Inversion Reconstruction of Signals Measured by the NMR Techniques

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1 PIERS ONLINE, VOL. 4, NO. 1, Inversion Reconstruction of Signals Measured by the NMR Techniques Eva Kroutilova 1, Miloslav Steinbauer 1, Premysl Dohal 1 Michal Hadinec 1, Eva Gescheidtova 1, and Karel Bartušek 2 1 Brno University of Technology, Czech Republic 2 Academy of Science of the Czech Republic Abstract The paper describes the magnetic resonance imaging method applicable mainly in MRI and MRS in vivo studies. There is discussed and solved the effect of changes of magnetic fields in MR tomography. This article deals with the reverse reconstruction results obtained from the numerical simulation of MR signals by various techniques, which will be usable for the experimental results verification. 1. INTRODUCTION Nuclear Magnet Resonance (NMR) is well known diagnostic non-destructive and non-invasive method [2 6]. It is used to investigation of the materials properties. One of the often use of NMR is medical application [8, 11]. The magnetic resonance imaging (MRI) is used to the propel a ferromagnetic core. The concept was studied for future development of microdevices designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascular system. A mathematical model is described [3] taking into account various parameters such as the size of blood vessels, the velocities and viscous properties of blood, the magnetic properties of the materials, the characteristics of MRI gradient coils, as well as the ratio between the diameter of a spherical core and the diameter of the blood vessels. Other paper [4] present a MRI-compatible micromanipulator, which can be employed to provide medical and biological scientists with the ability to concurrently manipulate and observe micron-scale objects inside an MRI gantry. The micromanipulator formed a two-finger micro hand, and it could handle a micron-scale object using a chopstick motion. The material engineering use the NMR too. For example NMR logging is an advanced method in formation evaluation and oil field production. It can provide the porosity, permeability, bound water volume, free fluid volume and oil viscosity. NMR logging is playing more and more important roles in oil and gas exploitation. (a) (b) Figure 1: The sample of two MRI results, the right results (a), the results with imaging loss. The results of the NMR method and signal processing are sensitive to used materials with extreme differences like a susceptibility, conductivity and also permeability from the macroscopic view to the mater. It is going to deformations and it makes the NMR can not be use. The Fig. 1 shows information losses effect.

2 PIERS ONLINE, VOL. 4, NO. 1, The paper brings the design of the hybrid numerical-experimental inverse method, which can reduce influence of the materials with extreme differences of the properties. The inverse methods are used in different applications [1, 7]. There is problem with task nonlinearity. It is described in [1]. The authors develop two nonlinear inverse methods to reconstruct the conductivity profile from electromagnetic induction (EMI) measurements: the improved two-step inverse method based on the extended Born approximation (EBA) and the combination of the EBA and the contrast source inversion (CSI) method. In the first method, the nonlinear problem is recast as a two-step linear inversion and is solved by using the extended Born approximation. The application of inverse method in the NMR techniques is in the temperature measurements, for the direct identification of the surface heat flux. The temperature measurements are not always possible considering an aggressive environment or an inaccessible zone. That is why an inverse method has been developed: the direct problem with the unknown boundary condition (wall heat flux) is solved by adding an observation equation given by temperature measurements on the opposite face of the wall [7]. The next step is to find simply model for numerical modeling and NMR experiment-verification. There can be changed material properties and next experimentally measured. The idea of increase of MRI is in the hybrid experimental and numerical inverse method. The numerical results are used in the MRI experimentally obtained data. The application of numerical results to the NMR post-processing can much more increase the final images. 2. GEOMETRICAL MODEL Fig. 2 describes the simply geometry for the numerical modeling. On both sides, the sample is surrounded by the referential medium. During the real experiment, the reference is represented by water, which is ideal for obtaining the MR signal. As shown in Fig. 2, in the model there are defined four volumes with different susceptibilities. The materials are defined by their permeabilites : material No. 1 the medium outside the cube (air), χ = 0, material No. 2 the cube walls (sodium glass), χ = 11, , material No. 3 is the sample material (sodium glass), χ = 11, , quartz glass, χ = 8, , the simax glass (commercial name), χ = 8, , material No. 4 is the medium inside the cube (water with nickel sulfate solution NiSO4, χ = 12, ). The permeability rate was set with the help of the relation µ = 1 + χ. For the sample geometry according to Fig. 1, the geometrical model was built in the system. In the model there was applied the discretization mesh with nodes and elements, type Solid96 (Ansys). The boundary conditions (1) were selected for the induction value of the static elementary field to be B 0 = 4, 7000 T in the direction of the z coordinate (the cube axis) corresponds with the real experiment carried out using the MR tomograph at the Institute of Scientific Instruments, ASCR Brno. Figure 2: The sample geometry for numerical modeling. Figure 3: The geometrical model in the system ansys.

3 PIERS ONLINE, VOL. 4, NO. 1, NUMERICAL ANALYSIS The numerical modelling was realized using the finite element method (FEM) together with the Ansys system and described in paper [11]. As the boundary condition, there was set the scalar magnetic potential ϕ m by solving Laplace s equation on the geometrical model in Fig. 3 together with the Dirichlet boundary conditon and the Neumann boundary condition 4. NUMERICAL MODEL ϕ m = div µ( grad ϕ m ) = 0 (1) ϕ m = konst. on the areas Γ 1 and Γ 2 (2) u n grad ϕ m = 0 on the areas Γ 3 and Γ 4. (3) The numerical modelling results are represented in Fig. 3 and Fig. 7. The numerical modelling results were then used for the representation of the module of magnetic induction B along the defined path. For the model meshing, the element size selected as optimum was 0, m. The boundary conditions ±ϕ/2 were set to the model edges, to the external left and right boundaries of the air medium, as represented in Fig. 1. The excitation value ±ϕ/2 was set using again the relation (21). This is derived for the assumption that, in the entire area, there are no exciting currents, therefore there holds for the rot H = 0 and the field is irrotational. Consequently, for the scalar magnetic potential ϕ m holds H = grad ϕ m (4) The potential of the exciting static field with intensity H 0 is by applying (4) ϕ m = H 0 u z dz = H 0 z (5) 5. EXPERIMENTAL VERIFICATION Figure 4: Elementary configuration of the MR magnet for the 200 MHz tomograph, ISI ASCR. Figure 5: The measured preparation. The preparation seating in the tomograph. The experimental measuring was realized using the MR tomograph at the Institute of Scientific Instruments, ASCR Brno. The tomograph elementary field B 0 = 4, 7000 T is generated by the superconductive solenoidal horizontal magnet produced by the Magnex Scientific company. The corresponding resonance frequency for the 1 H cores is 200 MHz. The Fig. 6 bring the numerical results of simply model solution without tested material. In the Fig. 7. is shoed result of numerical model with the tested material. The different of these results is showed in Fig. 8. The final result very good correspond with the theoretical conditions publicated in the thesis [10].

4 PIERS ONLINE, VOL. 4, NO. 1, , Characteristic of the Magnetic induction change into reference material 4, , , , , , ,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 Figure 6: The magnetic flux density B pattern, without sample material. 4,70002 Characteristic of the Magnetic induction change into material specimen (there isn't subtract reference backgroud) 4, , , , , , ,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 Figure 7: The magnetic flux density B pattern, with sample material Characteristic of the Magnetic induction change into specimen ,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 Figure 8: The magnetic flux density B pattern, differential result.

5 PIERS ONLINE, VOL. 4, NO. 1, CONCLUSION The numerical modelling and analysis of the task have verified the experimental results and, owing to the modificability of the numerical model, we have managed to advance further in the experimental qualitative NMR image processing realized at the ISI ASCR. This numerical and experimental models showed the possibility of inverse hybrid use. ACKNOWLEDGMENT The research described in the paper were financially supported by FRV S by research plan No. MSM ELCOM, No. MSM of the Ministry of Education, Youth and Sports of the Czech Republic and grant GAAV No. B and GA102/07/0389. REFERENCES 1. Zhang, Z. Q. and Q. H. Liu, Two nonlinear inverse methods for electromagnetic induction measurements, IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 6, , June Trakic, A., H. Wang, F. Liu, H. S. Lopez, and S. Crozier, Analysis of transient eddy currents in MRI using a cylindrical FDTD method, IEEE Transactions on Applied Superconductivity, Vol. 16, Issue 3, , ISSN: , Sept Mathieu, J.-B., G. Beaudoin, and S. Martel, Method of propulsion of a ferromagnetic core in the cardiovascular system through magnetic gradients generated by an MRI system, IEEE Transactions on Biomedical Engineering, Vol. 53, Issue 2, , ISSN: , Feb Yoshihiko, K., T. Tanikawa, and C. Kiyoyuki, MRI-compatible micromanipulator design and implementation and MRI-compatibility tests, 29th Annual International Conference of the IEEE, Engineering in Medicine and Biology Society, EMBS 2007, , Lyon, France, ISSN: X, Aug , Arima, H., S. Kato, K. Maehata, K. Ishibashi, T. Nakamoto, and T. Shintomi, Multipole analysis for absolute magnetic field measured by multi-probe pulsed-nmr method, IEEE Transactions on Applied Superconductivity, Vol. 10, No. 1, , March Long, H. F., Z. Li, Z. Xiao, and Y. Zhang, Numerical simulation of NMR logging tools antenna, 7th International Symposium on Antennas, Propagation & EM Theory, ISAPE 06, China, 1 3, Oct Reulet, P., D. Nortershauser, and P. Millan, Inverse method using infrared thermography for surface temperature and heat flux measurements, 20th International Congress on Instrumentation in Aerospace Simulation Facilities, ICIASF 03, , Aug , Vaughan, J. T., D. N. Haupt, P. J. Noa, J. M. Vaughn, and G. M. Pohost, RF front end for a 4.1 tesla clinical NMR spectrometer, IEEE Transactions on Nuclear Science, Vol. 42, No. 4, , August Fiala, P., E. Kroutilová, and T. Bachorec, Modelování elektromagnetických polí, počítačová cvičení, FEKT, VUT v Brnĕ, Údolní 53, , Brno, s. 1 69, Steinbauer, M., Mĕ rení magnetické susceptibility technikami tomografie magnetické rezonance, PhD Thesis, FEKT, VUT v Brnĕ, Údolní 53, , Brno, Fiala, P., E. Kroutilova, M. Steinbauer, M. Hadinec, and K. Bartusek, The effect of nonhomogenous parts into materials, PIERS Online, Vol. 3, No. 5, , 2007.