| Biological tissues show electromagnetic (EM) properties, i.e., the magnetic and electric properties,whenloaded in EM field. The magnetic property is magnetic permeability μ. Because the human tissues are nonmagnetic material, the permeability values of human tissues usually equal to the permeability of vacuum and can be regarded as a constant. Electric properties include permittivity ε and conductivity a, in which the conductivity can be regarded as the reciprocal of impedance. The values of electric properties are influenced by a variety of factors. Firstly, conductivity and permittivity are frequency dependent. Secondly, the values of electric properties changes with temperature. The electric properties of biological tissues are various at different temperatures. Thirdly, electric properties of biological tissues are also influenced by the ion concentration, the protein content and the proportion of water and free water within the tissues. Once the physiological or pathological state of tissue changed, its electric property values also changed correspondingly. Literatures have shown that the difference between the dielectric properties of human cancer tissue and its corresponding normal tissue reach to more than 30% or even several times. For example, the conductivity and relative permittivity (relative permittivity is the ratio of the permittivity and vacuum) of normal breast tissue are 0.12 S/m and 20.2, while the corresponding values of cancerous breast tissue are 0.79 S/m and 60.5 respectively (25℃,200 MHz). The conductivity and relative permittivity of cancerous breast tissue are respectively about 7 and 3 times to that of normal breast tissue. Thus, the changes of electric properties due to physiological or pathological changes of tissues or organs may provide valuable information for the early diagnosis of cancer, and may even help monitor the whole process that normal tissue deteriorate to cancer tissue. Therefore, biological tissue electric property imaging has great potential for clinical application. Magnetic resonance electric property tomography (MR EPT) is a novel electric property imaging approach developed after open-ended coaxial line method, electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT). MREPT provides electric property images at the Larmor frequency using a standard magnetic resonance imaging system and several RF coils without the requirement of additional measuring electrode and the current injected into the human body. The quality of electric properties imaging mainly depends on the three elements of MR EPT technology, i.e., magnetic resonance image quality, B1 mapping technology and MR EPT reconstruction algorithm. Compared to other imaging techniques, MR EPT has more advantages. Currently popular algorithm of MR EPT which is based on the modified Helmholtz equation was proposed by Wen. Using the algorithm, the electric properties of object can be calculated with known radio frequency (RF) field. Derivation of currently popular algorithm of MR EPT is under the assumption that the dielectric properties of object are locally constant. In homogeneous tissues, the reconstructed error (RE) is small and can be neglected using currently popular algorithm of MR EPT. However, the RE caused by this assumption is inherent when applying the algorithm in the tissues with inhomogeneous electric property distributions. Previous literature showed that the RE in tissue with inhomogeneous electric properties was severe at the frequency of 3 T. In recent years, the resonance frequency used in the research about MR EPT mainly among 1.5 T and 3 T and 7 T. In currently popular algorithm of MR EPT, the relation between electric properties and RF field is influenced by the resonance frequency used. In addition, the signal-to-noise ratio (SNR) of obtained magnetic resonance image also increases with resonance frequency in magnetic resonance imaging engineering practice. Therefore, applying currently popular algorithm of MR EPT in inhomogeneous tissue at different resonance frequency, RE may not be same. To date, the RE was investigated only at 3 T, and at 1.5 T and 7 T there is no literature quantitatively analyzing this error. The purpose of this paper is to quantitatively analyze RE of currently popular algorithm of MR EPT at the resonance frequencies of 1.5 T,3 T and 7 T using an inhomogeneous model, and then to compare the RE occurred at those three different resonance frequencies.B1 mapping technology is an important element related to the accuracy of the MR EPT technique. It provides basic data for subsequent MR EPT reconstruction algorithm. The RF field data obtained by B1 mapping technology directly affects the quality of the reconstructed results of electric properties. At present, through the B1 mapping technique can easily get the magnitude of the RF field, while the phase cannot be directly measured using existing technology. Furthermore, measurement error cannot be avoided in engineering practice. Therefore, in order to obtain accurate field data to quantitatively analyze the RE of currently popular algorithm of MR EPT, EM simulation experiment was chosen in this investigation. SEMCAD is a three-dimensional EM simulation software based on the finite difference time domain (Time-Domain Finite-Difference, FDTD) algorithm. In this study, EM simulation was implemented using SEMCAD, and the whole experiment was implemented according to the following five steps. Firstly, to build a high pass birdcage coil in the SEMCAD. The birdcage coil contained 16 pillars, two rings, two unit current sources and 32 capacitors. The 16 pillars that parallel to each other were between the two rings, and had equal interval between adjacent pillars. Each ring had 16 capacitors. The two current sources that had opposite current directions were located at one of the two rings. Secondly, to build an EM model that has inhomogeneous electric property distributions. The model was a cuboid, consisted of 40 uniform slices with different electric properties. Electric properties of the model varied linearly along x-direction and were constant along y-direction and z-direction (Z- direction was the direction parallel to the birdcage coil cavity). Electric property ranges of the model covered the electric properties (37℃,128 MHz) of mainly components in human brain, i.e., white matter, gray matter and cerebrospinal fluid (CSF). Thirdly, to obtain RF field data of the model at 1.5 T,3 T and 7 T. In this step, the cuboids model was posited at the center of birdcage coil. By regulating the capacitance values of capacitors on the 2 rings of birdcage, the resonance frequency of the coil could reach at 64 MHz (1.5T), 128 MHz (3T) and 298 MHz (7T) respectively. After the electromagnetic calculation zone was meshed, running the software, and waiting to obtain the RF field data of the EM model. Fourthly, to calculate the electric property distributions of the EM model using currently popular algorithm of MR EPT. In the magnetic resonance imaging system, the load interacts with EM field, therefore the signal detected in the resonance imaging system is bound to carry the electric property information of the load. Currently popular algorithm of MR EPT established the direct relation between the electric properties and the RF field of load. The electric property distributions of load can be calculated with the obtained RF field using currently popular algorithm of MR EPT. Fifthly, to calculate RE of electric properties. In SEMCAD, ideal electric property distributions of model can also be obtained. Using the ideal results, we computed distributions of absolute RE (aRE) and relative RE (rRE). Additionally, the maximum and mean REs of each reconstructed map were also calculated.In this study, we reconstructed electric property distributions of the model in the planes respectively perpendicular to the x-, y- and z-directions. The rRE of the reconstructed results on the same section was decrease with resonance frequency. When the resonance frequency were 1.5 T,3 T and 7 T, mean REs in the plane perpendicular to the x-direction were respectively 3.33%,2.21% and 1.28% for conductivity, and 20.70%,11.22% and 5.21% for relative permittivity. Mean REs in the plane perpendicular to the y-direction were respectively 7.06%,6.85% and 5.14% for conductivity, and 18.24%,6.3% and 2.51% for relative permittivity. Mean REs in the plane perpendicular to the z-direction were respectively 8.15%,7.12% and 5.47% for conductivity, and 25.72%,10.57% and 3.98% for relative permittivity.This paper compared the RE of currently popular algorithm of MR EPT at the resonance frequencies of 1.5 T,3 T and 7 T using a model with inhomogeneous distributions of electric properties. At different resonance frequencies, the RE of the algorithm was various. The RE decreased with resonance frequency. When the resonance frequency is 7 T, the mean rRE of conductivity and relative permittivity can be reduced to 1.28% and 2.51% respectively. This study may be helpful for the effort to improve the accuracy of the MR EPT technique, which is important for the potential early detection of cancer at clinic. |
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