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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳義裕(Yih-Yuh Chen),龐寧寧(Ning-Ning Pang) | |
| dc.contributor.author | Geng-Ming Hu | en |
| dc.contributor.author | 胡耿銘 | zh_TW |
| dc.date.accessioned | 2021-05-17T09:16:41Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.available | 2021-05-17T09:16:41Z | - |
| dc.date.copyright | 2012-08-01 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-31 | |
| dc.identifier.citation | [1] Chang, H. H., Hemberg, M., Barahona, M., Ingber, D. E., Huang, S.(2008) Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature, 453 , 544-548.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6709 | - |
| dc.description.abstract | 具有異質性的族群是自然界中常見的一種複雜系統，而其中一種讓人感興趣的簡單模型就是僅有兩個子群但彼此會互相競爭且可互相轉換的系統。在本篇的工作中，我們發展了一套描述這樣子的二態成長且具有互相轉換性質系統的數學模型，並且應用這個模型對應到了前列腺癌症腫瘤球在治療之下的真實成長數據。 | zh_TW |
| dc.description.abstract | Heterogeneous population is common among complex systems in nature. A simple heterogeneous growth model of interest is one with two states which not only compete with each other but exhibit transition phenomenon. In this work, we develop a mathematical model to describe such a system and apply it to fit the real growth data of the prostate cancer spheroid under treatments. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-17T09:16:41Z (GMT). No. of bitstreams: 1 ntu-101-D94222006-1.pdf: 14154602 bytes, checksum: 9ba7d35b804e50dad81688f5cc61e6ef (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | I A two-state growth model with transition probability 1
1 Introduction 2 2 Mathematical model of two-state growth with transition probability 6 2.1 The general Growth and transition model . . . . . . . . . . . . . . . 7 2.1.1 The time evolution equation of x1 and x2 . . . . . . . . . . . 7 2.1.2 Transforming x1 and x2 to xt and w1 . . . . . . . . . . . . . . 7 2.1.3 Some simplified cases. . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The general two-state growth and transition model with auto/paracrine signaling pathway . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 The auto/para-crine signaling pathway and it mathematical form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 The nullclines and fixed points in general autocrine transition case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.3 Jacobian matrix in general autocrine transition case. . . . . . 13 2.3 fi is a constant, the exponential growth model . . . . . . . . . . . . 16 2.3.1 Two-state exponential growth and autocrine transition model 16 2.3.2 The exact solution . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 When fi is a linear function- the general logistic growth model . . . 18 2.4.1 A general form of two-state logistic growth and autocrine transition model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 i 2.4.2 The xt nullcline for the general logistic growth . . . . . . . . 19 2.4.3 w˜1(xt) in a general logistic growth and autocrine transition model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.4 The fixed point formula in general logistic growth and autocrine transition model . . . . . . . . . . . . . . . . . . . . . 28 2.4.5 The stability and possible spiral behavior in general logistic growth and autocrine transition model . . . . . . . . . . . . . 40 2.5 The classification of logistic growth model. . . . . . . . . . . . . . . . 41 2.6 LH-0 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6.1 The exact solution when r1 = r2 . . . . . . . . . . . . . . . . 43 2.6.2 The nullclines . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.6.3 The fixed point condition . . . . . . . . . . . . . . . . . . . . 45 2.6.4 The stability of the fixed point . . . . . . . . . . . . . . . . . 45 2.6.5 The phase portraits of LH-0 . . . . . . . . . . . . . . . . . . . 45 2.7 LH-A model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.7.1 The nullclines . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.7.2 The fixed point condition . . . . . . . . . . . . . . . . . . . . 48 2.7.3 The stability of fixed point . . . . . . . . . . . . . . . . . . . 48 2.7.4 The phase portraits of LH-A . . . . . . . . . . . . . . . . . . 49 2.8 LH-B model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.8.1 The nullclines . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.8.2 The fixed point condition . . . . . . . . . . . . . . . . . . . . 52 2.8.3 The stability of fixed point . . . . . . . . . . . . . . . . . . . 53 2.8.4 The phase portraits of LH-B . . . . . . . . . . . . . . . . . . 53 2.9 LH-C model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.9.1 The nullclines . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.9.2 The fixed point condition . . . . . . . . . . . . . . . . . . . . 57 2.9.3 The stability of fixed point . . . . . . . . . . . . . . . . . . . 58 2.9.4 The phase diagram and phase portraits of LH-C . . . . . . . 60 2.10 LH-D model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 ii 2.10.1 The phase diagram and phase portraits of LH-D . . . . . . . 60 3 Conclusion 61 II An application to cancer growth system and treatment development 62 4 A simple introduction of carcinomatous process 63 5 A heterogeneous cancer growth with autocrine signaling pathway and fitting the growth curves of prostate tumor spheriod 65 5.1 Fitting idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.2 Result and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.1 Some simple properties of this model . . . . . . . . . . . . . . 68 5.2.2 A comparison of the numerical results and real data from tumor growth with treatments . . . . . . . . . . . . . . . . . . . . . . 72 6 IAS treatment simulation by the mathematical model and the planning of optimized therapy. 78 6.1 The clinical prostate cancer therapy of human- IAS (Intermittent Androgen Suppression) therapy . . . . . . . . . . . . . . . . . . . . . . . 78 7 Conclusion 81 A Statistical methods to make out sub-state from a whole system. 82 A.1 Least squares method . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.2 Maximum likelihood method . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.1 Maximum Likelihood . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.2 Logarithmic likelihood ratio test . . . . . . . . . . . . . . . . . 85 A.3 Numerical simulation method . . . . . . . . . . . . . . . . . . . . . . 87 iii A.3.1 Generation of non-uniform random number . . . . . . . . . . . 87 A.3.2 Optimum method . . . . . . . . . . . . . . . . . . . . . . . . 92 A.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.4.1 1-D data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.4.2 Application of 2-D data analysis . . . . . . . . . . . . . . . . . 111 B The phase portraits of two-state logistic growth and autocrine transition model 120 B.1 The phase portraits of LH-0 . . . . . . . . . . . . . . . . . . . . . . . 120 B.2 The phase portraits of LH-A . . . . . . . . . . . . . . . . . . . . . . 133 B.3 The phase portraits of LH-B . . . . . . . . . . . . . . . . . . . . . . 179 B.4 The phase portraits of LH-C . . . . . . . . . . . . . . . . . . . . . . 183 B.5 The phase portraits of LH-D . . . . . . . . . . . . . . . . . . . . . . 232 C Simple analysis of the time evolution of the cancer system model 248 iv | |
| dc.language.iso | en | |
| dc.title | 二態成長與躍遷模型及其在癌症成長系統及療法開發的應用 | zh_TW |
| dc.title | Two-state growth with transition model and its application to cancer growth system and therapy development | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 陳宣毅(Hsuan-Yi Chen),陳啟明(Chi-Ming Chen),李世炳(Sai-Ping Li) | |
| dc.subject.keyword | 二態系統,成長與躍遷模型,異質性系統,癌症,療法, | zh_TW |
| dc.subject.keyword | two-state system,growth with transition model,heterogeneous system,cancer,therapy, | en |
| dc.relation.page | 257 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2012-08-01 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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