Reconstruction of conductivity distribution of brain tissue from two components magnetic flux density

ABSTRACT

In this paper the recent Magnetic resonance electrical impedance imaging (MREIT) technique is used to image non-invasively the three-dimensional continuous conductivity distribution of the head tissues. With the feasibility of the human head being rotated twice in the magnetic resonance imaging (MRI) system, a continuous conductivity reconstruction MREIT algorithm based on two components of the measured magnetic flux density is introduced. The reconstructed conductivity image could be obtained through solving iter- atively a non-linear matrix equation. According to the present algorithm of using two magnetic flux den- sity components, numerical simulations were per- formed on a concentric three-sphere and realistic human head model (consisting of the scalp, skull and brain) with the uniform and non-uniform isotropic target conductivity distributions. Based on the algorithm, the reconstruction of scalp and brain conductivity ratios could be figured out even under the condition that only one current is injected into the brain. The present results show that the three-dimensional continuous conductivity reconstruction method with two magnetic flux density components for the realistic head could get better results than the method with only one magnetic flux density component. Given the skull conductivity ratio, the relative errors of scalp and brain conductivity values were reduced to less than 1% with the uniform conductivity distribution and less than 6.5% with the non-uniform distribution for different noise levels. Furthermore, the algorithm also shows fast convergence and improved robustness against noise.

In this paper the recent Magnetic resonance electrical impedance imaging (MREIT) technique is used to image non-invasively the three-dimensional continuous conductivity distribution of the head tissues. With the feasibility of the human head being rotated twice in the magnetic resonance imaging (MRI) system, a continuous conductivity reconstruction MREIT algorithm based on two components of the measured magnetic flux density is introduced. The reconstructed conductivity image could be obtained through solving iter- atively a non-linear matrix equation. According to the present algorithm of using two magnetic flux den- sity components, numerical simulations were per- formed on a concentric three-sphere and realistic human head model (consisting of the scalp, skull and brain) with the uniform and non-uniform isotropic target conductivity distributions. Based on the algorithm, the reconstruction of scalp and brain conductivity ratios could be figured out even under the condition that only one current is injected into the brain. The present results show that the three-dimensional continuous conductivity reconstruction method with two magnetic flux density components for the realistic head could get better results than the method with only one magnetic flux density component. Given the skull conductivity ratio, the relative errors of scalp and brain conductivity values were reduced to less than 1% with the uniform conductivity distribution and less than 6.5% with the non-uniform distribution for different noise levels. Furthermore, the algorithm also shows fast convergence and improved robustness against noise.

Cite this paper

nullXu, W. and Yan, D. (2010) Reconstruction of conductivity distribution of brain tissue from two components magnetic flux density.*Journal of Biomedical Science and Engineering*, **3**, 742-749. doi: 10.4236/jbise.2010.37099.

nullXu, W. and Yan, D. (2010) Reconstruction of conductivity distribution of brain tissue from two components magnetic flux density.

References

[1] Goncalves, S., de Munck, J.C., Heethaar, R.M., Lopes, da Silva, F.H. and van Dijk, B.W. (2000) The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem-a simulation study. Physiological Measurement, 21(3), 379-393.

[2] Zhang, N.P. (1992) Electrical impedance tomography based on current density imaging. MSc Thesis University of Toronto, Toronto.

[3] Birgül, ?. and ?der, Y.Z. (1996) Electrical impedance tomography using magnetic field generated by internal current distribution. Proceedings of IEEE Engineering in Medicine and Biology, 18th Annual International Conference, Amsterdam, 784-785.

[4] Birgül, ?., Eyübo?lu, B.M. and ?der, Y.Z. (2001) New technique for high resolution absolute conductivity ima- ging using magnetic resonance-electrical impedance to- mography (MR-EIT). Proceedings of SPIE International Symposium on Medical Imaging, Florida, 880-888.

[5] Khang, H.S., Lee, B.I., Oh, S.H., Woo, E.J., Lee, S.Y., Cho, M.H., et al. (2002) J-substitution algorithm in ma- gnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images. IEEE Transactions on Medical Imaging, 21(21), 695-702.

[6] Kwon, O., Lee, J.Y. and Yoo, J.R. (2002) Equipotential line method for magnetic resonance electrical impedance tomography (MREIT). Inverse Problems, 18(2), 1089- 1100.

[7] ?zdemir, M.S., Eyübo?lu, B.M. and ?zbek, O. (2004) Equipotential projection-based magnetic resonance ele- ctrical impedance tomography and experimental reali- zation. Physics in Medicine and Biology, 49(21), 4765- 4783.

[8] Seo, J.K., Yoon, J.R., Woo, E.J. and Kwon, O. (2003) Reconstruction of conductivity and current density ima- ging using only one component of magnetic field mea- surements. IEEE Transactions on Biomedical Engin- eering, 50(9), 1121-1124.

[9] Oh, S.H., Lee, B.I., Woo, E.J., Lee, S.Y., Cho, M.H., Kwon, O., et al. (2003) Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography. Physics in Medicine and Biology, 48(19), 3101-3116.

[10] Oh, S.H., Lee, B.I., Woo, E.J., Lee, S.Y., Kim, T.S., Kwon, O., et al. (2005) Electrical conductivity images of biological tissue phantom in MREIT. Physiological Measurement, 26(2), S279-S288.

[11] Park, C., Kwon, O., Woo, E.J. and Seo, J.K. (2004) Electrical conductivity imaging using gradient Bz decomposition algorithm in magnetic resonance electri- cal impedance tomography (MREIT). IEEE Transactions on Medical Imaging, 23(3), 388-394.

[12] ?der, Y.Z. and Onart, S. (2004) Algebric reconstruction for 3D magnetic resonance-electrical impedance tomo- graphy (MREIT) using one component of magnetic flux density. Physiological Measurement, 25(1), 281-294.

[13] Gao, N., Zhu, S.A. and He, B. (2005) Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement. Physics in Medicine and Biology, 50(11), 2675-2687.

[14] Gao, N., Zhu, S.A. and He, B. (2006) A new magnetic resonance electrical impedance tomography (MREIT) algorithm: The RSM-MREIT algorithm with applications to estimation of human head conductivity. Phys Med Biol, 3067-3083.

[15] Gao, N., He, B. (2008) Noninvasive Imaging of Bio- impedance Distribution by Means of Current Recon- struction Magnetic Resonance Electrical Impedance Tomography. IEEE Trans Biomed Eng, 55(5), 1530-1539.

[16] Seo, J. K., Pyo, H. C., Park, C., Kwon, O. and Woo, E. J. (2004) Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study. Physics in Medicine and Biology, 49(18), 4371-4382.

[17] Oostendorp, T.F., Delbeke, J. and Stegeman, D.F. (2000) The conductivity of the human skull: results of in vivo and in vitro measurements. IEEE Transactions on Bio- medical Engineering, 47, 1487-1492.

[18] Yan D.D., Zhang X.T., Zhu S.A. and He, B. (2006) A reconstruction algorithm for head 3D magnetic resonance electrical impedance tomography: Simulation study. Acta Biophysica Sinica (in Chinese), 22(6), 461-470.

[19] Yan D.D., Zhang X.T., Zhu S.A. and He B. (2007) A Two-stop MREIT algorithm for head tissue based on radial basic function neural network, Space Medicine & Medical Engineering (in Chinese), 20(2), 126-130.

[20] Yan D.D., Zhang X.T., Zhu S.A. and He B. (2008) Simulation study on two-step magnetic resonance elec- trical impedance tomography of brain anomaly tissues, Journal of Zhejiang University (in Chinese), 42(4), 661- 666.

[21] ?der, Y.Z., Onart, S. and Lionheart, W.R.B. (2003) Uniqueness and reconstruction in magnetic resonance electrical impedance tomography (MREIT). Physio- logical Measurement, 24(2), 591-604.

[22] Scott, G.C., Joy, M.L.G., Armstrong, R.L. and Henke- lman, R.M. (1992) Sensitivity of magnetic-resonance current-density imaging. Journal of Magnetic Resonance, 97(2), 235-254.

[1] Goncalves, S., de Munck, J.C., Heethaar, R.M., Lopes, da Silva, F.H. and van Dijk, B.W. (2000) The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem-a simulation study. Physiological Measurement, 21(3), 379-393.

[2] Zhang, N.P. (1992) Electrical impedance tomography based on current density imaging. MSc Thesis University of Toronto, Toronto.

[3] Birgül, ?. and ?der, Y.Z. (1996) Electrical impedance tomography using magnetic field generated by internal current distribution. Proceedings of IEEE Engineering in Medicine and Biology, 18th Annual International Conference, Amsterdam, 784-785.

[4] Birgül, ?., Eyübo?lu, B.M. and ?der, Y.Z. (2001) New technique for high resolution absolute conductivity ima- ging using magnetic resonance-electrical impedance to- mography (MR-EIT). Proceedings of SPIE International Symposium on Medical Imaging, Florida, 880-888.

[5] Khang, H.S., Lee, B.I., Oh, S.H., Woo, E.J., Lee, S.Y., Cho, M.H., et al. (2002) J-substitution algorithm in ma- gnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images. IEEE Transactions on Medical Imaging, 21(21), 695-702.

[6] Kwon, O., Lee, J.Y. and Yoo, J.R. (2002) Equipotential line method for magnetic resonance electrical impedance tomography (MREIT). Inverse Problems, 18(2), 1089- 1100.

[7] ?zdemir, M.S., Eyübo?lu, B.M. and ?zbek, O. (2004) Equipotential projection-based magnetic resonance ele- ctrical impedance tomography and experimental reali- zation. Physics in Medicine and Biology, 49(21), 4765- 4783.

[8] Seo, J.K., Yoon, J.R., Woo, E.J. and Kwon, O. (2003) Reconstruction of conductivity and current density ima- ging using only one component of magnetic field mea- surements. IEEE Transactions on Biomedical Engin- eering, 50(9), 1121-1124.

[9] Oh, S.H., Lee, B.I., Woo, E.J., Lee, S.Y., Cho, M.H., Kwon, O., et al. (2003) Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography. Physics in Medicine and Biology, 48(19), 3101-3116.

[10] Oh, S.H., Lee, B.I., Woo, E.J., Lee, S.Y., Kim, T.S., Kwon, O., et al. (2005) Electrical conductivity images of biological tissue phantom in MREIT. Physiological Measurement, 26(2), S279-S288.

[11] Park, C., Kwon, O., Woo, E.J. and Seo, J.K. (2004) Electrical conductivity imaging using gradient Bz decomposition algorithm in magnetic resonance electri- cal impedance tomography (MREIT). IEEE Transactions on Medical Imaging, 23(3), 388-394.

[12] ?der, Y.Z. and Onart, S. (2004) Algebric reconstruction for 3D magnetic resonance-electrical impedance tomo- graphy (MREIT) using one component of magnetic flux density. Physiological Measurement, 25(1), 281-294.

[13] Gao, N., Zhu, S.A. and He, B. (2005) Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement. Physics in Medicine and Biology, 50(11), 2675-2687.

[14] Gao, N., Zhu, S.A. and He, B. (2006) A new magnetic resonance electrical impedance tomography (MREIT) algorithm: The RSM-MREIT algorithm with applications to estimation of human head conductivity. Phys Med Biol, 3067-3083.

[15] Gao, N., He, B. (2008) Noninvasive Imaging of Bio- impedance Distribution by Means of Current Recon- struction Magnetic Resonance Electrical Impedance Tomography. IEEE Trans Biomed Eng, 55(5), 1530-1539.

[16] Seo, J. K., Pyo, H. C., Park, C., Kwon, O. and Woo, E. J. (2004) Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study. Physics in Medicine and Biology, 49(18), 4371-4382.

[17] Oostendorp, T.F., Delbeke, J. and Stegeman, D.F. (2000) The conductivity of the human skull: results of in vivo and in vitro measurements. IEEE Transactions on Bio- medical Engineering, 47, 1487-1492.

[18] Yan D.D., Zhang X.T., Zhu S.A. and He, B. (2006) A reconstruction algorithm for head 3D magnetic resonance electrical impedance tomography: Simulation study. Acta Biophysica Sinica (in Chinese), 22(6), 461-470.

[19] Yan D.D., Zhang X.T., Zhu S.A. and He B. (2007) A Two-stop MREIT algorithm for head tissue based on radial basic function neural network, Space Medicine & Medical Engineering (in Chinese), 20(2), 126-130.

[20] Yan D.D., Zhang X.T., Zhu S.A. and He B. (2008) Simulation study on two-step magnetic resonance elec- trical impedance tomography of brain anomaly tissues, Journal of Zhejiang University (in Chinese), 42(4), 661- 666.

[21] ?der, Y.Z., Onart, S. and Lionheart, W.R.B. (2003) Uniqueness and reconstruction in magnetic resonance electrical impedance tomography (MREIT). Physio- logical Measurement, 24(2), 591-604.

[22] Scott, G.C., Joy, M.L.G., Armstrong, R.L. and Henke- lman, R.M. (1992) Sensitivity of magnetic-resonance current-density imaging. Journal of Magnetic Resonance, 97(2), 235-254.