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      Estimating Dose Painting Effects in Radiotherapy: A Mathematical Model

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          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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          A restricted cell population propagates glioblastoma growth following chemotherapy

          Glioblastoma multiforme (GBM) is the most common primary malignant brain tumor, with a median survival of about one year 1 . This poor prognosis is due to therapeutic resistance and tumor recurrence following surgical removal. Precisely how recurrence occurs is unknown. Using a genetically-engineered mouse model of glioma, we identify a subset of endogenous tumor cells that are the source of new tumor cells after the drug, temozolomide (TMZ), is administered to transiently arrest tumor growth. A Nestin-ΔTK-IRES-GFP (Nes-ΔTK-GFP) transgene that labels quiescent subventricular zone adult neural stem cells also labels a subset of endogenous glioma tumor cells. Upon arrest of tumor cell proliferation with TMZ, pulse-chase experiments demonstrate a tumor re-growth cell hierarchy originating with the Nes-ΔTK-GFP transgene subpopulation. Ablation of the GFP+ cells with chronic ganciclovir administration significantly arrested tumor growth and combined TMZ-ganciclovir treatment impeded tumor development. These data indicate the existence of a relatively quiescent subset of endogenous glioma cells that are responsible for sustaining long-term tumor growth through the production of transient populations of highly proliferative cells.
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            Genetic instabilities in human cancers.

            Whether and how human tumours are genetically unstable has been debated for decades. There is now evidence that most cancers may indeed be genetically unstable, but that the instability exists at two distinct levels. In a small subset of tumours, the instability is observed at the nucleotide level and results in base substitutions or deletions or insertions of a few nucleotides. In most other cancers, the instability is observed at the chromosome level, resulting in losses and gains of whole chromosomes or large portions thereof. Recognition and comparison of these instabilities are leading to new insights into tumour pathogenesis.
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              The linear-quadratic formula and progress in fractionated radiotherapy.

              J. Fowler (1989)
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2014
                26 February 2014
                : 9
                : 2
                : e89380
                Affiliations
                [1 ]Department of Applied Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain
                [2 ]Institut National de Recherche en Informatique et en Automatique (INRIA), Domaine de Voluceau - Rocquencourt, Paris, France
                [3 ]Institute of Computational Biology, Helmholtz Center Munich, German Research Center for Environmental Health, Neuherberg, Germany
                [4 ]Radiophysics Department, Hospital Universitario Puerta de Hierro, Majadahonda, Madrid, Spain
                [5 ]University of Paris 6 (UPMC), CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France
                [6 ]Interdisciplinary Center for Bioinformatics (IZBI), University of Leipzig, Leipzig, Germany
                Fondazione Edmund Mach, Research and Innovation Centre, Italy
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: JCLA LN MAH DD. Performed the experiments: JCLA NJ. Analyzed the data: JCLA LN MAH DD. Contributed reagents/materials/analysis tools: JCLA NJ MAH DD. Wrote the paper: JCLA NJ MAH LN DD. Final approval of the version to be published: JCLA NJ LN MAH DD.

                Article
                PONE-D-13-27961
                10.1371/journal.pone.0089380
                3935877
                24586734
                7ccbc09a-44b7-468f-b321-fbcb5c330489
                Copyright @ 2014

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 6 July 2013
                : 20 January 2014
                Page count
                Pages: 21
                Funding
                Juan Carlos López Alfonso, Luis Núñez, and Miguel A. Herrero have been supported in part by MINECO Grant 2011-22656. Nick Jagiella and Dirk Drasdo gratefully acknowledge support by LUNGSYS II (BMBF), PhysCancer and INVADE (INSERM). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology
                Computational biology
                Molecular cell biology
                Cell division
                Cell growth
                Radiobiology
                Systems biology
                Computer science
                Computer modeling
                Mathematics
                Applied mathematics
                Medicine
                Oncology
                Cancer treatment
                Radiotherapy
                Radiology
                Medical physics

                Uncategorized
                Uncategorized

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