Practical Implementation of Optimized Tissue-Specific Prescribed Signal Evolutions for Improved Turbo-Spin-Echo Imaging
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`J. P. Mugler, III1, H. Meyer2, B. Kiefer2
`1University of Virginia, Charlottesville, VA, United States, 2Siemens Medical Solutions, Erlangen, Germany
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`Synopsis: Tissue-specific prescribed signal evolutions, achieved by variable refocusing RF-pulse flip angles, have been used to decrease acquisition
`time and SAR for turbo/fast spin-echo imaging. Because the required flip angles depend on the sequence configuration and relaxation times for the
`reference tissue, practical use demands a rapid calculation algorithm that is integrated into the sequence. We developed such an algorithm and
`demonstrated its integration into the TSE sequence on a commercial MR system. With calculation times below one second for up to 300 echoes, this
`implementation provides the flexibility necessary to make prescribed evolutions practical for routine imaging.
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`Introduction: Tissue-specific prescribed signal evolutions have been used to substantially decrease the acquisition time for single-slab 3D turbo-spin-
`echo imaging [1] and significantly reduce power deposition for real-time single-shot fast-spin-echo imaging [2]. Prescribed signal evolutions are
`achieved by a series of continuously-variable refocusing RF-pulse flip angles that are calculated using an iterative Bloch-equation-based theoretical
`simulation and whose values depend on the relaxation times for the reference tissue as well as the timing parameters for the pulse sequence. Because
`of these dependencies on the relaxation times and pulse-sequence configuration, practical use of prescribed signal evolutions demands a method that is
`integrated into the pulse sequence and can rapidly calculate the associated flip angle values based on parameter selections from the user.
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`Theory: The central task for deriving a prescribed signal evolution is to calculate the refocusing RF-pulse flip angle αn that yields a prescribed signal
`given the magnetization state immediately preceding this RF pulse. The desired signal S can be written [3]:
`S = T* sin2(αn/2) + T cos2(αn/2) + L* sin(αn)/2,
`where T* is the signal from a pure refocusing RF pulse (180˚), T is the signal from no RF pulse (0˚) and L* is the signal from encoded longitudinal
`magnetization (90˚). This equation can be solved for αn in closed form, and therefore the prescribed signal evolution for a specific overall signal level
`can be calculated directly by using a Bloch-equation-based numerical simulation of a CPMG echo train wherein, to prevent aliasing, the number of
`isochromats in the simulation is at least twice the number of echoes plus two. To find the prescribed signal evolution that is optimized to yield the
`highest overall signal, the closed form solution must be iterated. For this we use a standard interval bisection method with imbedded constraints for the
`number of iterations and, for providing control over the power deposition, the flip angle value at any selected position(s) along the echo train.
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`Methods: The theoretical approach described above was implemented in C++, the same programming language as that used for pulse sequences on
`our MR scanners. The flip-angle calculation program included three main components: (1) a function for calculating the prescribed signal evolution
`shape (e.g., an initial period of exponential decay, a central section of uniform signal and finally another period of exponential decay); (2) a base class
`for performing magnetization manipulations (e.g., RF pulses, dephasing [application of a gradient], relaxation, signal calculation); and (3) a derived class
`for calculating the variable flip-angle series that yields the desired prescribed signal evolution optimized to generate the maximum signal level subject to
`the iteration and flip-angle constraints. This C++ code was integrated into the turbo-spin-echo pulse-sequence code for Siemens MR scanners
`(Siemens Medical Solutions, Erlangen, Germany), which is compatible with 1.0T, 1.5T and 3T systems.
`To minimize the required execution time, the flip-angle program was configured to calculate two optimized prescribed signal evolutions for a given
`use of the pulse sequence. When the user first selects the sequence protocol, the program calculates a reference variable flip-angle series
`corresponding to a large number of echoes (e.g., 300). In terms of the maximum flip-angle value at any temporal position along an echo train of fixed
`duration, this series represents the limiting case for any smaller number of echoes. As the user changes parameters, the reference flip-angle values are
`used to rapidly estimate the flip angles for the current settings so that the estimated power deposition can be continually updated. Subsequently, when
`the user submits the desired protocol to the system for execution, the exact flip-angle values for the final parameter set are calculated.
`The calculation speed of the program was benchmarked using a 1.1 GHz Pentium III processor and 512 MB of memory. The turbo-spin-echo pulse
`sequence containing the flip-angle calculation program was used to obtain single-slab 3D image sets of the brain from healthy volunteers on 1.5T and
`3T MR systems (Symphony, Sonata, Trio; Siemens Medical Solutions) after obtaining informed written consent.
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`Results: The flip-angle calculation time as a function of the number of echoes is presented in Table 1 for an iteration limit of 25 and a maximum flip-
`angle constraint of 160˚ for any pulse in the echo train. Even for 300 echoes, the calculation time is well under one second. Within the user interface,
`the presence of the calculation program did not introduce a noticeable degradation in performance. A representative T2-weighted 3D turbo-spin-echo
`image, acquired using a 250-echo prescribed signal evolution, is shown in Figure 2.
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`Table 1. Flip-angle calculation time versus number of echoes.
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`Number of Echoes
`
`Calculation Time [ms]
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`50
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`100
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`200
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`300
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`18
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`70
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`250
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`452
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`Fig. 2. Coronal T2-weighted 3D
`turbo-spin-echo image of the brain.
`The prescribed signal evolution
`(exponential decay, uniform,
`exponential decay) was 900 ms in
`duration and included 250 echoes.
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`Conclusions: An algorithm for rapidly calculating the variable flip-angle refocusing RF pulses that yield optimized prescribed signal evolutions for
`turbo/fast spin-echo imaging has been developed and integrated into the turbo-spin-echo pulse sequence on a commercial MR system. Having
`calculation times well under 1 second, this program permitted prescribed signal evolutions to be implemented for single-slab 3D turbo-spin-echo imaging
`without a significant impact on the response time of the user interface. This implementation provides the necessary flexibility to make optimized
`prescribed signal evolutions practical for routine MR imaging applications.
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`References: 1. Mugler JP, Kiefer B, Brookeman JR. Proc Intl Soc Mag Reson Med 8 (2000); 687. 2. Busse RF, Riederer SJ. Proc Intl Soc Mag
`Reson Med 9 (2001); 1790. 3. Woessner DE. J Chem Phys 1961; 34:2057-2061.
`Acknowledgements: Supported in part by National Institutes of Health grant NS-35142.
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`Proc. Intl. Soc. Mag. Reson. Med. 11 (2003)
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