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研究生:甘弘暐
研究生(外文):Hong-Wei Kan
論文名稱:多頻率同步驅動光源之三維頻域式擴散光學斷層造影數值計算研究
指導教授:潘敏俊
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:109
中文關鍵詞:三維擴散光學斷層造影多頻率同步驅動光源方波驅動光源有限元素法Tikhonov正則化腫瘤特徵辨識影像重建影像評估
外文關鍵詞:three-dimensional diffuse optical tomographymulti-frequency synchronous driving light sourcesquare wave driven light sourcefinite element methodTikhonov regularizationidentification of tumorimage reconstructionquantitative evaluation of image
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近紅外光擴散光學斷層造影(Near infrared diffuse optical tomography, NIR DOT),將近紅外光打入組織,藉由量測近紅外光穿透組織之光強度變化,重建出組織內部之光學係數影像,並利用其光學係數差異,區別腫瘤與正常組織。本論文以多頻率同步驅動光源進行三維頻域式擴散光學斷層造影,藉由方波達成多頻率同步驅動。組織光學重建以擴散方程式為模型,將演算法分為前向計算與逆向計算兩個部分。前向計算,使用有限元素法(Finite element method, FEM)求解擴散方程式以獲得光強度與相位分佈。逆向計算,將前向計算得到之光資訊與量測得到之光資訊透過牛頓法疊代,求出量測與理論的光資訊差異最小化,進而估測光學係數的分佈。由於逆向計算的病態特性(ill-posed characteristics),故使用Tikhonov正則化穩定重建結果,其中多組頻率之光資訊,於雅可比矩陣以縱向擺放。
實驗中分為二維平面與三維立體模擬,分別採用直徑80 mm圓型,與底圓直徑80 mm、高度80 mm的仿乳作為模型,藉由設計不同乳房仿體光學特性之案例,驗證多組頻率資訊相較單組頻率資訊的重建能力。結果顯示,二維平面頻率DOT,對於離心距離15 mm置入物皆可順利重建,而對於離心距離25 mm置入物,其半徑大於7.5 mm重較效果最好;三維立體多頻率DOT,對於離心距離10 mm置入物,半徑大於7 mm可順利重建,而對於離心距離20 mm置入物,其半徑需大於10 mm重較效果較好。多頻率DOT對於較小及位於深層的置入物具有更好重建效果,同時雜訊與光學係數串擾現象對其影響較低。
Near infrared Diffuse optical tomography (NIR DOT), using the intensity of the infrared light reflecting on the tissue; and rebuild of optical coefficient image inside the tissue to differentiate tumor or regular tissue. The study focuses on three dimensional frequency domain diffuse optical tomography using multi-frequency driving light source, where the driving light source are using square wave. Reconstruction of tissue optics is based on the diffusion equation as model, and involves both the forward calculation and the inverse reconstruction. The forward calculation using Finite element method (FEM) for calculating the distribution of the light intensity and phase. The inverse calculation reconstructs the distribution of the optical coefficient by using Newton’s to minimize the difference between the theory obtained by forward calculation and measurement obtained by measured data. Due to ill-posed characteristics of the inverse calculation, Tikhonov regularization is utilized to stabilize the reconstruction result. The multi-sets of frequency of measurement data were placed in vertically in the Jacobian matrix.
The experiment includes 2 dimensional and 3 dimensional simulation, using 80 mm diameter circle and 80 mm diameter breast-like phantom as 2D and 3D geometry. For verification the ability of reconstruction with multi frequency module compare to single frequency module, different designated simulation cases , including different position of inclusion, size, and contrast ratio of absorption and reduced scattering coefficient of inclusion respect to background were used. As the result display, 2D plane DOT can reconstruction successfully with off-center to be 15mm; ideally, it is most efficient for the off-center to be 25mm and the radius to be more than 7.5mm. For the 3D DOT, the radius has to be larger than 7mm if the off-center is 10mm to be successfully planted; if the off-center is 20mm, then the radius needs to be larger than 10 mm to operate most efficiently. Multi-frequency DOT operates much more efficient with smaller and deeper placement. Additionally, it minimizes the noise and optical coefficient error.
摘要 I
Abstract II
誌謝 IV
目錄 V
圖目錄 VII
表目錄 XI
第一章 緒論 1
1-1 研究動機與目的 1
1-2 乳房組織光學特性與醫學影像造影 3
1-3 方波驅動光源 7
1-4 文獻回顧 8
1-4 論文架構 12
第二章 前向問題 13
2-1 擴散方程式 13
2-2 有限元素法求解擴散方程式 14
第三章 逆向問題 18
3-1 逆向問題之建立 18
3-2 雅可比(Jacobian)矩陣 20
3-3 雅可比矩陣正規化(normalization) 21
3-4 逆向問題正則化(regularization) 22
第四章 數值模擬驗證 23
4-1 模擬資料建立 23
4-2影像重建 28
4-3 模擬資料驗證 32
4-3-1幾何特徵辨識 33
4-3-2光學特徵辨識 58
4-4 影像評估與分析 76
第五章 結論 88
參考文獻 89
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