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.
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 linearquadratic 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 offtarget 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. Ó2016 AACR.
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.
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