使用碎形維度分析於胎兒之磁振影像大腦皮質表面的複雜度量測

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研究生：	陳張宗榮 Tzong-Rong Chen
論文名稱：	使用碎形維度分析於胎兒之磁振影像大腦皮質表面的複雜度量測 Complexity Measurement of Fetal Cortical Surfaces from Magnetic Resonance Images using Fractal Dimension Analysis
指導教授：	徐國鎧 Kuo-Kai Shyu 吳育德 Yu-Te Wu
口試委員:
學位類別：	博士 Doctor
系所名稱：	資訊電機學院 - 電機工程學系 Department of Electrical Engineering
畢業學年度：	98
語文別：	英文
論文頁數：	74
中文關鍵詞：	碎形維度、磁振影像、胎兒、腦皮質複雜度
外文關鍵詞：	Magnetic resonant images, Fractal dimension, Fetus, Cortical complexity
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雖然成年人大腦表面複雜度的碎形分析已經被研究了許多年；碎形維度分析的使用，對於發育中胎兒的大腦表面的複雜度測量，卻未曾被探索。這篇論文意在使用碎形維度分析的概念，來測量發育中胎兒的大腦表面的複雜度。為了量化碎形維度，進而能清楚了解胎兒大腦表面複雜度，文中探討從二維擴展到三維的四種碎形維度分析方法。這三維碎形維度分析的方法，應用在分析32個正常胎兒大腦及6個受試胎兒大腦，孕齡在22到37週間，並估測其碎形維度。由正常胎兒大腦結果顯示：胎兒腦皮質複雜度, 隨胎兒的懷孕週數增長而增加。在相同懷孕週數下, 雙胞胎的碎形維度結果比正常胎兒為低, 顯示雙胞胎的發育會有二到三週的延遲。大腦發展遲緩的胎腦也具有低的碎形維度, 顯示發展的遲緩意味著較少的大腦表面複雜度。這些結果與胎兒大腦的發育是一致的, 且證明三維碎形維度分析的方法，對胎兒大腦的表面複雜度量測是一個有效的方法。

Although fractal dimension (FD) analyses of adult human brain complexity have been performed for several years; the use of FD analysis for complexity measurement of the developmental fetal cortical surface has not been investigated. This work aims to measure complexity of the developmental fetal cortical surface from magnetic resonant images (MRI) using the concept of FD analysis. To quantify the FD that clarifies the complexity of fetal cortical surface, four methods of FD analysis were presented and extended from 2D to 3D. The presented 3D methods of FD analysis were then adopted to estimate the FD for complexity of developmental fetal cortical surface of 32 normal brains and 6 testing brains at a gestational age (GA) of 27–37 weeks. The results for normal brains reveal that the increase in complexity of cortical surface is correlated with the gestational age of the fetus. The FD results of the twins are lower than that of normal cases, showing a delay of 2-3 weeks may occur in the twins. Observation of cortical dysplasia has low FD, indicating that cortical dysplasia may mean less cortical complexity. These results are in good agreement with fetal brain development and demonstrate that the proposed methods of FD analysis are an effective means for complexity measurement of fetal cortical surface.

中文摘要 ............................................... ii
Abstract .............................................. iii
List of Contents ....................................... iv
List of Figures ........................................ vi
List of Tables ....................... ................. ix
Chapter 1.  Introduction ................................ 1
1.1  Motivation and Background .......................... 1
1.2  Review of Previous Works ……....................... 3
1.3  Purpose and Contribution ........................... 5
1.4  Organization of the Dissertation ................... 7
Chapter 2.  System Architecture for Complexity Measurement of Fetal Brains ......................................... 8
2.1  Subjects and Data Acquisition ...................... 8
2.2  The Processing Steps for Measuring Complexity of Fetal MR Images ......................................... 9
2.3  Theory of Fractal Dimension Analysis............... 14
Chapter 3.  Methods of Fractal Dimension Estimation .... 19
3.1  The Box-Counting Fractal Dimension Method ......... 19
3.1.1  The Traditional 2D Box-Counting Method .......... 19
3.1.2  The 3D Box-Counting Method ...................... 21
3.1.3  The 3D Modified Box-Counting Method ............. 22
3.2  The Entropy Based Information Fractal Dimension Method ................................................. 25
3.2.1  The 2D Entropy-Based Information Method.......... 25
3.2.2  The 3D Entropy-Based Information Method.......... 29
3.3  The 3D FFT Fractal Dimension Method ............... 31
3.4.1  The Correlation Dimension Method ................ 31
3.4.2  The 3D FFT Fractal Dimension Method ............. 32
3.3  The 3D Box-Counting Method with Local FD Measure .. 34
3.3.1  The Linear Regression Analysis .................. 34
3.3.2  The Local FD Measure Box-counting Method ........ 36
Chapter 4.  Results and Discussion ..................... 39
4.1  Results ........................................... 39
4.1.1  The FD Results of the Phantom Fractal Images .... 39
4.1.2  Results of Preprocessing of Fetal Cortical Brain MR images ................................................. 41
4.1.3  The FD Results of a Fetal Cortical Brain ........ 44
4.1.4  The FD Results of Developmental Fetal Cortical Surface ................................................ 47
4.2  Discussion ........................................ 49
Chapter 5. Conclusions and Future Works ................ 52
5.1 Conclusions ........................................ 52
5.2 Future Works ....................................... 55
References ............................................. 56
Appendix …............................................. 63
List of Publications ................................... 64

                                

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