Phase and intensity anomalies in fourier transform NMR

Freeman, Ray; Hill, H. A. O.

doi:10.1016/0022-2364(71)90047-3

Cited by 218 publications

(193 citation statements)

References 10 publications

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“…, [12] a result also known from previous publications (14,16,18,19), which reflects the often-cited dependence of the TrueFISP steady-state signal on the ratio T 2 /T 1 .…”

Section: Steady Statesupporting

confidence: 79%

“…[10] This expression appears rather compact in comparison but, as shown in Fig. 6a, it appears to be a suitable approximation for the exact formulation found in the literature (11)(12)(13)(14)(15)(16)(17)(18)(19), here adapted to sequences with alternating phase:…”

Section: Steady Statementioning

confidence: 62%

“…While a longer but also closed form expression has been available for many years (11)(12)(13)(14), the result presented here appears to be a good approximation and has proven valuable for further analysis. With its use, an analytical formula was derived for the decay rate of the signal time course in the transient TrueFISP phase.…”

Section: Discussionmentioning

confidence: 84%

“…Hence, ideally no positiondependent dephasing takes place so that it is appropriate to describe the magnetization at a certain frequency by a single vector. With use of matrix notation, an analytic expression can be derived for the steady-state signal of TrueFISP sequences, which is a rather complex function of the parameters involved (T 1 , T 2 , M 0 , TR, flip angle, and frequency offset) (11)(12)(13)(14)(15)(16)(17)(18)(19). Recently, matrix-based mathematics were successfully used to assess the TrueFISP signal decay in the transient phase at off-resonance frequencies, applied in combination with suitable approximations and rather abstract mathematical procedures based on spinor formalism and perturbation theory (20,21).…”

mentioning

confidence: 99%

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A simple geometrical description of the TrueFISP ideal transient and steady‐state signal

Schmitt

Griswold

Gulani

et al. 2005

Magnetic Resonance in Med

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The TrueFISP sequence (1) (also referred to as balanced or fully refocused SSFP, balanced FFE, or FIESTA) is best known for its high SNR efficiency in the steady state, particularly for compartments with a high T 2 /T 1 ratio. Useful information may also be provided by signal acquisition during the transient phase before the steady state is reached. This first became feasible with introduction of the ␣/2 RF preparation pulse, preceding the acquisition module at a time TR/2 (2). In this context, an inversion-prepared TrueFISP sequence was presented for T 1 -weighted imaging, a principle that was proposed later for T 1 quantification (3). However, it was thereupon demonstrated that the temporal evolution of the transient signal actually depends on both longitudinal and transverse relaxation and that this property can be exploited for simultaneous quantification of T 1 and T 2 (4). For magnetization at resonance frequency and for TR Ͻ Ͻ T 1,2 , the transient signal behavior can be described with a simple closed formula (5). Recently, analytic expressions were presented for the calculation of T 1 , T 2 , and spin density from the fit parameters that are obtained by fitting an IR TrueFISP signal time course to a three-parameter monoexponential function (6). The technique works well on the human brain, but the presence of off-resonances poses problems in that it yields modified relaxation parameters and the ␣/2 preparation scheme is suboptimal so that signal fluctuations may impair the early echoes.Various preparation schemes have been proposed for avoiding these initial signal oscillations even for off-resonant magnetization, such as the use of a series RF pulses with linearly increasing flip angles (7,8). An elaborate procedure was also presented for the development of tailored preparation schemes, employing the ShinnarLeRoux (SLR) algorithm for selective RF pulse design and combined with preceding magnitude calibration (9). It is based on eigenvector calculations, using a matrix formalism that was introduced as an early tool for the assessment of signal behavior in periodic pulse sequences (10). The approach is particularly useful for analysis of the True-FISP sequence, since here the net integrals of all gradients within a TR cycle are zero. Hence, ideally no positiondependent dephasing takes place so that it is appropriate to describe the magnetization at a certain frequency by a single vector. With use of matrix notation, an analytic expression can be derived for the steady-state signal of TrueFISP sequences, which is a rather complex function of the parameters involved (T 1 , T 2 , M 0 , TR, flip angle, and frequency offset) (11)(12)(13)(14)(15)(16)(17)(18)(19). Recently, matrix-based mathematics were successfully used to assess the TrueFISP signal decay in the transient phase at off-resonance frequencies, applied in combination with suitable approximations and rather abstract mathematical procedures based on spinor formalism and perturbation theory (20,21).In this paper, the behavior of the magnetization vecto...

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“…, [12] a result also known from previous publications (14,16,18,19), which reflects the often-cited dependence of the TrueFISP steady-state signal on the ratio T 2 /T 1 .…”

Section: Steady Statesupporting

confidence: 79%

Section: Steady Statementioning

confidence: 62%

Section: Discussionmentioning

confidence: 84%

mentioning

confidence: 99%

See 2 more Smart Citations

A simple geometrical description of the TrueFISP ideal transient and steady‐state signal

Schmitt

Griswold

Gulani

et al. 2005

Magnetic Resonance in Med

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show abstract

“…This concept separates the Bloch equations (1) into repetitive units of RF excitation and interpulse delays (2) and thereby allows the derivation of closed form solutions to steady state free precession (SSFP) sequences in the steady state (3)(4)(5)(6)(7) and the transient phase (8)(9)(10)(11). In practice, however, RF pulses have a finite duration (T RF ) and may cause systematic deviations from the solutions derived in the limit of quasi-instantaneous RF pulses (12,13).…”

mentioning

confidence: 99%

Superbalanced steady state free precession

Bieri

2011

Magnetic Resonance in Med

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Steady state free precession (SSFP) signal theory is commonly derived in the limit of quasi-instantaneous radiofrequency (RF) excitation. SSFP imaging protocols, however, are frequently set up with minimal pulse repetition times and RF pulses can thus constitute a considerable amount to the actual pulse repetition time. As a result, finite RF pulse effects can lead to 10-20% signal deviation from common SSFP theory in the transient and in the steady state which may impair the accuracy of SSFP-based quantitative imaging techniques. In this article, a new and generic approach for intrinsic compensation of finite RF pulse effects is introduced. Compensation is based on balancing relaxation effects during finite RF excitation, similar to flow or motion compensation of gradient moments. RF pulse balancing, in addition to the refocusing of gradient moments with balanced SSFP, results in a superbalanced SSFP sequence free of finite RF pulse effects in the transient and in the steady state; irrespective of the RF pulse duration, flip angles, relaxation times, or off-resonances. In multipulse experiments, the time evolution of spins is commonly analyzed in the limit of quasi-instantaneously acting radiofrequency (RF) pulses. This concept separates the Bloch equations (1) into repetitive units of RF excitation and interpulse delays (2) and thereby allows the derivation of closed form solutions to steady state free precession (SSFP) sequences in the steady state (3-7) and the transient phase (8-11). In practice, however, RF pulses have a finite duration (T RF ) and may cause systematic deviations from the solutions derived in the limit of quasi-instantaneous RF pulses (12,13). An introductory example of this behavior is presented in Fig. 1 for balanced SSFP (bSSFP). The range of finite RF pulse effects is illustrated for the steady state amplitude (Fig. 1a) and for the decay factor of the transient (Fig. 1b) as a function of the flip angle (a) for the two extremes of quasi-instantaneous (T RF ! 0) and quasi-continuous (T RF ! pulse repetition time [TR]) excitation. Generally, finite RF pulse effects increase with increasing flip angle and relaxation time ratio (L :¼ T 1 /T 2 ) and show a smooth transition with the fractional RF pulse duration (l :¼ T RF /TR) (12). However, neither bSSFP contrast nor its spin-echo nature is affected by finite RF pulse effects (13).Following the common doctrine, SSFP imaging protocols have minimal TR and short excitation periods. Short RF pulses, however, lead to pronounced magnetization transfer (MT) effects in tissues (14) which may impair the accuracy of common SSFP-based quantitative MR imaging techniques, such as fast relaxation time mapping with inversion recovery SSFP (15,16) or variable nutation SSFP (17). Thus, long RF pulses were proposed to be used with these techniques to suppress MT effects (18,19), but it also became evident that signal modulations from finite RF pulses can no longer be neglected (18,20,21). In principle, signal models of quantitative SSFP imaging techniques c...

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