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| Title: | The model of the movement of tumor cells and health cells |
| Authors: | 林育如
Lin, Yu-Ju |
| Contributors: | 李明融
Li,Meng-Rong
林育如
Lin, Yu-Ju |
| Keywords: | random-walk
flux motion
cell movement |
| Date: | 2005 |
| Issue Date: | 2009-09-18 18:29:29 (UTC+8) |
| Abstract: | 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 |
| Reference: | [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. |
| Description: | 碩士
國立政治大學
應用數學研究所
92751011
94 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0927510111 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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