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Model of Tumor Growth and Response to Radiation

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Applications of Electrochemistry in Medicine

Part of the book series: Modern Aspects of Electrochemistry ((MAOE,volume 56))

Abstract

Biological membranes have developed to separate different compartments of organisms and cells. There is a large number of rather different functions which membranes have to fulfil: (1) they control the material and energy fluxes of metabolic processes, (2) they provide a wrapping protecting the compartments from chemical and physical attacks of the environment, (3) they provide interfaces at which specific biochemical machineries can operate (e.g., membrane bound enzymes), (4) they are equipped for signal transduction, (5) they possess the necessary stability and flexibility to allow cell division, and endo- and exocytosis as well as migration, (6) they present anchoring structures that enable cell-to-cell and cell-to-matrix physical interactions and intercellular communication. These are certainly not all functions of membranes as new functionalities are continuously reported. Since the biological membranes separate essentially aqueous solutions, such separating borders—if they should possess a reasonable stability and also flexibility combined with selective permeability—have to be built up of hydrophobic molecules exposing to both sides a similar interface. It was one of the most crucial and most lucky circumstances for the development and existence of life that certain amphiphilic molecules are able to assemble in bilayer structures (membranes), which—on one side—possess a rather high physical and chemical stability, and—on the other side—are able to incorporate foreign molecules for modifying both the physical properties as well as the permeability of the membranes for defined chemical species. The importance of the chemical function of membranes and all its constituents, e.g., ion channels, pore peptides, transport peptides, etc., is generally accepted. The fluid-mosaic model proposed by Singer and Nicolson [1] is still the basis to understand the biological, chemical, and physical properties of biological membranes. The importance of the purely mechanical properties of membranes came much later into the focus of research. The reasons are probably the dominance of biochemical thinking and biochemical models among biologists and medical researchers, as well as a certain lack of appropriate methods to probe mechanical properties of membranes. The last decades have changed that situation due to the development of techniques like the Atomic Force Microscopy, Fluorescence Microscopy, Micropipette Aspiration, Raman Microspectroscopy, advanced Calorimetry, etc. This chapter is aimed at elucidating how the properties of membranes can be investigated by studying the interaction of vesicles with a very hydrophobic surface, i.e., with the surface of a mercury electrode. This interaction is unique as it results in a complete disintegration of the bilayer membrane of the vesicles and the formation of an island of adsorbed lipid molecules, i.e., a monolayer island. This process can be followed by current-time measurements (chronoamperometry), which allow studying the complete disintegration process in all its details: the different steps of that disintegration can be resolved on the time scale and the activation parameters can be determined. Most interestingly, the kinetics of vesicle disintegration on mercury share important features with the process of vesicle fusion and, thus, sheds light also on mechanisms of endocytosis and exocytosis. Most importantly, not only artificial vesicles (liposomes) can be studied with this approach, but also reconstituted plasma membrane vesicles and even intact mitochondria. Hence, one can expect that the method may provide in future studies also information on the membrane properties of various other vesicles, including exosomes, and may allow investigating various aspects of drug action in relation to membrane properties (transmembrane transport, tissue targeting, bioavailability, etc.), and also the impact of pathophysiological conditions (e.g., oxidative modification) on membrane properties, on a hitherto not or only hardly accessible level.

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References

  1. Busalmen JP, de Sánchez SR. Electrochemical polarization-induced changes in the growth of individual cells and biofilms of Pseudomonas fluorescens (ATCC 17552). Appl Environ Microbiol. 2005;71:6235–40.

    Article  CAS  Google Scholar 

  2. Thomlinson RH, Gray LH. The histological structure of some human lung cancers and the possible implications for radiotherapy. Br J Cancer. 1955;9:539–49.

    Article  CAS  Google Scholar 

  3. Hall EJ, Giaccia AJ. Radiobiology for the radiologist. 6th ed. Philadelphia: Lippincott Williams & Wilkins; 2006. p. 90–103.

    Google Scholar 

  4. Burton AC. Rate of growth of solid tumours as a problem of diffusion. Growth. 1966;30:157–76.

    CAS  Google Scholar 

  5. Araujo RP, McElwain DLS. A history of the study of solid tumor growth: the contribution of mathematical modelling. Bull Math Biol. 2004;66:1039–91.

    Article  CAS  Google Scholar 

  6. Greenspan HP. Models for the growth of a solid tumor by diffusion. Stud Appl Math. 1972;52:317–40.

    Google Scholar 

  7. Tiina Roose S, Chapman J, Maini PK. Mathematical models of avascular tumor growth. SIAM Rev. 2007;49:179–208.

    Article  Google Scholar 

  8. Ferreira Jr SC, Martins ML, Vilela MJ. Reaction–diffusion model for the growth of avascular tumor. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;65:021907.

    Article  Google Scholar 

  9. Bertuzzi A, Fasano A, Gandolfi A, Marangi D. Cell kinetics in tumor cords studied by a model with variable cell cycle length. Math Biosci. 2002;177:103–25.

    Article  Google Scholar 

  10. Ward J, King J. Mathematical modelling of avascular-tumour growth. IMA J Math Appl Med Biol. 1997;14(1):39–69.

    Article  CAS  Google Scholar 

  11. Fernández Slezak D, Suárez C, Soba A, Risk M, Marshall G. Numerical simulation of avascular tumor growth. J Phys Conf Ser. 2007;90:012049.

    Article  Google Scholar 

  12. Chaplain MAJ, Graziano L, Preziosi L. Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumor development. Math Med Biol. 2006;23:197–229.

    Article  CAS  Google Scholar 

  13. Basan M, Risler T, Joanny J-F, Sastre-Garau X, Prost J. Homeostatic competition drives tumor growth and metastasis nucleation. HFSP J. 2009;1:98.

    Google Scholar 

  14. Deroulers C, Aubert M, Badoual M, Grammaticos B. Modeling tumor cell migration: From microscopic to macroscopic models. Phys Rev E Stat Nonlin Soft Matter Phys. 2009;7(9):031917.

    Article  Google Scholar 

  15. Lo Stochastic CF. Gompertz model of tumor cell growth. J Theor Biol. 2007;248:317–21.

    Article  Google Scholar 

  16. Kim PS, Lee PP, Levy D. A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia. Bull Math Biol. 2008;70:1994–2016.

    Article  Google Scholar 

  17. Gatenby RA, Vincent TL. Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies. Mol Cancer Ther. 2003;2:919–27.

    CAS  Google Scholar 

  18. Albert PS, Shih JH, Tumor M. Growth with random onset. Biometrics. 2003;59:897–906.

    Article  Google Scholar 

  19. Delsanto PP, Condat CA, Pugno N, Gliozzi AS, Griffa M. A multilevel approach to cancer growth modeling. J Theor Biol. 2008;250:16–24.

    Article  CAS  Google Scholar 

  20. Byrne H, Drasdo D. Individual-based and continuum models of growing cell populations: a comparison. J Math Biol. 2009;58:657–87.

    Article  Google Scholar 

  21. Barbolosi D, Benabdallah A, Hubert F, Verga F. Mathematical and numerical analysis for a model of growing metastatic tumors. Math Biosci. 2009;218:1–14.

    Article  Google Scholar 

  22. Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 1999;59:4770–5.

    CAS  Google Scholar 

  23. Jain RK, Tong RT, Munn LL. Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model. Cancer Res. 2007;6(7):2729.

    Article  Google Scholar 

  24. Sutherland RM. Cell and environment interactions in tumor microregions: the multicell spheroid model. Science. 1988;240:177–84.

    Article  CAS  Google Scholar 

  25. Yorke ED, Fuks Z, Norton L, Whitmore W, Ling CC. Modeling the development of metastases from primary and locally, recurrent tumors: comparison with a clinical database for prostatic cancer. Cancer Res. 1993;53:2987–93.

    CAS  Google Scholar 

  26. Laird AK. Dynamics of tumor growth. Br J Cancer. 1964;18:490–502.

    Article  Google Scholar 

  27. Demidem A, Morvan D, Papon J, De Latour M, Madelmont JC. Cystemustine induces redifferentiation of primary tumor and confers protection against secondary tumor growth in a melanoma murine model. Cancer Res. 2001;6(1):2294.

    Google Scholar 

  28. Steel GG. Growth kinetics of tumors. Oxford: Clarendon; 1977.

    Google Scholar 

  29. Wheldon TE. Mathematical models in cancer research. Bristol: Adam Hilger; 1988.

    Google Scholar 

  30. West GB, Brown JH, Enquist BJ. A general model for ontogenetic growth. Nature. 2001;413:628–31.

    Article  CAS  Google Scholar 

  31. Kleiber M. Body size and metabolic rate. Physiol Rev. 1947;27:511–41.

    CAS  Google Scholar 

  32. Guiot C, Degiorgis PG, Delsanto PP, Gabriele P, Deisboeck TS. Does tumor growth follow a “universal law”? J Theor Biol. 2003;225:147–51.

    Article  Google Scholar 

  33. Colombo F, Baldan F, Mazzucchelli S, Martin-Padura I, Marighetti P, et al. Evidence of distinct tumour-propagating cell populations with different properties in primary human hepatocellular carcinoma. PLoS One. 2011;6:e21369. doi:10.1371/journal.pone.

    Article  CAS  Google Scholar 

  34. González-García I, Solé RV, Costa J. Metapopulation dynamics and spatial heterogeneity in cancer. Proc Natl Acad Sci USA. 2002;99:13085–9.

    Article  Google Scholar 

  35. Liu LJ, Brown SL, Ewing JR, Schlesinger M. Phenomenological model of interstitial fluid pressure in a solid tumor. Phys Rev E Stat Nonlin Soft Matter Phys. 2011;84:021919.

    Article  CAS  Google Scholar 

  36. West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science. 1999;284:1677–9.

    Article  CAS  Google Scholar 

  37. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science. 1997;276:122–6.

    Article  CAS  Google Scholar 

  38. Savage VM, Allen AP, Brown JH, Gillooly JF, Herman AB, Woodruff WH, et al. Scaling of number, size, and metabolic rate of cells with body size in mammals. Proc Natl Acad Sci USA. 2007;104:4718–23.

    Article  CAS  Google Scholar 

  39. Schmidt-Nielsen K. Scaling: why is animal size so important. Cambridge: Cambridge University Press; 1984.

    Book  Google Scholar 

  40. Calder III WA. Size, function and life history. Cambridge: Harvard University Press; 1984.

    Google Scholar 

  41. Feldman HA, McMahon TA. The 3/4 mass exponent for energy metabolism is not a statistical artefact. Respir Physiol. 1983;52:149.

    Article  CAS  Google Scholar 

  42. Charnov EL. Life history invariants: some explorations of symmetry in evolutionary ecology. Oxford: Oxford University Press; 1993.

    Google Scholar 

  43. Stearns SC. The evolution of life histories. Oxford: Oxford University Press; 1992.

    Google Scholar 

  44. Reiss MJ. The allometry of growth and reproduction. Cambridge: Cambridge University Press; 1989.

    Book  Google Scholar 

  45. von Bertalanffy L. Quantitative laws in metabolism and growth. Q Rev Biol. 1957;32:217–31.

    Article  Google Scholar 

  46. Al-Hajj M, Wicha MS, Benito-Hernandez A, Morrison SJ, Clarke MF. Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci USA. 2003;100:3983.

    Article  CAS  Google Scholar 

  47. Reya T, Morrison SJ, Clarke MF, Weissman IL. Stem cells, cancer, and cancer stem cells. Nature. 2001;414:105–11.

    Article  CAS  Google Scholar 

  48. Lapidot T, Sirard C, Vormoor J, Murdoch B, Hoang T, Caceres-Cortes J, et al. A cell initiating human acute myeloid leukaemia after transplantation into SCID mice. Nature. 1994;367:645–8.

    Article  CAS  Google Scholar 

  49. Singh SK, Clarke ID, Terasaki M, Bonn VE, Hawkins C, Squire J, et al. Identification of a cancer stem cell in human brain tumors. Cancer Res. 2003;63:5821–8.

    CAS  Google Scholar 

  50. Hall EJ, Giaccia AJ. Radiobiology for the Radiologist. 6th ed. Philadelphia: Lippincott Williams & Wilkins; 2006.

    Google Scholar 

  51. Skargard LD, Skwarchuk MW, Wouters BG. The survival of asynchronous V79 cells at low radiation doses: modeling the response of mixed cell populations. Radiat Res. 1994;138:S72–5.

    Article  Google Scholar 

  52. Astrahan M. Some implications of linear-quadratic-linear radiation dose–response with regard to hypofractionation. Med Phys. 2008;3(5):4161.

    Article  Google Scholar 

  53. Chadwick KH, Leenhouts HP. A molecular theory of cell survival. Phys Med Biol. 1973;18:78–87.

    Article  CAS  Google Scholar 

  54. Bradly G. Cells at intermediate oxygen levels can be more important than the “hypoxic fraction” in determining tumor response to fractionated radiotherapy. Radiat Res. 1997;147:541–50.

    Article  Google Scholar 

  55. Garcia LM, Wilkins DE, Raaphorst GP. α/β ratio: a dose range dependence study. Int J Radiat Oncol Biol Phys. 2007;67:587–93.

    Article  Google Scholar 

  56. Guerrero M, Carlone M. Mechanistic formulation of a linear-quadratic-linear (LQL) model: split-dose experiments and exponentially decaying sources. Med Phys. 2010;3(7):4173.

    Article  Google Scholar 

  57. Curtis SB. Lethal and potentially lethal lesions induced by radiation—a unified repair model. Radiat Res. 1986;106:252–70.

    Article  CAS  Google Scholar 

  58. Elkind MM, Sutton H. X-ray damage and recovery in mammalian cells in culture. Nature. 1959;184:1293–5.

    Article  CAS  Google Scholar 

  59. Stone K, Wunderli H, Mickey G, Paulson D. Isolation of a human prostate carcinoma cell line (DU-145). Int J Cancer. 1978;21:274–81.

    Article  CAS  Google Scholar 

  60. Leith J, et al. Radiobiological studies of PC-3 and DU-145 human prostate cancer cells, x-ray sensitivity in vitro and hypoxic fractions of xenografted tumors in vivo. Int J Radiat Oncol Biol Phys. 1993;25:283–7.

    Article  CAS  Google Scholar 

  61. Siemann DW. Tumour size: a factor influencing the isoeffect analysis of tumour response to combined modalities. Br J Cancer. 1980;41(Suppl IV):294.

    Google Scholar 

  62. Barendsen GW, Koot CJ, van Kersen GR, Bewley DK, Field SB, Parnell CJ. The effect of oxygen on impairment of the proliferative capacity of human cells in culture by ionizing radiations of different LET. Int J Radiat Biol. 1966;10:317–27.

    Article  CAS  Google Scholar 

  63. McNally NJ, de Ronde J, Folkard M. Interaction between X-ray and α-particle damage in V79 cells. Int J Radiat Biol. 1988;53:917–20.

    Article  CAS  Google Scholar 

  64. Wenzl T. and Jan J Wilkens, Modelling of the oxygen enhancement ratio for ion beam radiation therapy. Phys Med Biol. 2011;56:3251–68.

    Article  Google Scholar 

  65. Hieber L, Ponsel G, Roos H, Fenn S, Fromke E, Kellerer AM. Absence of a dose-rate effect in the transformation of C3H 10T1/2 cells by α-particles. Int J Radiat Biol. 1987;52:859–69.

    Article  CAS  Google Scholar 

  66. Beaton LA, Trevor B, Stocki TJ, Vinita C, Wilkins RC. Development and characterization of an in vitro alpha radiation exposure system. Phys Med Biol. 2011;56:3645–58.

    Article  Google Scholar 

  67. Durante M, Grossi GF, Gialanella G, Pugliese M, Nappo M, Yang TC. Effects of α-particles on survival and chromosomal aberrations in human mammary epithelial cells. Radiat Environ Biophys. 1995;34:195–204.

    Article  CAS  Google Scholar 

  68. Martin SG, Miller RC, Geard CR, Hall EJ. The biological effectiveness of radon-progeny alpha particles. IV. Morphological transformation of Syrian hamster embryo cells at low doses. Radiat Res. 1995;142:70–7.

    Article  CAS  Google Scholar 

  69. Thomas P, Tracy B, Ping T, Baweja A, Wickstrom M, Sidhu N, et al. Relative biological effectiveness (RBE) of alpha radiation in cultured porcine aortic endothelial cells. Int J Radiat Biol. 2007;83:171–9.

    Article  CAS  Google Scholar 

  70. Lloyd EL, Gemmell MA, Henning CB, Gemmell DS, Zabransky BJ. Transformation of mammalian cells by alpha particles. Int J Radiat Biol. 1979;36:467.

    Article  CAS  Google Scholar 

  71. Zhou H, Randers-Pehrson G, Waldren CA, Vannais D, Hall EJ, Hei TK. Induction of a bystander mutagenic effect of alpha particles in mammalian cells. Proc Natl Acad Sci USA. 2000;97:2099–104.

    Article  CAS  Google Scholar 

  72. Hei TK, Wu LJ, Liu SX, Vannais D, Waldren CA, Randers-Pehrson G. Mutagenic effects of a single and an exact number of α particles in mammalian cells. Proc Natl Acad Sci USA. 1997;94:3765.

    Article  CAS  Google Scholar 

  73. Walicka MA, Vaidyanathan G, Zalutsky MR, James Adelstein S, Kassis AI. Survival and DNA damage in Chinese hamster V79 cells exposed to alpha particles emitted by DNA-incorporated astatine-211. Radiat Res. 1998; 150:263–8.

    Article  CAS  Google Scholar 

  74. Hall EJ, Gross W, Dvorak RF, Kellerer AM, Rossi HH. Survival curves and age response functions for Chinese hamster cells exposed to x-ray or high LET alpha-particles. Radiat Res. 1972;52:88–98.

    Article  CAS  Google Scholar 

  75. Powers WE, Tolmach LJ. A multicomponent x-ray survival curve for mouse lymphosarcoma cells irradiated in vivo. Nature. 1963;197:710–1.

    Article  CAS  Google Scholar 

  76. Newman HC, Prise KM, Folkard M, Michael BD. DNA double-strand break distributions in X-ray and α-particle irradiated V79 cells: evidence for non-random breakage. Int J Radiat Biol. 1997;71:347–63.

    Article  CAS  Google Scholar 

  77. Blöcher D. DNA double-strand break repair determines the RBE of α-particles. Int J Radiat Biol. 1988;54:761–71.

    Article  Google Scholar 

  78. Wouters BG, Skarsgard LD. The response of a human tumor cell line to low radiation doses: evidence of enhanced sensitivity. Radiat Res. 1994;138:S76–80.

    Article  CAS  Google Scholar 

  79. Skarsgard LD, Hill AA, Acheson DK. Evidence for two forms of substructure in the cell survival curve. Acta Oncol. 1999;38:895–902.

    Article  CAS  Google Scholar 

  80. Howell RW, Neti PV. Modeling multicellular response to nonuniform distribution of radioactivity: Differences in cellular response to self-dose and cross-dose. Radiat Res. 2005;163:216–21.

    Article  CAS  Google Scholar 

  81. Rich JN, Stem C. Cells in radiation resistance. Cancer Res. 2007;67:8980–4.

    Article  CAS  Google Scholar 

  82. Liu G, Yuan X, Zeng Z, et al. Analysis of gene expression and chemoresistance of CD133+ cancer stem cells in glioblastoma. Mol Cancer. 2006;5:67. doi:10.1186/1476-4598-5-67.

    Article  Google Scholar 

  83. Belli JA, Piro AJ. The interaction between radiation and adriamycin damage in mammalian cells. Cancer Res. 1977;37:1624–30.

    CAS  Google Scholar 

  84. Pentheroudakis G, Briasoulis E, Pavlidis N. Cancer of unknown primary site: missing primary or missing biology? Oncologist. 2007;12:418–25.

    Article  CAS  Google Scholar 

  85. Briasoulis E, Pavilidis N. Cancer of unknown primary origin. Oncologist. 1997;2:142–52.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Windsor, Windsor, ON, N9B 3P4, Canada

    L. J. Liu & M. Schlesinger

  2. Henry Ford Hospital, Detroit, MI, 48202, USA

    S. L. Brown

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  1. L. J. Liu
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Correspondence to L. J. Liu .

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  1. , Dept. of Physics, University of Windsor, Sunset Avenue, Windsor, N9B 3P4, Canada

    Mordechay Schlesinger

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Liu, L.J., Brown, S.L., Schlesinger, M. (2013). Model of Tumor Growth and Response to Radiation. In: Schlesinger, M. (eds) Applications of Electrochemistry in Medicine. Modern Aspects of Electrochemistry, vol 56. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6148-7_11

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