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Peters J, van Dijck JA, Elias SG, Otten JD, Broeders MJ. The prognostic potential of mammographic growth rate of invasive breast cancer in the Nijmegen breast cancer screening cohort. J Med Screen 2024; 31:166-175. [PMID: 38295359 PMCID: PMC11330081 DOI: 10.1177/09691413231222765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2023] [Accepted: 11/15/2023] [Indexed: 02/02/2024]
Abstract
OBJECTIVES Insight into the aggressiveness of potential breast cancers found in screening may optimize recall decisions. Specific growth rate (SGR), measured on mammograms, may provide valuable prognostic information. This study addresses the association of SGR with prognostic factors and overall survival in patients with invasive carcinoma of no special type (NST) from a screened population. METHODS In this historic cohort study, 293 women with NST were identified from all participants in the Nijmegen screening program (2003-2007). Information on clinicopathological factors was retrieved from patient files and follow-up on vital status through municipalities. On consecutive mammograms, tumor volumes were estimated. After comparing five growth functions, SGR was calculated using the best-fitting function. Regression and multivariable survival analyses described associations between SGR and prognostic factors as well as overall survival. RESULTS Each one standard deviation increase in SGR was associated with an increase in the Nottingham prognostic index by 0.34 [95% confidence interval (CI): 0.21-0.46]. Each one standard deviation increase in SGR increased the odds of a tumor with an unfavorable subtype (based on histologic grade and hormone receptors; odds ratio 2.14 [95% CI: 1.45-3.15]) and increased the odds of diagnosis as an interval cancer (versus screen-detected; odds ratio 1.57 [95% CI: 1.20-2.06]). After a median of 12.4 years of follow-up, 78 deaths occurred. SGR was not associated with overall survival (hazard ratio 1.12 [95% CI: 0.87-1.43]). CONCLUSIONS SGR may indicate prognostically relevant differences in tumor aggressiveness if serial mammograms are available. A potential association with cause-specific survival could not be determined and is of interest for future research.
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Affiliation(s)
- Jim Peters
- Department for Health Evidence, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Jos A.A.M. van Dijck
- Department for Health Evidence, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Sjoerd G. Elias
- Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht University, Utrecht, The Netherlands
| | - Johannes D.M. Otten
- Department for Health Evidence, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Mireille J.M. Broeders
- Department for Health Evidence, Radboud University Medical Center, Nijmegen, The Netherlands
- Dutch Expert Centre for Screening (LRCB), Nijmegen, The Netherlands
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Classical mathematical models for prediction of response to chemotherapy and immunotherapy. PLoS Comput Biol 2022; 18:e1009822. [PMID: 35120124 PMCID: PMC8903251 DOI: 10.1371/journal.pcbi.1009822] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Revised: 03/08/2022] [Accepted: 01/10/2022] [Indexed: 01/02/2023] Open
Abstract
Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models. Mathematical oncology uses quantitative models for prediction of tumor growth and treatment response. The theoretical foundation of mathematical oncology is provided by six classical mathematical models: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. These models have been introduced decades ago, have been used in thousands of scientific articles and are part of textbooks and curricula in mathematical oncology. However, these models have not been systematically tested in clinical data from actual patients. In this study, we have collected quantitative tumor volume measurements from thousands of patients in five large clinical trials of cancer immunotherapy. We use this dataset to systematically investigate how accurately mathematical models can describe tumor growth, showing that there are pronounced differences between models. In addition, we show that two of these models can predict tumor response to immunotherapy and chemotherapy at later time points when trained on early tumor growth dynamics. Thus, our article closes a conceptual gap in the literature and at the same time provides a simple tool to predict response to chemotherapy and immunotherapy on the level of individual patients.
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Kiwumulo HF, Muwonge H, Ibingira C, Kirabira JB, Ssekitoleko RT. A systematic review of modeling and simulation approaches in designing targeted treatment technologies for Leukemia Cancer in low and middle income countries. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:8149-8173. [PMID: 34814293 DOI: 10.3934/mbe.2021404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Virtual experimentation is a widely used approach for predicting systems behaviour especially in situations where resources for physical experiments are very limited. For example, targeted treatment inside the human body is particularly challenging, and as such, modeling and simulation is utilised to aid planning before a specific treatment is administered. In such approaches, precise treatment, as it is the case in radiotherapy, is used to administer a maximum dose to the infected regions while minimizing the effect on normal tissue. Complicated cancers such as leukemia present even greater challenges due to their presentation in liquid form and not being localised in one area. As such, science has led to the development of targeted drug delivery, where the infected cells can be specifically targeted anywhere in the body. Despite the great prospects and advances of these modeling and simulation tools in the design and delivery of targeted drugs, their use by Low and Middle Income Countries (LMICs) researchers and clinicians is still very limited. This paper therefore reviews the modeling and simulation approaches for leukemia treatment using nanoparticles as an example for virtual experimentation. A systematic review from various databases was carried out for studies that involved cancer treatment approaches through modeling and simulation with emphasis to data collected from LMICs. Results indicated that whereas there is an increasing trend in the use of modeling and simulation approaches, their uptake in LMICs is still limited. According to the review data collected, there is a clear need to employ these tools as key approaches for the planning of targeted drug treatment approaches.
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Affiliation(s)
| | - Haruna Muwonge
- Department of Medical Physiology, Makerere University, Kampala, Uganda
| | - Charles Ibingira
- Department of Human Anatomy, Makerere University, Kampala, Uganda
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Kaushik V, Kulkarni Y, Felix K, Azad N, Iyer AKV, Yakisich JS. Alternative models of cancer stem cells: The stemness phenotype model, 10 years later. World J Stem Cells 2021; 13:934-943. [PMID: 34367485 PMCID: PMC8316871 DOI: 10.4252/wjsc.v13.i7.934] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Revised: 05/05/2021] [Accepted: 07/09/2021] [Indexed: 02/06/2023] Open
Abstract
The classical cancer stem cell (CSCs) theory proposed the existence of a rare but constant subpopulation of CSCs. In this model cancer cells are organized hierarchically and are responsible for tumor resistance and tumor relapse. Thus, eliminating CSCs will eventually lead to cure of cancer. This simplistic model has been challenged by experimental data. In 2010 we proposed a novel and controversial alternative model of CSC biology (the Stemness Phenotype Model, SPM). The SPM proposed a non-hierarchical model of cancer biology in which there is no specific subpopulation of CSCs in tumors. Instead, cancer cells are highly plastic in term of stemness and CSCs and non-CSCs can interconvert into each other depending on the microenvironment. This model predicts the existence of cancer cells ranging from a pure CSC phenotype to pure non-CSC phenotype and that survival of a single cell can originate a new tumor. During the past 10 years, a plethora of experimental evidence in a variety of cancer types has shown that cancer cells are indeed extremely plastic and able to interconvert into cells with different stemness phenotype. In this review we will (1) briefly describe the cumulative evidence from our laboratory and others supporting the SPM; (2) the implications of the SPM in translational oncology; and (3) discuss potential strategies to develop more effective therapeutic regimens for cancer treatment.
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Affiliation(s)
- Vivek Kaushik
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States
| | - Yogesh Kulkarni
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States
| | - Kumar Felix
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States
| | - Neelam Azad
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States
| | - Anand Krishnan V Iyer
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States
| | - Juan Sebastian Yakisich
- School of Pharmacy, Department of Pharmaceutical Sciences, Hampton University, Hampton, VA 23668, United States.
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5
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Solé R, Aguadé-Gorgorió G. The ecology of cancer differentiation therapy. J Theor Biol 2020; 511:110552. [PMID: 33309530 DOI: 10.1016/j.jtbi.2020.110552] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Revised: 10/21/2020] [Accepted: 11/17/2020] [Indexed: 11/29/2022]
Abstract
A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.
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Affiliation(s)
- Ricard Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe NM 87501, USA
| | - Guim Aguadé-Gorgorió
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain
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6
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Buller M, Chapple KM, Bird CR. Brain Metastases: Insights from Statistical Modeling of Size Distribution. AJNR Am J Neuroradiol 2020; 41:579-582. [PMID: 32241770 DOI: 10.3174/ajnr.a6496] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2019] [Accepted: 02/12/2020] [Indexed: 11/07/2022]
Abstract
BACKGROUND AND PURPOSE Brain metastases are a common finding on brain MRI. However, the factors that dictate their size and distribution are incompletely understood. Our aim was to discover a statistical model that can account for the size distribution of parenchymal metastases in the brain as measured on contrast-enhanced MR imaging. MATERIALS AND METHODS Tumor volumes were calculated on the basis of measured tumor diameters from contrast-enhanced T1-weighted spoiled gradient-echo images in 68 patients with untreated parenchymal metastatic disease. Tumor volumes were then placed in rank-order distributions and compared with 11 different statistical curve types. The resultant R 2 values to assess goodness of fit were calculated. The top 2 distributions were then compared using the likelihood ratio test, with resultant R values demonstrating the relative likelihood of these distributions accounting for the observed data. RESULTS Thirty-nine of 68 cases best fit a power distribution (mean R 2 = 0.938 ± 0.050), 20 cases best fit an exponential distribution (mean R 2 = 0.957 ± 0.050), and the remaining cases were scattered among the remaining distributions. Likelihood ratio analysis revealed that 66 of 68 cases had a positive mean R value (1.596 ± 1.316), skewing toward a power law distribution. CONCLUSIONS The size distributions of untreated brain metastases favor a power law distribution. This finding suggests that metastases do not exist in isolation, but rather as part of a complex system. Furthermore, these results suggest that there may be a relatively small number of underlying variables that substantially influence the behavior of these systems. The identification of these variables could have a profound effect on our understanding of these lesions and our ability to treat them.
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Affiliation(s)
- M Buller
- From the Department of Neuroradiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, Arizona
| | - K M Chapple
- From the Department of Neuroradiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, Arizona
| | - C R Bird
- From the Department of Neuroradiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, Arizona.
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7
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Sigal D, Przedborski M, Sivaloganathan D, Kohandel M. Mathematical modelling of cancer stem cell-targeted immunotherapy. Math Biosci 2019; 318:108269. [DOI: 10.1016/j.mbs.2019.108269] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 09/17/2019] [Accepted: 10/05/2019] [Indexed: 12/15/2022]
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Brady R, Enderling H. Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to. Bull Math Biol 2019; 81:3722-3731. [PMID: 31338741 PMCID: PMC6764933 DOI: 10.1007/s11538-019-00640-x] [Citation(s) in RCA: 79] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Accepted: 07/02/2019] [Indexed: 12/27/2022]
Abstract
The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735-1741, 1977; Norton in Can Res 48:7067-7071, 1988; Hahnfeldt et al. in Can Res 59:4770-4775, 1999; Anderson et al. in Comput Math Methods Med 2:129-154, 2000. https://doi.org/10.1080/10273660008833042 ; Michor et al. in Nature 435:1267-1270, 2005. https://doi.org/10.1038/nature03669 ; Anderson et al. in Cell 127:905-915, 2006. https://doi.org/10.1016/j.cell.2006.09.042 ; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800 ). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.
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Affiliation(s)
- Renee Brady
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, 33647, USA
| | - Heiko Enderling
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, 33647, USA.
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Afenya EK, Ouifki R, Mundle SD. Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II. J Theor Biol 2019; 460:37-55. [PMID: 30296448 DOI: 10.1016/j.jtbi.2018.10.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 09/28/2018] [Accepted: 10/01/2018] [Indexed: 12/31/2022]
Abstract
The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.
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Affiliation(s)
- Evans K Afenya
- Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, USA.
| | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
| | - Suneel D Mundle
- Department of Biochemistry, Rush University Medical Center, 1735 W. Harrison St, Chicago, IL 60612, USA.
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Emerging functional markers for cancer stem cell-based therapies: Understanding signaling networks for targeting metastasis. Semin Cancer Biol 2018; 53:90-109. [PMID: 29966677 DOI: 10.1016/j.semcancer.2018.06.006] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 06/20/2018] [Accepted: 06/28/2018] [Indexed: 12/18/2022]
Abstract
Metastasis is one of the most challenging issues in cancer patient management, and effective therapies to specifically target disease progression are missing, emphasizing the urgent need for developing novel anti-metastatic therapeutics. Cancer stem cells (CSCs) gained fast attention as a minor population of highly malignant cells within liquid and solid tumors that are responsible for tumor onset, self-renewal, resistance to radio- and chemotherapies, and evasion of immune surveillance accelerating recurrence and metastasis. Recent progress in the identification of their phenotypic and molecular characteristics and interactions with the tumor microenvironment provides great potential for the development of CSC-based targeted therapies and radical improvement in metastasis prevention and cancer patient prognosis. Here, we report on newly uncovered signaling mechanisms controlling CSC's aggressiveness and treatment resistance, and CSC-specific agents and molecular therapeutics, some of which are currently under investigation in clinical trials, gearing towards decisive functional CSC intrinsic or surface markers. One special research focus rests upon subverted regulatory pathways such as insulin-like growth factor 1 receptor signaling and its interactors in metastasis-initiating cell populations directly related to the gain of stem cell- and EMT-associated properties, as well as key components of the E2F transcription factor network regulating metastatic progression, microenvironmental changes, and chemoresistance. In addition, the study provides insight into systems biology tools to establish complex molecular relationships behind the emergence of aggressive phenotypes from high-throughput data that rely on network-based analysis and their use to investigate immune escape mechanisms or predict clinical outcome-relevant CSC receptor signaling signatures. We further propose that customized vector technologies could drastically enhance systemic drug delivery to target sites, and summarize recent progress and remaining challenges. This review integrates available knowledge on CSC biology, computational modeling approaches, molecular targeting strategies, and delivery techniques to envision future clinical therapies designed to conquer metastasis-initiating cells.
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A Multiscale Approach to the Migration of Cancer Stem Cells: Mathematical Modelling and Simulations. Bull Math Biol 2016; 79:209-235. [DOI: 10.1007/s11538-016-0233-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Accepted: 11/04/2016] [Indexed: 11/29/2022]
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12
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Mathematical Modelling of Bacterial Quorum Sensing: A Review. Bull Math Biol 2016; 78:1585-639. [PMID: 27561265 DOI: 10.1007/s11538-016-0160-6] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Accepted: 03/15/2016] [Indexed: 12/21/2022]
Abstract
Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.
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Marcu LG, Marcu D, Filip SM. In silico study of the impact of cancer stem cell dynamics and radiobiological hypoxia on tumour response to hyperfractionated radiotherapy. Cell Prolif 2016; 49:304-14. [PMID: 27079860 DOI: 10.1111/cpr.12251] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2016] [Accepted: 02/10/2016] [Indexed: 02/05/2023] Open
Abstract
OBJECTIVES Advanced head and neck carcinomas (HNCs) are aggressive tumours, mainly due to hypoxia and a cancer stem cell (CSC) subpopulation. The aim of this study was to simulate tumour growth and behaviour during radiotherapy of three HNC groups (governed by different growth kinetics, hypoxia levels and CSC division pattern) to determine correlation between resistance factors and responses to hyperfractionated radiotherapy. METHODS An in silico HNC model was developed based on biologically realistic input parameters. During radiotherapy simulation, three parameters were studied: growth kinetics, hypoxia and probability of CSC symmetrical division. Both independent and combined effects on tumour response to hyperfractionated radiotherapy were assessed. RESULTS Oxic and very mildly hypoxic HNCs were revealed to be controlled by hyperfractionated radiotherapy, irrespective of growth kinetics and CSC division pattern. Moderately hypoxic tumours had different responses to radiotherapy: while slowly proliferating HNCs were still controllable, tumours with higher cell turnover were more resistant. In rapidly proliferating tumours, the number of fractions needed for tumour control increased exponentially with the probability of CSC symmetrical division, whereas in moderately growing HNC, this behaviour was linear. Severely hypoxic tumours could not be controlled by radiotherapy alone. Tumours with CSCs in a severely hypoxic niche required adjuvant therapies to be eradicated. CONCLUSIONS Growth kinetics strongly influence tumour responses to treatment. Slowly growing tumours showed linear dependence between dose and hypoxia/CSC, whereas rapidly growing tumours followed exponential behaviour.
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Affiliation(s)
- L G Marcu
- Faculty of Science, University of Oradea, Oradea, 410087, Romania.,School of Physical Sciences, The University of Adelaide, Adelaide, South Australia, 5005, Australia
| | - D Marcu
- Faculty of Science, University of Oradea, Oradea, 410087, Romania
| | - S M Filip
- Faculty of Science, University of Oradea, Oradea, 410087, Romania
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Modeling the Treatment of Glioblastoma Multiforme and Cancer Stem Cells with Ordinary Differential Equations. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2016; 2016:1239861. [PMID: 27022405 PMCID: PMC4745194 DOI: 10.1155/2016/1239861] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Revised: 11/12/2015] [Accepted: 12/22/2015] [Indexed: 11/24/2022]
Abstract
Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this paper, we study the application of the CSC Hypothesis to the treatment of glioblastoma multiforme by immunotherapy. We extend the work of Kogan et al. (2008) to incorporate the dynamics of CSCs, prove the existence of a recurrence state, and provide an analysis of possible cancerous states and their dependence on treatment levels.
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Afenya EK, Ouifki R, Camara BI, Mundle SD. Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I. Math Biosci 2016; 274:83-93. [PMID: 26877072 DOI: 10.1016/j.mbs.2016.01.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 01/08/2016] [Accepted: 01/28/2016] [Indexed: 01/08/2023]
Abstract
Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture.
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Affiliation(s)
- Evans K Afenya
- Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, USA.
| | - Rachid Ouifki
- DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, 19 Jonkershoek Rd, Stellenbosch, 7600, South Africa.
| | - Baba I Camara
- Laboratoire Interdisciplinaire des Environnements Continentaux, Universit de Lorraine, CNRS UMR 7360, 8 rue du General Delestraint, Metz 57070, France.
| | - Suneel D Mundle
- Department of Biochemistry, Rush University Medical Center, 1735 W. Harrison St, Chicago, IL 60612, USA.
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16
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Monteagudo Á, Santos J. Treatment Analysis in a Cancer Stem Cell Context Using a Tumor Growth Model Based on Cellular Automata. PLoS One 2015; 10:e0132306. [PMID: 26176702 PMCID: PMC4503350 DOI: 10.1371/journal.pone.0132306] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2015] [Accepted: 06/11/2015] [Indexed: 12/31/2022] Open
Abstract
Cancer can be viewed as an emergent behavior in terms of complex system theory and artificial life, Cellular Automata (CA) being the tool most used for studying and characterizing the emergent behavior. Different approaches with CA models were used to model cancer growth. The use of the abstract model of acquired cancer hallmarks permits the direct modeling at cellular level, where a cellular automaton defines the mitotic and apoptotic behavior of cells, and allows for an analysis of different dynamics of the cellular system depending on the presence of the different hallmarks. A CA model based on the presence of hallmarks in the cells, which includes a simulation of the behavior of Cancer Stem Cells (CSC) and their implications for the resultant growth behavior of the multicellular system, was employed. This modeling of cancer growth, in the avascular phase, was employed to analyze the effect of cancer treatments in a cancer stem cell context. The model clearly explains why, after treatment against non-stem cancer cells, the regrowth capability of CSCs generates a faster regrowth of tumor behavior, and also shows that a continuous low-intensity treatment does not favor CSC proliferation and differentiation, thereby allowing an unproblematic control of future tumor regrowth. The analysis performed indicates that, contrary to the current attempts at CSC control, trying to make CSC proliferation more difficult is an important point to consider, especially in the immediate period after a standard treatment for controlling non-stem cancer cell proliferation.
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Affiliation(s)
- Ángel Monteagudo
- Department of Computer Science, University of A Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain
| | - José Santos
- Department of Computer Science, University of A Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain
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17
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Norton KA, Popel AS. An agent-based model of cancer stem cell initiated avascular tumour growth and metastasis: the effect of seeding frequency and location. J R Soc Interface 2015; 11:20140640. [PMID: 25185580 DOI: 10.1098/rsif.2014.0640] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
It is very important to understand the onset and growth pattern of breast primary tumours as well as their metastatic dissemination. In most cases, it is the metastatic disease that ultimately kills the patient. There is increasing evidence that cancer stem cells are closely linked to the progression of the metastatic tumour. Here, we investigate stem cell seeding to an avascular tumour site using an agent-based stochastic model of breast cancer metastatic seeding. The model includes several important cellular features such as stem cell symmetric and asymmetric division, migration, cellular quiescence, senescence, apoptosis and cell division cycles. It also includes external features such as stem cell seeding frequency and location. Using this model, we find that cell seeding rate and location are important features for tumour growth. We also define conditions in which the tumour growth exhibits decremented and exponential growth patterns. Overall, we find that seeding, senescence and division limit affect not only the number of stem cells, but also their spatial and temporal distribution.
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Affiliation(s)
- Kerri-Ann Norton
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA
| | - Aleksander S Popel
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA Department of Oncology and Sidney Kimmel Comprehensive Cancer Center, Baltimore, MD 21205, USA
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18
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Khan IS, Ehtesham M. Laboratory models for central nervous system tumor stem cell research. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2015; 853:69-83. [PMID: 25895708 DOI: 10.1007/978-3-319-16537-0_5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
Abstract
Central nervous system (CNS) tumors are complex organ systems comprising of a neoplastic component with associated vasculature, inflammatory cells, and reactive cellular and extracellular components. Research has identified a subset of cells in CNS tumors that portray defining properties of neural stem cells, namely, that of self-renewal and multi-potency. Growing evidence suggests that these tumor stem cells (TSC) play an important role in the maintenance and growth of the tumor. Furthermore, these cells have also been shown to be refractory to conventional therapy and may be crucial for tumor recurrence and metastasis. Current investigations are focusing on isolating these TSC from CNS tumors to investigate their unique biological processes. This understanding will help identify and develop more effective and comprehensive treatment strategies. This chapter provides an overview of some of the most commonly used laboratory models for CNSTSC research.
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Affiliation(s)
- Imad Saeed Khan
- Section of Neurosurgery, Geisel School of Medicine at Dartmouth, Lebanon, NH, USA
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19
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Dynamic regulation of the cancer stem cell compartment by Cripto-1 in colorectal cancer. Cell Death Differ 2015; 22:1700-13. [PMID: 26343543 PMCID: PMC4563784 DOI: 10.1038/cdd.2015.19] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2014] [Revised: 01/27/2015] [Accepted: 02/02/2015] [Indexed: 12/20/2022] Open
Abstract
Stemness was recently depicted as a dynamic condition in normal and tumor cells. We found that the embryonic protein Cripto-1 (CR1) was expressed by normal stem cells at the bottom of colonic crypts and by cancer stem cells (CSCs) in colorectal tumor tissues. CR1-positive populations isolated from patient-derived tumor spheroids exhibited increased clonogenic capacity and expression of stem-cell-related genes. CR1 expression in tumor spheroids was variable over time, being subject to a complex regulation of the intracellular, surface and secreted protein, which was related to changes of the clonogenic capacity at the population level. CR1 silencing induced CSC growth arrest in vitro with a concomitant decrease of Src/Akt signaling, while in vivo it inhibited the growth of CSC-derived tumor xenografts and reduced CSC numbers. Importantly, CR1 silencing in established xenografts through an inducible expression system decreased CSC growth in both primary and metastatic tumors, indicating an essential role of CR1 in the regulation the CSC compartment. These results point to CR1 as a novel and dynamically regulated effector of stem cell functions in colorectal cancer.
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20
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Day RS. What Tumor Dynamics Modeling Can Teach us About Exploiting the Stem-Cell View for Better Cancer Treatment. Cancer Inform 2015; 14:25-36. [PMID: 25780337 PMCID: PMC4345852 DOI: 10.4137/cin.s17294] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Revised: 01/19/2015] [Accepted: 01/22/2015] [Indexed: 12/26/2022] Open
Abstract
The cancer stem cell hypothesis is that in human solid cancers, only a small proportion of the cells, the cancer stem cells (CSCs), are self-renewing; the vast majority of the cancer cells are unable to sustain tumor growth indefinitely on their own. In recent years, discoveries have led to the concentration, if not isolation, of putative CSCs. The evidence has mounted that CSCs do exist and are important. This knowledge may promote better understanding of treatment resistance, create opportunities to test agents against CSCs, and open up promise for a fresh approach to cancer treatment. The first clinical trials of new anti-CSC agents are completed, and many others follow. Excitement is mounting that this knowledge will lead to major improvements, even breakthroughs, in treating cancer. However, exploitation of this phenomenon may be more successful if informed by insights into the population dynamics of tumor development. We revive some ideas in tumor dynamics modeling to extract some guidance in designing anti-CSC treatment regimens and the clinical trials that test them.
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Affiliation(s)
- Roger S Day
- Department of Biomedical Informatics, University of Pittsburgh, Pittsburgh, PA, USA
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21
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Abstract
This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.
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Affiliation(s)
- Heiko Enderling
- Department of Integrated Mathematical Oncology
- H. Lee Moffitt Cancer Center & Research Institute
- Tampa
- USA
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22
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23
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Abstract
Differentiation therapy for tumors refers to treating malignant tumors via the induction of cell differentiation. The best characterized clinical application of differentiation therapy is the use of all-trans retinoic acid in the treatment of acute promyelocytic leukemia (APL), which markedly improved the outcome of this disease. Unlike the situation with APL, the development of differentiation therapy for solid tumors is far from satisfactory. To date, no differentiation-inducing agents have been demonstrated to exert a curative effect on solid tumors. However, over the past decade progress in understanding the differentiation pathways and the development of differentiation-inducing agents might shed new light on the differentiation therapy for solid tumors.
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Affiliation(s)
- Wen Ping Xu
- Department of Gastroenterology, Changzheng Hospital, Second Military Medical University, Shanghai, China
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24
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Pei QM, Zhan X, Yang LJ, Bao C, Cao W, Li AB, Rozi A, Jia Y. Fluctuations of cell population in a colonic crypt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032715. [PMID: 24730882 DOI: 10.1103/physreve.89.032715] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Indexed: 06/03/2023]
Abstract
The number of stem cells in a colonic crypt is often very small, which leads to large intrinsic fluctuations in the cell population. Based on the model of cell population dynamics with linear feedback in a colonic crypt, we present a stochastic dynamics of the cell population [including stem cells (SCs), transit amplifying cells (TACs), and fully differentiated cells (FDCs)]. The Fano factor, covariance, and susceptibility formulas of the cell population around the steady state are derived by using the Langevin theory. In the range of physiologically reasonable parameter values, it is found that the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the reproductions of TACs and FDCs can be classified into three regimens: controlled, crossover, and uncontrolled. With the increasing of the net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e., the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and the net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.
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Affiliation(s)
- Qi-ming Pei
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and School of Physical Science and Technology, Yangtze University, Jingzhou 434023, China
| | - Xuan Zhan
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Li-jian Yang
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Chun Bao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Wei Cao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - An-bang Li
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Anvar Rozi
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and Department of Physics, Kashgar Teachers College, Kashgar 844007, China
| | - Ya Jia
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
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25
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López Alfonso JC, Jagiella N, Núñez L, Herrero MA, Drasdo D. Estimating dose painting effects in radiotherapy: a mathematical model. PLoS One 2014; 9:e89380. [PMID: 24586734 PMCID: PMC3935877 DOI: 10.1371/journal.pone.0089380] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2013] [Accepted: 01/20/2014] [Indexed: 12/25/2022] Open
Abstract
Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature. In this work we discuss the effects of different radiation dose distributions on heterogeneous tumors by means of an individual cell-based model. To that end, a case is considered where two tumor cell phenotypes are present, which we assume to strongly differ in their respective cell cycle duration and radiosensitivity properties. We show herein that, as a result of such differences, the spatial distribution of the corresponding phenotypes, whence the resulting tumor heterogeneity can be predicted as growth proceeds. In particular, we show that if we start from a situation where a majority of ordinary cancer cells (CCs) and a minority of cancer stem cells (CSCs) are randomly distributed, and we assume that the length of CSC cycle is significantly longer than that of CCs, then CSCs become concentrated at an inner region as tumor grows. As a consequence we obtain that if CSCs are assumed to be more resistant to radiation than CCs, heterogeneous dosimetries can be selected to enhance tumor control by boosting radiation in the region occupied by the more radioresistant tumor cell phenotype. It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts. Finally, limitations to our assumptions and their resulting clinical implications will be discussed.
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Affiliation(s)
- Juan Carlos López Alfonso
- Department of Applied Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain
| | - Nick Jagiella
- Institut National de Recherche en Informatique et en Automatique (INRIA), Domaine de Voluceau - Rocquencourt, Paris, France
- Institute of Computational Biology, Helmholtz Center Munich, German Research Center for Environmental Health, Neuherberg, Germany
| | - Luis Núñez
- Radiophysics Department, Hospital Universitario Puerta de Hierro, Majadahonda, Madrid, Spain
| | - Miguel A. Herrero
- Department of Applied Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain
- * E-mail:
| | - Dirk Drasdo
- Institut National de Recherche en Informatique et en Automatique (INRIA), Domaine de Voluceau - Rocquencourt, Paris, France
- University of Paris 6 (UPMC), CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France
- Interdisciplinary Center for Bioinformatics (IZBI), University of Leipzig, Leipzig, Germany
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26
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Dynamics between cancer cell subpopulations reveals a model coordinating with both hierarchical and stochastic concepts. PLoS One 2014; 9:e84654. [PMID: 24416258 PMCID: PMC3886990 DOI: 10.1371/journal.pone.0084654] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2013] [Accepted: 11/18/2013] [Indexed: 02/04/2023] Open
Abstract
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy.
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27
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Monteagudo Á, Santos J. Studying the capability of different cancer hallmarks to initiate tumor growth using a cellular automaton simulation. Application in a cancer stem cell context. Biosystems 2013; 115:46-58. [PMID: 24262634 DOI: 10.1016/j.biosystems.2013.11.001] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2013] [Revised: 10/29/2013] [Accepted: 11/03/2013] [Indexed: 02/06/2023]
Abstract
We used a cellular automaton model for cancer growth simulation at cellular level, based on the presence of different cancer hallmarks acquired by the cells. The presence of the hallmarks in each of the cells determines cell mitotic and apoptotic behaviors. Depending on the presence of the different hallmarks and some associated parameters of the hallmarks, the system can evolve to different dynamics. We used the cellular automaton model to inspect the capability of different hallmarks to generate tumor growth in different conditions, using this study in a cancer stem cell context to analyze the capability of the hallmarks to tumor regrowth in different circumstances.
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Affiliation(s)
- Ángel Monteagudo
- University of A Coruña, Department of Computer Science, Campus de Elviña s/n, 15071 A Coruña, Spain
| | - José Santos
- University of A Coruña, Department of Computer Science, Campus de Elviña s/n, 15071 A Coruña, Spain.
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28
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Gentry SN, Jackson TL. A mathematical model of cancer stem cell driven tumor initiation: implications of niche size and loss of homeostatic regulatory mechanisms. PLoS One 2013; 8:e71128. [PMID: 23990931 PMCID: PMC3747196 DOI: 10.1371/journal.pone.0071128] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2013] [Accepted: 06/28/2013] [Indexed: 12/23/2022] Open
Abstract
Hierarchical organized tissue structures, with stem cell driven cell differentiation, are critical to the homeostatic maintenance of most tissues, and this underlying cellular architecture is potentially a critical player in the development of a many cancers. Here, we develop a mathematical model of mutation acquisition to investigate how deregulation of the mechanisms preserving stem cell homeostasis contributes to tumor initiation. A novel feature of the model is the inclusion of both extrinsic and intrinsic chemical signaling and interaction with the niche to control stem cell self-renewal. We use the model to simulate the effects of a variety of types and sequences of mutations and then compare and contrast all mutation pathways in order to determine which ones generate cancer cells fastest. The model predicts that the sequence in which mutations occur significantly affects the pace of tumorigenesis. In addition, tumor composition varies for different mutation pathways, so that some sequences generate tumors that are dominated by cancerous cells with all possible mutations, while others are primarily comprised of cells that more closely resemble normal cells with only one or two mutations. We are also able to show that, under certain circumstances, healthy stem cells diminish due to the displacement by mutated cells that have a competitive advantage in the niche. Finally, in the event that all homeostatic regulation is lost, exponential growth of the cancer population occurs in addition to the depletion of normal cells. This model helps to advance our understanding of how mutation acquisition affects mechanisms that influence cell-fate decisions and leads to the initiation of cancers.
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Affiliation(s)
- Sara N. Gentry
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Trachette L. Jackson
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan, United States of America
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29
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Bagci EZ, Sen SM, Camurdan MC. Analysis of a mathematical model of apoptosis: individual differences and malfunction in programmed cell death. J Clin Monit Comput 2013; 27:465-79. [DOI: 10.1007/s10877-013-9468-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Accepted: 04/02/2013] [Indexed: 12/13/2022]
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30
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Fábián Á, Vereb G, Szöllősi J. The hitchhikers guide to cancer stem cell theory: Markers, pathways and therapy. Cytometry A 2012; 83:62-71. [DOI: 10.1002/cyto.a.22206] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2012] [Revised: 08/22/2012] [Accepted: 08/23/2012] [Indexed: 12/25/2022]
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