Concomitant gradient terms in phase contrast MR: Analysis and correction

Bernstein, Matt A.; Zhou, Xiaohong Joe; Polzin, Jason A.; King, Kevin F.; Ganin, Alexander; Pelc, Norbert J.; Glover, Gary H.

doi:10.1002/mrm.1910390218

Cited by 495 publications

(612 citation statements)

References 15 publications

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“…We estimate ε > 6.5 (residual fields add to the applied static field). As expected, in this regime of strong concomitant gradients, Fourier encoding breaks down and the image bears no resemblance to the phantom [5][6][7] . We can generalize our zero-field technique to the case of a uniform ambient field B a , which imposes conditions on both the gradient and π pulses.…”

supporting

confidence: 66%

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Distortion-free magnetic resonance imaging in the zero-field limit

Kelso¹,

Lee²,

Bouchard³

et al. 2009

Journal of Magnetic Resonance

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In MRI, the Larmor precession frequency ω(x, y, z) = γB(x, y, z) of the proton spins in the position-dependent magnetic field B(x, y, z) frequency-and phase-encodes the proton density distribution into a magnetic signal that is subsequently decoded to form an image 4 (γ is the magnetogyric ratio). In clinical MRI machines 4 the strength of the applied homogeneous static magnetic field B 0 = B 0 ẑ is typically 1.5 T. There has been recent interest, however, in systems operating in magnetic fields of the order of 10 -4 T (for example [13][14][15][16][17][18] ), where T 1 -weighted contrast is significantly enhanced 16 (T 1 is the longitudinal relaxation time). The loss of polarization is compensated-at least in part-by 3 prepolarizing 19 the spins at a much higher field, or by hyperpolarization techniques using lasers 20 , dynamic nuclear polarization 21,22 or parahydrogen-induced polarization 23 . The loss of signal amplitude inherent in Faraday-Law detection is mitigated by detecting the nuclear magnetization with either a Superconducting QUantum Interference Device (SQUID) 9 or an atomic magnetometer 24 , both of which respond to the magnetic flux itself, rather than its time rate of change. Regardless of the magnitude of B 0 , all currently used imaging processes involve the superposition of magnetic field gradients on a static field to impose spatial variations of the total field across the subject or sample. In the zero static field regime reported here, conventional MRI gradients are unable to encode the spins along a given direction and Fourier encoding breaks down.In conventional MRI techniques, the applied magnetic field gradients are assumed to be linear and unidirectional so that the field due to gradients is given by B(x, y, z) = (G x x + G y y + G z z) ẑ , where G x = ∂B z /∂x, G y = ∂B z /∂y, and G z = ∂B z /∂z are constants 4 . As an example, B(x, y, z) = G z z ẑ is shown in Fig. 1a. In reality, however, such idealized gradients are forbidden by the Maxwell equations divB = curlB = 0 for any magnetic field B in free space. In fact, any gradient must be accompanied by concomitant gradients in at least one additional direction, as illustrated in Fig The gradient field B(y, z) = (∂B y /∂y)y ŷ + (∂B z /∂z)z ẑ is turned on, and subsequently turned off nonadiabatically at time τ (point B). During this time interval, the spin precesses about B(y′, z′). The time τ is chosen to satisfy the requirement τ << 1/γG z L.Consequently, the precession during the interval τ is small, and we can treat it as the sum of precessions around ẑ and ŷ : δ z = γ(∂B z /∂z)z'τ around ẑ (Fig. 2b) and δ y = γ(∂B y /∂y)y'τ around ŷ (Fig. 2c). After the gradient pulse, a π pulse of uniform field Β π is applied along the z-axis with amplitude and duration adjusted to produce a precession angle of π around ẑ . This pulse flips the spin to the point C in Figs. 2b and 2c. 5Subsequently, a second gradient pulse brings the spin to D, and a second π pulse to E. This sequence of pulses produces a net precession of the spin about B z , ...

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supporting

confidence: 66%

“…1b. At very low static fields the undesired gradient components perpendicular to B 0 induce severe, essentially intractable image distortions [5][6][7] . The degree of distortion is characterized by a parameter ε = GL/B 0 , where G is the magnitude of the field gradient and L is the image field of view (FOV) 7 .…”

mentioning

confidence: 99%

Distortion-free magnetic resonance imaging in the zero-field limit

Kelso¹,

Lee²,

Bouchard³

et al. 2009

Journal of Magnetic Resonance

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“…All measurements were performed within 5 cm of the isocenter to minimize the Maxwell terms, and retrospective gating was used to minimize temporal differences in the background due to eddy currents (30). In regions of interest (ROIs) defined in the surrounding static gel, the mean difference and standard deviation (SD) from zero phases corresponded to less than 1.5% and 3.5% of the VENC, respectively; therefore, no measures were taken to further reduce these effects.…”

Section: Resultsmentioning

confidence: 99%

Laser Doppler velocimetry (LDV) and 3D phase‐contrast magnetic resonance angiography (PC‐MRA) velocity measurements: Validation in an anatomically accurate cerebral artery aneurysm model with steady flow

Hollnagel

Summers

Kollias

et al. 2007

Magnetic Resonance Imaging

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Purpose:To verify the accuracy of velocity mapping with three-dimensional (3D) phase-contrast magnetic resonance angiography (PC-MRA) for steady flow in a realistic model of a cerebral artery aneurysm at a 3T scanner. Materials and Methods:Steady flow through an original geometry model of a cerebral aneurysm was mapped at characteristic positions by state-of-the-art laser Doppler velocimetry (LDV) as well as 3D PC-MRA at 3T. The spatial distributions and local values of two velocity components obtained with these two measurement methods were compared. Results:The 3D PC-MRA velocity field distribution and mean velocity values exhibited only minor differences to compare to the LDV measurements in straight artery regions for both main and secondary velocities. The differences increased in regions with disturbed flow and in cases where the measurement plane was not perpendicular to the main flow direction.Conclusion: 3D PC-MRA can provide reliable measurements of velocity components of steady flow in small arteries. The accuracy of such measurements depends on the artery size and the measurement plane positioning.

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“…system for the effects of concomitant gradient fields (22). Correction for eddy current effects was achieved by subtracting the velocity field measured without rotation from the velocity field with rotation.…”

Section: Figurementioning

confidence: 99%

Improving computation of cardiovascular relative pressure fields from velocity MRI

Ebbers

Farnebäck

2009

Magnetic Resonance Imaging

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Purpose: To evaluate a multigrid-based solver for the pressure Poisson equation (PPE) with Galerkin coarsening, which works directly on the specified domain, for the computation of relative pressure fields from velocity MRI data. Materials and Methods:We compared the proposed structure-defined Poisson solver to other popular Poisson solvers working on unmodified rectangular and modified quasirectangular domains using synthetic and in vitro phantoms in which the mathematical solution of the pressure field is known, as well as on in vivo MRI velocity measurements of aortic blood flow dynamics.Results: All three PPE solvers gave accurate results for convex computational domains. Using a rectangular or quasirectangular domain on a more complicated domain, like a c-shape, revealed a systematic underestimation of the pressure amplitudes, while the proposed PPE solver, working directly on the specified domain, provided accurate estimates of the relative pressure fields. Conclusion:Popular iterative approaches with quasirectangular computational domains can lead to significant systematic underestimation of the pressure amplitude. We suggest using a multigrid-based PPE solver with Galerkin coarsening, which works directly on the structure-defined computational domain. This solver provides accurate estimates of the relative pressure fields for both simple and complex geometries with additional significant improvements with respect to execution speed.

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Concomitant gradient terms in phase contrast MR: Analysis and correction

Cited by 495 publications

References 15 publications

Distortion-free magnetic resonance imaging in the zero-field limit

Distortion-free magnetic resonance imaging in the zero-field limit

Laser Doppler velocimetry (LDV) and 3D phase‐contrast magnetic resonance angiography (PC‐MRA) velocity measurements: Validation in an anatomically accurate cerebral artery aneurysm model with steady flow

Improving computation of cardiovascular relative pressure fields from velocity MRI

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