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      Hybrid modeling frameworks of tumor development and treatment

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          Abstract

          Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

          This article is characterized under:

          • Analytical and Computational Methods > Computational Methods

          • Translational, Genomic, and Systems Medicine > Therapeutic Methods

          • Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

          Abstract

          Hybrid modeling framework of cancer combines three classes of mathematical models: data‐driven, physics‐based, and optimization for development of a clinically relevant and quantitative decision‐making system for personalized medicine.

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          Most cited references74

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          The mathematics of cancer: integrating quantitative models.

          Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
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            Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer

            Abiraterone treats metastatic castrate-resistant prostate cancer by inhibiting CYP17A, an enzyme for testosterone auto-production. With standard dosing, evolution of resistance with treatment failure (radiographic progression) occurs at a median of ~16.5 months. We hypothesize time to progression (TTP) could be increased by integrating evolutionary dynamics into therapy. We developed an evolutionary game theory model using Lotka–Volterra equations with three competing cancer “species”: androgen dependent, androgen producing, and androgen independent. Simulations with standard abiraterone dosing demonstrate strong selection for androgen-independent cells and rapid treatment failure. Adaptive therapy, using patient-specific tumor dynamics to inform on/off treatment cycles, suppresses proliferation of androgen-independent cells and lowers cumulative drug dose. In a pilot clinical trial, 10 of 11 patients maintained stable oscillations of tumor burdens; median TTP is at least 27 months with reduced cumulative drug use of 47% of standard dosing. The outcomes show significant improvement over published studies and a contemporaneous population.
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              Spatial Heterogeneity and Evolutionary Dynamics Modulate Time to Recurrence in Continuous and Adaptive Cancer Therapies

              Treatment of advanced cancers has benefited from new agents that supplement or bypass conventional therapies. However, even effective therapies fail as cancer cells deploy a wide range of resistance strategies. We propose that evolutionary dynamics ultimately determine survival and proliferation of resistant cells. Therefore, evolutionary strategies should be used with conventional therapies to delay or prevent resistance. Using an agent-based framework to model spatial competition among sensitive and resistant populations, we applied anti-proliferative drug treatments to varying ratios of sensitive and resistant cells. We compared a continuous maximum tolerated dose schedule with an adaptive schedule aimed at tumor control via competition between sensitive and resistant cells. Continuous treatment cured mostly sensitive tumors, but with any resistant cells, recurrence was inevitable. We identified two adaptive strategies that control heterogeneous tumors: dose modulation controls most tumors with less drug, while a more vacation-oriented schedule can control more invasive tumors. These findings offer potential modifications to treatment regimens that may improve outcomes and reduce resistance and recurrence.
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                Author and article information

                Contributors
                kasia.rejniak@moffitt.org
                Journal
                Wiley Interdiscip Rev Syst Biol Med
                Wiley Interdiscip Rev Syst Biol Med
                10.1002/(ISSN)1939-005X
                WSBM
                Wiley Interdisciplinary Reviews. Systems Biology and Medicine
                John Wiley & Sons, Inc. (Hoboken, USA )
                1939-5094
                1939-005X
                17 July 2019
                Jan-Feb 2020
                : 12
                : 1 ( doiID: 10.1002/wsbm.v12.1 )
                : e1461
                Affiliations
                [ 1 ] Department of Integrated Mathematical Oncology H. Lee Moffitt Cancer Center and Research Institute Tampa Florida
                [ 2 ] Department of Oncologic Sciences, Morsani College of Medicine University of South Florida Tampa Florida
                Author notes
                [*] [* ] Correspondence

                Katarzyna A. Rejniak, Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL.

                Email: kasia.rejniak@ 123456moffitt.org

                Author information
                https://orcid.org/0000-0002-7005-8692
                https://orcid.org/0000-0003-2093-2422
                Article
                WSBM1461
                10.1002/wsbm.1461
                6898741
                31313504
                fba110a0-a5ac-4d48-82ab-b1ae69866428
                © 2019 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc.

                This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

                History
                : 29 April 2019
                : 13 June 2019
                : 13 June 2019
                Page count
                Figures: 4, Tables: 0, Pages: 16, Words: 12504
                Funding
                Funded by: Florida Department of Health , open-funder-registry 10.13039/100006827;
                Funded by: Bankhead‐Coley Cancer Research
                Award ID: 9BC05
                Funded by: National Institutes of Health , open-funder-registry 10.13039/100000002;
                Award ID: U01 CA202229‐04
                Funded by: Moffitt Team Science Award
                Funded by: Moffitt Center for Immunization and Infection Research in Cancer (CIIRC)
                Categories
                Computational Methods
                Therapeutic Methods
                Organ, Tissue, and Physiological Models
                Update
                Updates
                Custom metadata
                2.0
                January/February 2020
                Converter:WILEY_ML3GV2_TO_JATSPMC version:5.7.3 mode:remove_FC converted:17.12.2019

                Molecular medicine
                mathematical modeling,mathematical oncology
                Molecular medicine
                mathematical modeling, mathematical oncology

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