劉 陽, 于孝輝, 郭建炎

(1. 廈門理工學院 電氣工程與自動化學院,福建 廈門 361024；2. 休斯頓衛(wèi)理公會派醫(yī)院研究中心 系統(tǒng)醫(yī)藥與生物工程系,德克薩斯 休斯頓 77030；3. 廈門理工學院 光電與通信工程學院,福建 廈門 361024)

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磁共振電特性成像人體腹腔癌癥仿真研究

劉 陽1, 于孝輝2, 郭建炎3

(1. 廈門理工學院 電氣工程與自動化學院,福建 廈門 361024；2. 休斯頓衛(wèi)理公會派醫(yī)院研究中心 系統(tǒng)醫(yī)藥與生物工程系,德克薩斯 休斯頓 77030；3. 廈門理工學院 光電與通信工程學院,福建 廈門 361024)

將磁共振電特性成像(MREPT)方法用于人體腹腔部位,考察該成像方式用于人體腹腔肝癌及胰腺癌診斷的可行性.采用鳥籠線圈同時作為射頻發(fā)射和接收,基于射頻發(fā)射場測量值重構(gòu)人體腹腔內(nèi)組織的電導率和相對介電率.包含10種組織的人體腹腔模型上的仿真結(jié)果表明：在信噪比SNR=30的情況下,MREPT能夠檢測出位于組織內(nèi)部半徑為3 cm的肝癌腫瘤和半徑為1 cm的胰腺癌腫瘤；由于逆問題重構(gòu)公式中均質(zhì)電特性的假設(shè)及拉普拉斯卷積的共同作用,可能無法檢測出位于組織邊界處的小體積癌癥腫瘤.拉普拉斯卷積核的大小對重構(gòu)結(jié)果的影響很大,在無噪聲情況下,3×3×3的卷積核的重構(gòu)效果最好,但當SNR=30～120時,5×5×5的卷積核是最佳選擇.

磁共振；電特性；電導率；介電率

人體組織的電導率和介電率取決于細胞成分、密度及細胞內(nèi)部結(jié)構(gòu)[1-2].大量研究結(jié)果表明：癌癥與正常組織之間的電特性存在顯著差別[3-5].人體組織內(nèi)電特性分布信息對于臨床疾病診斷具有潛在的應用價值.此外,電導率和介電率是合理設(shè)計和開展電磁場相關(guān)的疾病治療,如腫瘤熱療及射頻切除等所必須的[6-7].

在過去的幾十年中,研究人員一直致力于非入侵式人體組織電導率和介電率成像方法的研究.電阻抗斷層成像(electrical impedance tomography, EIT)[8]是該領(lǐng)域最早被提出的一種成像方法,但由于該技術(shù)中表面電壓測量值的個數(shù)遠遠小于待重構(gòu)未知數(shù)的個數(shù),逆問題表現(xiàn)出嚴重的病態(tài)性,最終導致重構(gòu)圖像精度和分辨率較低.盡管這一問題在后來發(fā)展起來的磁共振電阻抗成像(magnetic resonance electrical impedance tomography, MREIT)[9-10]中得到克服,但為了在測量磁場信號中取得較高的信噪比(signal to noise, SNR),要求注入電流的強度遠遠超過IEC安全標準,這成為該技術(shù)走向臨床應用的最大障礙.

磁共振電特性成像(magnetic resonance electrical impedance tomography, MREPT)[11-12]是根據(jù)人體組織與射頻磁場之間的相互作用所引起的不均勻射頻磁場測量值來重構(gòu)組織內(nèi)電導率和相對介電率分布的一種成像方式.與MREIT相比,該成像方式無需向待成像物體注入電流,既簡化了對成像系統(tǒng)硬件設(shè)備的要求,也從根本上解決了MREIT中注入電流所引起的安全性問題.MREPT的思想最早由Haacke等[13]提出.直到最近,得益于MRI設(shè)備性能的不斷提高及新的射頻脈沖序列的研發(fā),MREPT才被用于人體活體實驗.

目前,根據(jù)所應用于射頻發(fā)射和接收的射頻線圈的種類的不同,MREPT可以分為以鳥籠線圈做發(fā)射和接收[14-16]及以陣列線圈做發(fā)射和接收[17]兩類.其中前者是3.0 T及以下磁場強度的MRI設(shè)備上最常用的射頻收發(fā)方式；后者往往為了達到更好的勻場效果,用在7.0 T及以上磁場強度的MRI設(shè)備上.無論采用何種射頻收發(fā)方式,目前幾乎所有的MREPT研究都集中于人體頭部,僅有極少數(shù)幾項研究嘗試將MREPT用于人體子宮頸癌[18]和乳腺癌[19]的檢測.

本文將MREPT技術(shù)用于成像人體腹腔電特性分布,通過計算機仿真考察該技術(shù)基于目前臨床廣泛使用的MRI設(shè)備(1.5 T磁場強度,鳥籠線圈作為射頻發(fā)射和接收)用于人體腹腔肝癌及胰腺癌檢測的可行性.仿真結(jié)果表明,該成像方法具有較高的成像精度和分辨率,顯示了該方法對于未來腹腔癌癥檢測的潛在應用價值,也為與射頻電磁場相關(guān)的癌癥治療提供了一條新途徑.

1 方法簡介

1.1 正問題

(1)

對于線性、各向同性、非散射材料,MREPT正問題可以采用以下Maxwell旋度方程來描述：

×E=-iωB，

(2)

×B=μ0(σ+iωε0εr).

(3)

(4)

(5)

式中：“*”表示復共軛.基于式(6)構(gòu)造在實際中可以獲得的復數(shù)射頻發(fā)射場分布,基于該仿真測量值求解逆問題.

(6)

1.2 逆問題

(7)

(8)

2 仿真設(shè)計

在包含皮膚、脂肪、肌肉、肋骨及脊椎骨、肝臟、胰腺、腎臟、大腸、脾臟及胃等10種組織的真實人體腹腔模型上進行仿真,仿真模型如圖1所示.采用16條腿的低通鳥籠線圈產(chǎn)生64 MHz的射頻激勵,并接收射頻磁場信號.除肝臟和胰腺外,腹腔內(nèi)其他組織均為正常組織.在64 MHz的頻率下,正常及癌癥組織的電特性取值請見文獻[22,23].為了考察MREPT對不同大小的癌癥組織的檢測能力,分別在肝臟和胰腺中構(gòu)造半徑為3和1 cm的兩個癌癥腫瘤.

圖1 人體腹腔模型Fig.1 Human abdominal model

(9)

式中：P為組織電導率σ或相對介電率εr,下標tar表示目標電特性,re表示重構(gòu)電特性.

3 實驗結(jié)果

圖3、4分別給出肝癌及胰腺癌腫瘤所在平面的目標及不同噪聲水平下的重構(gòu)電導率及相對介電率分布.可見,不同噪聲水平下的重構(gòu)結(jié)果相差不大,這是由于采用核卷積的方法來實現(xiàn)拉普拉斯運算,有效地抑制了噪聲對重構(gòu)結(jié)果的影響.由圖4可以看出,在SNR=60的情況下,能夠從重構(gòu)圖像中分辨出半徑為1 cm胰腺癌的位置.式(7)和(8)是在假定待成像物體內(nèi)電特性均質(zhì)的情況下得到的[7,15-16],即式(7)、(8)中忽略了電導率和相對介電率的梯度,因此導致在不同媒質(zhì)交界面處重構(gòu)出的電特性誤差較大,這一點可以從圖3、4看出.這意味著較小的癌癥組織如果位于器官的邊界處,可能無法檢測得到.

圖2 仿真系統(tǒng)配置及射頻場仿真結(jié)果Fig.2 Simulation system configuration and radiofrequency field simulation results

圖3 肝癌所在平面目標及不同噪聲水平下基于5×5×5卷積核的重構(gòu)電特性分布Fig.3 Target and reconstructed electrical property distributions with different noise levels based on5×5×5 revolution kernel on liver cancer located plane

圖4 胰腺癌所在平面目標及不同噪聲水平下基于5×5×5卷積核的重構(gòu)電特性分布Fig.4 Target and reconstructed electrical property distributions with different noise levels based on5×5×5 revolution kernel on pancreas cancer located plane

圖5 肝癌所在平面目標及不同大小卷積核重構(gòu)電導率分布Fig.5 Target and reconstructed conductivity distributions achieved with different size of revolution kernels on liver cancer located plane

圖6 胰腺癌所在平面目標及不同大小卷積核時重構(gòu)電導率分布Fig.6 Target and reconstructed conductivity distributions achieved with different size of revolution kernels on pancreas cancer located plane

為了定量地評價重構(gòu)結(jié)果,圖7給出不同噪聲水平及不同卷積核大小時,肝臟和胰臟區(qū)域重構(gòu)電特性與目標電特性之間的相對誤差R曲線圖.可以看出,在無噪聲的情況下,基于3×3×3的卷積核計算得到的重構(gòu)電特性與目標電特性之間的相對誤差遠遠小于基于5×5×5和9×9×9兩個卷積核所獲得的；相反,當SNR=30時,3×3×3的卷積核的重構(gòu)效果最差.這與圖5、6所展示的定性結(jié)果一致.當存在噪聲時,即使在SNR=120時,3×3×3的卷積核已無優(yōu)勢；除了胰腺介電率SNR=30這種情況之外,5×5×5的卷積核往往能夠獲得最好的重構(gòu)效果.

圖7 不同噪聲水平和卷積核大小時重構(gòu)電特性與目標電特性之間的相對誤差曲線Fig.7 Relative error curves between reconstructed and target electrical properties with different noise levels and different sizes of convolution kernels

4 結(jié) 語

本文將目前電特性成像領(lǐng)域最新的成像方法MREPT應用于人體腹腔部位,通過計算機仿真考察該成像方式用于人體肝癌及胰腺癌檢測的可行性.仿真結(jié)果表明：在信噪比SNR=30的情況下,MREPT能夠準確檢測出位于組織內(nèi)部半徑為3 cm的肝癌腫瘤和半徑為1 cm的胰腺癌腫瘤.由于逆問題重構(gòu)公式中所作的均質(zhì)電特性假設(shè)及拉普拉斯卷積的共同作用,對于位于邊界處的小體積腫瘤檢測的準確性相對降低,甚至根本無法檢出.提出新的MREPT算法,有效地克服不同媒質(zhì)交界面處電特性重構(gòu)誤差較大的問題,是未來MREPT的一個重要研究方向.

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下期論文摘要預登

金屬橡膠復合齒輪副振動特性分析及實驗

黃 偉1， 王家序1,2, 徐 濤1， 肖 科1， 李俊陽1， 吳會超3

(1．重慶大學 機電傳動與運載裝備研究所，重慶 400044；2．四川大學 空天科學與工程學院，四川 成都 610065；3. 唐山軌道客車有限責任公司，河北 唐山 063000 )

摘 要: 以少齒差行星減速器核心部件金屬橡膠復合齒輪副為研究對象，綜合考慮時變嚙合剛度、嚙合阻尼、齒輪誤差激勵、軸承支撐剛度、支撐阻尼、傳動軸扭轉(zhuǎn)剛度、扭轉(zhuǎn)阻尼及金屬橡膠徑向支撐剛度和支撐阻尼等因素，采用集中質(zhì)量法建立彎-扭耦合的6自由度非線性振動模型.采用可變階次的多步Adams PECE法對動力學方程進行求解，研究復合齒輪副的振動特性.通過實驗驗證了金屬齒輪副和復合齒輪副的振動響應.結(jié)果表明，復合齒輪齒圈的振動位移和振動速度最大，經(jīng)過金屬橡膠彈性體后，輪轂的振動位移和振動速度均有明顯的減小；輪轂的扭轉(zhuǎn)振動角位移和扭轉(zhuǎn)振動角速度較齒圈有一定的衰減；復合齒輪副振動平穩(wěn)性優(yōu)于金屬齒輪副；仿真結(jié)果和實驗結(jié)果基本一致.

關(guān)鍵詞： 行星減速器；金屬橡膠；復合齒輪副；振動特性

Simulation study on magnetic resonance electrical property tomography of human abdominal cancer

LIU Yang1, YU Xiao-hui2, GUO Jian-yan3

(1.SchoolofElectricalEngineeringandAutomation,XiamenUniversityofTechnology,Xiamen361024,China;2.DepartmentofSystemsMedicineandBioengineering,HoustonMethodistHospitalResearchInstitute，Houston77030,USA;3.SchoolofOpto-ElectronicandCommunicationEngineering,XiamenUniversityofTechnology,Xiamen361024,China)

The magnetic resonance electrical property tomography (MREPT) method was applied to human abdomen. The birdcage coil was used for radio frequency (RF) transmission and reception. The conductivity and relative permittivity of abdominal tissues were reconstructed based on the RF field measurement. The simulation results conducted on human abdominal model including 10 types of tissues show that the MREPT can detect the 3cm-radius liver cancer tumor and 1cm-radius pancreas tumor located in the central area of tissues. MREPT may fail to detect the small tumors located near the boundary of tissues due to the homogeneous electrical property assumption made in the reconstruction algorithm together with the adopted Laplacian revolution. The size of Laplacian revolution kernel has significant influence on the reconstruction result. When there is no noise, the 3×3×3 Laplacian revolution kernel can achieve the highest accuracy. The best performance can be achieved by 5×5×5 Laplacian revolution kernel with a SNR in the range of 30 to 120.

magnetic resonance; electrical property; conductivity; permittivity

2015-09-22.

福建省自然科學基金資助項目(2013J05102,2016J01323);福建省教育廳科研資助項目(JA15383).

劉陽(1980—), 女, 講師, 博士,從事生物電阻抗成像的研究. ORCID: 0000-0001-8631-0154.

E-mail: liuyang32201220@gmail.com

郭建炎, 男, 副教授. ORCID: 0000-0002-3508-0755. E-mail: guonetmail@163.com

10.3785/j.issn.1008-973X.2016.10.016

TM 15; TP 391

A

1008-973X(2016)10-1959-06

浙江大學學報(工學版)網(wǎng)址： www.zjujournals.com/eng