在灌注加權成像(PWI)中的選擇性圖像分割和組織風險評估

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研究生：	蘇克諦 Bal, Sukhdeep Singh
論文名稱：	在灌注加權成像(PWI)中的選擇性圖像分割和組織風險評估 Selective Image Segmentation and Tissue at Risk Assessment in Perfusion Weighted Imaging
指導教授：	楊梵孛 Yang, Fan-pei Gloria
口試委員:	N/A Alpers, Andreas N/A Colquitt, Daniel 彭家勛 Peng, Giia Sheun N/A Wu, Junjie 許靖涵 Hsu, Ching-Han
學位類別：	博士 Doctor
系所名稱：	教務處 - 跨院國際博士班學位學程 International Intercollegiate PhD Program
論文出版年：	2023
畢業學年度：	111
語文別：	英文
論文頁數：	144
中文關鍵詞：	圖像分割、電腦斷層掃描、核磁共振、灌注加權成像
外文關鍵詞：	PWI
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灌注加權成像(PWI) , 是一種非侵入式的磁振造影（MR）/電腦斷層造影檢查（CT）技術，用於評估各種血液動力學參數以檢驗腦區的血流狀態。這些參數通常用於定位中風病人的半影區或高風險的組織，透過再灌流療法進行搶救。某些電波與掃描器軟體所預估腦灌流參數的成像管道與分割方法有關。本論文著重於發展腦灌流參數估計與分割方法的影像分析路徑。我們聚焦於腦灌流權重影像上的動脈區域分割以及低對比度、非均質強度和非平滑邊緣影像上的腫瘤分割等困難問題。
我們首先在變分框架中開發動脈區域的分割模型。我們提出一套新的模型將幾何限制融入到距離函數當中。這套修正模型採用在距離項中的離散總變異，並通過最小化凸函數的能量來定位動脈區域，優於先前的選擇性分割方式，這些方式通常採用成本函數或基於叢集的方法。這種提升使得本模型能有效選擇識別高風險組織上表現良好的動脈區域。另一項研究調查是否將血液動力學模型擬合到從動脈分割獲得的動脈輸入函數(Arterial input function，AIF)並在選擇AIF時最小化部分體積效果，是否能改善對中風患者的核心和半影區的測定的估計。

在本論文的後半部分，我們提出了一套選擇性分割的高效率的架構，使用新區域力項和基於離散總變異公式的測地距離逞罰項。本研究所提出的模型是使用者獨立的，並允許在具有非均質、非平滑和粗糙邊緣的腫瘤影像和醫療影像中進行精確的分割。本研究另闢一章，專門討論將變分分割方法與深度學習整合。儘管近年來深度學習技術非常受歡迎，深度學習技術經常受到需要大量標籤數據集的限制。我們示範了如何使用變分方法作為半監督（或非監督）訓練演算法中的損失函數來補充標籤，以進行腦腫瘤的分割。

磁振造影（MR）
電腦斷層造影（CT）
動脈輸入函數（AIF）

ABSTRACT

Perfusion-weighted imaging (PWI) is a noninvasive Magnetic Resonance (MR)/Computed
Tomography (CT) technique that assesses various hemodynamic parameters to examine
blood flow in brain regions. These parameters are used in stroke patients to locate the
penumbra or the tissue at risk, which can be salvaged with reperfusion therapies. Certain
artefacts are associated with the imaging pipeline and segmentation methods used in scanner
software’s to estimate perfusion parameters. The focus of this thesis is the development of
an image analysis pipeline for perfusion parameter estimation and segmentation models. We
concentrate on difficult problems such as arterial region segmentation on perfusion weighted
images and tumor segmentation on images with low contrast, in-homogeneous intensity, and
non-smooth edges.

We begin with developing an arterial region segmentation model in the variational framework.
We propose a new model in which geometric constraints are incorporated into a
distance function. The modified model employs discrete total variation in the distance term
and locates arterial regions by minimizing the energy of a convex functional, outperforming
previous selective segmentation works that typically employ either a cost function or
a clustering-based approach. This enhancement enables our model to effectively select an
arterial region that performs well in identifying tissue at risk. Another work investigates
whether fitting a hemodynamic model to the Arterial input function (AIF) obtained from
arterial segmentation and minimizing the partial volume effect during AIF selection improves
volumetric estimation of core and penumbra in stroke patients.

In the second half of this thesis, we propose an efficient framework for selective segmentation
using a new region force term and a geodesic distance penalty based on a discrete TV
formulation. The proposed model is user-independent and allows for precise segmentation in
tumor images and medical images with non-homogeneous, non-smooth, and scraggy boundary edges. A chapter is dedicated to integrating the variational segmentation method with deep learning. Despite being extremely popular recently, deep learning techniques are frequently constrained by the need for sizable sets of labelled data. We demonstrate how labels can be supplemented by using a variational method as a loss function in a semi-supervised (or unsupervised) training algorithm for brain tumor segmentation.

Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Introduction 13
1 Project Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Perfusion Weighted Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Image Processing and Image Segmentation . . . . . . . . . . . . . . . . . . 17
4 Chapters of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Mathematical Preliminaries 22
1 Linear Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 Regularisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Calculus of Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Variation of a Functional . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Discretisation of Partial Differential Equations . . . . . . . . . . . . . . . . . 31
4.1 Finite Difference Schemes . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.1 Numerical methods to solve Linear Systems of Equations . . . . . . . 34
5.2 Numerical methods to solve Non-Linear Systems of Equations . . . . 36
Review of Segmentation Models 43
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.1 Variational Segmentation approach . . . . . . . . . . . . . . . . . . . 44
2 Global Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.1 Mumford and Shah Model . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2 Chan-Vese Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3 Level set Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4 Convex version of Chan Vese Model . . . . . . . . . . . . . . . . . . 52
3 Selective Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 Geodesic Active Contours . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Gout et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3 Badshah and Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Rada and Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 Spencer and Chen Model . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Convex Liu et.al . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Roberts Chen Convex Geodesic Selective Model . . . . . . . . . . . . 59
3.8 Additive Operator Splitting . . . . . . . . . . . . . . . . . . . . . . . 62
Arterial Input Function Segmentation based on a Contour Geodesic model
for Tissue at Risk identification in Ischemic Stroke 65
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.1 Proposed contour based AIF Segmentation method . . . . . . . . . . 67
2.2 Purposed Matrix analysis to find the potential AIF within the contour 70
2.3 Perfusion Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . 71
2.4 Statistical analysis and Perfusion parameter estimation . . . . . . . . 71
3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1 Statistical analysis of Curve Characteristics . . . . . . . . . . . . . . 72
3.2 Perfusion maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1 AIF and contour based models . . . . . . . . . . . . . . . . . . . . . 79
4.2 Tissue at risk and limitations . . . . . . . . . . . . . . . . . . . . . . 80
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Partial Volume Effects correction and Curve fitted Arterial Input Function
for Core and Penumbra estimation 81
1 Partial volume affect correction for Arterial Input Function (AIF) . . . . . . 83
1.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 84
1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2 Core and Penumbra estimation using Deep learning based AIF in association
with clinical measures in Computed Tomography Perfusion (CTP) . . . . . . 95
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Selective Geodesic Variational Segmentation Model with new Region force104
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2 Review of Selective Segmentation Model . . . . . . . . . . . . . . . . . . . . 106
3 Purposed Selective Segmentation Model . . . . . . . . . . . . . . . . . . . . 108
3.1 Mathematical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.1 Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2 Quantitative comparisons . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3 Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Deep Learning Segmentation and Future Work 126
1 Unsupervised Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
1.2 Deep Learning Implementation . . . . . . . . . . . . . . . . . . . . . 127
1.3 Predicted Results from Deep learning network . . . . . . . . . . . . . 129
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131


                                

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