中國醫藥大學機構典藏 China Medical University Repository, Taiwan:Item 310903500/26459

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行政院國家科學委員會專題研究計畫成果報告

以核磁共振乳房影像模擬乳房非線性變形壓縮:計算乳房密

度

研究成果報告(精簡版)

計畫類別：個別型

計畫編號： NSC 98-2221-E-039-009-

執行期間： 98 年 08 月 01 日至 99 年 07 月 31 日

執行單位：中國醫藥大學生物醫學影像暨放射科學學系

計畫主持人：施子卿

共同主持人：陳中和、何永仁

計畫參與人員：此計畫無其他參與人員

報告附件：出席國際會議研究心得報告及發表論文

處理方式：本計畫可公開查詢

中華民國 99 年 10 月 23 日

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計畫類別：■個別型計畫 □整合型計畫

計畫編號：NSC 98－2221－E－039 －009

執行期間： 98 年 8 月 1 日至 99 年 7 月 31 日

執行機構及系所：中國醫藥大學

生物醫學影像暨放射科學學系

計畫主持人：施子卿

共同主持人：陳中和、何永和、蘇敏瑩

報告目錄

成果報告封面 P2

報告內容 P3

參考文獻 P9

成果報告及計畫成果自評表 P13

出席國際學術會議心得報告 P15

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行政院國家科學委員會補助專題研究計畫

■成果報告

□期中進度報告

（計畫名稱）

以核磁共振乳房影像模擬乳房非線性變形壓縮

:計算乳房密度

Computational Simulation of Breast Compression

Based on Non-Linear Deformation by Using Magnetic

Resonance Images: to Measure Breast Density

計畫類別：■個別型計畫 □整合型計畫

計畫編號：NSC 98－2221－E－039 －009

執行期間： 98 年 8 月 1 日至 99 年 7 月 31 日

執行機構及系所：中國醫藥大學生物醫學影像暨放射科學學系

計畫主持人：施子卿

共同主持人：陳中和、何永和、蘇敏瑩

計畫參與人員：

成果報告類型(依經費核定清單規定繳交)：■精簡報告 □完整報告

本計畫除繳交成果報告外，另須繳交以下出國心得報告：

□赴國外出差或研習心得報告

□赴大陸地區出差或研習心得報告

■出席國際學術會議心得報告

□國際合作研究計畫國外研究報告

處理方式：

除列管計畫及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年□二年後可公開查詢

中華民國 99 年 10 月 23 日

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I. Introduction

Mammographic density is a quantitative estimate of the proportion of fibroglandular tissue to the total breast area analyzed on mammograms. The fat and fibroglandular tissues are two major components of the breast. The fibroglandular tissue is denser than the fatty tissue, and therefore shows brighter intensity on mammograms; and as such the percentage of the dense tissues in the breast area can be measured based on the contrast shown in the mammogram, termed “mammographic density”. There is well-established evidence that a higher mammographic density is associated with an increased risk of breast cancer [1-4], thus the breast density may play an important role in the evaluation of cancer risk. Women with mammographic density greater than 50% have 3- to 5-fold higher breast cancer risk than those with less than 25% density [4-8].

Despite the established role of breast density as one of the strongest predictors of breast cancer risk, the progress to build the density into the risk assessment model has been relatively slow. That is in part due to the lack of reliable measurement methods. Visual estimation has been still commonly used in recent publications [11-15]. Quantitative measurements by planimetry, computer-assisted thresholding, and clustering segmentation methods [16] have been reported, yet whether they are reliable for measuring changes over time remains to be determined.

Even if a reliable method can be developed, another fundamental problem is the nature of projection images in mammography. The measured density may depend upon the projection angle, compression level, patient position, and x-ray intensity. Recently, Kopans (2008) indicated that the use of two-dimensional (2D) mammograms alone to assess the ratio of dense to fatty tissue in the breast is inaccurate for determining the volume ratios of the soft tissues, and suggested that an accurate breast density should be obtained from the three-dimensional (3D) data (i.e., volumetric measurement of breast density) [1]. However, the value of breast density measured by mammography is currently under debate [17]. Recently, there are some efforts to estimate density on mammograms considering the overlapping tissue along the projection direction. For example, Ding et al. (2008) developed “standard mammogram form (SMF)” to estimate the density volumetrically [18], but it was found that SMF is not better compared to the thresholding method for cancer risk prediction. The thresholding method, a computer-assisted technique that uses the gray scale in the digitized images, is to calculate the percent area of breast covered in dense regions or is to compute the number of pixels in dense area and total breast area (i.e., measuring breast density) for assessing the risk of breast cancer [19-21]. Furthermore, the stepwise rises in a breast cancer risk associated with higher density was measured by the thresholding method [18].

Therefore, the variations in the measured density by mammography warrant more research. To investigate this variation, the mammograms taken from the same woman using different positions, compression angles, and compression levels should be compared; however, since radiation is given to the woman, it is not ethical to perform such a study due to concern for excessive radiation exposure. Instead, a simulation model may be used to investigate the dependence of measured density on mammograms based on the 3D distribution of fatty and fibroglandular tissues within the breast measured by MRI. The first step for such a simulation model is to account for the effects of breast compression. In this work, we applied a nonlinear deformation model to estimate the displacement of tissues based on different elastic properties of fibroglandular and fatty tissues.

II. Methods

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The MRI study was performed on a 1.5 T Eclipse scanner (Philips, Cleveland, OH) using a dedicated four-channel breast coil. The pre-contrast T1-weighted images without fat saturation were using a 3D SPGR (RF-FAST) pulse sequence, with TR=1.8 ms, TE=4.0 ms, slice thickness=4.0 mm, flip angle=20, matrix size=256256, FOV=380 mm. A total of thirty-two axial slices were used to cover the entire breast. Only normal breast was used for simulation. First, a computer-assisted algorithm was employed to segment the fatty and the fibroglandular tissues from MR images, based on the method reported in Nie et al. (2008) [22]. The breast was segmented from the body using the following procedures: (a) perform an initial V-shape cutting using three body landmarks to determine the posterior cutoff points of breast in the lateral boundary; (b) apply a fuzzy C-means (FCM) based segmentation algorithm(i.e., excluding air and lung tissue) with the B-spline curve fitting to obtain the breast boundary. Fuzzy C-means algorithm uses a fuzzy pixel classification to segment images [23-25]. The FCM clustering algorithm needs a priori information about the number of classes in the dataset [26-28]. The FCM clustering algorithm is also sensitive to the situation of the initialization and easy to fall into the local minimum or a saddle point while iterating. B-spline curve fitting is used to exclude chest wall muscle and dynamic searching to exclude skin. B-splines curve fitting is to compute a curve to a set of data points by basis function of a fixed order [29,30]. After the breast region is obtained, the fuzzy C-means clustering algorithm is applied for homogeneity correction and segmentation between the fibroglandular and fatty tissues. An example of the segmented breast region and the fibroglandular tissues from 32 imaging slices acquired from one patient is shown in Fig. 1.

Fig. 1. The segmented fatty tissue (white areas) and the fibroglandular tissue (red areas) using by the MRI-based segmentation method (Nie et al., 2008)[22].

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In order to generate the volume mesh of the breast, the outside surface of the whole breast needs to be determined first. Currently available medical imaging software for 3D reconstruction treats objects as surface components, and this is done using triangulation of the surface [31-36]. The surface triangulation uses a set of triangular facets (i.e., triangular surface elements) of different sizes and shapes to cover the surface of an object. The surface of breast tissues were covered with triangular elements by the Avizo® 6.0 software package (Visage Imaging Inc., Carlsbad, California, USA), in which the Delaunay triangulation was employed to build topological structures from MR images. The MR image set had 32 slices with the corresponding voxel size of 1.481.484 mm3. The Avizo® 6.0 software package (Visage Imaging Inc., Carlsbad, California, USA) was used to create the 3D surface of the breast, as shown in Fig. 2.

Fig. 2. The 3D surface of the whole breast and the fibroglandular tissues generated by using Avizo® 6.0 software package based on the segmentation results shown in Fig.1.

The 3D surface geometry of the fibroglandular tissue within the breast was also generated, as demonstrated in Fig. 3. The outside surface of the whole breast contained 56,098 points and 109,248 faces (i.e., triangular elements).

Fig. 3. The 3D surface generation of breast and fibroglandular tissues reconstructed by Avizo® 6.0 software to show coronal view (a, the front view from anterior to posterior), sagittal view (b, the side view from lateral to medial), and axial view (c, from superior to inferior).

II.C. Volume mesh generation

The finite element software package MSC.Marc® (MSC Software Corporation, Santa Ana, California, USA) was used to generate the volume mesh from the 3D surface geometry of the breast and the fibroglandular tissues, shown in Fig.2. The tetrahedral volume mesh with 4 nodes was defined as one element. The breast was meshed into 23,777

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elements, 21,417 for the fatty tissue and 2,360 for the fibroglandular tissue. After the volume mesh is generated, this allows simulation of breast deformation using the finite element (FE) method when an external force is applied.

Fig. 4. The volume mesh of the left breast and the fibroglandular tissues generated by using the finite element software package MSC.Marc® . The mesh lines indicate the finite elements used.

II.D. Nonlinear breast compression

For most medical applications with small tissue deformation less than 5% strain, the linear elasticity model has been used commonly. Using atomic force microscopy and finite element modeling, Kang et al. demonstrated changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor- [37]. Since the deformation of breast compression in mammography is much larger (i.e. over 5%), the nonlinear elastic model was employed [38-40]. The hyperelastic mode is the Mooney-Rivlin nonlinear elastic model to describe the constitutive law for large deformation of the soft tissue [41-43]. We implemented the hyperelastic model to simulate the deformation. The hyperelastic materials have a very small compressibility. It also can endure large elastic strain that is recoverable. A strain energy density function for quasi-incompressible hyperelastic materials in terms of the strain invariants is defined in Eq. (1). For the Moony-Rivilin materials, the strain-energy density function can be described as the simplest rational polynomial representation (Horgan, 2009) [44, 45]. The constitutive model reflects slight deviations from incompressibility on assuming that the material is homogeneous, isotropic and hyperelastic [44,45]. The strain energy density function is expressed using the polynomial constitutive model as follows



 





 





N j i j i i j

I

C

1 2 1

3

3 

(1) whe 2 3 2 2 2 1 1













I

and 21 2 3 2 3 2 2 2 2 2 1 2  

I are strain invariants,



₁,



₂,



3are the eigenvalues of the stretch

tensor, and N is the order of the polynomial. If N is set to 1, it represents the Mooney-Rivlin materials [46]. Based on the polynomial model, the measured strain energy coefficients of fatty and fibroglandular tissues were summarized in the report proposed by Tanner et al. (2006) and Samani and Plewes (2004) [39, 40]. The Mooney-Rivlin material constants used in our simulation model were: (N =1,

C

₀₁=1,333 Pa and

C

₁₀= 2,000 Pa) for fatty tissues, and (N =1,

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01

C

=2,333.3 Pa and

C

₁₀=3,500 Pa) fibroglandular tissues [47].

In order to simulate the nonlinear elastic deformation of breast compression, we used the von Mises strain and tangential Young’s modulus for each iteration step in the MSC.Marc® finite element software solver. The deformation-dependent tangential Young’s modulus is given by

e e

d

E







(2)

where



_e and



_e are the von Mises stress and strain, respectively. We also assumed all tissues are incompressible during deformation upon compression. Finally, we used the finite element software package MSC.Marc® to simulate breast compression at various compression ratios from 0 to 60%.

II.E. Boundary conditions for breast compression

The planar compression paddle was set as a rigid body. Notice that the compression paddle must need to select a 3-D surface object in Contact Bodies item in MSC.Marc software package due to the breast compression is in a 3-D deformation (i.e., the contact between compression paddles and the breast surface is a 3-D touching). The friction contact between the paddle and the breast was assumed based on Coulomb’s friction law and the friction coefficient was set to 0.2 for both contact bodies. In this study, the compression direction was set as the z-direction in either CC or MLO compression. Since the posterior surface of the breast was sitting on the ribcage, it gave another constraint not allowing the nodes to move along the y-axis direction. There are a total of 454 nodes on this surface, and they can only slide within the x-z plane during the deformation under breast compression, as shown in Fig. 5.

Fig. 5. The fixed y-direction displacement on the posterior breast surface during compression as the boundary condition. The red crosses indicate the posterior nodes with fixed displacement in the y-axis direction.

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Figure 6 shows the deformations of the breast in the x-axis, y-axis, and z-axis directions at 60% compression ratios in CC compression. The moving velocity of the two paddles toward each other was set at 0.02 cm s-1, and the time step for each iteration was 0.5 sec. When the time reached 133 sec, each compression paddle moved 2.66 cm. The thickness of the breast before compression was 13.3 cm, hence the compression ratio was approximately 40% at this time point (2.662/13.3=0.4). The color-coding indicates the relative extent of displacements in three directions. The MSC.Marc® software detects the maximum and the minimum values of the displacement and equally divides the range into 10 levels indicated by different colors. Therefore the colors can only be used for evaluating relative changes. The maximum and minimum displacements from all nodes in the whole compression volume were obtained to indicate the degree of movement and summarized in Table I. For example, in Fig.6 at 60% compression ratio, the minimum and maximum displacements in the z-axis were -4.0 cm in negative z direction and 4.0 cm in the positive z direction, and the range of displacements was from -1.8 to 2.7 cm in the x-axis, and from -1.7 to 0.7 cm in the y-axis. While the compression paddles were moving along the z-axis direction, the posterior breast (i.e., the chest wall on ribcage) was fixed as the boundary condition; thus, the breast tissue was pushed away from the chest wall. The range of displacement variations in x-, y-, and z-axis directions at 20%, 40%, and 60% compression ratio are listed in Table I.

Fig. 6. The side view of the breast deformation before compression and at 60% CC view compression ratios. The relative displacements at x-, y-, and z-direction are shown by colors on the same sagittal view images. The range between the minimum and maximum displacement values are equally divided into 10 levels, shown by different colors. The blue and yellow color bars indicate the minimum and maximum values of displacements, which is -1.8 to 2.7 cm in x-axis, -1.7 to 0.7 cm in y-axis, and -4.0 to 4.0 cm in z-axis at 60% compression ratio. The displacements in the z-direction (the compression direction between the two paddles) is greater compared to x- and y- displacements.

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IV. Conclusions

In this work we demonstrated our compression model and the simulation of tissue displacement by using two software packages, Avizo® 6.0 and MSC.Marc® . We need to further refine the model to mimic the way that a derived mammogram is taken. For example, for MLO view compression, we may also include the muscle in the analysis to match the typical MLO mammogram. Our simulation model may provide a suitable tool for analyzing the change of breast density at different compression situations to further understand the measurement variations due to technical factors that cannot be studied in humans. In order to achieve this goal, we will need to improve the spatial resolution of the compressed breast, and then to generate a derived mammogram based on the characteristic properties of x-ray sources and detectors.

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國科會補助專題研究計畫成果報告自評表

請就研究內容與原計畫相符程度、達成預期目標情況、研究成果之學術或應用價

值（簡要敘述成果所代表之意義、價值、影響或進一步發展之可能性）

、是否適

合在學術期刊發表或申請專利、主要發現或其他有關價值等，作一綜合評估。

1. 請就研究內容與原計畫相符程度、達成預期目標情況作一綜合評估

■ 達成目標

□ 未達成目標（請說明，以

100 字為限）

□ 實驗失敗

□ 因故實驗中斷

□ 其他原因

說明：部分結果已發表在國際著名期刊

Physics in Medicine & Biology

**T.C. Shih*, J.H. Chen, D. Liu, K. Nie, L. Sun, M. Lin, D. Chang, O. Nalcioglu,**

and M.Y. Su, “Computational Simulation of Breast Compression Based on

Segmented Breast and Fibroglandular Tissues on Magnetic Resonance

Images,” Physics in Medicine and Biology, vol. 55, no.14, pp.4153-4168,

July, 2010. (國科會計畫編號 NSC 98-2221-E-039-009)

2. 研究成果在學術期刊發表或申請專利等情形：

論文：■已發表 □未發表之文稿 □撰寫中 □無

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其他：

（以

100 字為限）

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3. 請依學術成就、技術創新、社會影響等方面，評估研究成果之學術或應用價

值（簡要敘述成果所代表之意義、價值、影響或進一步發展之可能性）（以

500 字為限）

學術成就

:部分研究成果已發表在國際著名期刊 Physics in Medicine and

Biology, July,2010.

技術創新

:本研究使用核磁共振乳房影像模擬乳房非線性大變形壓縮二項技

術，是醫學影像與生物力學結合之技術創新。

社會影響

:乳房攝影是在早期診斷乳癌有效的診斷方式。乳房攝影所得的乳房

攝影緻密度(乳房密度)即是纖維腺體組織在全部乳房組織的比值，其亦是一

評估乳癌風險之重要標誌。新證據顯示乳房攝影緻密度高的女性會增加

4~5

倍乳癌風險的罹患率。乳房壓縮是乳房攝影必要的方式，乳房壓縮不僅減少

乳房攝影厚度亦可減少病人輻射劑量並改善影像。然而，乳房密度會隨者壓

縮角度、壓縮率、病人的姿態和位置、放射人員的技術品質而改變。即使是

同一個病人同一放射師，不同投影角度也可能穫得不同的乳房密度。由於，

乳房壓縮是大變形(通常超過 20%變形，非線性變形)，本研究使用核磁共振

乳房影像模擬乳房非線性壓縮。結果顯示在壓縮方向的乳房組織位移變化比

其他兩個方向大。壓縮的組織厚度，

60％的壓縮比下，壓縮後乳房厚度約為

5-7 公分的範圍，這是典型的乳房 X 光檢查範圍。此研究提供一個有用的工

具的可靠性評估乳房密度方法可用於評估患乳腺癌的風險模型。

(16)

國科會補助專題研究計畫項下出席國際學術會議心得報告

日期：99 年 10 月 23 日

一、參加會議經過

參加

2010/5/1~2010/5/7 瑞典斯德哥爾摩國際醫用磁振造影學會(ISMRM)2010

年會及

ESMRMB,SMRT 大會聯合會所主辦，國際醫用磁振造影學會(ISMRM)是每年

最重要的醫用磁振造影大型學術會議。這次舉辦在瑞典首都典斯德哥爾摩，可說不

管是在醫用磁振造影學術界或產業最重要的會議之一。本次會議共有來自世界各地

的國家超過六千位的教授、學者、研究人員及產業界代表等參與，約超過

5000 篇被

接受為壁報展示或口頭報告，內容遍及醫學物理師應了解磁振造影基本物理、磁振

造影在工程上的應用、在臨床試驗前的磁振造影癌症研究、腦連結的磁振造影評估、

心臟磁振造影的現況應用、臨床需求、及其技術發展、磁振造影工程、分子與細胞

計畫編號

NSC 98－2221－E－039－009

計畫名稱

以核磁共振乳房影像模擬乳房非線性變形壓縮

:計算乳房密度

Computational Simulation of Breast Compression Based on

Non-Linear Deformation by Using Magnetic Resonance Images: to

Measure Breast Density

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姓名

施子卿

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