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) 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. Major findings A mathematical model was used to connect presurgical primary tumor volume and postsurgical metastatic burden and survival in two clinically relevant animal models of spontaneous metastasis and one clinical dataset of metastatic relapse probability in breast cancer patients. This model used one specific parameter to quantify differential metastatic aggressiveness, which could be of help for personalizing adjuvant therapy. Simulations revealed a highly nonlinear relationship between resected primary tumor size and metastatic recurrence. These results uncover a computable and patient-dependent threshold for evaluating the efficacy of surgery on overall survival.

Thousands of cancer patients are currently in clinical trials evaluating antiangiogenic therapy in the neoadjuvant setting, which is the treatment of localized primary tumors prior to surgical intervention. The rationale is that shrinking a tumor will improve surgical outcomes and minimize growth of occult micrometastatic disease—thus delaying post-surgical recurrence and improving survival. But approved VEGF pathway inhibitors have not been tested in clinically relevant neoadjuvant models that compare pre- and post-surgical treatment effects. Using mouse models of breast, kidney, and melanoma metastasis, we demonstrate that primary tumor responses to neoadjuvant VEGFR TKI treatment do not consistently correlate with improved post-surgical survival, with survival worsened in certain settings. Similar negative effects did not extend to protein-based VEGF pathway inhibitors and could be reversed with altered dose, surgical timing, and treatment duration, or when VEGFR TKIs are combined with metronomic ‘anti-metastatic’ chemotherapy regimens. These studies represent the first attempt to recapitulate the complex clinical parameters of neoadjuvant therapy in mice and identify a novel tool to compare systemic antiangiogenic treatment effects on localized and disseminated disease.

Sunitinib is an antiangiogenic therapy given as a first-line treatment for renal cell carcinoma (RCC). While treatment improves progression-free survival, most patients relapse. We hypothesized that patient relapse can stem from the development of a lymphatic network driven by the production of the main growth factor for lymphatic endothelial cells, VEGFC. In this study, we found that sunitinib can stimulate gene transcription and increase VEGFC mRNA half-life. In addition, sunitinib activated p38 MAPK, which resulted in the upregulation/activity of HuR and inactivation of tristetraprolin, two AU-rich element-binding proteins. Sunitinib stimulated a VEGFC-dependent development of lymphatic vessels in experimental tumors. This may explain our findings of increased lymph node invasion and new metastatic sites in 30% of sunitinib-treated patients and increased lymphatic vessels found in 70% of neoadjuvant treated patients. In summary, a therapy dedicated to destroying tumor blood vessels induced the development of lymphatic vessels, which may have contributed to the treatment failure..

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 populationlevel correlation between the Gompertz parameters was further confirmed in our analysis (R 2 > 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