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Volumn 53, Issue 3, 2014, Pages 449-464

Coupling of discrete random walks and continuous modeling for three-dimensional tumor-induced angiogenesis

Author keywords

Capillary growth; Isogeometric analysis; Numerical simulations; Random walk; Tumor angiogenesis

Indexed keywords

BIOCHEMISTRY; COMPUTER SIMULATION; CONTINUUM MECHANICS; ENDOTHELIAL CELLS; MEDICAL NANOTECHNOLOGY; NUMERICAL METHODS; RANDOM PROCESSES;

EID: 84898602268     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-013-0958-0     Document Type: Article
Times cited : (34)

References (75)
  • 1
    • 0142248828 scopus 로고    scopus 로고
    • A cellular automaton model for tumour growth in inhomogeneous environment
    • Alarcón T, Byrne HM, Maini PK (2003) A cellular automaton model for tumour growth in inhomogeneous environment. J Theor Biol 225(2):257-274
    • (2003) J Theor Biol , vol.225 , Issue.2 , pp. 257-274
    • Alarcón, T.1    Byrne, H.M.2    Maini, P.K.3
  • 4
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumor-induced angiogenesis
    • Anderson ARA, Chaplain MAJ (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 60(5):857-899
    • (1998) Bull Math Biol , vol.60 , Issue.5 , pp. 857-899
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 5
    • 0001257097 scopus 로고    scopus 로고
    • A mathematical model for capillary network formation in the absence of endothelial cell proliferation
    • Anderson ARA, Chaplain MAJ (1998) A mathematical model for capillary network formation in the absence of endothelial cell proliferation. Appl Math Lett 11(3):109-114
    • (1998) Appl Math Lett , vol.11 , Issue.3 , pp. 109-114
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 6
    • 33645287543 scopus 로고    scopus 로고
    • Local maximum-entropy approximation schemes: A seamless bridge between finite elements and meshfree methods
    • Arroyo M, OrtizM(2006) Local maximum-entropy approximation schemes: A seamless bridge between finite elements and meshfree methods. Int J Numer Methods Eng 65(13):2167-2202
    • (2006) Int J Numer Methods Eng , vol.65 , Issue.13 , pp. 2167-2202
    • Arroyo, M.1    Ortiz, M.2
  • 7
    • 34247569970 scopus 로고    scopus 로고
    • A cell-basedmodel exhibiting branching and anastomosis during tumor-induced angiogenesis
    • Bauer AL, Jackson TL, Jiang Y (2007) A cell-basedmodel exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys J 92(9):3105-3121
    • (2007) Biophys J , vol.92 , Issue.9 , pp. 3105-3121
    • Bauer, A.L.1    Jackson, T.L.2    Jiang, Y.3
  • 9
    • 33745677813 scopus 로고    scopus 로고
    • Isogeometric fluid-structure interaction analysis with applications to arterial blood flow
    • Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38(4-5):310-322
    • (2006) Comput Mech , vol.38 , Issue.4-5 , pp. 310-322
    • Bazilevs, Y.1    Calo, V.M.2    Zhang, Y.3    Hughes, T.J.R.4
  • 10
    • 74049137363 scopus 로고    scopus 로고
    • Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes
    • BazilevsY, Michler C, CaloVM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199(13-16):780-790
    • (2010) Comput Methods Appl Mech Eng , vol.199 , Issue.13-16 , pp. 780-790
    • Bazilevs, Y.1    Michler, C.2    Calo, V.M.3    Hughes, T.J.R.4
  • 11
    • 73549120589 scopus 로고    scopus 로고
    • Tipping the balance: Robustness of tip cell selection, migration and fusion in angiogenesis
    • Bentley K, Mariggi G, Gerhardt H, Bates PA (2009) Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis. PLoS Comput Biol 5(10):e1000,549
    • (2009) PLoS Comput Biol , vol.5 , Issue.10
    • Bentley, K.1    Mariggi, G.2    Gerhardt, H.3    Bates, P.A.4
  • 12
    • 0037967272 scopus 로고    scopus 로고
    • Angiogenesis: Tumorigenesis and the angiogenic switch
    • Bergers G, Benjamin LE (2003) Angiogenesis: Tumorigenesis and the angiogenic switch. Nat Rev Cancer 3(6):401
    • (2003) Nat Rev Cancer , vol.3 , Issue.6 , pp. 401
    • Bergers, G.1    Benjamin, L.E.2
  • 13
    • 63249119539 scopus 로고    scopus 로고
    • Stochastic modelling of tumourinduced angiogenesis
    • Capasso V, Morale D (2009) Stochastic modelling of tumourinduced angiogenesis. J Math Biol 58(1-2):219-233
    • (2009) J Math Biol , vol.58 , Issue.1-2 , pp. 219-233
    • Capasso, V.1    Morale, D.2
  • 14
    • 0034470377 scopus 로고    scopus 로고
    • Mathematical modelling of angiogenesis
    • Chaplain MAJ (2000) Mathematical modelling of angiogenesis. J Neuro-Oncol 50(1-2):37-51
    • (2000) J Neuro-Oncol , vol.50 , Issue.1-2 , pp. 37-51
    • Chaplain, M.A.J.1
  • 15
    • 0030404170 scopus 로고    scopus 로고
    • Mathematical modelling, simulation and prediction of tumour-induced angiogenesis
    • Chaplain MAJ, Anderson ARA (1996) Mathematical modelling, simulation and prediction of tumour-induced angiogenesis. Invasion Metastasis 16(4-5):222-234
    • (1996) Invasion Metastasis , vol.16 , Issue.4-5 , pp. 222-234
    • Chaplain, M.A.J.1    Anderson, A.R.A.2
  • 16
    • 0027610910 scopus 로고
    • A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method
    • Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method. J Appl Mech 60:371-375
    • (1993) J Appl Mech , vol.60 , pp. 371-375
    • Chung, J.1    Hulbert, G.M.2
  • 19
    • 34547629767 scopus 로고    scopus 로고
    • Studies of refinement and continuity in isogeometric structural analysis
    • Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196(41-44):4160-4183
    • (2007) Comput Methods Appl Mech Eng , vol.196 , Issue.41-44 , pp. 4160-4183
    • Cottrell, J.A.1    Hughes, T.J.R.2    Reali, A.3
  • 21
    • 70249127275 scopus 로고    scopus 로고
    • Smooth, second order, nonnegative meshfree approximants selected by maximum entropy
    • Cyron CJ, Arroyo M, Ortiz M (2009) Smooth, second order, nonnegative meshfree approximants selected by maximum entropy. Int J Numer Methods Eng 79(13):1605-1632
    • (2009) Int J Numer Methods Eng , vol.79 , Issue.13 , pp. 1605-1632
    • Cyron, C.J.1    Arroyo, M.2    Ortiz, M.3
  • 22
    • 33645985153 scopus 로고    scopus 로고
    • The effective dispersion of nanovectors within the tumor microvasculature
    • Decuzzi P, Causa F, Ferrari M, Netti PA (2006) The effective dispersion of nanovectors within the tumor microvasculature. Ann Biomed Eng 34(4):633-641
    • (2006) Ann Biomed Eng , vol.34 , Issue.4 , pp. 633-641
    • Decuzzi, P.1    Causa, F.2    Ferrari, M.3    Netti, P.A.4
  • 24
    • 0037025251 scopus 로고    scopus 로고
    • Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
    • Engel G, Garikipati K, Hughes TJR, Larson MG, Mazzei L, Taylor RL (2002) Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput Methods Appl Mech Eng 191(34):3669-3750
    • (2002) Comput Methods Appl Mech Eng , vol.191 , Issue.34 , pp. 3669-3750
    • Engel, G.1    Garikipati, K.2    Hughes, T.J.R.3    Larson, M.G.4    Mazzei, L.5    Taylor, R.L.6
  • 26
    • 85013312416 scopus 로고
    • Tumor angiogenesis: Therapeutic implications
    • Folkman J (1971) Tumor angiogenesis: Therapeutic implications. New Engl J Med 285(21):1182-1186
    • (1971) New Engl J Med , vol.285 , Issue.21 , pp. 1182-1186
    • Folkman, J.1
  • 28
    • 84874526323 scopus 로고    scopus 로고
    • A computational model for predicting nanoparticle accumulation in tumor vasculature
    • Frieboes H, Wu M, Lowengrub J, Decuzzi P, Cristini V (2013) A computational model for predicting nanoparticle accumulation in tumor vasculature. PLoS ONE 8(2):e5687
    • (2013) PLoS ONE , vol.8 , Issue.2
    • Frieboes, H.1    Wu, M.2    Lowengrub, J.3    Decuzzi, P.4    Cristini, V.5
  • 29
    • 77952954625 scopus 로고    scopus 로고
    • Three-dimensionalmultispecies nonlinear tumor growth- II: Tumor invasion and angiogenesis
    • Frieboes HB, Jin F, Chuang YL,Wise SM, Lowengrub JS, Cristini V(2010) Three-dimensionalmultispecies nonlinear tumor growth- II: Tumor invasion and angiogenesis. J Theor Biol 264(4):1254- 1278
    • (2010) J Theor Biol , vol.264 , Issue.4 , pp. 1254-1278
    • Frieboes, H.B.1    Jin, F.2    Chuang, Y.L.3    Wise, S.M.4    Lowengrub, J.S.5    Cristini, V.6
  • 30
    • 3042604836 scopus 로고    scopus 로고
    • On lung endothelial cell heterogeneity
    • Gebb S, Stevens T (2004) On lung endothelial cell heterogeneity. Microvasc Res 68(1):1-12
    • (2004) Microvasc Res , vol.68 , Issue.1 , pp. 1-12
    • Gebb, S.1    Stevens, T.2
  • 33
    • 84873297512 scopus 로고    scopus 로고
    • Threedimensional simulation of unstable gravity-driven infiltration of water into a porous medium
    • Gomez H, Cueto-Felgueroso L, Juanes R (2013) Threedimensional simulation of unstable gravity-driven infiltration of water into a porous medium. J Comput Phys 238:217-239
    • (2013) J Comput Phys , vol.238 , pp. 217-239
    • Gomez, H.1    Cueto-Felgueroso, L.2    Juanes, R.3
  • 34
    • 79955469960 scopus 로고    scopus 로고
    • Provably unconditionally stable, second-order time-accurate, mixed variational methods for phasefield models
    • Gomez H, Hughes TJR (2011) Provably unconditionally stable, second-order time-accurate, mixed variational methods for phasefield models. J Comput Phys 230:5310-5327
    • (2011) J Comput Phys , vol.230 , pp. 5310-5327
    • Gomez, H.1    Hughes, T.J.R.2
  • 35
    • 77952553498 scopus 로고    scopus 로고
    • Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
    • Gomez H, Hughes TJR, Nogueira X, Calo VM (2010) Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations. Comput Methods Appl Mech Eng 199(25-28):1828-1840
    • (2010) Comput Methods Appl Mech Eng , vol.199 , Issue.25-28 , pp. 1828-1840
    • Gomez, H.1    Hughes, T.J.R.2    Nogueira, X.3    Calo, V.M.4
  • 36
    • 84869880123 scopus 로고    scopus 로고
    • An unconditionally energy-stable method for the phase field crystal equation
    • Gomez H, Nogueira X (2012) An unconditionally energy-stable method for the phase field crystal equation. Comput Methods Appl Mech Eng 249-252:52-61
    • (2012) Comput Methods Appl Mech Eng , vol.249-252 , pp. 52-61
    • Gomez, H.1    Nogueira, X.2
  • 37
    • 79961060240 scopus 로고    scopus 로고
    • Numerical simulation of asymptotic states of the damped Kuramoto-Sivashinsky equation
    • Gomez H, París J (2011) Numerical simulation of asymptotic states of the damped Kuramoto-Sivashinsky equation. Phys Rev E 83:046,702
    • (2011) Phys Rev e , vol.83
    • Gomez, H.1    París, J.2
  • 38
    • 84898597791 scopus 로고
    • In: Schmidt R, Thews G (eds) Hum Physiol. Springer, Berlin Heidelberg
    • Grote J (1989) Tissue respiration. In: Schmidt R, Thews G (eds) Hum Physiol. Springer, Berlin Heidelberg, pp 598-612
    • (1989) Tissue Respiration. , pp. 598-612
    • Grote, J.1
  • 39
    • 0034614637 scopus 로고    scopus 로고
    • The hallmarks of cancer
    • Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100(1):57-70
    • (2000) Cell , vol.100 , Issue.1 , pp. 57-70
    • Hanahan, D.1    Weinberg, R.A.2
  • 40
    • 79952284127 scopus 로고    scopus 로고
    • Hallmarks of cancer: The next generation
    • Hanahan D, Weinberg RA (2011) Hallmarks of cancer: The next generation. Cell 144(5):646-674
    • (2011) Cell , vol.144 , Issue.5 , pp. 646-674
    • Hanahan, D.1    Weinberg, R.A.2
  • 42
    • 0031582488 scopus 로고    scopus 로고
    • A biased random walk model for the trajectories of swimming micro-organisms
    • Hill N, Häder DP (1997) A biased random walk model for the trajectories of swimming micro-organisms. J Theor Biol 186(4):503- 526
    • (1997) J Theor Biol , vol.186 , Issue.4 , pp. 503-526
    • Hill, N.1    Häder, D.P.2
  • 43
    • 21044443461 scopus 로고    scopus 로고
    • Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
    • Hughes TJR, Cottrell JA, BazilevsY(2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39-41):4135-4195
    • (2005) Comput Methods Appl Mech Eng , vol.194 , Issue.39-41 , pp. 4135-4195
    • Hughes, T.J.R.1    Cottrell, J.A.2    Bazilevs, Y.3
  • 44
    • 0034287408 scopus 로고    scopus 로고
    • A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method
    • Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190(3-4):305-319
    • (2000) Comput Methods Appl Mech Eng , vol.190 , Issue.3-4 , pp. 305-319
    • Jansen, K.E.1    Whiting, C.H.2    Hulbert, G.M.3
  • 45
  • 47
    • 0002178791 scopus 로고
    • A numerical approach to three-dimensional dendritic solidification
    • Kobayashi R (1994) A numerical approach to three-dimensional dendritic solidification. Exp Math 3(1):59-81
    • (1994) Exp Math , vol.3 , Issue.1 , pp. 59-81
    • Kobayashi, R.1
  • 48
    • 34147171490 scopus 로고    scopus 로고
    • Endothelial cell migration during angiogenesis
    • Lamalice L, Le Boeuf F, Huot J (2007) Endothelial cell migration during angiogenesis. Circ Res 100(6):782-794
    • (2007) Circ Res , vol.100 , Issue.6 , pp. 782-794
    • Lamalice, L.1    Le Boeuf, F.2    Huot, J.3
  • 49
    • 0000271120 scopus 로고
    • Two-dimensional fully adaptive solutions of reaction-diffusion equations
    • Lang J (1995) Two-dimensional fully adaptive solutions of reaction-diffusion equations. Appl NumerMath 18(1-3):223-240
    • (1995) Appl NumerMath , vol.18 , Issue.1-3 , pp. 223-240
    • Lang, J.1
  • 50
    • 70350234933 scopus 로고    scopus 로고
    • Numerical simulation of a nanoparticle focusing lens in amicrofluidic channel by using immersed finite element method
    • Lee TR, Chang YS, Choi JB, Liu WK, Kim YJ (2009) Numerical simulation of a nanoparticle focusing lens in amicrofluidic channel by using immersed finite element method. J Nanosci Nanotechnol 9(12):7407-7411
    • (2009) J Nanosci Nanotechnol , vol.9 , Issue.12 , pp. 7407-7411
    • Lee, T.R.1    Chang, Y.S.2    Choi, J.B.3    Liu, W.K.4    Kim, Y.J.5
  • 51
    • 0034845581 scopus 로고    scopus 로고
    • Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
    • Levine HA, Pamuk S, Sleeman BD, Nilsen-Hamilton M (2001) Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma. Bull Math Biol 63:801-863
    • (2001) Bull Math Biol , vol.63 , pp. 801-863
    • Levine, H.A.1    Pamuk, S.2    Sleeman, B.D.3    Nilsen-Hamilton, M.4
  • 52
    • 0035287283 scopus 로고    scopus 로고
    • Mathematical modeling of the onset of capillary formation initiating angiogenesis
    • Levine HA,Sleeman BD,Nilsen-HamiltonM(2001) Mathematical modeling of the onset of capillary formation initiating angiogenesis. J Math Biol 42(3):195-238
    • (2001) J Math Biol , vol.42 , Issue.3 , pp. 195-238
    • Levine, H.A.1    Sleeman, B.D.2    Nilsen-Hamilton, M.3
  • 53
    • 84877906231 scopus 로고    scopus 로고
    • Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier-Stokes-Korteweg equations
    • Liu J, Gomez H, Evans JA, Hughes TJR, Landis CM(2013) Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier-Stokes-Korteweg equations. J Comput Phys 248:47-86
    • (2013) J Comput Phys , vol.248 , pp. 47-86
    • Liu, J.1    Gomez, H.2    Evans, J.A.3    Hughes, T.J.R.4    Landis, C.M.5
  • 56
    • 16644400591 scopus 로고    scopus 로고
    • Mathematical modeling of tumor-induced angiogenesis
    • MantzarisNV,Webb S,OthmerHG(2004) Mathematical modeling of tumor-induced angiogenesis. J Math Biol 49(2):111-187
    • (2004) J Math Biol , vol.49 , Issue.2 , pp. 111-187
    • Mantzaris, N.V.1    Webb, S.2    Othmer, H.G.3
  • 57
    • 84866463851 scopus 로고    scopus 로고
    • A Hybrid Discrete continuum mathematical model of pattern prediction in the developing retinal vasculature
    • McDougall SR, Watson MG, Devlin AH, Mitchell CA, Chaplain MAJ (2012) A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature. Bull Math Biol 74(10):2272-2314
    • (2012) Bull Math Biol , vol.74 , Issue.10 , pp. 2272-2314
    • McDougall, S.R.1    Watson, M.G.2    Devlin, A.H.3    Mitchell, C.A.4    Chaplain, M.A.J.5
  • 58
    • 55949094110 scopus 로고    scopus 로고
    • A hybrid model for three-dimensional simulations of sprouting angiogenesis
    • Milde F, Bergdorf M, Koumoutsakos P (2008) A hybrid model for three-dimensional simulations of sprouting angiogenesis. Biophys J 95(7):3146-3160
    • (2008) Biophys J , vol.95 , Issue.7 , pp. 3146-3160
    • Milde, F.1    Bergdorf, M.2    Koumoutsakos, P.3
  • 59
    • 0031230846 scopus 로고    scopus 로고
    • Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies
    • Orme ME, Chaplain MAJ (1997) Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. Math Med Biol 14(3):189-205
    • (1997) Math Med Biol , vol.14 , Issue.3 , pp. 189-205
    • Orme, M.E.1    Chaplain, M.A.J.2
  • 60
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup, and collapse: The abc's of taxis in reinforced random walks
    • Othmer HG, Stevens A (1997) Aggregation, blowup, and collapse: The abc's of taxis in reinforced random walks. Siam J Appl Math 57(4):1044-1081
    • (1997) Siam J Appl Math , vol.57 , Issue.4 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 61
    • 0042863949 scopus 로고    scopus 로고
    • A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies
    • Plank MJ, Sleeman BD (2003) A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. Math Med Biol 20(2):135-181
    • (2003) Math Med Biol , vol.20 , Issue.2 , pp. 135-181
    • Plank, M.J.1    Sleeman, B.D.2
  • 62
    • 7444258529 scopus 로고    scopus 로고
    • Lattice and non-lattice models of tumour angiogenesis
    • Plank MJ, Sleeman BD (2004) Lattice and non-lattice models of tumour angiogenesis. Bull Math Biol 66(6):1785-1819
    • (2004) Bull Math Biol , vol.66 , Issue.6 , pp. 1785-1819
    • Plank, M.J.1    Sleeman, B.D.2
  • 63
    • 84887212532 scopus 로고    scopus 로고
    • Second-order convexmaximum entropy approximants with applications to high-order PDE
    • Rosolen A,Millán D, ArroyoM(2013) Second-order convexmaximum entropy approximants with applications to high-order PDE. Int J Numer Methods Eng 94(2):150-182
    • (2013) Int J Numer Methods Eng , vol.94 , Issue.2 , pp. 150-182
    • Rosolen, A.1    Millán, D.2    Arroyo, M.3
  • 64
    • 84880699962 scopus 로고    scopus 로고
    • A review of mathematical models for the formation of vascular networks
    • Scianna M, Bell C, Preziosi L (2013) A review of mathematical models for the formation of vascular networks. J Theor Biol 333:174-209
    • (2013) J Theor Biol , vol.333 , pp. 174-209
    • Scianna, M.1    Bell, C.2    Preziosi, L.3
  • 65
    • 80051671525 scopus 로고    scopus 로고
    • A multiscale hybrid approach for vasculogenesis and related potential blocking therapies
    • Scianna M, Munaron L, Preziosi L (2011) A multiscale hybrid approach for vasculogenesis and related potential blocking therapies. Prog Biophys Mol Biol 106(2):450-462
    • (2011) Prog Biophys Mol Biol , vol.106 , Issue.2 , pp. 450-462
    • Scianna, M.1    Munaron, L.2    Preziosi, L.3
  • 66
    • 84874745309 scopus 로고    scopus 로고
    • A cellular potts model simulating cell migration on and in matrix environments
    • Scianna M, Preziosi L,Wolf K (2013) A cellular potts model simulating cell migration on and in matrix environments. Math Biosci Eng 10(1):235-261
    • (2013) Math Biosci Eng , vol.10 , Issue.1 , pp. 235-261
    • Scianna, M.1    Preziosi, L.2    Wolf, K.3
  • 69
    • 0037119531 scopus 로고    scopus 로고
    • Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation
    • Sleeman B, Wallis IP (2002) Tumour induced angiogenesis as a reinforced random walk: modelling capillary network formation without endothelial cell proliferation. Math Comput Model 36(3):339-358
    • (2002) Math Comput Model , vol.36 , Issue.3 , pp. 339-358
    • Sleeman, B.1    Wallis, I.P.2
  • 70
    • 26844479092 scopus 로고    scopus 로고
    • Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies
    • Stephanou A, McDougall SR, Anderson ARA, Chaplain MAJ (2005) Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies. Math Comput Model 41(10):1137-1156
    • (2005) Math Comput Model , vol.41 , Issue.10 , pp. 1137-1156
    • Stephanou, A.1    McDougall, S.R.2    Anderson, A.R.A.3    Chaplain, M.A.J.4
  • 71
    • 13744260837 scopus 로고    scopus 로고
    • A deterministic model of growth factor-induced angiogenesis
    • Sun S, Wheeler MF, Obeyesekere M, Patrick CW (2005) A deterministic model of growth factor-induced angiogenesis. Bull Math Biol 67(2):313-337
    • (2005) Bull Math Biol , vol.67 , Issue.2 , pp. 313-337
    • Sun, S.1    Wheeler, M.F.2    Obeyesekere, M.3    Patrick, C.W.4
  • 73
    • 84885481235 scopus 로고    scopus 로고
    • Capillary networks in tumor angiogenesis: From discrete endothelial cells to phasefield averaged descriptions via isogeometric analysis
    • Vilanova G, Colominas I, Gomez H (2013) Capillary networks in tumor angiogenesis: From discrete endothelial cells to phasefield averaged descriptions via isogeometric analysis. Int J Numer Methods Biomed Eng 29(10):1015-1160
    • (2013) Int J Numer Methods Biomed Eng , vol.29 , Issue.10 , pp. 1015-1160
    • Vilanova, G.1    Colominas, I.2    Gomez, H.3
  • 75
    • 35348877949 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
    • Xia Y, Xu Y, Shu CW (2007) Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. J Comput Phys 227(1):472-491
    • (2007) J Comput Phys , vol.227 , Issue.1 , pp. 472-491
    • Xia, Y.1    Xu, Y.2    Shu, C.W.3


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