臺灣博碩士論文加值系統

　　皮膚細胞的基層主要有兩種細胞生長於其上。其一是幹細胞(stem cell)，另一種則是transit amplifying cell(TA cell)。正常的表皮細胞之生長行為會使細胞的總數維持在穩態，然而癌症細胞則傾向於自我分裂，而使得stem cell的總數異常增加，最終形成細胞密度較大的腫瘤。
　　本篇論文的模擬內容分兩部分：皮膚傷口的癒合模擬以及皮膚腫瘤的生長模擬。前者的主旨在於印證我們所引用的文獻的合理性，後者則是我們主要的研究內容。
　　透過巨觀尺度的模擬，我們的最終發現到了皮膚腫瘤的半徑大約是以每年10~20mm的速率逐漸擴張，當細胞的生長機制異變的越嚴重，腫瘤擴張的速率也會較高。而透過微觀的粒子模擬，我們解釋了惡性腫瘤以及良性腫瘤的差異：腫瘤的生長形貌和細胞的遷徙運動行為有著密不可分的關係！
　　此外，我們也針對細胞的異變係數做穩定性的分析，發現到異變係數存在著臨界值。倘若細胞異變的情況過於嚴重，癌細胞將會破壞掉皮膚組織應該維持的細胞總數之穩定性，進而毀壞掉整層組織。

　　On the basal layer of epidermis, there are two types of cells – stem cells (Stem) and transit amplifying cells (TA). The density of cells on the healthy epidermis must be const. But cancer cells tend to proliferate – the density of cancerous stem cells will increase, finally it will become tumor.
　　In this paper, the simulations can be divided into two parts: Modeling wound-healing and modeling tumor growth. Wound-healing model was used to check the accuracy our simulation. Our main idea was to simulation the growth of tumor.
　　In the simulation of macroscopic, we found that the growth rate of tumor was about 10~20 mm per year. When the mutant factor was increase, the growth rate will increase too. In microscopic, we can describe the difference of malignant tumor and benign tumor – the morphology of tumor were influenced by the migration parameter of cells.
　　In addition, we analysis the stability of mutant factor, found that if the mutant factor was greater than critical value, the behavior of these cancer cells will destroy whole epidermis thoroughly.

　第一章：研究背景
1.1 簡介.........................1
1.2 研究目的.....................3
1.3 研究背景知識.................5
　1.3.1 表皮細胞增生模型.........6
　1.3.2 細胞更新模型.............7
　1.3.3 細胞遷徙模型............10
　1.3.4 癌細胞的生長行為........11
1.4 研究構思....................13
　1.4.1 正常細胞的生長情形......13
　1.4.2 癌細胞的生長模型........15

　第二章：研究內容
2.1 正常細胞的生長理論模型之建立.........16
　2.1.1 細胞增生模型的引用以及印證.......16
　2.1.2 細胞擴散模型的引用以及結合.......22
　2.1.3 巨觀尺度下之細胞模型的印證.......26
　2.1.4 微觀尺度下之細胞遷徙模型的抉擇...29
　2.1.5 細胞遷徙模型之介紹...............30
　2.1.6 微觀模型的整合...................34
　2.1.7 微觀模型的印證...................36
2.2 癌細胞以及腫瘤的生長理論模型之建立...38
　2.2.1 癌細胞的生長行為.................38
　2.2.2 癌症腫瘤的模型...................39
　2.2.3 不計空間分布的初步估算...........40
2.3 研究議題.............................42

第三章：研究結果
3.1 傷口癒合模型之結果探討...............44
　3.1.1 巨觀傷口的癒合模型結果...........44
　3.1.2 微觀傷口的癒合模型結果...........52
3.2 平均場下的癌細胞之生長行為...........60
　3.2.1異變係數J對細胞生長的影響.........61
　3.2.2 固定點的存有條件.................66
　3.2.3 固定點的穩定性分析...............67
　3.2.4 相圖.............................71
3.3 考慮空間分布下的癌細胞生長行為以及腫瘤之生成.....76
　3.3.1 巨觀狀態下的腫瘤之成長...........77
　3.3.2 微觀狀態下的腫瘤之成長...........82
　3.3.3 腫瘤模擬結果之探討...............95
　參考文獻...............................97

附錄：程式語言............99
　一、驗證參考文獻之模型的程式........99
　二、巨觀傷口癒合模型之程式.........101
　三、微觀傷口癒合模型之程式.........106
　四、平均場下的腫瘤模型程式式.......119
　五、巨觀腫瘤生長模型之程式.........120
　六、微觀腫瘤生成之程式.............126

[1] Elizabeth Clayton : A single type of progenitor cell maintains normal epidermis. Nature 446,185 (2007)
[2] Arthur D. Lander : Spatial Dynamics of Multistage Cell Lineages in Tissue Stratification Biophysicl Journal Volume, 99 3145-3154 (2010)
[3] Rowland, B. D. : KLF4, p21 and context-dependent opposing forces in cancer. Nature Rev. Cancer 6, 11–23 (2006)
[4] Robert, E. M. : Oral and Maxillofacial Pathology. 1-st (edn) Quintessence Publishing Co, Inc. Carol Stream, Illinois. ISBN: 0-86715-390-3(2003)
[5] Yu-Jung Li. : A Theoretical Model for Both Embryogenesis and Carcinogenesis. Institute of Biophysics National Central University. June (2009)
[6] Patrick B. Warren : Cells, cancer, and rare events: Homeostatic metastability in stochastic nonlinear dynamical models of skin cell proliferation. PHYSICAL REVIEW E 80, 030903 (2009)
[7] Christophe Deroulers : Modeling tumor cell migration: From microscopic to macroscopic models PHYSICAL REVIEW E 79, 031917 (2009)
[8] Leonard M. Sander :Dynamics and Pattern Formation in Invasive Tumor Growth PRL 96, 188103 (2006)
[9] C. A. Condat : Cancer growth: Predictions of a realistic model. PHYSICAL REVIEW E 78, 022901 (2008)
[10] Shinya Yamanaka : Induction of Pluripotent Stem Cells from Mouse Embryonic and Adult Fibroblast Cultures by Defined Factors. Cell 126, 663–676 (2006)
[11] Shinya Yamanaka : Elite and stochastic models for induced pluripotent stem cell generation. Nature vol.460 08180 (2009)
[12] Foster, K. W : Induction of KLF4 in basal keratinocytes blocks the proliferation differentiation switch and initiates squamous epithelial dysplasia. Oncogene 24, 1491–1500 (2005).
[13] J.D Murray: Mathematical Biology II. Spatial Models and Biomedical Applications, Third Edition.
[14] Van Den Brenk :Studies in restorative growth processes in mammalian wound healing.
[15] Ashkin, J : Statistics of Two-Dimensional Lattices with Four Components. Physical Review. Vol. 64, No. 5 and 6 (1943).
[16] Potts Renfrey. Some Generalized Order-Disorder Transformations. Proceedings of the Cambridge Philosophical Society, Vol. 48, pp. 106−109. (1952).
[17] Thomas E. Cell Migration Driven by Cooperative Substrate Deformation Patterns PRL 104, 168104 (2010)
[18] Charles Kittel: Thermal Physics second edition.
[19] Bruce Alberts: Molecular Biology of the Cell.
[20] Steven H. Stogatz : Nonlinear dynamics and chaos.
[21] Allon M. Klein: Kinetics of cell division in epidermal maintenance. PHYSICAL REVIEW E 76, 021910 (2007)
[22] Weinberg, Robert E: The biology of cancer. New York Garland Science. 2007. (ISBN 0-8153-4076-1)
[23] Sergei Fedotov : Probabilistic approach to a proliferation and migration dichotomy in tumor cell invasion PHYSICAL REVIEW E 77, 031911 (2008)
[24] Chiu Fan Lee : Predicting rare events in chemical reactions: Application to skin cell proliferation. PHYSICAL REVIEW E 82, 021103 (2010)
[25] Arthur D. Lander : Pattern, Growth, and Control DOI 10.1016/j.cell.2011.03.009
[26] M. Ben Amar : Contour Instabilities in Early Tumor Growth Models PRL 106, 148101 (2011)