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題名 The model of the movement of tumor cells and health cells
作者 林育如
Lin, Yu-Ju
貢獻者 李明融
Li,Meng-Rong
林育如
Lin, Yu-Ju
關鍵詞 random-walk
flux motion
cell movement
日期 2005
上傳時間 18-九月-2009 18:29:29 (UTC+8)
摘要 This study concludes two parts. In the first part, we establish
     the model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.
This study concludes two parts. In the first part, we establish
     the model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.
Contents
     Abstract...i
     1 Introduction...1
     2 Modelling of the interaction between two cell populations following the random-walk concept
     2.1 The movement of one cell population...3
     2.2 The interaction between two cell populations...6
     3 Analysis of the model of the interaction between two cell populations
     3.1 The behavior and the meaning ofν(x,t) =ν(z) as z→0...10
     3.2 The behavior and the meaning ofν(x,t) =ν(z) as z→∞...15
     4 Modelling of the interaction between two cell populations following the flux motion
     4.1 The movement of one cell population under space limitation...18
     4.2 The interaction between two cell populations under space limitation...21
     5 Analysis of the model of the interaction between two cell populations
     5.1 The properties of total cells as time far into the future...25
     5.2 The behavior of single cell population as time far into the future...28
     References...32
參考文獻 [1] D. C. Bottino and L. J. Fauci (1998). A computational model of ameboid deformation and locomotion. European Biophysics Journal with Biophysics Letters, 27(5), 532-539.
[2] D. Bottino, A. Mogilner, T. Roberts, M. Stewart and G. Oster (2002). How nematode sperm crawl. Journal of Cell Science, 115(2), 367-384.
[3] M. A. J. Chaplain and A. M. Stuart (1993). A model mechanism for the chemotactic response of endothelial cells to tumor angiogenesis factor. IMA Journal of Mathematical Applied in Medicine and Biology, 10(3), 149-168.
[4] T. Hillen and H. G. Othmer (2000). The diffusion limit of transport equations derived from velocity-jump processes. SIAM Journal of Applied Mathematics, 61(3), 751-775.
[5]T. Höfer, J. A. Sherratt and P. K. Maini (1995). Dyctyostelium discoideum: cellular self-organisation in an excitable biological medium. Proc. R. Soc. Lond., B259, 249-257.
[6] E. F. Keller and L. A. Segel (1970). Initiation of slide mold aggregation viewed as an instability. Journal of Theoretical Biology, 26, 99415.
[7] J. Mazumdar (1999). An introduction to mathematical physiology and biology. Combridge University Press, Combridge.
[8] G. Oster (1984). On the crawling of cells. Journal of Embryology and Experimental Morphology, 83, 329-364.
[9] G. Oster and A. Perelson (1985). Cell spreading and motility: a model lamellipod. Journal of Mathematical Biology, 21, 383-388.
[10] K. J. Painter, P. K. Maini and H. G. Othmer (2000). A chemotactic model for the advance and retreat of the primitive streak in avian development. Bulletin of Mathematical Biology, 62, 501-525.
[11] K. J. Painter and J. A. Sherratt (2003). Modelling the movement of interacting cell populations. Journal of Theoretical Biology, 225, 327-339.
[12] G. J. Pettet, H. M. Byrne, D. L. S. Mcelwain and J. Norbury (1996). A model of wound-healing angiogenesis in soft tissue. Mathematical Bioscience, 136(1), 35-63.
描述 碩士
國立政治大學
應用數學研究所
92751011
94
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0927510111
資料類型 thesis
dc.contributor.advisor 李明融zh_TW
dc.contributor.advisor Li,Meng-Rongen_US
dc.contributor.author (作者) 林育如zh_TW
dc.contributor.author (作者) Lin, Yu-Juen_US
dc.creator (作者) 林育如zh_TW
dc.creator (作者) Lin, Yu-Juen_US
dc.date (日期) 2005en_US
dc.date.accessioned 18-九月-2009 18:29:29 (UTC+8)-
dc.date.available 18-九月-2009 18:29:29 (UTC+8)-
dc.date.issued (上傳時間) 18-九月-2009 18:29:29 (UTC+8)-
dc.identifier (其他 識別碼) G0927510111en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36405-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 92751011zh_TW
dc.description (描述) 94zh_TW
dc.description.abstract (摘要) This study concludes two parts. In the first part, we establish
     the model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.
zh_TW
dc.description.abstract (摘要) This study concludes two parts. In the first part, we establish
     the model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.
en_US
dc.description.abstract (摘要) Contents
     Abstract...i
     1 Introduction...1
     2 Modelling of the interaction between two cell populations following the random-walk concept
     2.1 The movement of one cell population...3
     2.2 The interaction between two cell populations...6
     3 Analysis of the model of the interaction between two cell populations
     3.1 The behavior and the meaning ofν(x,t) =ν(z) as z→0...10
     3.2 The behavior and the meaning ofν(x,t) =ν(z) as z→∞...15
     4 Modelling of the interaction between two cell populations following the flux motion
     4.1 The movement of one cell population under space limitation...18
     4.2 The interaction between two cell populations under space limitation...21
     5 Analysis of the model of the interaction between two cell populations
     5.1 The properties of total cells as time far into the future...25
     5.2 The behavior of single cell population as time far into the future...28
     References...32
-
dc.description.tableofcontents Contents
     Abstract...i
     1 Introduction...1
     2 Modelling of the interaction between two cell populations following the random-walk concept
     2.1 The movement of one cell population...3
     2.2 The interaction between two cell populations...6
     3 Analysis of the model of the interaction between two cell populations
     3.1 The behavior and the meaning ofν(x,t) =ν(z) as z→0...10
     3.2 The behavior and the meaning ofν(x,t) =ν(z) as z→∞...15
     4 Modelling of the interaction between two cell populations following the flux motion
     4.1 The movement of one cell population under space limitation...18
     4.2 The interaction between two cell populations under space limitation...21
     5 Analysis of the model of the interaction between two cell populations
     5.1 The properties of total cells as time far into the future...25
     5.2 The behavior of single cell population as time far into the future...28
     References...32
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0927510111en_US
dc.subject (關鍵詞) random-walken_US
dc.subject (關鍵詞) flux motionen_US
dc.subject (關鍵詞) cell movementen_US
dc.title (題名) The model of the movement of tumor cells and health cellszh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] D. C. Bottino and L. J. Fauci (1998). A computational model of ameboid deformation and locomotion. European Biophysics Journal with Biophysics Letters, 27(5), 532-539.zh_TW
dc.relation.reference (參考文獻) [2] D. Bottino, A. Mogilner, T. Roberts, M. Stewart and G. Oster (2002). How nematode sperm crawl. Journal of Cell Science, 115(2), 367-384.zh_TW
dc.relation.reference (參考文獻) [3] M. A. J. Chaplain and A. M. Stuart (1993). A model mechanism for the chemotactic response of endothelial cells to tumor angiogenesis factor. IMA Journal of Mathematical Applied in Medicine and Biology, 10(3), 149-168.zh_TW
dc.relation.reference (參考文獻) [4] T. Hillen and H. G. Othmer (2000). The diffusion limit of transport equations derived from velocity-jump processes. SIAM Journal of Applied Mathematics, 61(3), 751-775.zh_TW
dc.relation.reference (參考文獻) [5]T. Höfer, J. A. Sherratt and P. K. Maini (1995). Dyctyostelium discoideum: cellular self-organisation in an excitable biological medium. Proc. R. Soc. Lond., B259, 249-257.zh_TW
dc.relation.reference (參考文獻) [6] E. F. Keller and L. A. Segel (1970). Initiation of slide mold aggregation viewed as an instability. Journal of Theoretical Biology, 26, 99415.zh_TW
dc.relation.reference (參考文獻) [7] J. Mazumdar (1999). An introduction to mathematical physiology and biology. Combridge University Press, Combridge.zh_TW
dc.relation.reference (參考文獻) [8] G. Oster (1984). On the crawling of cells. Journal of Embryology and Experimental Morphology, 83, 329-364.zh_TW
dc.relation.reference (參考文獻) [9] G. Oster and A. Perelson (1985). Cell spreading and motility: a model lamellipod. Journal of Mathematical Biology, 21, 383-388.zh_TW
dc.relation.reference (參考文獻) [10] K. J. Painter, P. K. Maini and H. G. Othmer (2000). A chemotactic model for the advance and retreat of the primitive streak in avian development. Bulletin of Mathematical Biology, 62, 501-525.zh_TW
dc.relation.reference (參考文獻) [11] K. J. Painter and J. A. Sherratt (2003). Modelling the movement of interacting cell populations. Journal of Theoretical Biology, 225, 327-339.zh_TW
dc.relation.reference (參考文獻) [12] G. J. Pettet, H. M. Byrne, D. L. S. Mcelwain and J. Norbury (1996). A model of wound-healing angiogenesis in soft tissue. Mathematical Bioscience, 136(1), 35-63.zh_TW