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From the guest editors
Investigating the steady state of multicellular spheroids by revisiting the two-fluid model
1. | Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 Firenze |
2. | Dipartimento di Matematica "U. Dini", Universita' di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy |
3. | Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" - CNR, Viale Manzoni 30, 00185 Roma, Italy |
References:
[1] |
D. Ambrosi and L. Preziosi, Cell adhesion mechanisms and stress relaxation in the mechanics of tumours, Biomech. Model. MechanoBiol., 8 (2009), 397-413.
doi: 10.1007/s10237-008-0145-y. |
[2] |
S. Astanin and L. Preziosi, Multiphase models of tumour growth, in "Selected Topics in Cancer Modelling'' (eds. N. Bellomo, M. Chaplain and E. De Angelis), Birkhauser, (2008), 223-250.
doi: 10.1007/978-0-8176-4713-1_9. |
[3] |
S. Astanin and L. Preziosi, Mathematical modelling of the Warburg effect in tumour cords, J. Theor. Biol., 258 (2009), 578-590.
doi: 10.1016/j.jtbi.2009.01.034. |
[4] |
A. Bertuzzi, A. Fasano and A. Gandolfi, A free boundary problem with unilateral constraints describing the evolution of a tumour cord under the influence of cell killing agents, SIAM J. Math. Analysis, 36 (2004), 882-915.
doi: 10.1137/S003614002406060. |
[5] |
A. Bertuzzi, A. Fasano, A. Gandolfi and C. Sinisgalli, Necrotic core in EMT6/Ro tumor spheroids: Is it caused by an ATP deficit?, J. Theor. Biol., 262 (2010), 142-150.
doi: 10.1016/j.jtbi.2009.09.024. |
[6] |
A. Bertuzzi, C. Bruni, A. Fasano, A. Gandolfi, F. Papa and C. Sinisgalli, Response of tumor spheroids to radiation: Modeling and parameter identification, Bull. Math. Biol., 72 (2010), 1069-1091.
doi: 10.1007/s11538-009-9482-y. |
[7] |
A. Bredel-Geissler, U. Karbach, S. Walenta, L. Vollrath and W. Mueller-Klieser, Proliferation-associated oxygen consumption and morphology of tumour cells in monolayer and spheroid culture, J. Cell. Physiol., 153 (1992), 44-52.
doi: 10.1002/jcp.1041530108. |
[8] |
H. M. Byrne and M. A. J. Chaplain, Growth of nonnecrotic tumors in the presence and absence of inhibitors, Math. Biosci., 130 (1995), 151-181.
doi: 10.1016/0025-5564(94)00117-3. |
[9] |
H. M. Byrne and M. A. J. Chaplain, Growth of necrotic tumors in the presence and absence of inhibitors, Math. Biosci., 135 (1996), 187-216.
doi: 10.1016/0025-5564(96)00023-5. |
[10] |
H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures, Math. Med. Biol., 20 (2003), 341-366.
doi: 10.1093/imammb/20.4.341. |
[11] |
H. M. Byrne, J. R. King, D. L. S. McElwain and L. Preziosi, A two-phase model of solid tumour growth, Appl. Math. Lett., 16 (2003), 567-573.
doi: 10.1016/S0893-9659(03)00038-7. |
[12] |
J. J. Casciari, S. V. Sotirchos and R. M. Sutherland, Variation in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH, J. Cell. Physiol., 151 (1992), 386-394.
doi: 10.1002/jcp.1041510220. |
[13] |
V. Cristini, X. Li, J. S. Lowengrub and S. M. Wise, Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching, J. Math. Biol., 58 (2009), 723-763.
doi: 10.1007/s00285-008-0215-x. |
[14] |
A. Fasano, A. Gandolfi and M. Gabrielli, The energy balance in stationary multicellular spheroids, Far East J. Math. Sci., 39 (2010), 105-128. |
[15] |
A. Friedman and F. Reitich, Symmetry-breaking bifurcations of analytic solutions to free boundary problems: An application to a model of tumor growth, Trans. Amer. Math. Soc., 353 (2000), 1587-1634.
doi: 10.1090/S0002-9947-00-02715-X. |
[16] |
J. P. Freyer and R. M. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth, J. Cell. Physiol., 124 (1985), 516-524.
doi: 10.1002/jcp.1041240323. |
[17] |
J. P. Freyer and R. M. Sutherland, Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply, Cancer Res., 46 (1986), 3504-3512. |
[18] |
G. Hamilton, Multicellular spheroids as an in vitro tumor model, Cancer Lett., 131 (1998), 29-34.
doi: 10.1016/S0304-3835(98)00198-0. |
[19] |
G. Helmlingen, P. A. Netti, H. C. Lichtembeld, R. J. Melder and R. K. Jain, Solid stress inhibits the growth of multicellular tumor spheroids, Nature Biotech., 15 (1997), 778-783.
doi: 10.1038/nbt0897-778. |
[20] |
A. Iordan, A. Duperray and C. Verdier, A fractal approach to the rheology of concentrated cell suspensions, Phis. Rev. E, 77 (2008), 011911.
doi: 10.1103/PhysRevE.77.011911. |
[21] |
P. A. Netti and R. K. Jain, Interstitial transport in solid tumours, in "Cancer Modelling and Simulation'' (ed. L. Preziosi), Chapman&Hall/CRC, (2003), 51-74.
doi: 10.1201/9780203494899.ch3. |
[22] |
K. A. Landman and C. P. Please, Tumour dynamics and necrosis: surface tension and stability, IMA J. Math. Appl. Med. Biol., 18 (2001), 131-158.
doi: 10.1093/imammb/18.2.131. |
[23] |
G. Lemon, J. R. King, H. M. Byrne, O. E. Jensen and K. M. Shakesheff, Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory, J. Math. Biol., 52 (2008), 571-594.
doi: 10.1007/s00285-005-0363-1. |
[24] |
W. Mueller-Klieser, Method for the determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids, Biophysical Journal, 46 (1984), 343-348.
doi: 10.1016/S0006-3495(84)84030-8. |
[25] |
M. Neeman, K. A. Jarrett, L. O. Sillerud and J. P. Freyer, Self-diffusion of water in multicellular spheroids measured by magnetic resonance microimaging, Cancer Res., 51 (1991), 4072-4079. |
[26] |
K. R. Rajagopal and L. Tao, "Mechanics of Mixtures,'' World Scientific, Singapore, 1995. |
[27] |
K. Smallbone, R. A. Gatenby, R. J. Gillies, P. K. Maini and D. J. Gavaghan, Metabolic changes during carcinogenesis: Potential impact on invasiveness, J. Theor. Biol., 244 (2007), 703-713.
doi: 10.1016/j.jtbi.2006.09.010. |
[28] |
J. P. Ward and J. R. King, Mathematical modelling of avascular tumor growth I, IMA J. Math. Appl. Med. Biol., 14 (1997), 36-69.
doi: 10.1093/imammb/14.1.39. |
[29] |
J. P. Ward and J. R. King, Mathematical modelling of avascular tumor growth II. Modelling growth saturation, IMA J. Math. Appl. Med. Biol., 16 (1999), 171-211.
doi: 10.1093/imammb/16.2.171. |
show all references
References:
[1] |
D. Ambrosi and L. Preziosi, Cell adhesion mechanisms and stress relaxation in the mechanics of tumours, Biomech. Model. MechanoBiol., 8 (2009), 397-413.
doi: 10.1007/s10237-008-0145-y. |
[2] |
S. Astanin and L. Preziosi, Multiphase models of tumour growth, in "Selected Topics in Cancer Modelling'' (eds. N. Bellomo, M. Chaplain and E. De Angelis), Birkhauser, (2008), 223-250.
doi: 10.1007/978-0-8176-4713-1_9. |
[3] |
S. Astanin and L. Preziosi, Mathematical modelling of the Warburg effect in tumour cords, J. Theor. Biol., 258 (2009), 578-590.
doi: 10.1016/j.jtbi.2009.01.034. |
[4] |
A. Bertuzzi, A. Fasano and A. Gandolfi, A free boundary problem with unilateral constraints describing the evolution of a tumour cord under the influence of cell killing agents, SIAM J. Math. Analysis, 36 (2004), 882-915.
doi: 10.1137/S003614002406060. |
[5] |
A. Bertuzzi, A. Fasano, A. Gandolfi and C. Sinisgalli, Necrotic core in EMT6/Ro tumor spheroids: Is it caused by an ATP deficit?, J. Theor. Biol., 262 (2010), 142-150.
doi: 10.1016/j.jtbi.2009.09.024. |
[6] |
A. Bertuzzi, C. Bruni, A. Fasano, A. Gandolfi, F. Papa and C. Sinisgalli, Response of tumor spheroids to radiation: Modeling and parameter identification, Bull. Math. Biol., 72 (2010), 1069-1091.
doi: 10.1007/s11538-009-9482-y. |
[7] |
A. Bredel-Geissler, U. Karbach, S. Walenta, L. Vollrath and W. Mueller-Klieser, Proliferation-associated oxygen consumption and morphology of tumour cells in monolayer and spheroid culture, J. Cell. Physiol., 153 (1992), 44-52.
doi: 10.1002/jcp.1041530108. |
[8] |
H. M. Byrne and M. A. J. Chaplain, Growth of nonnecrotic tumors in the presence and absence of inhibitors, Math. Biosci., 130 (1995), 151-181.
doi: 10.1016/0025-5564(94)00117-3. |
[9] |
H. M. Byrne and M. A. J. Chaplain, Growth of necrotic tumors in the presence and absence of inhibitors, Math. Biosci., 135 (1996), 187-216.
doi: 10.1016/0025-5564(96)00023-5. |
[10] |
H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures, Math. Med. Biol., 20 (2003), 341-366.
doi: 10.1093/imammb/20.4.341. |
[11] |
H. M. Byrne, J. R. King, D. L. S. McElwain and L. Preziosi, A two-phase model of solid tumour growth, Appl. Math. Lett., 16 (2003), 567-573.
doi: 10.1016/S0893-9659(03)00038-7. |
[12] |
J. J. Casciari, S. V. Sotirchos and R. M. Sutherland, Variation in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH, J. Cell. Physiol., 151 (1992), 386-394.
doi: 10.1002/jcp.1041510220. |
[13] |
V. Cristini, X. Li, J. S. Lowengrub and S. M. Wise, Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching, J. Math. Biol., 58 (2009), 723-763.
doi: 10.1007/s00285-008-0215-x. |
[14] |
A. Fasano, A. Gandolfi and M. Gabrielli, The energy balance in stationary multicellular spheroids, Far East J. Math. Sci., 39 (2010), 105-128. |
[15] |
A. Friedman and F. Reitich, Symmetry-breaking bifurcations of analytic solutions to free boundary problems: An application to a model of tumor growth, Trans. Amer. Math. Soc., 353 (2000), 1587-1634.
doi: 10.1090/S0002-9947-00-02715-X. |
[16] |
J. P. Freyer and R. M. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth, J. Cell. Physiol., 124 (1985), 516-524.
doi: 10.1002/jcp.1041240323. |
[17] |
J. P. Freyer and R. M. Sutherland, Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply, Cancer Res., 46 (1986), 3504-3512. |
[18] |
G. Hamilton, Multicellular spheroids as an in vitro tumor model, Cancer Lett., 131 (1998), 29-34.
doi: 10.1016/S0304-3835(98)00198-0. |
[19] |
G. Helmlingen, P. A. Netti, H. C. Lichtembeld, R. J. Melder and R. K. Jain, Solid stress inhibits the growth of multicellular tumor spheroids, Nature Biotech., 15 (1997), 778-783.
doi: 10.1038/nbt0897-778. |
[20] |
A. Iordan, A. Duperray and C. Verdier, A fractal approach to the rheology of concentrated cell suspensions, Phis. Rev. E, 77 (2008), 011911.
doi: 10.1103/PhysRevE.77.011911. |
[21] |
P. A. Netti and R. K. Jain, Interstitial transport in solid tumours, in "Cancer Modelling and Simulation'' (ed. L. Preziosi), Chapman&Hall/CRC, (2003), 51-74.
doi: 10.1201/9780203494899.ch3. |
[22] |
K. A. Landman and C. P. Please, Tumour dynamics and necrosis: surface tension and stability, IMA J. Math. Appl. Med. Biol., 18 (2001), 131-158.
doi: 10.1093/imammb/18.2.131. |
[23] |
G. Lemon, J. R. King, H. M. Byrne, O. E. Jensen and K. M. Shakesheff, Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory, J. Math. Biol., 52 (2008), 571-594.
doi: 10.1007/s00285-005-0363-1. |
[24] |
W. Mueller-Klieser, Method for the determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids, Biophysical Journal, 46 (1984), 343-348.
doi: 10.1016/S0006-3495(84)84030-8. |
[25] |
M. Neeman, K. A. Jarrett, L. O. Sillerud and J. P. Freyer, Self-diffusion of water in multicellular spheroids measured by magnetic resonance microimaging, Cancer Res., 51 (1991), 4072-4079. |
[26] |
K. R. Rajagopal and L. Tao, "Mechanics of Mixtures,'' World Scientific, Singapore, 1995. |
[27] |
K. Smallbone, R. A. Gatenby, R. J. Gillies, P. K. Maini and D. J. Gavaghan, Metabolic changes during carcinogenesis: Potential impact on invasiveness, J. Theor. Biol., 244 (2007), 703-713.
doi: 10.1016/j.jtbi.2006.09.010. |
[28] |
J. P. Ward and J. R. King, Mathematical modelling of avascular tumor growth I, IMA J. Math. Appl. Med. Biol., 14 (1997), 36-69.
doi: 10.1093/imammb/14.1.39. |
[29] |
J. P. Ward and J. R. King, Mathematical modelling of avascular tumor growth II. Modelling growth saturation, IMA J. Math. Appl. Med. Biol., 16 (1999), 171-211.
doi: 10.1093/imammb/16.2.171. |
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