compared with concomitant dosing, p < 0.05) and reduced metastatic spreading. Additionally, bevacizumab alone could lead to more aggressive metastatic disease with shorter survival in animals. Our model was able to fit the experimental data and provided insights on the underlying dynamics of the vasculature's ability to deliver the cytotoxic agent. Final simulations suggested a new, data-informed optimal gap of 2.2 days. Our experimental data suggest that current concomitant dosing between bevacizumab and paclitaxel could be a sub-optimal strategy at bedside. In addition, this proof of concept study suggests that mathematical modelling could help to identify the optimal interval among a variety of possible alternate treatment modalities, thus refining the way experimental or clinical studies are conducted.

Positron emission tomography with (18)F fludeoxyglucose integrated with CT ((18)F-FDG PET/CT) is a recommended imaging procedure in the evaluation of non-small-cell lung cancers (NSCLCs). Radiochemotherapy (RCT) is a mainstay for treatment of locally advanced NSCLC, for which overall survival still remains poor. Early evaluation of treatment response may help in decision-making to complete radiotherapy (RT) or to switch to other treatment modalities. The present study aimed to evaluate the performance of new metabolic parameters based on a simplified kinetic analysis on a single time point (SKA-S)-derived mathematical method, as compared with standardized uptake value (SUV) measurement during RT.Four patients treated with RT or RCT for NSCLC were evaluated using (18)F-FDG PET/CT during RT and after treatment completion. Whole-body (18)F-FDG PET/CT was performed followed by four additional list-mode acquisitions centered over the target lesion. Response was evaluated at four times (i.e. PET1-PET4) by calculating standard SUV values and T80%, the time taken to reach 80% of (18)F-FDG metabolized fraction using a SKA-S-derived mathematical method.Data from SUV and T80% calculations were found to be controversial. T80% was found to be more predictive of clinical outcome.Although results from this pilot study should be further confirmed in a large prospective study, the data suggest that T80% is a promising metabolic biomarker for assessing early response to RT.In this proof of concept study, we show that T80% defined from a mathematic model taking into account the net influx rate constant and vascular volume could be consider as a promising biomarker as compared with the maximum SUV.

International audience; Computational oncology is a generic term that encompasses any form of computer-based modelling relating to tumour biology and cancer therapy. Mathematical modelling can be used to probe the pharmacokinetics and pharmacodynamics relationships of the available anticancer agents in order to improve treatment. As a result of the ever-growing numbers of druggable molecular targets and possible drug combinations, obtaining an optimal toxicity-efficacy balance is an increasingly complex task. Consequently, standard empirical approaches to optimizing drug dosing and scheduling in patients are now of limited utility; mathematical modelling can substantially advance this practice through improved rationalization of therapeutic strategies. The implementation of mathematical modelling tools is an emerging trend, but remains largely insufficient to meet clinical needs; at the bedside, anticancer drugs continue to be prescribed and administered according to standard schedules. To shift the therapeutic paradigm towards personalized care, precision medicine in oncology requires powerful new resources for both researchers and clinicians. Mathematical modelling is an attractive approach that could help to refine treatment modalities at all phases of research and development, and in routine patient care. Reviewing preclinical and clinical examples, we highlight the current achievements and limitations with regard to computational modelling of drug regimens, and discuss the potential future implementation of this strategy to achieve precision medicine in oncology.

Rapid improvements in the detection and tracking of early-stage tumor progression aim to guide decisions regarding cancer treatments as well as predict metastatic recurrence in patients following surgery. Mathematical models may have the potential to further assist in estimating metastatic risk, particularly when paired with in vivo tumor data that faithfully represent all stages of disease progression. Herein, we describe mathematical analysis that uses data from mouse models of spontaneous metastasis developing after surgical removal of orthotopically implanted primary tumors. Both presurgical (primary tumor) growth and postsurgical (metastatic) growth were quantified using bioluminescence and were then used to generate a mathematical formalism based on general laws of the disease (i.e., dissemination and growth). The model was able to fit and predict pre/postsurgical data at the level of the individual as well as the population. Our approach also enabled retrospective analysis of clinical data describing the probability of metastatic relapse as a function of primary tumor size. In these data-based models, interindividual variability was quantified by a key parameter of intrinsic metastatic potential. Critically, our analysis identified a highly nonlinear relationship between primary tumor size and postsurgical survival, suggesting possible threshold limits for the utility of tumor size as a predictor of metastatic recurrence. These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential and may guide optimal timing of treatments in neoadjuvant (presurgical) and adjuvant (postsurgical) settings to maximize patient benefit. Cancer Res; 76(3); 535–47. ©2015 AACR.

Combining radiotherapy with immune checkpoint blockade may offer considerable therapeutic impact if the immunosuppressive nature of the tumor microenvironment (TME) can be relieved. In this study, we used mathematical models, which can illustrate the potential synergism between immune checkpoint inhibitors and radiotherapy. A discrete-time pharmacodynamic model of the combination of radiotherapy with inhibitors of the PD1–PDL1 axis and/or the CTLA4 pathway is described. This mathematical framework describes how a growing tumor first elicits and then inhibits an antitumor immune response. This antitumor immune response is described by a primary and a secondary (or memory) response. The primary immune response appears first and is inhibited by the PD1–PDL1 axis, whereas the secondary immune response happens next and is inhibited by the CTLA4 pathway. The effects of irradiation are described by a modified version of the linear-quadratic model. This modeling offers an explanation for the reported biphasic relationship between the size of a tumor and its immunogenicity, as measured by the abscopal effect (an off-target immune response). Furthermore, it explains why discontinuing immunotherapy may result in either tumor recurrence or a durably sustained response. Finally, it describes how synchronizing immunotherapy and radiotherapy can produce synergies. The ability of the model to forecast pharmacodynamic endpoints was validated retrospectively by checking that it could describe data from experimental studies, which investigated the combination of radiotherapy with immune checkpoint inhibitors. In summary, a model such as this could be further used as a simulation tool to facilitate decision making about optimal scheduling of immunotherapy with radiotherapy and perhaps other types of anticancer therapies. Cancer Res; 76(17); 4931–40. ©2016 AACR.

International audience; Tumours with high (18)F-FDG uptake values on static late PET images do not always exhibit high proliferation indices. These discrepancies might be related to high proportion of unmetabolised (18)F-FDG components in the tissues. We propose a method that enables to calculate different (18)F-FDG kinetic parameters based on a new mathematical approach that integrates a measurement error model. Six patients with diagnosed non-metastatic paragangliomas (PGLs) and six control patients with different types of lesions were investigated in this pilot study using (18)F-FDG PET/CT. In all cases, a whole-body acquisition was followed by four static acquisitions centred over the target lesions, associated with venous blood samplings. We used an extension of the Hunter's method to calculate the net influx rate constant (K H). The exact net influx rate constant and vascular volume fraction (K i and V, respectively) were subsequently obtained by the method of least squares. Next, we calculated the mean percentages of metabolised (PM) and unmetabolised (PUM) (18)F-FDG components, and the times required to reach 80 % of the amount of metabolised (18)F-FDG (T80%). A test-retest evaluation indicated that the repeatability of our approach was accurate; the coefficients of variation were below 2 % regardless of the kinetic parameters considered. We observed that the PGLs were characterised by high dispersions of the maximum standardised uptake value SUVmax (9.7 ± 11, coefficient of variation CV = 114 %), K i (0.0137 ± 0.0119, CV = 87 %), and V (0.292 ± 0.306, CV = 105 %) values. The PGLs were associated with higher PUM (p = 0.02) and T80% (p = 0.02) values and lower k 3 (p = 0.02) values compared to the malignant lesions despite the similar SUVmax values (p = 0.55). The estimations of these new kinetic parameters are more accurate than SUVmax or K i for in vivo metabolic assessment of PGLs at the molecular level.

Bevacizumab-containing protocols are all based upon the concomitant administration of the drugs given in a row. Bevacizumab is expected to induce a transient normalization of the tumor neo-vasculature prior to exert its anti-angiogenic properties. The resulting increase in blood flow could lead to higher drug delivery to the tumors and therefore to higher efficacy, provided that cytotoxics are administered after bevacizumab. Determining this time-window cannot be performed by empirical practice, but mathematical modeling can help to achieve this goal. To this end, we have developed an original mathematical PK/PD model that enables the description of the effect of bevacizumab on the quality of the vasculature and the resulting effects of drugs sequential administration on tumor growth. The model was able to simulate a variety of scheduling and suggested that a 5-days lag between bevacizumab and cytotoxics should achieve higher antiproliferative efficacy as compared with standard administration. To test the predictivity of the model, a comparative study was undertaken in tumor-bearing mice. Human H460 NSCLC cells stably transfected with luciferase were ectotopically implanted in swiss nude mice. Treatment consisted in the combo bevacizumab (20 mg/kg) plus pemetrexed (100 mg/kg) and cisplatin (3 mg/kg) given as 3 cycles administered every 2 weeks following different scheduling. Mice were randomly allocated into 4 groups (n = 12 mice per group): control, concomitant (bevacizumab and chemo given the same day), sequence-1 (chemo followed by bevacizumab 5 days later) and sequence-2 (bevacizumab followed by chemo 5 days later). Tumor growth was monitored twice a week by bioluminescence imaging after i.p. injection of 150 mg/kg luciferine. As predicted by our mathematical model, results showed that the sequential administration of bevacizumab followed 5 days later by the pemetrexed/cisplatin doublet led to a better efficacy (-42% reduction in tumor growth at treatment completion and -35% at study conclusion, p Citation Format: Joseph Ciccolini, Sebastien Benzekry, Sarah Giacometti, Fabrice Barlesi, Dominique Barbolosi. Model-riven optimization of anti-angiogenics combined with chemotherapy: application to bevacizumab + pemetrexed/cisplatin doublet in NSCLC-bearing mice. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2099.