基于生成对抗网络的膝关节模型构建与局部比吸收率估计
Knee Joint Model Construction and Local Specific Absorption Rate Estimation Based on Generative Adversarial Networks
通讯作者: * Tel: 010-64437805, E-mail:xiaoliang@mail.buct.edu.cn.
收稿日期: 2023-01-15
基金资助: |
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Corresponding authors: * Tel: 010-64437805, E-mail:xiaoliang@mail.buct.edu.cn.
Received: 2023-01-15
局部比吸收率(SAR)是衡量高场磁共振成像安全性的重要指标.目前主要的方法是对扫描获得的磁共振图像进行组织分割,从而构建个体特异性模型,对其进行电磁仿真以计算局部SAR.针对仿真中膝关节模型长度影响局部SAR估计准确度的问题,本文提出了一种基于条件生成对抗网络(CGAN)的膝关节磁共振图像分割与视野扩展方法,将膝关节图像简化归类为肌肉、脂肪和骨骼三种组织,通过CGAN进行像素的语义分割,采用注意力机制以提高分割的准确度,并且沿头-足方向在图像两端生成扩展区域,构建出更长的模型.实验中对所提方法以及各种对比方法得到的膝关节模型进行电磁仿真,计算它们与人工标注模型的局部SAR的相对误差,结果验证了所提方法可以获得相对精确的膝关节局部SAR估计.
关键词:
The local specific absorption rate (SAR) is an essential metric when assessing the safety of high-field magnetic resonance imaging (MRI). Usually, the subject-specific model is created from segmented magnetic resonance (MR) images, followed by SAR estimates. However, the length of knee joint model affects the accuracy of local SAR estimation in simulation. To address the issue, this paper proposed a knee joint MR image segmentation and field-of-view extension method based on conditional generative adversarial nets (CGAN). The image of knee joint was classified into images of three tissues, namely, muscle, fat, and bone. And pixel semantic segmentation was performed using CGAN with attention mechanism to improve accuracy. The method also generated extension areas at both ends of the image along the head-foot direction to construct a longer model. The knee joint models by using the proposed method and various comparison methods were electromagnetically simulated, and the relative error of their local SAR compared to the manually annotated model was calculated. Results verified that the proposed method can achieve a relatively accurate estimation of local SAR in the knee joint.
Keywords:
本文引用格式
任宏晋, 马岩, 肖亮.
REN Hongjin, MA Yan, XIAO Liang.
引言
当前膝关节局部SAR估计的主要方法是通过构建特异性的膝关节模型并以此进行电磁仿真[7],这就需要基于膝关节MR图像进行组织分割以重建模型. 一些情况下可以根据获得的低场MR图像重建模型,以此进行高场扫描前的电磁仿真与局部SAR估计. 低场图像组织对比度较低,且由于膝关节结构复杂,一些组织在图像上模糊且间断,难以准确分割. 组织简化可以适应信噪比较低的图像,减少人工标注的误差与时间消耗.学术界经常采用组织简化策略来进行局部SAR估计[8,9].Carluccio等[10]使用只有肌肉、脂肪和肺的简化模型,与原始模型相比得出了较接近的局部SAR估计[11].表明当用肌肉替换除骨骼、脂肪和肺以外的所有组织类型时,人体躯干模型中的局部SAR值无显著差异. 对于膝关节,考虑到组织的介电特性[12],可以简化为肌肉、脂肪和骨骼三种有代表性的组织,这适用于图像信噪比较低的情况.
我们前期基于230 mm视野图像进行了图像分割与局部SAR估计的研究[23]. 为了提高小视野图像构建模型的局部SAR估计的准确度,本文针对常用的150 mm视野图像,提出了一种基于条件生成对抗网络的图像分割和视野扩展方法,该方法采用“肌肉-脂肪-骨骼”组织简化,集成了融合注意力机制的U型网络(U-Net)为生成网络,将对抗损失和绝对值损失函数(L1损失)结合作为目标损失函数,对输入图像进行语义分割,并在图像两端生成组织扩展到230 mm视野,从而构建更长的模型.实验中,分别对所提方法和三种对比方法构建的膝关节模型进行了电磁仿真和局部SAR估计.
1 方法
1.1 数据集
本研究使用的膝关节数据集与之前的研究[23]采用的数据集相同,为矢位纵向弛豫(T1)加权自旋回波图像,来自于67位志愿者,志愿者的平均年龄为46.3岁. 选择数据集中48位志愿者的图像作为训练集,19位志愿者的图像作为测试集. 图像的扫描于2019年在张家口仁爱医院的0.35 T MRI系统上进行,获得了院方许可,实验之前均对每一位志愿者进行了告知,并获得了他们的同意,实验中由影像科医生负责扫描,以确保安全.
扫描图像的视野为230 mm×230 mm,层厚为4 mm,每位志愿者的图像切片数为30,图像尺寸为384×384,体素尺寸为0.6 mm×0.6 mm×4 mm.在本研究中,电磁仿真所采用的鸟笼线圈长度为180 mm,这样基于230 mm视野所构建模型的局部SAR基本上接近整个人腿的情况,可以作为对比的基准.实际扫描时的图像视野常为150 mm×150 mm,对于230 mm而言属于视野较小的情况,因此这里研究从150 mm视野扩展到230 mm视野.在网络训练与测试中,根据视野扩展的需求将原始数据集的视野修剪为150 mm×150 mm.
所有的图像由专业影像人员标注为肌肉、脂肪、半月板、软骨、皮质骨和松质骨六种组织,在此基础上进行组织简化,将骨骼与脂肪之外的组织全部归为肌肉,因此得到肌肉、脂肪和骨骼三种组织的标注图像.
1.2 所提方法的总体结构
所提膝关节模型构建方法的整体流程图如图1所示,训练集中视野为150 mm×150 mm的原始图像与其对应的视野为230 mm×230 mm的人工标注“肌肉-脂肪-骨骼”图像作为输入数据,以训练条件生成对抗网络. 该网络对三种组织进行分割的同时,在图像头-足方向的两端生成包含三种组织的区域,从而扩展视野. 在测试时,每一位志愿者的所有图像输入网络,得到视野为230 mm×230 mm的“肌肉-脂肪-骨骼”分类图像,将每一位志愿者的所有分类图像切片合在一起,得到长度为230 mm而非150 mm的膝关节模型,将膝关节模型放置在射频发射线圈模型中,进行电磁仿真并计算局部SAR分布.
图1
图1
所提方法的膝关节模型构建整体流程图
Fig. 1
The whole flowchart of knee joint model construction using the proposed method
1.3 条件生成对抗网络(CGAN)
CGAN由生成网络G和判别网络D两个子网络组成,生成网络G负责从噪声中生成具有先验信息的合成样本,判别网络D是一个分类器,负责判别传入网络的数据是真实数据还是合成样本.在训练过程中,两个子网络同时训练但目标相反.CGAN的优化目标如(1)式 [22]所示:
其中x表示真实数据,y表示条件,z表示随机噪声,
本文使用的CGAN的结构如图2所示. 生成网络以原始小视野图像(Fov为150 mm×150 mm)作为条件y,从噪声z中合成原始MR图像的分割扩展图像
图2
图2
所提出的CGAN的结构. 根据判别网络输出的0/1矩阵计算对抗损失,误差反向传播给生成网络和判别网络,使用人工标注图像和生成网络生成结果计算L1损失,反向传播给生成网络,根据梯度下降原理不断调整网络参数
Fig. 2
The architecture of the proposed CGAN. The countermeasure loss is calculated according to the 0/1 matrix of the output of the discriminator network. The error is propagated back to the generator network and the discriminator network, and the L1 loss is calculated by using the artificially labeled image and the generating result of the generator network, transmitting back to the generator network, and the network parameters are continuously adjusted according to the gradient descent principle
1.4 生成网络
如图3所示,本文使用的生成网络为一个4层的U-Net,采用原始小视野MR图像作为条件y输入,而输入的随机噪声z体现在网络训练与测试的dropout步骤中. 每层进行两次卷积操作,使用边缘0填充的卷积方式,可保持网络的输入图像与输出图像大小一致. 使用步长为2的卷积操作代替池化操作进行下采样,可以避免边缘特征在传播中逐渐消失. 每次卷积操作后都进行批归一化和线性整流激活(ReLu激活).在上采样过程中每个跳跃连接末端加入注意力模块,较浅层的特征图监督较深层的特征图,将权重主要分配在待分割的区域,减小背景的权重来优化分割. 最后一个解码器层的输出附加了softmax激活函数,该函数为每个输出标签生成输出概率图.
图3
图3
生成网络的结构. 网络的输入为原始灰度图像,输出肌肉、脂肪、骨骼与背景4种图像
Fig. 3
The structure of generator network. The network input is the original gray-scale image, and the output consists of muscle, fat, bone and background images
1.5 注意力模块
在电磁仿真中,如果背景区域被错误分类为某种膝关节组织,会导致SAR估计产生明显的错误.为此,在网络设计中引入注意力模块[24],可以将注意力集中在特定的区域,抑制背景区域的特征激活.注意力模块的结构如图4所示.使用上一层编码部分的输出特征图el-1作为门控信号,解码部分特征图dl进行上采样获得同样的尺寸,对它们进行卷积操作从而实现线性变换,然后使用ReLu函数激活,经过卷积层后采用sigmoid激活函数能够在训练过程中使参数更好的收敛,输出注意力系数矩阵α,使其与dl相乘,能够确定感兴趣区域.在U-Net的跳跃连接中加入注意力模块,从浅层次的特征图提取上下文信息,并突出显示感兴趣区域的位置,随后通过跳跃连接将以多个比例提取的特征图合并,可以实现更精确的分割.
图4
图4
生成网络中使用的注意力模块. 根据解码部分特征图dl与其上一层编码部分特征图el-1作为输入,计算注意力系数矩阵α,el-1与注意力系数矩阵α逐像素相乘来选择聚焦区域
Fig. 4
The attention modules used in generator network. The attention coefficient matrix α is calculated by using the decoded partial characteristic graph dl and the coded partial characteristic graph el-1 as the input, el-1 multiplies the attention coefficient matrix α pixel by pixel to select the focus region
1.6 判别网络
判别网络采用了patch-GAN的思想,为5层的卷积神经网络结构,采用小视野原始MR图像与大视野人工标注图像的组合,或其与生成网络生成的分割扩展图像(Fov为230 mm×230 mm)的组合作为输入,使用步长为2的卷积实现每层的下采样,对每次卷积后的结果均进行了ReLu激活与批归一化,最后一层为一个卷积层,其输出后接sigmoid函数,最终输出为一个由0与1组成的二维矩阵,矩阵中的每一个数字都对应了输入图像组合的一个区域的判别结果,矩阵越大,对应的区域越小,这样训练可以使模型更关注图像的细节. 判别网络的网络结构如图5所示.
图5
1.7 损失函数的设计
在训练中要解决(1)式的极大极小问题:固定生成网络,通过合成和人工标注的分割扩展图像训练判别网络,使判别网络的损失函数最大化;或者固定判别网络,通过合成分割扩展图像训练生成网络,使生成网络的损失函数最小化,这两个损失为对抗损失.
除对抗损失外,在损失函数中添加L1损失,可以帮助生成器捕捉上下文信息,这有利于补充图像中头-足方向需要生成的扩展区域.损失函数的定义如(2)式所示:
上式中λ为L1损失的权重系数.
2 实验
2.1 网络训练
使用Python语言编写网络模型,在TensorFlow平台上训练和预测. 用于实验的计算机配置有4核英特尔i7-4 770处理器和具有16 GB内存的GeForce GTX显卡. 生成网络包含4个编码层和解码层,在跳跃连接中加入了注意力模块,卷积核大小为3×3. 判别网络为5层的卷积神经网络,卷积内核大小为3×3,初始卷积核数量设置为16. 生成网络和判别网络都使用自适应矩估计优化器(ADAM优化器)训练,学习率为0.001,L1损失函数的权重λ设置为10.在训练过程中,为了使生成网络与判别网络的性能尽量均衡,我们试验了不同的生成网络训练次数与判别网络训练次数之比,最终设置为每训练3次生成网络就训练一次判别网络.
2.2 分割的评价指标
以人工标注结果作为基准,图像分割性能通过Dice系数(DCC)与真阳性率(TPR)进行评估,这两项指标计算公式如(3)和(4)式所示:
其中T是人工标注结果,U是网络的分割结果.
2.3 电磁仿真与SAR计算
将生成对抗网络的输出结果逐片组合,形成最终的膝关节模型.在电磁仿真中,采用3 T的膝关节发射线圈模型,这是一个正交鸟笼线圈,采用集总电容模式.其长度和半径分别为180 mm和87.5 mm.
构造的膝关节模型置于线圈的中心.两个1 V幅度的正交正弦波分别注入线圈的两个端口.线圈内部的电场是两个端口产生的电场的总和.
电磁仿真完成后,即可基于仿真结果计算局部SAR分布.
SAR计算公式如(5)式[25]所示:
其中σ是组织的电导率,ρ是组织的密度,
局部SAR值是SAR的平均,用SAR10g表达,是指某一体素p周边10 g组织的SAR的平均值,其计算公式如(6)式[25]所示:
其中V代表一个立方区域,该立方区域以p为中心并有10 g质量,mq代表V中任意一体素q的质量.
3 结果与讨论
3.1 分割结果
对150 mm视野区域磁共振图像的准确分割确保了所构建的模型在中心150 mm范围内与原始模型的相似度,对于局部SAR的精准估计是必要的. 为了评估所提出的架构的分割性能,对所提方法与经典的U-Net,以及融合注意力模块的U型网络Attention U-Net[24]进行比较(U-Net网络和Attention U-Net网络为4层,卷积核大小为7×7),基于原始的150 mm×150 mm视野图像测试集,计算了各方法的分割性能评价指标,如表1所示.根据表1可以看出,比起U-Net与Attention U-Net,所提方法总体上的分割性能是最佳的,肌肉与脂肪的DCC、脂肪与骨骼的TPR明显大于另外两种方法.
表1 各种方法的分割结果评价指标(所提方法、U-Net、Attention U-Net相比人工标注结果)
Table 1
分割方法 | 评价指标 | 肌肉 | 脂肪 | 骨骼 |
---|---|---|---|---|
所提方法 | DCC | 0.8798 | 0.9135 | 0.9022 |
TPR | 0.8915 | 0.9198 | 0.9114 | |
U-Net | DCC | 0.8472 | 0.9040 | 0.9006 |
TPR | 0.8841 | 0.8785 | 0.8921 | |
Attention U-Net | DCC | 0.8578 | 0.9022 | 0.9058 |
TPR | 0.9059 | 0.8611 | 0.8991 |
图6
图6
一位志愿者(女性,21岁)的一个膝关节MR切片基于不同方法的分割结果. 其中黄色代表脂肪,红色代表肌肉,白色代表骨骼,视野为150 mm×150 mm
Fig. 6
Segmentation results of one knee section of a female volunteer based on different methods, where yellow represents fat, red represents muscle, and white represents bone, with a field of view of 150 mm×150 mm
3.2 SAR估计结果
3.1节已经验证了本文提出的架构在分割中优于经典的U-Net和比较先进的Attention U-Net,由于本文在对膝关节磁共振图像进行分割的同时,还在头-足两端生成了扩展的部分,对于模型的合理外推可以使模型长度大于线圈长度,同时避免在模型边界处的问题,防止电流在截断处形成伪环,导致该区域的局部SAR升高[26],为了验证所提出的方法生成的更长模型对SAR估计的改进,我们将所提方法与以下三种方法做局部SAR估计的对比.
(1)方法1,使用U-Net网络将Fov为150 mm×150 mm的小视野膝关节图像分割为肌肉、脂肪和骨骼三种组织,基于网络输出结果构建150 mm长的膝关节模型,该对比的目的在于研究膝关节模型外推对局部SAR估计精度的影响.
(3)方法3,在U-Net分割的基础上采用头-足方向两端的重复外推,具体做法是:使用U-Net网络分割的视野为150 mm×150 mm的图像,沿头-足方向由两端边界图像向外重复外扩,两端分别扩展40 mm,进而构建230 mm长度的膝关节模型.采用这种方法可以保持边界上组织分布的连续性.
使用所提方法与对比方法得到的膝关节模型的示例如图7所示.
图7
图7
对一位志愿者(女性,21岁)使用各种不同方法构建的膝关节模型. (a)人工标注;(b)所提方法;(c)方法1;(d)方法2;(e)方法3
Fig. 7
Models of the knee joint of a female volunteer constructed with different methods. (a) artificial labeling; (b) the proposed method;(c) method 1; (d) method 2; (e) method 3
以人工标注的230 mm膝关节模型(六种组织)为基准,所提方法与对比方法的SAR10g最大值的相对误差的统计值如表2所示.
表2 最大SAR10g的相对误差的统计(所提方法和对比方法相比人工标注结果)
Table 2
所提方法 | 方法1 | 方法2 | 方法3 | |
---|---|---|---|---|
平均值 | 0.0696 | 0.2932 | 0.0783 | 0.1066 |
标准差 | 0.0542 | 0.1206 | 0.0527 | 0.0525 |
方法2与方法3均为在150 mm视野区域分割的基础上进行扩展以构建模型,尽管方法3两端最后一层重复外推的结果包含了肌肉、脂肪与骨骼三种组织,但最后一层的组织分布与外推区域实际的组织分布有一定差异,这种差异对局部SAR的估计精度会造成影响.这种情况在方法2中也存在,由于局部SAR取决于体内电场分布,而导致电场分布的因素比较复杂,因此通过电磁仿真进行两个方法的比较.
表3 不同模型的最大SAR10g的统计
Table 3
模型 | Duke左腿 | Duke右腿 | Ella左腿 | Ella右腿 |
---|---|---|---|---|
230 mm-全组织 | 1.4973 | 1.2078 | 1.0765 | 1.3145 |
230 mm-简化 | 1.4404 | 1.3555 | 1.1862 | 1.4363 |
230 mm-肌肉 | 1.4500 | 1.3261 | 1.1587 | 1.3676 |
230 mm-两端重复外推 | 1.5249 | 1.3940 | 1.2387 | 1.4592 |
150 mm-简化 | 1.9746 | 1.9019 | 1.5773 | 1.8345 |
根据表3,计算每一种模型与230mm-全组织模型的SAR10g最大值的相对误差,并且求出相对误差的平均值,可以得出150 mm-简化模型与230 mm-全组织模型的相对误差为0.438 6,说明模型长度对局部SAR有较大影响.对于不同外推方法,230 mm-肌肉和230 mm-两端重复外推模型与230 mm-全组织模型的相对误差分别为0.061 6和0.108 3,采用肌肉填充的方法误差更小,与前文的结论是一致的.此外,230 mm-简化模型与全组织模型的相对误差为0.088 7,这也证明了“肌肉-脂肪-骨骼”的组织简化方法对局部SAR没有显著影响.
我们前期的研究[23]是基于230 mm视野的原始图像分割六种组织以构建模型,得到的局部SAR最大值的相对误差的均值为0.036 6,标准差为0.035 7.与本文所提方法的偏差为0.033±0.035 7,这表明图像视野扩展与组织简化确实对局部SAR的估计精度有一定影响,这可以归因于以下事实:之前研究[23]是采用230 mm视野图像重建模型,由于所用鸟笼线圈长度为180 mm,所以不需要扩展图像.然而,实际临床膝关节扫描中大部分是采用150 mm甚至更小的视野.本文针对这种情况,采用230 mm视野图像数据集(与文献[23]相同)作为对照的基准,从中裁剪得到150 mm视野图像以模拟实际临床扫描得到的图像,再通过生成头-足各40 mm的组织得到230 mm模型,因此局部SAR预测精度会有下降.另一方面,采用“肌肉-脂肪-骨骼”的组织简化方案,必然会导致局部SAR估计结果与高度详细的模型之间有偏差,然而简化可以适应信噪比较低的图像,减少人工标注的误差与时间消耗,具有较强的实用意义.
图8
图8
同一位志愿者(女性,21岁)的膝关节SAR10g分布图.从上到下为连续5层的分布,从左到右的每一列分别为基于人工标注、所提方法、方法1、方法2和方法3的结果
Fig. 8
SAR10g distribution of the same volunteer’s knee. From top to bottom are the distribution of five consecutive MR slices, from left to right, are the results based on artificially labeling, the proposed method, method 1, method 2 and method 3 respectively
图9显示了该志愿者的各种方法所建模型的SAR10g的最大密度投影. 人工标注、所提方法、方法1、方法2以及方法3的SAR10g的最大值分别为1.390 W/kg、1.456 W/kg、1.773 W/kg、1.477 W/kg和1.522 W/kg. 所提方法与人工标注的结果最为接近,同时,热点区域的位置基本相同. 这说明了所提方法的有效性.
图9
图9
同一位志愿者(女性,21岁)的各种方法重建模型的SAR10g的最大密度投影图. (a)人工标注;(b)所提方法;(c)方法1;(d)方法2;(e)方法3
Fig. 9
The same volunteer’s maximum intensity projection of SAR10g by (a) artificially labeling; (b) the proposed method; (c) method 1; (d) method 2; (e) method 3
3.3 讨论
为了准确地估计局部SAR,快速而精准地构建个体特异性的膝关节模型具有重要意义.考虑到临床实际扫描中采集的膝关节图像视野主要在150 mm及以下,当采用180 mm长的鸟笼线圈时,基于该视野图像构建的模型的局部SAR估计误差较大.针对这种情况,要求对膝关节MR图像进行自动分割,对分割结果进行图像区域的扩展,构建更长的膝关节模型以实现更准确的局部SAR估计.
近年来,一些基于全卷积神经网络的模型如用于图像分割的深度卷积编码器-解码器架构(SegNet)、U-Net等广泛用于膝关节磁共振图像分割. 不同于这种类型的网络,生成对抗网络是由生成网络和判别网络两个网络组成,期待的结果是由生成网络学习原始数据分布得到的,判别网络在训练过程中对生成网络的结果进行判别,指导生成网络生成数据.通过对抗训练使生成网络模拟原始数据分布,可以生成更加逼真的图像. 此外视野扩展与分割采用同一生成对抗网络架构,在该网络中外推扩展与图像分割相互促进,对于图像分割任务来说,可以在生成外推部分的组织分布时更好的学习分割部分的特征图,提升磁共振图像上的分割性能.通过分割任务,网络可以更好地学习图像的语义信息和上下文关系,更好地理解图像中的结构从而帮助外推扩展更好地生成外扩的部分,提高所构建模型的外推部分的相似度.因此不仅能够在膝关节磁共振图像的组织分割中取得好的结果,也能够在小视野的膝关节图像的头-足两端生成更接近真实组织分布的扩展区域,从而构建更接近实际人腿的模型.
电磁仿真与局部SAR估计结果表明,采用“肌肉-脂肪-骨骼”组织简化,基于条件生成对抗网络进行分割与视野扩展所构建的膝关节模型,得到的SAR10g最大值与人工标注模型相对误差较小,热点区域基本相同,这说明所提出的方法在一定程度上能够得到比较接近人工标注的局部SAR估计.未来我们将扩大数据集,丰富志愿者的类型,对所提方法进一步验证与优化,得到更好的局部SAR估计结果.
4 结论
本文提出了一种基于条件生成对抗网络的全自动组织分割与视野扩展方法,用于更精准的膝关节局部SAR估计. 在将膝关节MR图像简化分类为肌肉、脂肪和骨骼三种组织的同时,还在头-足方向的两端生成包含组织的图像区域,扩大了膝关节模型的尺寸,使其更接近于实际人腿的情况. 局部SAR估计的结果表明了所提方法的有效性.
利益冲突
无
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