Magnetic Field Distribution and Signal Decay in Functional MRI in Very High Fields (up to 9.4 T) Using Monte Carlo Diffusion Modeling

Mueller-Bierl, Bernd Michael; Uludag, Kamil; Pereira, Philippe L.; Schick, Fritz

doi:https://doi.org/10.1155/2007/70309

International Journal of Biomedical Imaging

On this page

Abstract References Copyright Related Articles

Special Issue

Mathematics in Biomedical Imaging

View this Special Issue

Research Article | Open Access

Volume 2007 | Article ID 070309 | https://doi.org/10.1155/2007/70309

Magnetic Field Distribution and Signal Decay in Functional MRI in Very High Fields (up to 9.4 T) Using Monte Carlo Diffusion Modeling

Bernd Michael Mueller-Bierl,¹Kamil Uludag,¹Philippe L. Pereira,²and Fritz Schick³

Academic Editor: Tie Zhou

Received28 Sept 2006

Revised30 May 2007

Accepted25 Aug 2007

Published30 Sept 2007

Abstract

Extravascular signal decay rate R2 or R2∗ as a function of blood oxygenation, geometry, and field strength was calculated using a Monte Carlo (MC) algorithm for a wider parameter range than hitherto by others. The relaxation rates of gradient-recalled-echo (GRE) and Hahn-spin-echo (HSE) imaging in the presence of blood vessels (ranging from capillaries to veins) have been computed for a wide range of field strengths up to 9.4 T and 50% blood deoxygenation. The maximum HSE decay was found to be shifted to lower radii in higher compared to lower field strengths. For GRE, however, the relaxation rate was greatest for large vessels at any field strength. In addition, assessments of computational reliability have been carried out by investigating the influence of the time step, the Monte Carlo step procedure, boundary conditions, the number of angles between the vessel and the exterior field B0, the influence of neighboring vessels having the same orientation as the central vessel, and the number of proton spins. The results were compared with those obtained from a field distribution of the vessel computed by an analytic formula describing the field distribution of an ideal object (an infinitely long cylinder). It was found that the time step is not critical for values equal to or lower than 200 microseconds. The choice of the MC step procedure (three-dimensional Gaussian diffusion, constant one- or three-dimensional diffusion step) also failed to influence the results significantly; in contrast, the free boundary conditions, as well as taking too few angles into account, did introduce errors. Next neighbor vessels with the same orientation as the main vessel did not contribute significantly to signal decay. The total number of particles simulated was also found to play a minor role in computing R2/ R2∗.

References

B. E. Hoppel, R. M. Weisskoff, K. R. Thulborn, J. B. Moore, K. K. Kwong, and B. R. Rosen, “Measurement of regional blood oxygenation and cerebral hemodynamics,” Magnetic Resonance in Medicine, vol. 30, no. 6, pp. 715–723, 1993.
View at: Publisher Site | Google Scholar
B. M. Müller-Bierl, H. Graf, U. Lauer, G. Steidle, and F. Schick, “Numerical modeling of needle tip artifacts in MR gradient echo imaging,” Medical Physics, vol. 31, no. 3, pp. 579–587, 2004.
View at: Publisher Site | Google Scholar
C. R. Fisel, J. L. Ackerman, R. B. Buxton et al., “MR contrast due to microscopically heterogeneous magnetic susceptibility: numerical simulations and applications to cerebral physiology,” Magnetic Resonance in Medicine, vol. 17, no. 2, pp. 336–347, 1991.
View at: Publisher Site | Google Scholar
R. M. Weisskoff, C. S. Zuo, J. L. Boxerman, and B. R. Rosen, “Microscopic susceptibility variation and transverse relaxation: theory and experiment,” Magnetic Resonance in Medicine, vol. 31, no. 6, pp. 601–610, 1994.
View at: Publisher Site | Google Scholar
S. Ogawa, R. S. Menon, D. W. Tank et al., “Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model,” Biophysical Journal, vol. 64, no. 3, pp. 803–812, 1993.
View at: Google Scholar
R. P. Kennan, J. Zhong, and J. C. Gore, “Intravascular susceptibility contrast mechanisms in tissues,” Magnetic Resonance in Medicine, vol. 31, no. 1, pp. 9–21, 1994.
View at: Publisher Site | Google Scholar
J. L. Boxerman, L. M. Hamberg, B. R. Rosen, and R. M. Weisskoff, “MR contrast due to intravascular magnetic susceptibility perturbations,” Magnetic Resonance in Medicine, vol. 34, no. 4, pp. 555–566, 1995.
View at: Publisher Site | Google Scholar
N. Fujita, “Extravascular contribution of blood oxygenation level-dependent signal changes: a numerical analysis based on a vascular network model,” Magnetic Resonance in Medicine, vol. 46, no. 4, pp. 723–734, 2001.
View at: Publisher Site | Google Scholar
W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C++. The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 2nd edition, 2002.
S. Balac, G. Caloz, G. Cathelineau, B. Chauvel, and J. D. de Certaines, “Integral method for numerical simulation of MRI artifacts induced by metallic implants,” Magnetic Resonance in Medicine, vol. 45, no. 4, pp. 724–727, 2001.
View at: Publisher Site | Google Scholar
R. Bhagwandien, R. van Ee, R. Beersma, C. J. G. Bakker, M. A. Moerland, and J. J. W. Lagendijk, “Numerical analysis of the magnetic field for arbitrary magnetic susceptibility distributions in 2D,” Magnetic Resonance Imaging, vol. 10, no. 2, pp. 299–313, 1992.
View at: Publisher Site | Google Scholar
K. M. Lüdeke, P. Röschmann, and R. Tischler, “Susceptibility artefacts in NMR imaging,” Magnetic Resonance Imaging, vol. 3, no. 4, pp. 329–343, 1985.
View at: Publisher Site | Google Scholar
C. J. G. Bakker, R. Bhagwandien, M. A. Moerland, and M. Fuderer, “Susceptibility artifacts in 2DFT spin-echo and gradient-echo imaging: the cylinder model revisited,” Magnetic Resonance Imaging, vol. 11, no. 4, pp. 539–548, 1993.
View at: Publisher Site | Google Scholar
B. M. Müller-Bierl, H. Graf, P. L. Pereira, and F. Schick, “Numerical simulations of intra-voxel dephasing effects and signal voids in gradient echo MR imaging using different sub-grid sizes,” Magnetic Resonance Materials in Physics, Biology and Medicine, vol. 19, no. 2, pp. 88–95, 2006.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2007 Bernd Michael Mueller-Bierl et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation Order printed copies

Views

357

Downloads

991

Citations