Analytical solution to the transient phase of steady‐state free precession sequences

Ganter, Carl

doi:10.1002/mrm.21968

Cited by 15 publications

(30 citation statements)

References 23 publications

(76 reference statements)

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“…Using analogy with the effective field in the spin-lock experiment, proven earlier, the two relaxation components are:

R_{1 ρ} = {cos}^{2} false(normalΘ false) R_{1} + {sin}^{2} false(normalΘ false) R_{2}

R_{2 ρ} = {sin}^{2} false(normalΘ false) R_{1} + {cos}^{2} false(normalΘ false) R_{2}

These expressions are in agreement with the relaxation expressions in bSSFP derived in Ref. [24]. Using these two relaxation components the steady-state magnetization becomes:

M_{s s} = - D Λ^{- 1} D^{- 1} R_{1} M_{0}

where D is the diagonalization matrix of the H eff and is given in Appendix B.…”

Section: Theorysupporting

confidence: 85%

Balanced Steady-State Free Precession (bSSFP) from an effective field perspective: Application to the detection of chemical exchange (bSSFPX)

Shu

Liu

Grant

et al. 2017

Journal of Magnetic Resonance

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Chemical exchange saturation transfer (CEST) is a novel contrast mechanism and it is gaining increasing popularity as many promising applications have been proposed and investigated. Fast and quantitative CEST imaging techniques are further needed in order to increase the applicability of CEST for clinical use as well as to derive quantitative physiological and biological information. Steady-state methods for fast CEST imaging have been reported recently. Here, we observe that an extreme case of these methods is a balanced steady-state free precession (bSSFP) sequence. The bSSFP in itself is sensitive to the exchange processes; hence, no additional saturation or preparation is needed for CEST-like data acquisition. The bSSFP experiment can be regarded as observation during saturation, without separate saturation and acquisition modules as used in standard CEST and similar experiments. One of the differences from standard CEST methods is that the bSSFP spectrum is an XY-spectrum not a Z-spectrum. As the first proof-of-principle step, we have implemented the steady state bSSFP sequence for chemical exchange detection (bSSFPX) and verified its feasibility in phantom studies. These studies have shown that bSSFPX can achieve exchange-mediated contrast comparable to the standard CEST experiment. Therefore, the bSSFPX method has a potential for fast and quantitative CEST data acquisition.

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“…Using analogy with the effective field in the spin-lock experiment, proven earlier, the two relaxation components are:

R_{1 ρ} = {cos}^{2} false(normalΘ false) R_{1} + {sin}^{2} false(normalΘ false) R_{2}

R_{2 ρ} = {sin}^{2} false(normalΘ false) R_{1} + {cos}^{2} false(normalΘ false) R_{2}

These expressions are in agreement with the relaxation expressions in bSSFP derived in Ref. [24]. Using these two relaxation components the steady-state magnetization becomes:

M_{s s} = - D Λ^{- 1} D^{- 1} R_{1} M_{0}

where D is the diagonalization matrix of the H eff and is given in Appendix B.…”

Section: Theorysupporting

confidence: 85%

Balanced Steady-State Free Precession (bSSFP) from an effective field perspective: Application to the detection of chemical exchange (bSSFPX)

Shu

Liu

Grant

et al. 2017

Journal of Magnetic Resonance

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“…The novel non-equilibrium B 1 mapping method (16) makes use of a recently observed linear relation between the frequency of oscillations in the transient phase of unbalanced steady-state free precession sequences and the actual flip angle (17). For sufficient repetitive deviation from steady state in the dynamic 3D acquisitions (matrix, 64 · 52 · 4; isotropic resolution, 5 mm), software triggering (period, 500 ms) was applied to alternate trains of steady-state free precession blocks (57 Cine phases) with idle periods.…”

Section: Mr Radiofrequency Field Homogeneitymentioning

confidence: 99%

Performance Measurements of the Siemens mMR Integrated Whole-Body PET/MR Scanner

Delso¹,

Fürst²,

Jakoby³

et al. 2011

J Nucl Med

Self Cite

784

606

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These results compare favorably with other state-of-the-art PET/CT and PET/MR scanners, indicating that the integration of the PET detectors in the MR scanner and their operation within the magnetic field do not have a perceptible impact on the overall performance. The MR subsystem performs essentially like a standalone system. However, further work is necessary to evaluate the more advanced MR applications, such as functional imaging and spectroscopy.

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“…The symbol “” signifies the Hermitian conjugate of vectors and matrices. The similarity transformation matrices are defined as

S = true(\begin{matrix} 1 & + i & 0 \\ 1 & - i & 0 \\ 0 & 0 & 1 \end{matrix} true)

{boldS}^{- 1} = \frac{1}{2} true[\begin{matrix} 1 & 1 & 0 \\ - i & + i & 0 \\ 0 & 0 & 2 \end{matrix} true] .

In some situations, such as in the investigation of transient phase behavior of steady state sequences as performed by Ganter , the unitary transformation in Eqs. and may be more convenient; however, its disadvantage is that the scaling factor

ρ = 1 / \sqrt{2}

occurs in some components of all further vectors and operator matrices.…”

Section: The Main Challenge: Understanding Echo Generationmentioning

confidence: 99%

“…The key concept of configuration states was previously based on the Fourier decomposition of transverse magnetization. Now, the full complex system of reference [M + , M − , M z ] T is expressed by means of Fourier decompositions and transforms :

\begin{matrix} left \\ {\overset{F}{true}}_{+} (boldk) = \int_{V} (M_{x} (boldr) + i M_{y} (boldr)) e^{- i k r} d^{3} r = \int_{V} M_{+} (boldr) e^{- i k r} d^{3} r \\ \Leftrightarrow M_{x} (boldr) + i M_{y} (boldr) = M_{+} (boldr) = \int_{V} {\overset{F}{true}}_{+} (boldk) e^{i k r} d^{3} k, \end{matrix}

\begin{matrix} left \\ {\overset{F}{true}}_{-} (boldk) = \int_{V} (M_{x} (boldr) - i M_{y} (boldr)) e^{- i k r} d^{3} r = \int_{V} M_{-} (boldr) e^{- i k r} d^{3} r \\ \Leftrightarrow M_{x} (boldr) - i M_{y} (boldr) = M_{-} (boldr) = \int_{V} {\overset{F}{true}}_{-} (boldk) e^{i k r} d^{3} k, \end{matrix}

…”

Section: The Main Challenge: Understanding Echo Generationmentioning

confidence: 99%

Extended phase graphs: Dephasing, RF pulses, and echoes ‐ pure and simple

Weigel

2014

Magnetic Resonance Imaging

354

422

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The extended phase graph (EPG) concept represents a powerful tool for depicting and understanding the magnetization response of a broad variety of MR sequences. EPGs focus on echo generation as well as on classification and use a Fourier based magnetization description in terms of "configurations states". The effect of gradients, radiofrequency (RF) pulses, relaxation, and motion phenomena during the MR sequence is characterized as the action of a few matrix operations on these configuration states. Thus, the EPG method allows for fast and precise quantitation of echo intensities even if several gradients and RF pulses are applied. EPG diagrams aid in the comprehension of different types of echoes and their corresponding echo time. Despite its several benefits in regard to a large number of problems and issues, researchers and users still often refrain from applying EPGs. It seems that "phase graphing" is still seen as a kind of "magic." The present review investigates the foundation of EPGs and sheds light on prerequisites for adding more advanced phenomena such as diffusion. The links between diagrams and calculations are discussed. A further focus is on limitations and simplifications as well recent extensions within the EPG concept. To make the review complete, representative software for EPG coding is provided.

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Analytical solution to the transient phase of steady‐state free precession sequences

Cited by 15 publications

References 23 publications

Balanced Steady-State Free Precession (bSSFP) from an effective field perspective: Application to the detection of chemical exchange (bSSFPX)

Balanced Steady-State Free Precession (bSSFP) from an effective field perspective: Application to the detection of chemical exchange (bSSFPX)

Performance Measurements of the Siemens mMR Integrated Whole-Body PET/MR Scanner

Extended phase graphs: Dephasing, RF pulses, and echoes ‐ pure and simple

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