Computational markers for personalized prediction of outcomes in non-small cell lung cancer patients with brain metastases

Intracranial progression after curative treatment of early-stage non-small cell lung cancer (NSCLC) occurs from 10 to 50% and is difficult to manage, given the heterogeneity of clinical presentations and the variability of treatments available. The objective of this study was to develop a mechanistic model of intracranial progression to predict survival following a first brain metastasis (BM) event occurring at a time [Formula: see text]. Data included early-stage NSCLC patients treated with a curative intent who had a BM as the first and single relapse site (N = 31). We propose a mechanistic mathematical model able to derive computational markers from primary tumor and BM data at [Formula: see text] and estimate the amount and sizes of (visible and invisible) BMs, as well as their future behavior. These two key computational markers are [Formula: see text], the proliferation rate of a single tumor cell; and [Formula: see text], the per day, per cell, probability to metastasize. The predictive value of these individual computational biomarkers was evaluated. The model was able to correctly describe the number and size of metastases at [Formula: see text] for 20 patients. Parameters [Formula: see text] and [Formula: see text] were significantly associated with overall survival (OS) (HR 1.65 (1.07-2.53) p = 0.0029 and HR 1.95 (1.31-2.91) p = 0.0109, respectively). Adding the computational markers to the clinical ones significantly improved the predictive value of OS (c-index increased from 0.585 (95% CI 0.569-0.602) to 0.713 (95% CI 0.700-0.726), p < 0.0001). We demonstrated that our model was applicable to brain oligoprogressive patients in NSCLC and that the resulting computational markers had predictive potential. This may help lung cancer physicians to guide and personalize the management of NSCLC patients with intracranial oligoprogression.

Reuniting philosophy and science to advance cancer research

Cancers rely on multiple, heterogeneous processes at different scales, pertaining to many biomedical fields. Therefore, understanding cancer is necessarily an interdisciplinary task that requires placing specialised experimental and clinical research into a broader conceptual, theoretical, and methodological framework. Without such a framework, oncology will collect piecemeal results, with scant dialogue between the different scientific communities studying cancer. We argue that one important way forward in service of a more successful dialogue is through greater integration of applied sciences (experimental and clinical) with conceptual and theoretical approaches, informed by philosophical methods. By way of illustration, we explore six central themes: (i) the role of mutations in cancer; (ii) the clonal evolution of cancer cells; (iii) the relationship between cancer and multicellularity; (iv) the tumour microenvironment; (v) the immune system; and (vi) stem cells. In each case, we examine open questions in the scientific literature through a philosophical methodology and show the benefit of such a synergy for the scientific and medical understanding of cancer.

Mechanistic modeling of metastatic relapse in early breast cancer to investigate the biological impact of prognostic biomarkers

BACKGROUND AND OBJECTIVE

Estimating the risk of metastatic relapse is a major challenge to decide adjuvant treatment options in early-stage breast cancer (eBC). To date, distant metastasis-free survival (DMFS) analysis mainly relies on classical, agnostic, statistical models (e.g., Cox regression). Instead, we propose here to derive mechanistic models of DMFS.

METHODS

The present series consisted of eBC patients who did not receive adjuvant systemic therapy from three datasets, composed respectively of 692 (Bergonié Institute), 591 (Paoli-Calmettes Institute, IPC), and 163 (Public Hospital Marseille, AP-HM) patients with routine clinical annotations. The last dataset also contained expression of three non-routine biomarkers. Our mechanistic model of DMFS relies on two mathematical parameters that represent growth (α) and dissemination (μ). We identified their population distributions using mixed-effects modeling. Critically, we propose a novel variable selection procedure allowing to: (i) identify the association of biological parameters with either α, μ or both, and (ii) generate an optimal candidate model for DMFS prediction.

RESULTS

We found that Ki67 and Thymidine Kinase-1 were associated with α, and nodal status and Plasminogen Activator Inhibitor-1 with μ. The predictive performances of the model were excellent in calibration but moderate in discrimination, with c-indices of 0.72 (95% CI [0.48, 0.95], AP-HM), 0.63 ([0.44, 0.83], Bergonié) and 0.60 (95% CI [0.54, 0.80], IPC).

CONCLUSIONS

Overall, we demonstrate that our novel method combining mechanistic and advanced statistical modeling is able to unravel the biological roles of clinicopathological parameters from DMFS data.

Abstract 2737: A mechanistic model for prediction of metastatic relapse in early-stage breast cancer using routine clinical features

Estimation of the risk of metastatic relapse is a major challenge to decide treatment options for early-stage breast cancer patients. To date, metastasis free survival (MFS) analysis mainly relies on classical - agnostic - statistical models (e.g., Cox regression). Instead, we propose to derive mechanistic models to predict MFS.

The data consisted of patients who did not receive adjuvant systemic therapy from two databases: one (data 1, N = 163) with routine clinical features and the PAI-1 and uPA biomarkers and two (data 2, N = 692) with 11 routine clinical features. The mathematical models are based on a partial differential equation describing a size-structured population of metastases. They predict MFS from the size of the tumor at diagnosis and two mathematical parameters, α and μ describing respectively the tumor growth speed and metastatic dissemination potential. Using mixed-effects modeling, the population distributions of α and μ were assumed to be lognormal and to depend on routine clinical variables, whereas the observation error was assumed lognormal on the time-to-relapse. Variable selection consisted first in a univariate Wald test for all covariates with effect either on α or μ. We then used a backward elimination procedure. Significance of the covariates in the final model was assessed by a multivariable Wald test. Concordance indexes (c-index) were computed to assess the predictive power in cross-validation procedures as well as test sets.

The model was implemented as an R package using optimized C++ code for the mechanistic part and enabling parallelization, resulting in a 4-fold reduction of the computing compared to a former python implementation. Nevertheless, over 4 hours are still needed to run a 100 samples bootstrap on a distributed computing cluster. The model selection procedure on data 1 revealed an association of PAI1 and age with μ, and of Estrogen receptor level with alpha, consistent with the established biological link between PAI-1 and tumor invasiveness. The resulting model achieved good prediction performances with a c-index of 0.72 in 5 folds cross-validation. Using only routine clinical markers, the algorithm on data 2 selected a model with the grade and Progesterone Receptors in α, Ki67 and node status in μ. These were able to adequately describe the data on calibration plots but performed poorly in prediction with a cross validated c-index of 0.60.

Mechanistic modeling was able to unravel the biological and predictive role of PAI-1 but showed limited predictive power when using only on routine clinical features.

Citation Format: Célestin Bigarré, Pascal Finetti, François Bertucci, Xavier Muracciole, Sébastien Benzekry. A mechanistic model for prediction of metastatic relapse in early-stage breast cancer using routine clinical features [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2737.

Development and Validation of a Prediction Model of Overall Survival in High-Risk Neuroblastoma Using Mechanistic Modeling of Metastasis

Prognosis of high-risk neuroblastoma (HRNB) remains poor despite multimodal therapies. Better prediction of survival could help to refine patient stratification and better tailor treatments. We established a mechanistic model of metastasis in HRNB relying on two processes: growth and dissemination relying on two patient-specific parameters: the dissemination rate μ and the minimal visible lesion size S_vis. This model was calibrated using diagnosis values of primary tumor size, lactate dehydrogenase circulating levels, and the meta-iodobenzylguanidine International Society for Paediatric Oncology European (SIOPEN) score from nuclear imaging, using data from 49 metastatic patients. It was able to describe the data of total tumor mass (lactate dehydrogenase, R² > 0.99) and number of visible metastases (SIOPEN, R² = 0.96). A prediction model of overall survival (OS) was then developed using Cox regression. Clinical variables alone were not able to generate a model with sufficient OS prognosis ability (P = .507). The parameter μ was found to be independent of the clinical variables and positively associated with OS (P = .0739 in multivariable analysis). Critically, addition of this computational biomarker significantly improved prediction of OS with a concordance index increasing from 0.675 (95% CI, 0.663 to 0.688) to 0.733 (95% CI, 0.722 to 0.744, P < .0001), resulting in significant OS prognosis ability (P = .0422).

Machine Learning and Mechanistic Modeling for Prediction of Metastatic Relapse in Early-Stage Breast Cancer

PURPOSE

For patients with early-stage breast cancer, predicting the risk of metastatic relapse is of crucial importance. Existing predictive models rely on agnostic survival analysis statistical tools (eg, Cox regression). Here we define and evaluate the predictive ability of a mechanistic model for time to distant metastatic relapse.

METHODS

The data we used for our model consisted of 642 patients with 21 clinicopathologic variables. A mechanistic model was developed on the basis of two intrinsic mechanisms of metastatic progression: growth (parameter α) and dissemination (parameter μ). Population statistical distributions of the parameters were inferred using mixed-effects modeling. A random survival forest analysis was used to select a minimal set of five covariates with the best predictive power. These were further considered to individually predict the model parameters by using a backward selection approach. Predictive performances were compared with classic Cox regression and machine learning algorithms.

RESULTS

The mechanistic model was able to accurately fit the data. Covariate analysis revealed statistically significant association of Ki67 expression with α (P = .001) and EGFR expression with μ (P = .009). The model achieved a c-index of 0.65 (95% CI, 0.60 to 0.71) in cross-validation and had predictive performance similar to that of random survival forest (95% CI, 0.66 to 0.69) and Cox regression (95% CI, 0.62 to 0.67) as well as machine learning classification algorithms.

CONCLUSION

By providing informative estimates of the invisible metastatic burden at the time of diagnosis and forward simulations of metastatic growth, the proposed model could be used as a personalized prediction tool for routine management of patients with breast cancer.

Abstract 6244: Turning poorly vascularized tumors into highly vascularized tumors with nanoparticles: Proof of concept and pharmacometric analysis

Combinatorial regimen are a mainstay in oncology. Taxanes and trastuzumab are both gold standards for HER2 positive breast cancer. To what extent they could reshape tumor micro-environment remains to be elucidated. The aim of this study was to compare in breast cancer mice models the antiproliferative efficacy and impact on tumor neo-angiogenesis of trastuzumab stealth immunoliposomes encapsulating docetaxel and stealth liposomal docetaxel associated with free trastuzumab. Nude mice bearing human MDA-MB-231 breast cancer tumors were treated by saline (control), docetaxel liposome (5mg/kg) associated with free trastuzumab (1.9 mg/kg) or trastuzumab immunoliposome (eq. 5 mg/kg docetaxel and 1.9 mg/kg trastuzumab) QW for 4 consecutive weeks. Tumor growth was monitored twice a week by volumetric measurement using a caliper. Blodd vessels density was evaluated in vivo by fluorescence imaging using Angiosense as a vascular probe plus ex-vivo using anti-CD31 antibodies and electronic microscopy at 2, 4 and 6 weeks. A specific algorithm was developed on MatLab for imaging analysis. No treatment-induced toxicities was observed. After 4 weeks of dosing, no difference in efficacy was seen between treatments (p=0.798) and Angiosense imaging did not show differences either (p=0.628). However electronic microscopy showed that both immunoliposomes and liposomes increased tumor vascular density as compared with control. In addition, a difference between treatments was evidenced because a marked increase in vascularization of central tumors VS. peripheral tumors was observed with trastuzumab immunoliposome as compared with standard docetaxel liposome (p=0.00023). A numerical model based on porous medium theory combined with multi-scale approaches has been derived to describe the spatial distribution of the drugs within tissues. Overall our data suggest that trastuzumab stealth immunoliposomes induce a normalization of tumor vessels with an increase in blood vessels density in central tumors. This could pave the way for sequencing combinatorial strategies so as to improve drug delivery into tumors of the associated treatments.

Citation Format: Guillaume Sicard, Anne Rodallec, Florian Correard, Cristina Vaghi, Clair Poignard, Joseph Ciccolini, Sébastien Benzekry, Arnauld Sergé, Raphaelle Fanciullino. Turning poorly vascularized tumors into highly vascularized tumors with nanoparticles: Proof of concept and pharmacometric analysis [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 6244.

Deciphering the response and resistance to immune-checkpoint inhibitors in lung cancer with artificial intelligence-based analysis: when PIONeeR meets QUANTIC

This project aims to generate dense longitudinal data in lung cancer patients undergoing anti-PD1/PDL1 therapy. Mathematical modelling with mechanistic learning algorithms will help decipher the mechanisms underlying the response or resistance to immunotherapy. A better understanding of these mechanisms should help identifying actionable items to increase the efficacy of immune-checkpoint inhibitors.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer

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 further 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.

Turning cold tumors into hot tumors: harnessing the potential of tumor immunity using nanoparticles

INTRODUCTION

Immune checkpoint inhibitors have considerably changed the landscape of oncology. However apart from world-acclaimed success stories limited to melanoma and lung cancer, many solid tumors failed to respond to immune checkpoint inhibitors due to limited immunogenicity, unfavorable tumor micro-environments (TME), lack of infiltrating T lymphocytes or increases in Tregs. Areas covered: Combinatorial strategies are foreseen as the future of immunotherapy and using cytotoxics or modulating agents is expected to boost the efficacy of immune checkpoint inhibitors. In this respect, nanoparticles displaying unique pharmacokinetic features such as tumor targeting properties, optimal payload delivery and long-lasting interferences with TME, are promising candidates for such combinations. This review covers the basis, expectancies, limits and pitfalls of future combination between nanoparticles and immune check point inhibitors. Expert opinion: Nanoparticles allow optimal delivery of variety of payloads in tumors while sparing healthy tissue, thus triggering immunogenic cell death. Depleting tumor stroma could further help immune cells and monoclonal antibodies to better circulate in the TME, plus immune-modulating properties of the charged cytotoxics. Finally, nanoparticles themselves present immunogenicity and antigenicity likely to boost immune response at the tumor level.

Abstract 4264: Mathematical modeling of differential effects of sunitinib on primary tumor and metastatic growth

Sunitinib is a drug with anti-angiogenic activity used in the treatment of patients with metastases from renal cell carcinoma or gastrointestinal tumors. However, despite clear efficacy in reducing established tumor growth, recent preclinical studies have shown limited, or even opposing, efficacies in preventing metastatic spread.

In this work, we evaluated a mathematical metastatic model to describe primary tumor and metastatic dynamics in response to sunitinib in a clinically relevant mouse model of spontaneous metastatic breast cancer that develops after surgical removal of an orthotopically implanted primary tumor. Mice received either vehicle or sunitinib in the neoadjuvant (presurgical) setting according to different schedules. The experimental dataset comprises measurements of primary tumor kinetics, metastatic burden and pre-surgical molecular and cellular biomarkers, including vascular cell Ki67 and CD31 expression, circulating tumor cells (CTCs) and myeloid derived suppressor cells (MDSCs). Estimation of the model's parameters was performed using a mixed-effects population approach. To describe tumor growth under sunitinib treatment, a simple ordinary differential equation model of tumor growth inhibition was used.

Population fits obtained modeling the effect of treatment only on primary tumor growth described well the experimental data of all the treated groups considered. On the contrary, simulations of treatment also on metastasis could not reproduce the behavior of the data. By inserting in the model the available biomarkers as covariates, through a Wald-test, measurements of Ki67+/CD31+, CTCs and granulocytic MDSCs were found significantly correlated with the model parameter expressing the metastatic aggressiveness of the tumor.

Together, these mathematical models confirm a differential effect of sunitinib on primary (localized) tumors compared to secondary (metastatic) disease. Our results suggest that Ki67+/CD31+, CTCs and MDSCs measurements might help in predicting metastatic potential and thus aid in predicting benefit in overall survival for preoperative antiangiogenic treatments.

Citation Format: Chiara Nicolò, Michalis Mastri, Amanda Tracz, John M. Ebos, Sébastien Benzekry. Mathematical modeling of differential effects of sunitinib on primary tumor and metastatic growth [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 4264.

Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non-Small Cell Lung Carcinoma

Concomitant administration of bevacizumab and pemetrexed‐cisplatin is a common treatment for advanced nonsquamous non‐small cell lung cancer (NSCLC). Vascular normalization following bevacizumab administration may transiently enhance drug delivery, suggesting improved efficacy with sequential administration. To investigate optimal scheduling, we conducted a study in NSCLC‐bearing mice. First, experiments demonstrated improved efficacy when using sequential vs. concomitant scheduling of bevacizumab and chemotherapy. Combining this data with a mathematical model of tumor growth under therapy accounting for the normalization effect, we predicted an optimal delay of 2.8 days between bevacizumab and chemotherapy. This prediction was confirmed experimentally, with reduced tumor growth of 38% as compared to concomitant scheduling, and prolonged survival (74 vs. 70 days). Alternate sequencing of 8 days failed in achieving a similar increase in efficacy, thus emphasizing the utility of modeling support to identify optimal scheduling. The model could also be a useful tool in the clinic to personally tailor regimen sequences.

Next generation metronomic chemotherapy-report from the Fifth Biennial International Metronomic and Anti-angiogenic Therapy Meeting, 6-8 May 2016, Mumbai

The 5^th Biennial Metronomic and Anti-angiogenic Therapy Meeting was held on 6^th – 8^th May in the Indian city of Mumbai. The meeting brought together a wide range of clinicians and researchers interested in metronomic chemotherapy, anti-angiogenics, drug repurposing and combinations thereof. Clinical experiences, including many from India, were reported and discussed in three symposia covering breast cancer, head and neck cancers and paediatrics. On the pre-clinical side research into putative mechanisms of action, and the interactions between low dose metronomic chemotherapy and angiogenesis and immune responses, were discussed in a number of presentations. Drug repurposing was discussed both in terms of clinical results, particularly with respect to angiosarcoma and high-risk neuroblastoma, and in pre-clinical settings, particularly the potential for peri-operative interventions. However, it was clear that there remain a number of key areas of challenge, particularly in terms of definitions, perceptions in the wider oncological community, mechanisms of action and predictive biomarkers. While the potential for metronomics and drug repurposing in low and middle income countries remains a key theme, it is clear that there is also considerable potential for clinically relevant improvements in patient outcomes even in high income economies.

Host age is a systemic regulator of gene expression impacting cancer progression

Aging is the major determinant of cancer incidence, which, in turn, is likely dictated in large part by processes that influence the progression of early subclinical (occult) cancers. However, there is little understanding of how aging informs changes in aggregate host signaling that favor cancer progression. In this study, we provide direct evidence that aging can serve as an organizing axis to define cancer progression-modulating processes. As a model system to explore this concept, we employed adolescent (68 days), young adult (143 days), middle-aged (551 days), and old (736 days) C57BL/6 mice as syngeneic hosts for engraftment of Lewis lung cancer to identify signaling and functional processes varying with host age. Older hosts exhibited dysregulated angiogenesis, metabolism, and apoptosis, all of which are associated with cancer progression. TGFβ1, a central player in these systemic processes, was downregulated consistently in older hosts. Our findings directly supported the conclusion of a strong host age dependence in determining the host tumor control dynamic. Furthermore, our results offer initial mechanism-based insights into how aging modulates tumor progression in ways that may be actionable for therapy or prevention.

Classical mathematical models for description and prediction of experimental tumor growth

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Tumor growth curves display relatively simple time curves that can be quantified using mathematical models. Herein we exploited two experimental animal systems to assess the descriptive and predictive power of nine classical tumor growth models. Several goodness-of-fit metrics and a dedicated error model were employed to rank the models for their relative descriptive power. We found that the model with the highest descriptive power was not necessarily the most predictive one. The breast growth curves had a linear profile that allowed good predictability. Conversely, not one of the models was able to accurately predict the lung growth curves when using only a few data points. To overcome this issue, we considered a method that uses the parameter population distribution, informed from a priori knowledge, to estimate the individual parameter vector of an independent growth curve. This method was found to considerably improve the prediction success rates. These findings may benefit preclinical cancer research by identifying models most descriptive of fundamental growth characteristics. Clinical perspective is also offered on what can be expected from mathematical modeling in terms of future growth prediction.

Global dormancy of metastases due to systemic inhibition of angiogenesis

Autopsy studies of adults dying of non-cancer causes have shown that virtually all of us possess occult, cancerous lesions. This suggests that, for most individuals, cancer will become dormant and not progress, while only in some will it become symptomatic disease. Meanwhile, it was recently shown in animal models that a tumor can produce both stimulators and inhibitors of its own blood supply. To explain the autopsy findings in light of the preclinical research data, we propose a mathematical model of cancer development at the organism scale describing a growing population of metastases, which, together with the primary tumor, can exert a progressively greater level of systemic angiogenesis-inhibitory influence that eventually overcomes local angiogenesis stimulation to suppress the growth of all lesions. As a departure from modeling efforts to date, we look not just at signaling from and effects on the primary tumor, but integrate over this increasingly negative global signaling from all sources to track the development of total tumor burden. This in silico study of the dynamics of the tumor/metastasis system identifies ranges of parameter values where mutual angio-inhibitory interactions within a population of tumor lesions could yield global dormancy, i.e., an organism-level homeostatic steady state in total tumor burden. Given that mortality arises most often from metastatic disease rather than growth of the primary per se, this finding may have important therapeutic implications.

Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers

Although optimal control theory has been used for the theoretical study of anti-cancerous drugs scheduling optimization, with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously published model for metastatic development to define an optimal control problem at the scale of the entire organism of the patient. In silico study of the impact of different scheduling strategies for anti-angiogenic and cytotoxic agents (either in monotherapy or in combination) is performed to compare a low-dose, continuous, metronomic administration scheme with a more classical maximum tolerated dose schedule. Simulation results reveal differences between primary tumor reduction and control of metastases but overall suggest use of the metronomic protocol.