基于系统矩阵优化的二维磁性粒子成像研究
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摘要
磁性粒子成像(MPI)是一种新型高分辨率成像技术,利用磁性粒子在交变磁场中的非线性响应构建系统矩阵进而重建磁性纳米粒子的浓度分布,提高重建速度并降低存储空间需求和计算复杂度是实现实时成像的关键.本文将磁性粒子的非线性磁化响应特征与电磁感应定律相结合获取检测点电压信号,进一步考虑接受线圈的灵敏度可得电压信号与磁性粒子浓度的关系,利用傅里叶变换及频域矩阵展开分析了影响系统矩阵的因素,系统分析了系统矩阵频率分量的选取以及不同接收方向对重建图像的影响.结果表明,通过选取高频段信号可以优化系统矩阵分量的空间结构;通过增加频率分量可以构建线性无关方程组,使方程的解唯一化,提高重建精度和质量;通过不同接收方向系统矩阵的重组,使系统矩阵拥有更丰富的空间结构,进而提高浓度分布重建图像的质量.本研究对MPI技术进行磁性纳米粒子浓度重建起到了重要的指导作用,在新型生物医学成像领域有着广阔的应用前景.
Magnetic particle imaging(MPI)is a new medical imaging technology,which uses the nonlinear re-magnetization behavior of superparamagnetic nanoparticles to change magnetic field to determine their distribution. The key issues of the real-time PMI include the improvement of reconstruction speed and the reduction of storage requirement and computation complexity. By combining the nonlinear magnetization response characteristics of magnetic particles with the law of electromagnetic induction,the voltage signal was obtained. Furthermore,by considering the sensitivity of the receiving coil,the voltage signal shows a linear relationship with the concentration of magnetic particles. The fast Fourier transform is used to analyze the influence of the spectrum characteristics and the frequency resolution on the system matrix. Moreover,the influence of coding number,frequency component selection of the system function and the receiving direction on image reconstruction is studied systematically. It is proved that,the spatial structure of the system function can be optimized by selecting high frequency signals. The imaging accuracy and quality are improved by increasing the number of the frequency component and reconstructing the matrix using signals in different directions. More frequency components can be used to construct linearly independent equations to obtain a unique solution,and the system matrix reorganized by signals with different receiving directions has a richer spatial structure,which plays an important guiding role in MPI technology and exhibits promising prospect in new biomedical imaging.
Magnetic particle imaging(MPI)is a new medical imaging technology,which uses the nonlinear re-magnetization behavior of superparamagnetic nanoparticles to change magnetic field to determine their distribution. The key issues of the real-time PMI include the improvement of reconstruction speed and the reduction of storage requirement and computation complexity. By combining the nonlinear magnetization response characteristics of magnetic particles with the law of electromagnetic induction,the voltage signal was obtained. Furthermore,by considering the sensitivity of the receiving coil,the voltage signal shows a linear relationship with the concentration of magnetic particles. The fast Fourier transform is used to analyze the influence of the spectrum characteristics and the frequency resolution on the system matrix. Moreover,the influence of coding number,frequency component selection of the system function and the receiving direction on image reconstruction is studied systematically. It is proved that,the spatial structure of the system function can be optimized by selecting high frequency signals. The imaging accuracy and quality are improved by increasing the number of the frequency component and reconstructing the matrix using signals in different directions. More frequency components can be used to construct linearly independent equations to obtain a unique solution,and the system matrix reorganized by signals with different receiving directions has a richer spatial structure,which plays an important guiding role in MPI technology and exhibits promising prospect in new biomedical imaging.
引文
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[2] IANOS R,TACULESCU A,PACURARIU C,et al.Solution combustion synthesis and characterization of magnetite,Fe3O4,nanopowders[J].J Am Ceram Soc,2012,95:2236-2240.
[3] ABBASI A Z,GUTIERREZ L,DEL L L,et al.Magnetic capsules for NMR imaging:effect of magnetic nanoparticles spatial distribution and aggregation[J].J Phys Chem,2011,115:6257-6264.
[4] GOODWILL P,TAMRAZIAN A,CROFT L,et al.Ferrohydrodynamic relaxometry for magnetic particle imaging[J].Appl Phys Lett,2011,98:262502.
[5] GLEICH B,WEIZENECKER J.Tomographic imaging using the nonlinear response of magnetic particles[J].Nature,2005,435(7046):1214-1217.
[6] WEIZENECKER J,BORGERT J,GLEICH B.A simulation study on the resolution and sensitivity of magnetic particle imaging[J].Phys Med Biol,2007,52:6363-6374.
[7] KNOPP T,SATTEL T,BIEDERER S,et al.Model-based reconstruction for magnetic particle imaging[J].IEEE Trans Med Imaging,2010,29(1):12-18.
[8] PANAGIOTOPOULOS N,DUSCHKA R,AHLBORG M,et al.Magnetic particle imaging:current developments and future directions[J].Int J Nanomedicine,2015,10:3097-3114.
[9] BORGERT J,SCHMIDT J D,SCHMALE I,et al.Fundamentals and applications of magnetic particle imaging[J].J Cardiovasc Comput Tomogr,2012,6(3):149-153.
[10] GOODWILL P,SARITAS E U,CROFT L R,et al.X-Space MPI:magnetic nanoparticles for safe medical imaging[J].Adv Mater,2012,24(28):3870-3877.
[11] GLEICH B,WEIZENECKER J,BORGERT J.Experimental results on fast 2D-encoded magnetic particle imaging[J].Phys Med Biol,2008,53(6):81-84.
[12] KAETHNER C,AHLBORG M,KNOPP T,et al.Efficient gradient field generation providing a multi-dimensional arbitrary shifted field-free point for magnetic particle imaging[J].J Appl Phys,2014,115(4):0449101-0449105.
[13] VOGEL P,RUCKERT M A,KLAUER P,et al.Traveling wave magnetic particle imaging[J].IEEE Trans Med Imaging,2014,33(2):400-407.
[14] KNOPP T,BIEDERER S,SATTEL T F,et al.Trajectory analysis for magnetic particle imaging[J].Phys Med Biol,2008,54:385-397.
[15] WEIZENECKER J,GLEICH B,RAHMER J,et al.Three-dimensional real-time in vivo magnetic particle imaging[J].Phys Med Biol,2009,54:1-10.
[16] KNOPP T,BIEDERER S,SATTEL T F,et al.2D model-based reconstruction for magnetic particle imaging[J].Med Phys,2010,37(2):485-491.
[17] KNOPP T,SATTEL T F,BIEDERER S,et al.Field-free line formation in a magnetic field[J].J Phys Math Theor,2010,43(1):012002.
[18] ERBE M,WEBER M,SATTEL T F,et al.Experimental validation of an assembly of optimized curved rectangular coils for the use in dynamic field free line magnetic particle imaging[J].Curr Med Imaging Rev,2013,9(2):89-95.
[19] GOODWILL P,LU K,ZHENG B,et al.An X-Space magnetic particle imaging scanner[J].Rev Sci Instrum,2012,83:033708.
[20] TAY Z,GOODWILL P,HENSLEY D,et al.A high-throughput,arbitrary-waveform,MPI spectrometer and relaxometer for comprehensive magnetic particle optimization and characterization[J].Scientific reports,2016,6(1):34180.
[21] 谢迪,张朴,程晶晶.基于磁性粒子成像技术的一维建模仿真研究[J].计算机仿真,2013,30(9):410-414.
[22] 张金瑶.磁粒子成像信号分析与系统研制[D].西安:西安电子科技大学,2014.
[23] RAHMER J,WEIZENECKER J,GLEICH B,et al.Signal encoding in magnetic particle imaging:properties of the system function[J].BMC Med Imaging,2009,9:4-8.
[24] KNOPP T,RAHMER J,SATTEL T F,et al.Weighted iterative reconstruction for magnetic particle imaging[J].Phys Med Biol,2010,55(6):1577-1589.