On the growth and dissemination laws in a mathematical model of metastatic growth

International audienceMetastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive techniques such as longitudinal tracking of bioluminescent cells. The metastatic process was simplified here into two essential components – dissemination and colonization – which were mathematically formalized in terms of simple quantitative laws. The resulting mathematical model was confronted to in vivo experimental data of spontaneous metastasis after primary tumor resection. We discuss how much information can be inferred from confrontation of theories to the data with emphasis on identifiability issues. It is shown that two mutually exclusive assumptions for the secondary growth law (namely same or different from the primary tumor growth law) could fit equally well the data. Similarly, the fractal dimension coefficient in the dissemination law could not be uniquely determined from data on total metastatic burden only. Together, these results delimitate the range of information that can be recovered from fitting data of metastatic growth to already simplified mathematical models

Accelerated Metastasis after Short-Term Treatment with a Potent Inhibitor of Tumor Angiogenesis

SummaryHerein we report that the VEGFR/PDGFR kinase inhibitor sunitinib/SU11248 can accelerate metastatic tumor growth and decrease overall survival in mice receiving short-term therapy in various metastasis assays, including after intravenous injection of tumor cells or after removal of primary orthotopically grown tumors. Acceleration of metastasis was also observed in mice receiving sunitinib prior to intravenous implantation of tumor cells, suggesting possible “metastatic conditioning” in multiple organs. Similar findings with additional VEGF receptor tyrosine kinase inhibitors implicate a class-specific effect for such agents. Importantly, these observations of metastatic acceleration were in contrast to the demonstrable antitumor benefits obtained when the same human breast cancer cells, as well as mouse or human melanoma cells, were grown orthotopically as primary tumors and subjected to identical sunitinib treatments

Inverse correlation between VEGF and soluble VEGF receptor 2 in POEMS with AIDP responsive to intravenous immunoglobulin

POEMS (polyneuropathy, organomegaly, endocrinopathy, M-band, and skin changes) syndrome is characterized by chronic progressive polyneuropathy and plasma-cell dyscrasia. A major diagnostic criterion of POEMS is elevation of circulating vascular endothelial growth factor (VEGF), which is believed to play a pathogenic role in this disease. We report a case of POEMS that presented as relapsing acute inflammatory demyelinating polyneuropathy, in which complete remission after intravenous immunoglobulin (IVIg) treatment was unexpectedly observed. At clinical nadir, the VEGF level was 30-fold higher, and the soluble form of VEGF receptor 2 (sVEGFR2), which acts as a decoy for VEGF, was 2.7-fold lower than normal. These changes combined might contribute to the pathogenesis of POEMS, inducing vascular permeability and tissue edema. At 9-month follow-up, during clinical remission, VEGF and sVEGFR2 were near normal values. sVEGFR2 reduction is a new finding in POEMS. IVIg treatment may benefit POEMS patients with acute neuropathy by downgrading VEGF release induced by inflammatory cytokines

A reduced Gompertz model for predicting tumor age using a population approach

Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed for the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and-more notably-Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The population-level correlation between the Gompertz parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual parameter. Leveraging the population approach using bayesian inference, we estimated the time 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 was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line. These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summary Mathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis

Mathematical modeling of differential effects of neo-adjuvant Sunitinib on primary tumor and metastatic growth

International audienceSunitinib 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 [1, 2]. In this work, we evaluated a previously validated mechanistic mathematical model of metastasis [3] to describe primary tumor and metastatic dynamics in response to neoadjuvant anti-angiogenic treatment in clinically relevant mouse models of spontaneous metastatic breast and kidney cancers that develop after surgical removal of orthotopically implanted primary tumors. The data of more than 380 mice receiving either vehicle or sunitinib in the neoadjuvant (presurgical) setting according to different schedules was analyzed. The experimental datasets comprise measurements of primary tumor and metastatic burden kinetics as well as pre-surgical molecular and cellular biomarkers, including vascular cell Ki67 and CD31 expression, circulating tumor cells (CTCs) and myeloid derived suppressor cell counts (MDSCs). Estimation of the mathematical model's parameters was performed using a mixed-effects population approach. Population fits obtained modeling the effect of treatment only on primary tumor growth described well the experimental data of all the treated groups considered, suggesting a negligible effect of the neo-adjuvant treatment on early metastatic spread and growth. When inserting in the model the available biomarkers as covariates, measurements of Ki67+/CD31+, CTCs and granulocytic MDSCs were found significantly correlated with a specific model parameter expressing the metastatic aggressiveness of the tumor. Together, our mathematical model confirms a differential effect of sunitinib on primary (localized) tumors compared to secondary (metastatic) disease. Our results suggest that CTCs and MDSCs might help in predicting metastatic potential and provide a biologically-based computational model integrating these biomarkers into personalized predictions of metastatic benefit of pre-operative treatments. [1] Ebos, J. M. L., Lee, C. R., Cruz-Munoz, W., Bjarnason, G. A., Christensen, J. G., and Kerbel, R. S. (2009). Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. Cancer Cell, 15(3):232-239

The safety and efficacy of sunitinib before planned nephrectomy in metastatic clear cell renal cancer

Background: The safety and efficacy of upfront sunitinib, before nephrectomy in metastatic clear cell renal cancer (mCRC), has not been prospectively evaluated

Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach

International audienceRapid 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) and postsurgical (metastatic) growth was quantified using bioluminescence and was 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-/post-surgical 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, inter-individual 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

P-rex1 cooperates with PDGFRβ to drive cellular migration in 3D microenvironments

Expression of the Rac-guanine nucleotide exchange factor (RacGEF), P-Rex1 is a key determinant of progression to metastasis in a number of human cancers. In accordance with this proposed role in cancer cell invasion and metastasis, we find that ectopic expression of P-Rex1 in an immortalised human fibroblast cell line is sufficient to drive multiple migratory and invasive phenotypes. The invasive phenotype is greatly enhanced by the presence of a gradient of serum or platelet-derived growth factor, and is dependent upon the expression of functional PDGF receptor β. Consistently, the invasiveness of WM852 melanoma cells, which endogenously express P-Rex1 and PDGFRβ, is opposed by siRNA of either of these proteins. Furthermore, the current model of P-Rex1 activation is advanced through demonstration of P-Rex1 and PDGFRβ as components of the same macromolecular complex. These data suggest that P-Rex1 has an influence on physiological migratory processes, such as invasion of cancer cells, both through effects upon classical Rac1-driven motility and a novel association with RTK signalling complexes

Novel 1,4-benzoxazine and 1,4-benzodioxine inhibitors of angiogenesis.

Esters of 1,4-benzoxazine and 1,4-benzodioxine compounds 1 and 10, which combine thrombin inhibitory and GPIIb/IIIa antagonistic activity in one molecule are shown to inhibit endothelial cell migration and tube formation in vitro and angiogenesis in the chicken chorioallantoic membrane (CAM) assay. The corresponding carboxylic acids 1 (R2 = H) and 11 were devoid of antiangiogenic activity, most probably due to their insufficient entry into the cell. Although thrombin inhibition remains the most probable explanation for their inhibition of angiogenesis, VEGFR2 kinase assay suggest that other targets such as VEGFR2 might be involved