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Dhawan A, Kohandel M, Hill R, Sivaloganathan S. Tumour control probability in cancer stem cells hypothesis. PLoS One 2014; 9:e96093. [PMID: 24811314 PMCID: PMC4014481 DOI: 10.1371/journal.pone.0096093] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2013] [Accepted: 04/02/2014] [Indexed: 12/02/2022] Open
Abstract
The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCPS as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer or CD133 for glioma, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCPCD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations parameterized for the case of gliomas, to compare the theoretical TCPS and the measurable TCPCD+. We also use the measurable TCP to compare the effect of various radiation protocols.
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Affiliation(s)
- Andrew Dhawan
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- School of Medicine, Queen's University, Kingston, Ontario, Canada
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada
- * E-mail:
| | - Richard Hill
- Department of Medical Biophysics, Princess Margaret Hospital, Ontario Cancer Institute, University of Toronto, Toronto, Ontario, Canada
| | - Sivabal Sivaloganathan
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada
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Belmonte-Beitia J, Woolley T, Scott J, Maini P, Gaffney E. Modelling biological invasions: Individual to population scales at interfaces. J Theor Biol 2013; 334:1-12. [DOI: 10.1016/j.jtbi.2013.05.033] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2012] [Revised: 05/24/2013] [Accepted: 05/28/2013] [Indexed: 11/27/2022]
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Powathil GG, Adamson DJA, Chaplain MAJ. Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: clinical insights from a computational model. PLoS Comput Biol 2013; 9:e1003120. [PMID: 23874170 PMCID: PMC3708873 DOI: 10.1371/journal.pcbi.1003120] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2012] [Accepted: 05/13/2013] [Indexed: 11/24/2022] Open
Abstract
In this paper we use a hybrid multiscale mathematical model that incorporates both individual cell behaviour through the cell-cycle and the effects of the changing microenvironment through oxygen dynamics to study the multiple effects of radiation therapy. The oxygenation status of the cells is considered as one of the important prognostic markers for determining radiation therapy, as hypoxic cells are less radiosensitive. Another factor that critically affects radiation sensitivity is cell-cycle regulation. The effects of radiation therapy are included in the model using a modified linear quadratic model for the radiation damage, incorporating the effects of hypoxia and cell-cycle in determining the cell-cycle phase-specific radiosensitivity. Furthermore, after irradiation, an individual cell's cell-cycle dynamics are intrinsically modified through the activation of pathways responsible for repair mechanisms, often resulting in a delay/arrest in the cell-cycle. The model is then used to study various combinations of multiple doses of cell-cycle dependent chemotherapies and radiation therapy, as radiation may work better by the partial synchronisation of cells in the most radiosensitive phase of the cell-cycle. Moreover, using this multi-scale model, we investigate the optimum sequencing and scheduling of these multi-modality treatments, and the impact of internal and external heterogeneity on the spatio-temporal patterning of the distribution of tumour cells and their response to different treatment schedules. Anti-cancer treatments such as radiotherapy and chemotherapy have evolved through clinical trial-and-error over decades, and although they cure some cases and are partially effective in many, the majority of such cancers ultimately recur. Doctors turn to new, expensive drugs as they emerge, but perhaps fail to study and learn how to use the therapies they already have most effectively. This is partly because clinical trials are expensive to conduct, both in terms of time and money. The cancer cell is complicated, but many mechanisms that control its response to treatment are now understood. We show here how a mathematical model accurately reproduces the results of previous biological experiments of cancer treatment, opening up the possibility of using it to predict which combinations of drugs and radiotherapy would be best for patients.
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Affiliation(s)
- Gibin G Powathil
- Division of Mathematics, University of Dundee, Dundee, United Kingdom.
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Johnson D, McKeever S, Stamatakos G, Dionysiou D, Graf N, Sakkalis V, Marias K, Wang Z, Deisboeck TS. Dealing with diversity in computational cancer modeling. Cancer Inform 2013; 12:115-24. [PMID: 23700360 PMCID: PMC3653811 DOI: 10.4137/cin.s11583] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
This paper discusses the need for interconnecting computational cancer models from different sources and scales within clinically relevant scenarios to increase the accuracy of the models and speed up their clinical adaptation, validation, and eventual translation. We briefly review current interoperability efforts drawing upon our experiences with the development of in silico models for predictive oncology within a number of European Commission Virtual Physiological Human initiative projects on cancer. A clinically relevant scenario, addressing brain tumor modeling that illustrates the need for coupling models from different sources and levels of complexity, is described. General approaches to enabling interoperability using XML-based markup languages for biological modeling are reviewed, concluding with a discussion on efforts towards developing cancer-specific XML markup to couple multiple component models for predictive in silico oncology.
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Affiliation(s)
- David Johnson
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Steve McKeever
- Department of Informatics and Media, Uppsala University, Uppsala, Sweden
| | - Georgios Stamatakos
- Institute of Communication and Computer Systems, National Technical University of Athens, Athens, Greece
| | - Dimitra Dionysiou
- Institute of Communication and Computer Systems, National Technical University of Athens, Athens, Greece
| | - Norbert Graf
- Department of Paediatric Haematology and Oncology, Saarland University Hospital, Homburg, Germany
| | - Vangelis Sakkalis
- Institute of Computer Science at the Foundation for Research and Technology—Hellas, Heraklion, Crete, Greece
| | - Konstantinos Marias
- Institute of Computer Science at the Foundation for Research and Technology—Hellas, Heraklion, Crete, Greece
| | - Zhihui Wang
- Department of Pathology, University of New Mexico, Albuquerque, NM, USA
| | - Thomas S. Deisboeck
- Harvard-MIT (HST), Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, USA
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Wang CH, Rockhill JK, Mrugala M, Peacock DL, Lai A, Jusenius K, Wardlaw JM, Cloughesy T, Spence AM, Rockne R, Alvord EC, Swanson KR. Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. Cancer Res 2009; 69:9133-40. [PMID: 19934335 PMCID: PMC3467150 DOI: 10.1158/0008-5472.can-08-3863] [Citation(s) in RCA: 135] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Glioblastomas are the most aggressive primary brain tumors, characterized by their rapid proliferation and diffuse infiltration of the brain tissue. Survival patterns in patients with glioblastoma have been associated with a number of clinicopathologic factors including age and neurologic status, yet a significant quantitative link to in vivo growth kinetics of each glioma has remained elusive. Exploiting a recently developed tool for quantifying glioma net proliferation and invasion rates in individual patients using routinely available magnetic resonance images (MRI), we propose to link these patient-specific kinetic rates of biological aggressiveness to prognostic significance. Using our biologically based mathematical model for glioma growth and invasion, examination of serial pretreatment MRIs of 32 glioblastoma patients allowed quantification of these rates for each patient's tumor. Survival analyses revealed that even when controlling for standard clinical parameters (e.g., age and Karnofsky performance status), these model-defined parameters quantifying biological aggressiveness (net proliferation and invasion rates) were significantly associated with prognosis. One hypothesis generated was that the ratio of the actual survival time after whatever therapies were used to the duration of survival predicted (by the model) without any therapy would provide a therapeutic response index (TRI) of the overall effectiveness of the therapies. The TRI may provide important information, not otherwise available, about the effectiveness of the treatments in individual patients. To our knowledge, this is the first report indicating that dynamic insight from routinely obtained pretreatment imaging may be quantitatively useful in characterizing the survival of individual patients with glioblastoma. Such a hybrid tool bridging mathematical modeling and clinical imaging may allow for stratifying patients for clinical studies relative to their pretreatment biological aggressiveness.
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Affiliation(s)
| | - Jason K. Rockhill
- Department of Radiation Oncology, University of Washington, Seattle, WA, USA
| | - Maciej Mrugala
- Department of Neurology, University of Washington, Seattle, WA, USA
| | | | - Albert Lai
- Department of Neurology, University of California, Los Angeles, CA, USA
| | - Katy Jusenius
- Department of Radiation Oncology, University of Washington, Seattle, WA, USA
| | - Joanna M. Wardlaw
- Department of Clinical Neurosciences, Western General Hospital, University of Edinburgh, Edinburgh, Scotland, UK
| | - Timothy Cloughesy
- Department of Neurology, University of California, Los Angeles, CA, USA
| | | | - Russ Rockne
- Department of Pathology, University of Washington, Seattle, WA, USA
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