Time domain simulation of Fourier imaging by summation of isochromats
We have developed a time‐domain simulation of two‐dimensional Fourier imaging in which the signal is represented by a finite Fourier series. Each term corresponds to a spin isochromat and has a coefficient that evolves in response to radiofrequency and gradient pulses, and periods of free precession...
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| Published in | International journal of imaging systems and technology Vol. 8; no. 5; pp. 419 - 426 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Hoboken
Wiley Subscription Services, Inc., A Wiley Company
1997
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| Abstract | We have developed a time‐domain simulation of two‐dimensional Fourier imaging in which the signal is represented by a finite Fourier series. Each term corresponds to a spin isochromat and has a coefficient that evolves in response to radiofrequency and gradient pulses, and periods of free precession. An explicit calculation is performed to derive the number of isochromats required to achieve a specified degree of precision, permitting accurate results to be obtained in an efficient fashion. With this, the time‐domain signal throughout the entire experiment is calculated. The resulting time domain data is combined into the standard k‐space matrix and yields an image after two‐dimensional Fourier transformation. Multiple‐shot sequences such as spin warp and single‐shot experiments such as Burst are simulated in the same fashion. Our procedure makes no assumptions about transverse dephasing between pulses, so that complicated sequences of direct and stimulated echoes are correctly modeled. The influence of spin‐spin and spin‐lattice relaxation is included in a natural way. A number of artifacts can be quantitatively reproduced. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 419–426, 1997 |
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| AbstractList | We have developed a time‐domain simulation of two‐dimensional Fourier imaging in which the signal is represented by a finite Fourier series. Each term corresponds to a spin isochromat and has a coefficient that evolves in response to radiofrequency and gradient pulses, and periods of free precession. An explicit calculation is performed to derive the number of isochromats required to achieve a specified degree of precision, permitting accurate results to be obtained in an efficient fashion. With this, the time‐domain signal throughout the entire experiment is calculated. The resulting time domain data is combined into the standard k‐space matrix and yields an image after two‐dimensional Fourier transformation. Multiple‐shot sequences such as spin warp and single‐shot experiments such as Burst are simulated in the same fashion. Our procedure makes no assumptions about transverse dephasing between pulses, so that complicated sequences of direct and stimulated echoes are correctly modeled. The influence of spin‐spin and spin‐lattice relaxation is included in a natural way. A number of artifacts can be quantitatively reproduced. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 419–426, 1997 |
| Author | Shkarin, Pavel Spencer, Richard G. S. |
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| Copyright | Copyright © 1997 John Wiley & Sons, Inc. |
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| References | J. Hennig. "Echoes-how to generate, recognize, use or avoid them in MR-imaging sequences. Part II: Echoes in imaging sequences," Concepts Magn. Reson. 3, 179-192 (1991). D. B. Twieg. "The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods," Med. Phys. 10, 610-621 (1983). R. M. Summers, L. Axel and S. Israel. "A computer simulation of nuclear magnetic resonance imaging," Magn. Reson. Med. 3, 363-376 (1986). I. J. Lowe and R. E. Wysong. "DANTE Ultrafast Imaging Sequence (DUFIS)," J. Magn. Reson. Ser. B 101, 106-109 (1993). W. A. Edelstein, J. M. Hutchison, G. Johnson and T. Redpath. "Spin warp NMR imaging and its applications to human whole-body imaging," Phys. Med. Biol. 25, 751-756 (1980). J. A. Nyenhuis and O. P. Yee. "Simulation of nuclear magnetic resonance spin echoes using the Bloch equation: Influence of magnetic field inhomogeneities," J. Appl. Phys. 76, 6909-6911 (1994). J. Hennig. "Echoes-how to generate, recognize, use or avoid them in MR-imaging sequences. Part I: Fundamental and not so fundamental properties of spin echoes," Concepts Magn. Reson. 3, 125-143 (1991). J. Hennig and M. Hodapp. "Burst imaging," MAGMA 1, 39-48 (1993). J. S. Petersson, J.-O. Christoffersson and K. Golman. "MRI simulation using the k-space formalism," Magn. Reson. Imag. 11, 557-568 (1993). P. Shkarin and R. G. S. Spencer. "Direct stimulation of spin echoes by summation of isochromats," Concepts Magn. Reson. 8, 253-268 (1996). J. Bittoun, T. Taquin and M. Sauzade. "A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method," Magn. Reson. Imag. 2, 113-120 (1984). D. A. Feinberg, J. D. Hale, J. C. Watts, L. Kaufman and A. Mark. "Halving MR imaging time by conjugation: demonstration at 3.5 kG," Radiology 161, 527-531 (1986). 1991; 3 1983; 10 1980; 25 1993; 1 1984; 2 1996; 8 1993; 11 1986; 3 1986; 161 1994; 76 1993; 101 |
| References_xml | – volume: 161 start-page: 527 year: 1986 end-page: 531 article-title: Halving MR imaging time by conjugation: demonstration at 3.5 kG publication-title: Radiology – volume: 3 start-page: 179 year: 1991 end-page: 192 article-title: Echoes—how to generate, recognize, use or avoid them in MR‐imaging sequences. Part II: Echoes in imaging sequences publication-title: Concepts Magn. Reson. – volume: 25 start-page: 751 year: 1980 end-page: 756 article-title: Spin warp NMR imaging and its applications to human whole‐body imaging publication-title: Phys. Med. Biol. – volume: 3 start-page: 125 year: 1991 end-page: 143 article-title: Echoes—how to generate, recognize, use or avoid them in MR‐imaging sequences. Part I: Fundamental and not so fundamental properties of spin echoes publication-title: Concepts Magn. Reson. – volume: 1 start-page: 39 year: 1993 end-page: 48 article-title: Burst imaging publication-title: MAGMA – volume: 101 start-page: 106 year: 1993 end-page: 109 article-title: DANTE Ultrafast Imaging Sequence (DUFIS) publication-title: J. Magn. Reson. Ser. B – volume: 8 start-page: 253 year: 1996 end-page: 268 article-title: Direct stimulation of spin echoes by summation of isochromats publication-title: Concepts Magn. Reson. – volume: 2 start-page: 113 year: 1984 end-page: 120 article-title: A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method publication-title: Magn. Reson. Imag. – volume: 10 start-page: 610 year: 1983 end-page: 621 article-title: The k‐trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods publication-title: Med. Phys. – volume: 76 start-page: 6909 year: 1994 end-page: 6911 article-title: Simulation of nuclear magnetic resonance spin echoes using the Bloch equation: Influence of magnetic field inhomogeneities publication-title: J. Appl. Phys. – volume: 11 start-page: 557 year: 1993 end-page: 568 article-title: MRI simulation using the k‐space formalism publication-title: Magn. Reson. Imag. – volume: 3 start-page: 363 year: 1986 end-page: 376 article-title: A computer simulation of nuclear magnetic resonance imaging publication-title: Magn. Reson. Med. |
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| Title | Time domain simulation of Fourier imaging by summation of isochromats |
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