Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation

  • Jake C. Forster
    SA Medical Imaging, Department of Nuclear Medicine, The Queen Elizabeth Hospital, Woodville South, SA 5011, Australia

    Department of Physics, University of Adelaide, North Terrace, Adelaide SA 5005, Australia
    Search for articles by this author
  • Loredana G. Marcu
    Corresponding author at: Faculty of Science, University of Oradea, 410087, Romania.
    Faculty of Science, University of Oradea, Oradea 410087, Romania

    Cancer Research Institute and School of Health Sciences, University of South Australia, Adelaide SA 5001, Australia
    Search for articles by this author
  • Eva Bezak
    Department of Physics, University of Adelaide, North Terrace, Adelaide SA 5005, Australia

    Cancer Research Institute and School of Health Sciences, University of South Australia, Adelaide SA 5001, Australia
    Search for articles by this author


      • Despite advances in knowledge, tumour hypoxia remains a challenge in radiotherapy.
      • Several hypoxia-targeting methods exists, all with their advantages and drawbacks.
      • In silico models are complementary tools offering novel solutions to manage hypoxia.
      • The paper reviews the current landscape of hypoxia models and response to therapy.
      • Future models must consider connected vascular networks to simulate agent delivery.



      The negative impact of tumour hypoxia on cancer treatment outcome has been long-known, yet there has been little success combating it. This paper investigates the potential role of in silico modelling to help test emerging hypoxia-targeting treatments in cancer therapy.


      A Medline search was undertaken on the current landscape of in silico models that simulate cancer therapy and evaluate their ability to test hypoxia-targeting treatments. Techniques and treatments to combat tumour hypoxia and their current challenges are also presented.


      Hypoxia-targeting treatments include tumour reoxygenation, hypoxic cell radiosensitization with nitroimidazoles, hypoxia-activated prodrugs and molecular targeting. Their main challenges are toxicity and not achieving adequate delivery to hypoxic regions of the tumour. There is promising research toward combining two or more of these techniques. Different types of in silico therapy models have been developed ranging from temporal to spatial and from stochastic to deterministic models. Numerous models have compared the effectiveness of different radiotherapy fractionation schedules for controlling hypoxic tumours. Similarly, models could help identify and optimize new treatments for overcoming hypoxia that utilize novel hypoxia-targeting technology.


      Current therapy models should attempt to incorporate more sophisticated modelling of tumour angiogenesis/vasculature and vessel perfusion in order to become more useful for testing hypoxia-targeting treatments, which typically rely upon the tumour vasculature for delivery of additional oxygen, (pro)drugs and nanoparticles.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Physica Medica: European Journal of Medical Physics
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Schwartz G.
        Uber Desensibiliserung gegen Röntgen- und Radiumstrahlen.
        Munchener Medizinische Wochenschrift. 1909; 24: 1-2
        • Horsman M.R.
        • Overgaard J.
        The impact of hypoxia and its modification of the outcome of radiotherapy.
        J Radiat Res. 2016; 57: i90-i98
        • Folkman J.
        Tumor angiogenesis.
        Adv Cancer Res. 1985; 43: 175-203
        • Forster J.C.
        • Harriss-Phillips W.M.
        • Douglass M.J.
        • Bezak E.
        A review of the development of tumor vasculature and its effects on the tumor microenvironment.
        Hypoxia (Auckl). 2017; 5: 21-32
        • Jain R.K.
        Molecular regulation of vessel maturation.
        Nat Med. 2003; 9: 685-693
        • Clavo B.
        • Robaina F.
        • Fiuza D.
        • Ruiz A.
        • Lloret M.
        • Rey-Baltar D.
        • et al.
        Predictive value of hypoxia in advanced head and neck cancer after treatment with hyperfractionated radio-chemotherapy and hypoxia modification.
        Clin Transl Oncol. 2017; 19: 419-424
        • Nordsmark M.
        • Bentzen S.M.
        • Rudat V.
        • Brizel D.
        • Lartigau E.
        • Stadler P.
        • et al.
        Prognostic value of tumor oxygenation in 397 head and neck tumors after primary radiation therapy. An international multi-center study.
        Radiother Oncol. 2005; 77: 18-24
        • Nordsmark M.
        • Overgaard M.
        • Overgaard J.
        Pretreatment oxygenation predicts radiation response in advanced squamous cell carcinoma of the head and neck.
        Radiother Oncol. 1996; 41: 31-39
        • Marcu L.G.
        • Moghaddasi L.
        • Bezak E.
        Imaging of tumor characteristics and molecular pathways with PET: developments over the last decade toward personalized cancer therapy.
        Int J Radiat Oncol Biol Phys. 2018; 102: 1165-1182
        • Overgaard J.
        • Eriksen J.G.
        • Nordsmark M.
        • Alsner J.
        • Horsman M.R.
        • Danish H.
        • et al.
        Plasma osteopontin, hypoxia, and response to the hypoxia sensitiser nimorazole in radiotherapy of head and neck cancer: results from the DAHANCA 5 randomised double-blind placebo-controlled trial.
        Lancet Oncol. 2005; 6: 757-764
        • Overgaard J.
        • Hansen H.S.
        • Overgaard M.
        • Bastholt L.
        • Berthelsen A.
        • Specht L.
        • et al.
        A randomized double-blind phase III study of nimorazole as a hypoxic radiosensitizer of primary radiotherapy in supraglottic larynx and pharynx carcinoma. Results of the Danish Head and Neck Cancer Study (DAHANCA) Protocol 5–85.
        Radiother Oncol. 1998; 46: 135-146
        • Withers H.R.T.
        The 4 R’s of radiotherapy.
        in: Alder J.T.L.a.H. Advances in Radiation Biology. Academic Press, New York1975: 241-271
        • Mendenhall W.M.
        • Morris C.G.
        • Amdur R.J.
        • Mendenhall N.P.
        • Siemann D.W.
        Radiotherapy alone or combined with carbogen breathing for squamous cell carcinoma of the head and neck: a prospective, randomized trial.
        Cancer. 2005; 104: 332-337
        • Sealy R.
        Hyperbaric oxygen in the radiation treatment of head and neck cancers.
        Radiother Oncol. 1991; 20: 75-79
        • Castro C.I.
        • Briceno J.C.
        Perfluorocarbon-based oxygen carriers: review of products and trials.
        Artif Organs. 2010; 34: 622-634
        • Feldman L.A.
        • Fabre M.S.
        • Grasso C.
        • Reid D.
        • Broaddus W.C.
        • Lanza G.M.
        • et al.
        Perfluorocarbon emulsions radiosensitise brain tumors in carbogen breathing mice with orthotopic GL261 gliomas.
        PLoS ONE. 2017; 12e0184250
        • Li J.
        • Shang W.
        • Li Y.
        • Fu S.
        • Tian J.
        • Lu L.
        Advanced nanomaterials targeting hypoxia to enhance radiotherapy.
        Int J Nanomedicine. 2018; 13: 5925-5936
        • Alam F.
        • Yadav N.
        • Ahmad M.
        • Shadan M.
        Blood substitutes: possibilities with nanotechnology.
        Indian J Hematol Blood Transfus. 2014; 30: 155-162
        • Pittman R.N.
        Tissue Gas Transport.
        in: Pittman R.N. Regulation of Tissue Oxygenation. 1 ed. Morgan & Claypool Life Sciences, San Rafael2011
        • Song X.
        • Feng L.
        • Liang C.
        • Yang K.
        • Liu Z.
        Ultrasound triggered tumor oxygenation with oxygen-shuttle nanoperfluorocarbon to overcome hypoxia-associated resistance in cancer therapies.
        Nano Lett. 2016; 16: 6145-6153
        • Martin D.F.
        • Porter E.A.
        • Rockwell S.
        • Fischer J.J.
        Enhancement of tumor radiation response by the combination of a perfluorochemical emulsion and hyperbaric oxygen.
        Int J Radiat Oncol Biol Phys. 1987; 13: 747-751
        • Rockwell S.
        • Irvin C.G.
        • Kelley M.
        • Hughes C.S.
        • Yabuki H.
        • Porter E.
        • et al.
        Effects of hyperbaric oxygen and a perfluorooctylbromide emulsion on the radiation responses of tumors and normal tissues in rodents.
        Int J Radiat Oncol Biol Phys. 1992; 22: 87-93
        • Gao M.
        • Liang C.
        • Song X.
        • Chen Q.
        • Jin Q.
        • Wang C.
        • et al.
        Erythrocyte-membrane-enveloped perfluorocarbon as nanoscale artificial red blood cells to relieve tumor hypoxia and enhance cancer radiotherapy.
        Adv Mater. 2017; 29
        • Kwan J.J.
        • Kaya M.
        • Borden M.A.
        • Dayton P.A.
        Theranostic oxygen delivery using ultrasound and microbubbles.
        Theranostics. 2012; 2: 1174-1184
        • Song G.
        • Ji C.
        • Liang C.
        • Song X.
        • Yi X.
        • Dong Z.
        • et al.
        TaOx decorated perfluorocarbon nanodroplets as oxygen reservoirs to overcome tumor hypoxia and enhance cancer radiotherapy.
        Biomaterials. 2017; 112: 257-263
        • Song G.
        • Liang C.
        • Yi X.
        • Zhao Q.
        • Cheng L.
        • Yang K.
        • et al.
        Perfluorocarbon-loaded hollow Bi2Se3 nanoparticles for timely supply of oxygen under near-infrared light to enhance the radiotherapy of cancer.
        Adv Mater. 2016; 28: 2716-2723
        • Aldea M.
        • Florian I.A.
        • Kacso G.
        • Craciun L.
        • Boca S.
        • Soritau O.
        • et al.
        Nanoparticles for targeting intratumoral hypoxia: exploiting a potential weakness of glioblastoma.
        Pharm Res. 2016; 33: 2059-2077
        • Rey S.
        • Schito L.
        • Koritzinsky M.
        • Wouters B.G.
        Molecular targeting of hypoxia in radiotherapy.
        Adv Drug Deliv Rev. 2017; 109: 45-62
        • Secomb T.W.
        • Hsu R.
        • Ong E.T.
        • Gross J.F.
        • Dewhirst M.W.
        Analysis of the effects of oxygen supply and demand on hypoxic fraction in tumors.
        Acta Oncol. 1995; 34: 313-316
        • Wardman P.
        Chemical radiosensitizers for use in radiotherapy.
        Clin Oncol (R Coll Radiol). 2007; 19: 397-417
        • Wilson W.R.
        • Hay M.P.
        Targeting hypoxia in cancer therapy.
        Nat Rev Cancer. 2011; 11: 393-410
        • Wardman P.
        Nitroimidazoles as hypoxic cell radiosensitizers and hypoxia probes: misonidazole, myths and mistakes.
        Br J Radiol. 2018; (20170915)
        • Wardman P.
        The importance of radiation chemistry to radiation and free radical biology (The 2008 Silvanus Thompson Memorial Lecture).
        Br J Radiol. 2009; 82: 89-104
        • Wardman P.
        Time as a variable in radiation biology: the oxygen effect.
        Radiat Res. 2016; 185: 1-3
        • Overgaard J.
        • Horsman M.R.
        Modification of hypoxia-induced radioresistance in tumors by the use of oxygen and sensitizers.
        Semin Radiat Oncol. 1996; 6: 10-21
        • Thomson D.
        • Yang H.
        • Baines H.
        • Miles E.
        • Bolton S.
        • West C.
        • et al.
        NIMRAD – a phase III trial to investigate the use of nimorazole hypoxia modification with intensity-modulated radiotherapy in head and neck cancer.
        Clin Oncol (R Coll Radiol). 2014; 26: 344-347
        • Mistry I.N.
        • Thomas M.
        • Calder E.D.D.
        • Conway S.J.
        • Hammond E.M.
        Clinical advances of hypoxia-activated prodrugs in combination with radiation therapy.
        Int J Radiat Oncol Biol Phys. 2017; 98: 1183-1196
        • Dobrowsky W.
        • Huigol N.G.
        • Jayatilake R.S.
        • Kizilbash N.I.
        • Okkan S.
        • Kagiya V.T.
        • et al.
        AK-2123 (Sanazol) as a radiation sensitizer in the treatment of stage III cervical cancer: results of an IAEA multicentre randomised trial.
        Radiother Oncol. 2007; 82: 24-29
        • Wang Y.
        • Xie Y.
        • Li J.
        • Peng Z.H.
        • Sheinin Y.
        • Zhou J.
        • et al.
        Tumor-penetrating nanoparticles for enhanced anticancer activity of combined photodynamic and hypoxia-activated therapy.
        ACS Nano. 2017; 11: 2227-2238
        • Park K.
        Facing the truth about nanotechnology in drug delivery.
        ACS Nano. 2013; 7: 7442-7447
        • Wang Y.F.
        • Liu L.
        • Xue X.
        • Liang X.J.
        Nanoparticle-based drug delivery systems: what can they really do in vivo?.
        F1000Res. 2017; 6: 681
        • Xu Z.
        • Zhao J.
        • Gou S.
        • Xu G.
        Novel hypoxia-targeting Pt(iv) prodrugs.
        Chem Commun (Camb). 2017; 53: 3749-3752
        • Voss M.H.
        • Hussain A.
        • Vogelzang N.
        • Lee J.L.
        • Keam B.
        • Rha S.Y.
        • et al.
        A randomized phase II trial of CRLX101 in combination with bevacizumab versus standard of care in patients with advanced renal cell carcinoma.
        Ann Oncol. 2017; 28: 2754-2760
        • Huo D.
        • Liu S.
        • Zhang C.
        • He J.
        • Zhou Z.
        • Zhang H.
        • et al.
        Hypoxia-targeting, tumor microenvironment responsive nanocluster bomb for radical-enhanced radiotherapy.
        ACS Nano. 2017; 11: 10159-10174
        • Dewhirst M.W.
        • Lee C.T.
        • Ashcraft K.A.
        The future of biology in driving the field of hyperthermia.
        Int J Hyperthermia. 2016; 32: 4-13
        • Gao S.
        • Zheng M.
        • Ren X.
        • Tang Y.
        • Liang X.
        Local hyperthermia in head and neck cancer: mechanism, application and advance.
        Oncotarget. 2016; 7: 57367-57378
        • Elming P.B.
        • Sorensen B.S.
        • Oei A.L.
        • Franken N.A.P.
        • Crezee J.
        • Overgaard J.
        • et al.
        Hyperthermia: the optimal treatment to overcome radiation resistant hypoxia.
        Cancers (Basel). 2019; 11
        • Gerweck L.E.
        • Nygaard T.G.
        • Burlett M.
        Response of cells to hyperthermia under acute and chronic hypoxic conditions.
        Cancer Res. 1979; 39: 966-972
        • Sen A.
        • Capitano M.L.
        • Spernyak J.A.
        • Schueckler J.T.
        • Thomas S.
        • Singh A.K.
        • et al.
        Mild elevation of body temperature reduces tumor interstitial fluid pressure and hypoxia and enhances efficacy of radiotherapy in murine tumor models.
        Cancer Res. 2011; 71: 3872-3880
        • Xu Y.
        • Choi J.
        • Hylander B.
        • Sen A.
        • Evans S.S.
        • Kraybill W.G.
        • et al.
        Fever-range whole body hyperthermia increases the number of perfused tumor blood vessels and therapeutic efficacy of liposomally encapsulated doxorubicin.
        Int J Hyperthermia. 2007; 23: 513-527
        • Forster J.C.
        • Douglass M.J.J.
        • Phillips W.M.
        • Bezak E.
        Monte Carlo simulation of the oxygen effect in DNA damage induction by ionizing radiation.
        Radiat Res. 2018; 190: 248-261
        • Chen W.
        • Wang Y.
        • Qin M.
        • Zhang X.
        • Zhang Z.
        • Sun X.
        • et al.
        Bacteria-driven hypoxia targeting for combined biotherapy and photothermal therapy.
        ACS Nano. 2018;
        • Huang W.C.
        • Chiang W.H.
        • Cheng Y.H.
        • Lin W.C.
        • Yu C.F.
        • Yen C.Y.
        • et al.
        Tumortropic monocyte-mediated delivery of echogenic polymer bubbles and therapeutic vesicles for chemotherapy of tumor hypoxia.
        Biomaterials. 2015; 71: 71-83
        • Jiang P.S.
        • Yu C.F.
        • Yen C.Y.
        • Woo C.W.
        • Lo S.H.
        • Huang Y.K.
        • et al.
        Irradiation enhances the ability of monocytes as nanoparticle carrier for cancer therapy.
        PLoS ONE. 2015; 10e0139043
        • Antosh M.P.
        • Wijesinghe D.D.
        • Shrestha S.
        • Lanou R.
        • Huang Y.H.
        • Hasselbacher T.
        • et al.
        Enhancement of radiation effect on cancer cells by gold-pHLIP.
        Proc Natl Acad Sci U S A. 2015; 112: 5372-5376
        • Fan W.
        • Bu W.
        • Zhang Z.
        • Shen B.
        • Zhang H.
        • He Q.
        • et al.
        X-ray radiation-controlled NO-release for on-demand depth-independent hypoxic radiosensitization.
        Angew Chem Int Ed Engl. 2015; 54: 14026-14030
        • Harriss-Phillips W.M.
        • Bezak E.
        • Potter A.
        Stochastic predictions of cell kill during stereotactic ablative radiation therapy: do hypoxia and reoxygenation really matter?.
        Int J Radiat Oncol Biol Phys. 2016; 95: 1290-1297
        • Harriss-Phillips W.M.
        • Bezak E.
        • Yeoh E.K.
        Monte Carlo radiotherapy simulations of accelerated repopulation and reoxygenation for hypoxic head and neck cancer.
        Br J Radiol. 2011; 84: 903-918
        • Harriss-Phillips W.M.
        • Bezak E.
        • Yeoh E.K.
        Altered fractionation outcomes for hypoxic head and neck cancer using the HYP-RT Monte Carlo model.
        Br J Radiol. 2013; 86: 20120443
        • Tuckwell W.
        • Bezak E.
        • Yeoh E.
        • Marcu L.
        Efficient Monte Carlo modelling of individual tumour cell propagation for hypoxic head and neck cancer.
        Phys Med Biol. 2008; 53: 4489-4507
        • Marcu L.G.
        • Marcu D.
        In silico modelling of a cancer stem cell-targeting agent and its effects on tumour control during radiotherapy.
        Sci Rep. 2016; 6: 32332
        • Marcu L.G.
        • Marcu D.
        The effect of targeted therapy on recruited cancer stem cells in a head and neck carcinoma model.
        Cell Prolif. 2017; 50
        • Marcu L.G.
        • Marcu D.
        • Filip S.M.
        In silico study of the impact of cancer stem cell dynamics and radiobiological hypoxia on tumour response to hyperfractionated radiotherapy.
        Cell Prolif. 2016; 49: 304-314
        • Garau M.M.I.
        Radiobiology of stereotactic body radiation therapy (SBRT).
        Rep Pract Oncol Radi. 2017; 22: 86-95
        • Kelada O.J.
        • Decker R.H.
        • Nath S.K.
        • Johung K.L.
        • Zheng M.Q.
        • Huang Y.
        • et al.
        High single doses of radiation may induce elevated levels of hypoxia in early-stage non-small cell lung cancer tumors.
        Int J Radiat Oncol Biol Phys. 2018; 102: 174-183
        • Dasu A.
        • Toma-Dasu I.
        Theoretical simulation of tumour oxygenation–practical applications.
        Adv Exp Med Biol. 2006; 578: 357-362
        • Dasu A.
        • Toma-Dasu I.
        Vascular oxygen content and the tissue oxygenation–a theoretical analysis.
        Med Phys. 2008; 35: 539-545
        • Dasu A.
        • Toma-Dasu I.
        The relationship between vascular oxygen distribution and tissue oxygenation.
        Adv Exp Med Biol. 2009; 645: 255-260
        • Dasu A.
        • Toma-Dasu I.
        • Karlsson M.
        Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia.
        Phys Med Biol. 2003; 48: 2829-2842
        • Dasu A.
        • Toma-Dasu I.
        • Karlsson M.
        The effects of hypoxia on the theoretical modelling of tumour control probability.
        Acta Oncol. 2005; 44: 563-571
        • Toma-Dasu I.
        • Dasu A.
        • Brahme A.
        Dose prescription and optimisation based on tumour hypoxia.
        Acta Oncol. 2009; 48: 1181-1192
        • Antonovic L.
        • Lindblom E.
        • Dasu A.
        • Bassler N.
        • Furusawa Y.
        • Toma-Dasu I.
        Clinical oxygen enhancement ratio of tumors in carbon ion radiotherapy: the influence of local oxygenation changes.
        J Radiat Res. 2014; 55: 902-911
        • Lindblom E.
        • Dasu A.
        • Beskow C.
        • Toma-Dasu I.
        High brachytherapy doses can counteract hypoxia in cervical cancer-a modelling study.
        Phys Med Biol. 2017; 62: 560-572
        • Lindblom E.
        • Dasu A.
        • Toma-Dasu I.
        Optimal fractionation in radiotherapy for non-small cell lung cancer–a modelling approach.
        Acta Oncol. 2015; 54: 1592-1598
        • Lindblom E.
        • Toma-Dasu I.
        • Dasu A.
        Accounting for two forms of hypoxia for predicting tumour control probability in radiotherapy: an in silico study.
        Adv Exp Med Biol. 2018; 1072: 183-187
        • Toma-Dasu I.
        • Sandstrom H.
        • Barsoum P.
        • Dasu A.
        To fractionate or not to fractionate? That is the question for the radiosurgery of hypoxic tumors.
        J Neurosurg. 2014; 121: 110-115
        • Lindblom E.
        • Antonovic L.
        • Dasu A.
        • Lax I.
        • Wersall P.
        • Toma-Dasu I.
        Treatment fractionation for stereotactic radiotherapy of lung tumours: a modelling study of the influence of chronic and acute hypoxia on tumour control probability.
        Radiat Oncol. 2014; 9: 149
        • Antonovic L.
        • Dasu A.
        • Furusawa Y.
        • Toma-Dasu I.
        Relative clinical effectiveness of carbon ion radiotherapy: theoretical modelling for H&N tumours.
        J Radiat Res. 2015; 56: 639-645
        • Kocher M.
        • Treuer H.
        Reoxygenation of hypoxic cells by tumor shrinkage during irradiation. A computer simulation.
        Strahlentherapie und Onkologie: Organ der Deutschen Rontgengesellschaft [et al]. 1995; 171: 219-230
        • Kocher M.
        • Treuer H.
        • Muller R.P.
        Quantification of tumor reoxygenation during accelerated radiation therapy.
        Radiology. 1997; 205: 263-268
        • Kocher M.
        • Treuer H.
        • Voges J.
        • Hoevels M.
        • Sturm V.
        • Muller R.P.
        Computer simulation of cytotoxic and vascular effects of radiosurgery in solid and necrotic brain metastases.
        Radiother Oncol. 2000; 54: 149-156
        • Harting C.
        • Peschke P.
        • Borkenstein K.
        • Karger C.P.
        Single-cell-based computer simulation of the oxygen-dependent tumour response to irradiation.
        Phys Med Biol. 2007; 52: 4775-4789
        • Harting C.
        • Peschke P.
        • Karger C.P.
        Computer simulation of tumour control probabilities after irradiation for varying intrinsic radio-sensitivity using a single cell based model.
        Acta Oncol. 2010; 49: 1354-1362
        • Borkenstein K.
        • Levegrun S.
        • Peschke P.
        Modeling and computer simulations of tumor growth and tumor response to radiotherapy.
        Radiat Res. 2004; 162: 71-83
        • Kempf H.
        • Bleicher M.
        • Meyer-Hermann M.
        Spatio-Temporal Dynamics of Hypoxia during Radiotherapy.
        PLoS ONE. 2015; 10e0133357
        • Hamis S.
        • Nithiarasu P.
        • Powathil G.G.
        What does not kill a tumour may make it stronger: Iin silico insights into chemotherapeutic drug resistance.
        J Theor Biol. 2018; 454: 253-267
        • Powathil G.G.
        • Adamson D.J.
        • Chaplain M.A.
        Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: clinical insights from a computational model.
        PLoS Comput Biol. 2013; 9e1003120
        • Powathil G.G.
        • Gordon K.E.
        • Hill L.A.
        • Chaplain M.A.
        Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model.
        J Theor Biol. 2012; 308: 1-19
        • Powathil G.G.
        • Munro A.J.
        • Chaplain M.A.
        • Swat M.
        Bystander effects and their implications for clinical radiation therapy: Insights from multiscale in silico experiments.
        J Theor Biol. 2016; 401: 1-14
        • Paul-Gilloteaux P.
        • Potiron V.
        • Delpon G.
        • Supiot S.
        • Chiavassa S.
        • Paris F.
        • et al.
        Optimizing radiotherapy protocols using computer automata to model tumour cell death as a function of oxygen diffusion processes.
        Sci Rep. 2017; 7: 2280
        • Kolokotroni E.
        • Dionysiou D.
        • Veith C.
        • Kim Y.J.
        • Sabczynski J.
        • Franz A.
        • et al.
        In silico oncology: quantification of the in vivo antitumor efficacy of cisplatin-based doublet therapy in Non-Small Cell Lung Cancer (NSCLC) through a multiscale mechanistic model.
        PLoS Comput Biol. 2016; 12e1005093
        • Kolokotroni E.A.
        • Dionysiou D.D.
        • Uzunoglu N.K.
        • Stamatakos G.S.
        Studying the growth kinetics of untreated clinical tumors by using an advanced discrete simulation model.
        Math Comput Modell. 2011; 54: 1989-2006
        • Stamatakos G.S.
        • Kolokotroni E.A.
        • Dionysiou D.D.
        • Georgiadi E.
        • Desmedt C.
        An advanced discrete state-discrete event multiscale simulation model of the response of a solid tumor to chemotherapy: mimicking a clinical study.
        J Theor Biol. 2010; 266: 124-139
        • Kyroudis C.A.
        • Dionysiou D.D.
        • Kolokotroni E.A.
        • Stamatakos G.S.
        Studying the regression profiles of cervical tumours during radiotherapy treatment using a patient-specific multiscale model.
        Sci Rep. 2019; 9: 1081
        • Antipas V.P.
        • Stamatakos G.S.
        • Uzunoglu N.K.
        • Dionysiou D.D.
        • Dale R.G.
        A spatio-temporal simulation model of the response of solid tumours to radiotherapy in vivo: parametric validation concerning oxygen enhancement ratio and cell cycle duration.
        Phys Med Biol. 2004; 49: 1485-1504
        • Stamatakos G.
        • Antipas V.P.
        • Ozunoglu N.K.
        A patient-specific in vivo tumor and normal tissue model for prediction of the response to radiotherapy.
        Methods Inf Med. 2007; 46: 367-375
        • Stamatakos G.S.
        • Antipas V.P.
        • Uzunoglu N.K.
        A spatiotemporal, patient individualized simulation model of solid tumor response to chemotherapy in vivo: the paradigm of glioblastoma multiforme treated by temozolomide.
        IEEE Trans Biomed Eng. 2006; 53: 1467-1477
        • Stamatakos G.S.
        • Antipas V.P.
        • Uzunoglu N.K.
        Simulating chemotherapeutic schemes in the individualized treatment context: the paradigm of glioblastoma multiforme treated by temozolomide in vivo.
        Comput Biol Med. 2006; 36: 1216-1234
        • Espinoza I.
        • Peschke P.
        • Karger C.P.
        A voxel-based multiscale model to simulate the radiation response of hypoxic tumors.
        Med Phys. 2015; 42: 90-102
        • Gago-Arias A.
        • Sanchez-Nieto B.
        • Espinoza I.
        • Karger C.P.
        • Pardo-Montero J.
        Impact of different biologically-adapted radiotherapy strategies on tumor control evaluated with a tumor response model.
        PLoS ONE. 2018; 13e0196310
        • Crispin-Ortuzar M.
        • Jeong J.
        • Fontanella A.N.
        • Deasy J.O.
        A radiobiological model of radiotherapy response and its correlation with prognostic imaging variables.
        Phys Med Biol. 2017; 62: 2658-2674
        • Jeong J.
        • Oh J.H.
        • Sonke J.J.
        • Belderbos J.
        • Bradley J.D.
        • Fontanella A.N.
        • et al.
        Modeling the cellular response of lung cancer to radiation therapy for a broad range of fractionation schedules.
        Clin Cancer Res. 2017; 23: 5469-5479
        • Jeong J.
        • Shoghi K.I.
        • Deasy J.O.
        Modelling the interplay between hypoxia and proliferation in radiotherapy tumour response.
        Phys Med Biol. 2013; 58: 4897-4919
        • Chapman J.D.
        Single-hit mechanism of tumour cell killing by radiation.
        Int J Radiat Biol. 2009; 79: 71-81
        • Nahum A.E.
        • Movsas B.
        • Horwitz E.M.
        • Stobbe C.C.
        • Chapman J.D.
        Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: Implications for the α/β ratio.
        Int J Rad Oncol Biol Phys. 2003; 57: 391-401
        • Carlson D.J.
        • Stewart R.D.
        • Semenenko V.A.
        Effects of oxygen on intrinsic radiation sensitivity: A test of the relationship between aerobic and hypoxic linear-quadratic (LQ) model parameters.
        Med Phys. 2006; 33: 3105-3115
        • Forster J.C.
        • Douglass M.J.
        • Harriss-Phillips W.M.
        • Bezak E.
        Development of an in silico stochastic 4D model of tumor growth with angiogenesis.
        Med Phys. 2017; 44: 1563-1576
        • Forster J.C.
        • Douglass M.J.J.
        • Harriss-Phillips W.M.
        • Bezak E.
        Simulation of head and neck cancer oxygenation and doubling time in a 4D cellular model with angiogenesis.
        Sci Rep. 2017; 7: 11037
        • Carlson D.J.
        • Keall P.J.
        • Loo Jr., B.W.
        • Chen Z.J.
        • Brown J.M.
        Hypofractionation results in reduced tumor cell kill compared to conventional fractionation for tumors with regions of hypoxia.
        Int J Radiat Oncol Biol Phys. 2011; 79: 1188-1195
        • Strigari L.
        • Benassi M.
        • Sarnelli A.
        • Polico R.
        • D'Andrea M.
        A modified hypoxia-based TCP model to investigate the clinical outcome of stereotactic hypofractionated regimes for early stage non-small-cell lung cancer (NSCLC).
        Med Phys. 2012; 39: 4502-4514
        • Chvetsov A.V.
        • Rajendran J.G.
        • Zeng J.
        • Patel S.A.
        • Bowen S.R.
        • Kim E.Y.
        Theoretical effectiveness of cell survival in fractionated radiotherapy with hypoxia-targeted dose escalation.
        Med Phys. 2017; 44: 1975-1982
        • de la Cruz R.
        • Guerrero P.
        • Spill F.
        • Alarcon T.
        Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis.
        J Theor Biol. 2016; 407: 161-183
        • Saberian F.
        • Ghate A.
        • Kim M.
        A theoretical stochastic control framework for adapting radiotherapy to hypoxia.
        Phys Med Biol. 2016; 61: 7136-7161
        • Avanzo M.
        • Stancanello J.
        • Franchin G.
        • Sartor G.
        • Jena R.
        • Drigo A.
        • et al.
        Correlation of a hypoxia based tumor control model with observed local control rates in nasopharyngeal carcinoma treated with chemoradiotherapy.
        Med Phys. 2010; 37: 1533-1544
        • Strigari L.
        • Torriani F.
        • Manganaro L.
        • Inaniwa T.
        • Dalmasso F.
        • Cirio R.
        • et al.
        Tumour control in ion beam radiotherapy with different ions in the presence of hypoxia: an oxygen enhancement ratio model based on the microdosimetric kinetic model.
        Phys Med Biol. 2018; 63065012
        • Russo G.
        • Attili A.
        • Battistoni G.
        • Bertrand D.
        • Bourhaleb F.
        • Cappucci F.
        • et al.
        A novel algorithm for the calculation of physical and biological irradiation quantities in scanned ion beam therapy: the beamlet superposition approach.
        Phys Med Biol. 2016; 61: 183-214
        • Espinoza I.
        • Peschke P.
        • Karger C.P.
        A model to simulate the oxygen distribution in hypoxic tumors for different vascular architectures.
        Med Phys. 2013; 40081703
        • Cai Y.
        • Wu J.
        • Li Z.
        • Long Q.
        Mathematical modelling of a brain tumour initiation and early development: a coupled model of glioblastoma growth, pre-existing vessel co-option, Angiogenesis and Blood Perfusion.
        PLoS One. 2016; 11e0150296
        • Perfahl H.
        • Byrne H.M.
        • Chen T.
        • Estrella V.
        • Alarcon T.
        • Lapin A.
        • et al.
        Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions.
        PLoS ONE. 2011; 6e14790
        • Perfahl H.
        • Hughes B.D.
        • Alarcon T.
        • Maini P.K.
        • Lloyd M.C.
        • Reuss M.
        • et al.
        3D hybrid modelling of vascular network formation.
        J Theor Biol. 2017; 414: 254-268
        • Tang L.
        • van de Ven A.L.
        • Guo D.
        • Andasari V.
        • Cristini V.
        • Li K.C.
        • et al.
        Computational modeling of 3D tumor growth and angiogenesis for chemotherapy evaluation.
        PLoS ONE. 2014; 9e83962
        • Welter M.
        • Rieger H.
        Physical determinants of vascular network remodeling during tumor growth.
        Eur Phys J E Soft Matter. 2010; 33: 149-163
        • Welter M.
        • Rieger H.
        Interstitial fluid flow and drug delivery in vascularized tumors: a computational model.
        PLoS ONE. 2013; 8e70395
        • Zangooei M.H.
        • Habibi J.
        Hybrid multiscale modeling and prediction of cancer cell behavior.
        PLoS ONE. 2017; 12e0183810
        • Cai Y.
        • Zhang J.
        • Li Z.
        Multi-scale mathematical modelling of tumour growth and microenvironments in anti-angiogenic therapy.
        Biomed Eng Online. 2016; 15: 155
        • Bernal M.A.
        • Bordage M.C.
        • Brown J.M.C.
        • Davidkova M.
        • Delage E.
        • El Bitar Z.
        • et al.
        Track structure modeling in liquid water: a review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit.
        Phys Med. 2015; 31: 861-874
        • Incerti S.
        • Baldacchino G.
        • Bernal M.
        • Capra R.
        • Champion C.
        • Francis Z.
        • et al.
        The Geant4-DNA project.
        Int J Model Simul Sci Comput. 2010; 01: 157-178
        • Incerti S.
        • Ivanchenko A.
        • Karamitros M.
        • Mantero A.
        • Moretto P.
        • Tran H.N.
        • et al.
        Comparison of GEANT4 very low energy cross section models with experimental data in water.
        Med Phys. 2010; 37: 4692-4708
        • Friedland W.
        • Schmitt E.
        • Kundrat P.
        • Baiocco G.
        • Ottolenghi A.
        Track-structure simulations of energy deposition patterns to mitochondria and damage to their DNA.
        Int J Radiat Biol. 2018; 1–9
        • Friedland W.
        • Schmitt E.
        • Kundrat P.
        • Dingfelder M.
        • Baiocco G.
        • Barbieri S.
        • et al.
        Comprehensive track-structure based evaluation of DNA damage by light ions from radiotherapy-relevant energies down to stopping.
        Sci Rep. 2017; 7: 45161
        • Kreipl M.S.
        • Friedland W.
        • Paretzke H.G.
        Time- and space-resolved Monte Carlo study of water radiolysis for photon, electron and ion irradiation.
        Radiat Environ Biophys. 2009; 48: 11-20
        • Friedland W.
        • Dingfelder M.
        • Kundrat P.
        • Jacob P.
        Track structures, DNA targets and radiation effects in the biophysical Monte Carlo simulation code PARTRAC.
        Mutat Res. 2011; 711: 28-40
        • Plante I.
        • Cucinotta F.A.
        Simulation of the radiolysis of water using Green's functions of the diffusion equation.
        Radiat Prot Dosim. 2015; 166: 24-28
        • Plante I.
        • Devroye L.
        Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations.
        Radiat Phys Chem. 2017; 139: 157-172
        • Nikjoo H.
        • Emfietzoglou D.
        • Liamsuwan T.
        • Taleei R.
        • Liljequist D.
        • Uehara S.
        Radiation track, DNA damage and response-a review. Reports on progress in physics.
        Phys Soc (Great Britain). 2016; 79116601
        • Friedland W.
        • Kundrat P.
        Track structure based modelling of chromosome aberrations after photon and alpha-particle irradiation.
        Mutat Res. 2013; 756: 213-223
        • Friedland W.
        • Kundrat P.
        Chromosome aberration model combining radiation tracks, chromatin structure, DSB repair and chromatin mobility.
        Radiat Prot Dosim. 2015; 166: 71-74
        • Henthorn N.T.
        • Warmenhoven J.W.
        • Sotiropoulos M.
        • Mackay R.I.
        • Kirkby N.F.
        • Kirkby K.J.
        • et al.
        In silico non-homologous end joining following ion induced DNA double strand breaks predicts that repair fidelity depends on break density.
        Sci Rep. 2018; 8: 2654
        • Zhang Y.
        • Feng Y.
        • Wang W.
        • Yang C.
        • Wang P.
        An expanded multi-scale Monte Carlo simulation method for personalized radiobiological effect estimation in radiotherapy: a feasibility study.
        Sci Rep. 2017; 7: 45019