Most imaging modalities image an object's interior while all instrumentation, including sources and receivers, is externally located. One notable exception is ultra-sound (US), which can be miniaturized sufficiently to locate a US transducer within an object and gather data for image reconstruction. Another is cross-borehole geophysical imaging. The goal of any internal imaging modality is to provide images of greater fldelity while avoiding interfering structures. Due to the bulkiness of multi-coil magnetic induction tomography (MIT), transmitting and receiving coils are never placed within small targets (e.g., a human body). Here, we demonstrate a novel implementation of single-coil MIT that performs a scan all while the coil is located within the interior of a small, lab-created phantom consisting of salt-doped agarose. Phantom geometry is annular, consisting of a 6.0 cm diameter channel of depth 5.5 cm surrounded by a 3.0 cm thick cylindrical wall. A centrally located agarose gel annulus, 2.0 cm thick, is doped with sucient NaCl to elevate its conductivity above that of surrounding agarose. The resulting nearly axisymmetric phantoms consist of material having conductivity ranging from 0.11 to 10.55 S/m. A scan is accomplished robotically, with the coil stub-mounted on the positioning head of a 3-axis controller that positions the planar circular loop coil into 360 or 720 pre-programmed internal positions. Image reconstruction from gathered data is shown to correctly reveal the location, size and conductivity of the approximately axisymmetric inclusion.
Joe R. Feldkamp,
"Internal Magnetic Induction Tomography Using a Single Coil," Progress In Electromagnetics Research,
Vol. 164, 97-107, 2019. doi:10.2528/PIER18120408
2. Sikora, J., Boundary Element Method for Impedance and Optical Tomography, Oficyna Wydawnicza Politechniki Warszawskiej, 2007.
3. Sikora, J., S. Wojtowicz, and eds., Industrial and Biological Tomography: Theoretical Basis and Applications, Wydawnictwo Ksiazkowe Instytutu Elektrotechniki, 2010.
4. Wei, H. Y. and M. Soleimani, "Electromagnetic tomography for medical and industrial applications: Challenges and opportunities," Proc. IEEE, Vol. 101, 559-564, 2013. doi:10.1109/JPROC.2012.2237072
5. Stawicki, K. and S. Gratkowski, "Optimization of signal coils in the magnetic induction tomography system," Przeglad Elektrotechniczny, Vol. 86, No. 5, 74-77, 2010.
6. Zakaria, Z., et al., "Advancements in transmitters and sensors for biological tissue imaging in magnetic induction tomography," Sensors, Vol. 12, 7126-7156, 2012. doi:10.3390/s120607126
7. Al-Zeibak, S. and H. N. Saunders, "A feasibility study of in vivo electromagnetic imaging," Physics in Medicine and Biology, Vol. 38, No. 1, 151-160, 1993. doi:10.1088/0031-9155/38/1/011
8. Zhdanov, M. S. and K. Yoshioka, "Cross-well electromagnetic imaging in three dimensions," Exploration Geophysics, Vol. 34, 34-40, 2003. doi:10.1071/EG03034
9. Ma, L., H.-Y. Wei, and M. Soleimani, "Planar magnetic induction tomography for 3D near subsurface imaging," Progress In Electromagnetic Research, Vol. 138, 65-82, 2013. doi:10.2528/PIER12110711
10. Scharfetter, H., K. Hollaus, J. Rosell-Ferrer, and R. Merwa, "Single-step 3D image reconstruction in magnetic induction tomography: Theoretical limits of spatial resolution and contrast to noise ratio," Annals of Biomedical Engineering, Vol. 34, No. 11, 1786-1798, 2006. doi:10.1007/s10439-006-9177-6
11. Dekdouk, B., C. Ktistis, D. W. Armitage, and A. J. Peyton, "Absolute imaging of low conductivity material distributions using nonlinear reconstruction methods in magnetic induction tomography," Progress In Electromagnetic Research, Vol. 155, 1-18, 2016. doi:10.2528/PIER15071705
12. Feldkamp, J. R., "Single-coil magnetic induction tomographic three-dimensional imaging," J. Medical Imaging, Vol. 2, No. 1, 013502, 2015. doi:10.1117/1.JMI.2.1.013502
13. Feldkamp, J. R. and S. Quirk, "Validation of a convolution integral for conductivity imaging," Progress In Electromagnetic Research Letters, Vol. 67, 1-6, 2017. doi:10.2528/PIERL17011401
14. Feldkamp, J. R. and S. Quirk, "Coil geometry effects on single-coil magnetic induction tomography," Physics in Medicine and Biology, Vol. 62, 7097-7113, May 2017. doi:10.1088/1361-6560/aa807b
15. Joines, M. T., Y. Zhang, C. Li, and R. L. Jirtle, "The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz," Medical Physics, Vol. 21, No. 4, 547-550, 1994. doi:10.1118/1.597312
16. Sudduth, K. A., N. R. Kitchen, W. J. Wiebold, W. D. Batchelor, G. A. Bolero, D. E. Clay, H. L. Palm, F. J. Pierce, R. T. Schuler, and K. D. Thelen, "Relating apparent electrical conductivity to soil properties across the north-central U.S.A.," Computers and Electronics in Agriculture, Vol. 46, 263-283, 2005. doi:10.1016/j.compag.2004.11.010
17. Palacky, G. J., "Resistivity characteristics of geologic targets (Ch. 3)," Electromagnetic Methods in Applied Geophysics, Vol. 1, 53-129, 1988.
18. Feldkamp, J. R., "Inversion of an inductive loss convolution integral for conductivity imaging," Progress In Electromagnetic Research B, Vol. 74, 93-107, 2017. doi:10.2528/PIERB17021413
19. Parise, M., "On the surface fields of a small circular loop antenna placed on plane stratified earth," Intl. J. of Antennas and Propagation, Vol. 2015, Article ID 187806, 8 pages, http://dx.doi.org/10.1155/2015/187806, 2015.
20. Gradshteyn, I. S. and Ryzhik, Table of Integrals, Series and Products, Corrected and Enlarged Ed., A. Jeffrey, Academic Press, New York, NY, 1980.
21. Lapidus, L. and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley-Interscience, J. Wiley & Sons, NY, 1982.
22. Elden, L., "Algorithms for the regularization of ill-conditioned least squares problems," BIT, Vol. 17, 134-145, 1977. doi:10.1007/BF01932285
23. Donatelli, M., A. Neuman, and L. Reichel, "Square regularization matrices for large linear discrete ill-posed problems," Numerical Linear Algebra with Applications, Vol. 19, 896-913, 2012. doi:10.1002/nla.1833
24. Katamreddy, S. H. and P. K. Yalavarthy, "Model-resolution based regularization improves near infrared diffuse optical tomography," J. Opt. Soc. Am., Vol. 29, No. 5, 649-656, 2012. doi:10.1364/JOSAA.29.000649
25. Feldkamp, J. R. and S. Quirk, "Effects of tissue heterogeneity on single-coil, scanning MIT imaging," Proc. SPIE 9783, Medical Imaging: Physics of Medical Imaging, 978359, 2016.
26. Feldkamp, J. R. and S. Quirk, "Optically tracked, single-coil, scanning magnetic induction tomography," J. Medical Imaging, Vol. 4, No. 2, 023504, 2017. doi:10.1117/1.JMI.4.2.023504
27. Feldkamp, J. R. and S. Quirk, "Optically tracked, single-coil, scanning magnetic induction tomography," Proc. SPIE 10132, Medical Imaging: Physics of Medical Imaging, 10132172, 2017.