Questions and Answers ​in MRI
  • Home
  • Complete List of Questions
  • …Magnets & Scanners
    • Basic Electromagnetism >
      • What causes magnetism?
      • What is a Tesla?
      • Who was Tesla?
      • What is a Gauss?
      • How strong is 3.0T?
      • What is a gradient?
      • Aren't gradients coils?
      • What is susceptibility?
      • How to levitate a frog?
      • What is ferromagnetism?
      • Superparamagnetism?
    • Magnets - Part I >
      • Types of magnets?
      • Brands of scanners?
      • Which way does field point?
      • Which is the north pole?
      • Low v mid v high field?
      • Advantages to low-field?
      • Disadvantages?
      • What is homogeneity?
      • Why homogeneity?
      • Why shimming?
      • Passive shimming?
      • Active shimming?
    • Magnets - Part II >
      • Superconductivity?
      • Perpetual motion?
      • How to ramp?
      • Superconductive design?
      • Room Temp supercon?
      • Liquid helium use?
      • What is a quench?
      • Is field ever turned off?
      • Emergency stop button?
    • Gradients >
      • Gradient coils?
      • How do z-gradients work?
      • X- and Y- gradients?
      • Open scanner gradients?
      • Eddy current problems?
      • Active shielded gradients?
      • Active shield confusion?
      • What is pre-emphasis?
      • Gradient heating?
      • Gradient specifications?
      • Gradient linearity?
    • RF & Coils >
      • Many kinds of coils?
      • Radiofrequency waves?
      • Phase v frequency?
      • RF Coil function(s)?
      • RF-transmit coils?
      • LP vs CP (Quadrature)?
      • Multi-transmit RF?
      • Receive-only coils?
      • Array coils?
      • AIR Coils?
    • Site Planning >
      • MR system layout?
      • What are fringe fields?
      • How to reduce fringe?
      • Magnetic shielding?
      • Need for vibration testing?
      • What's that noise?
      • Why RF Shielding?
      • Wires/tubes thru wall?
  • ...Safety and Screening
    • Overview >
      • ACR Safety Zones?
      • MR safety screening?
      • Incomplete screening?
      • Passive v active implants?
      • Conditional implants?
      • Common safety issues?
      • Projectiles?
      • Metal detectors?
      • Pregnant patients?
      • Postop, ER & ICU patients?
      • Temperature monitoring?
      • Orbital foreign bodies?
      • Bullets and shrapnel?
    • Static Fields >
      • "Dangerous" metals?
      • "Safe" metals?
      • Magnetizing metal?
      • Object shape?
      • Forces on metal?
      • Most dangerous place?
      • Force/torque testing?
      • Static field bioeffects?
      • Dizziness/Vertigo?
      • Flickering lights?
      • Metallic taste?
    • RF Fields >
      • RF safety overview?
      • RF biological effects?
      • What is SAR?
      • SAR limits?
      • Operating modes?
      • How to reduce SAR?
      • RF burns?
      • Estimate implant heating?
      • SED vs SAR?
      • B1+rms vs SAR?
      • Personnel exposure?
      • Cell phones?
    • Gradient Fields >
      • Gradient safety overview
      • Acoustic noise?
      • Nerve stimulation?
      • Gradient vs RF heating?
    • Safety: Neurological >
      • Aneurysm coils/clips?
      • Shunts/drains?
      • Pressure monitors/bolts?
      • Deep brain stimulators?
      • Spinal cord stimulators?
      • Vagal nerve stimulators?
      • Cranial electrodes?
      • Carotid clamps?
      • Peripheral stimulators?
      • Epidural catheters?
    • Safety: Head & Neck >
      • Additional orbit safety?
      • Cochlear Implants?
      • Bone conduction implants?
      • Other ear implants?
      • Dental/facial implants?
      • ET tubes & airways?
    • Safety: Chest & Vascular >
      • Breast tissue expanders?
      • Breast biopsy markers?
      • Airway stents/valves/coils?
      • Respiratory stimulators?
      • Ports/vascular access?
      • Swan-Ganz catheters?
      • IVC filters?
      • Implanted infusion pumps?
      • Insulin pumps & CGMs?
      • Vascular stents/grafts?
      • Sternal wires/implants?
    • Safety: Cardiac >
      • Pacemaker dangers?
      • Pacemaker terminology?
      • New/'Safe" Pacemakers?
      • Old/Legacy Pacemakers?
      • Violating the conditions?
      • Epicardial pacers/leads?
      • Cardiac monitors?
      • Heart valves?
      • Miscellaneous CV devices?
    • Safety: Abdominal >
      • PIllCam and capsules?
      • Gastric pacemakers?
      • Other GI devices?
      • Contraceptive devices?
      • Foley catheters?
      • Incontinence devices?
      • Penile Implants?
      • Sacral nerve stimulators?
      • GU stents and other?
    • Safety: Orthopedic >
      • Orthopedic hardware?
      • External fixators?
      • Traction and halos?
      • Bone stimulators?
      • Magnetic rods?
  • …The NMR Phenomenon
    • Spin >
      • What is spin?
      • Why I = ½, 1, etc?
      • Proton = nucleus = spin?
      • Predict nuclear spin (I)?
      • Magnetic dipole moment?
      • Gyromagnetic ratio (γ)?
      • "Spin" vs "Spin state"?
      • Energy splitting?
      • Fall to lowest state?
      • Quantum "reality"?
    • Precession >
      • Why precession?
      • Who was Larmor?
      • Energy for precession?
      • Chemical shift?
      • Net magnetization (M)?
      • Does M instantly appear?
      • Does M also precess?
      • Does precession = NMR?
    • Resonance >
      • MR vs MRI vs NMR?
      • Who discovered NMR?
      • How does B1 tip M?
      • Why at Larmor frequency?
      • What is flip angle?
      • Spins precess after 180°?
      • Phase coherence?
      • Release of RF energy?
      • Rotating frame?
      • Off-resonance?
      • Adiabatic excitation?
      • Adiabatic pulses?
    • Relaxation - Physics >
      • Bloch equations?
      • What is T1?
      • What is T2?
      • Relaxation rate vs time?
      • Why is T1 > T2?
      • T2 vs T2*?
      • Causes of Relaxation?
      • Dipole-dipole interactions?
      • Chemical Exchange?
      • Spin-Spin interactions?
      • Macromolecule effects?
      • Which H's produce signal?
      • "Invisible" protons?
      • Magnetization Transfer?
      • Bo effect on T1 & T2?
      • How to predict T1 & T2?
    • Relaxation - Clincial >
      • T1 bright? - fat
      • T1 bright? - other oils
      • T1 bright? - cholesterol
      • T1 bright? - calcifications
      • T1 bright? - meconium
      • T1 bright? - melanin
      • T1 bright? - protein/mucin
      • T1 bright? - myelin
      • Magic angle?
      • MT Imaging/Contrast?
  • …Pulse Sequences
    • MR Signals >
      • Origin of MR signal?
      • Free Induction Decay?
      • Gradient echo?
      • TR and TE?
      • Spin echo?
      • 90°-90° Hahn Echo?
      • Stimulated echoes?
      • STEs for imaging?
      • 4 or more RF-pulses?
      • Partial flip angles?
      • How is signal higher?
      • Optimal flip angle?
    • Spin Echo >
      • SE vs Multi-SE vs FSE?
      • Image contrast: TR/TE?
      • Opposite effects ↑T1 ↑T2?
      • Meaning of weighting?
      • Does SE correct for T2?
      • Effect of 180° on Mz?
      • Direction of 180° pulse?
    • Inversion Recovery >
      • What is IR?
      • Why use IR?
      • Phase-sensitive IR?
      • Why not PSIR always?
      • Choice of IR parameters?
      • TI to null a tissue?
      • STIR?
      • T1-FLAIR
      • T2-FLAIR?
      • IR-prepped sequences?
      • Double IR?
    • Gradient Echo >
      • GRE vs SE?
      • Multi-echo GRE?
      • Types of GRE sequences?
      • Commercial Acronyms?
      • Spoiling - what and how?
      • Spoiled-GRE parameters?
      • Spoiled for T1W only?
      • What is SSFP?
      • GRASS/FISP: how?
      • GRASS/FISP: parameters?
      • GRASS vs MPGR?
      • PSIF vs FISP?
      • True FISP/FIESTA?
      • FIESTA v FIESTA-C?
      • DESS?
      • MERGE/MEDIC?
      • GRASE?
      • MP-RAGE v MR2RAGE?
    • Susceptibility Imaging >
      • What is susceptibility (χ)?
      • What's wrong with GRE?
      • Making an SW image?
      • Phase of blood v Ca++?
      • Quantitative susceptibility?
    • Diffusion: Basic >
      • What is diffusion?
      • Iso-/Anisotropic diffusion?
      • "Apparent" diffusion?
      • Making a DW image?
      • What is the b-value?
      • b0 vs b50?
      • Trace vs ADC map?
      • Light/dark reversal?
      • T2 "shine through"?
      • Exponential ADC?
      • T2 "black-out"?
      • DWI bright causes?
    • Diffusion: Advanced >
      • Diffusion Tensor?
      • DTI (tensor imaging)?
      • Whole body DWI?
      • Readout-segmented DWI?
      • Small FOV DWI?
      • IVIM?
      • Diffusion Kurtosis?
    • Fat-Water Imaging >
      • Fat & Water properties?
      • F-W chemical shift?
      • In-phase/out-of-phase?
      • Best method?
      • Dixon method?
      • "Fat-sat" pulses?
      • Water excitation?
      • STIR?
      • SPIR?
      • SPAIR v SPIR?
      • SPIR/SPAIR v STIR?
  • …Making an Image
    • From Signals to Images >
      • Phase v frequency?
      • Angular frequency (ω)?
      • Signal squiggles?
      • Real v Imaginary?
      • Fourier Transform (FT)?
      • What are 2D- & 3D-FTs?
      • Who invented MRI?
      • How to locate signals?
    • Frequency Encoding >
      • Frequency encoding?
      • Receiver bandwidth?
      • Narrow bandwidth?
      • Slice-selective excitation?
      • SS gradient lobes?
      • Cross-talk?
      • Frequency encode all?
      • Mixing of slices?
      • Two slices at once?
      • Simultaneous Multi-Slice?
    • Phase Encoding >
      • Phase-encoding gradient?
      • Single PE step?
      • What is phase-encoding?
      • PE and FE together?
      • 2DFT reconstruction?
      • Choosing PE/FE direction?
    • Performing an MR Scan >
      • What are the steps?
      • Automatic prescan?
      • Routine shimming?
      • Coil tuning/matching?
      • Center frequency?
      • Transmitter gain?
      • Receiver gain?
      • Dummy cycles?
      • Where's my data?
      • MR Tech qualifications?
    • Image Quality Control >
      • Who regulates MRI?
      • Who accredits?
      • Mandatory accreditation?
      • Routine quality control?
      • MR phantoms?
      • Geometric accuracy?
      • Image uniformity?
      • Slice parameters?
      • Image resolution?
      • Signal-to-noise?
      • Ghosting?
  • …K-space & Rapid Imaging
    • K-space (Basic) >
      • What is k-space?
      • Parts of k-space?
      • What does "k" stand for?
      • Spatial frequencies?
      • Locations in k-space?
      • Data for k-space?
      • Why signal ↔ k-space?
      • Spin-warp imaging?
      • Big spot in middle?
      • K-space trajectories?
      • Radial sampling?
    • K-space (Advanced) >
      • K-space grid?
      • Negative frequencies?
      • Field-of-view (FOV)
      • Rectangular FOV?
      • Partial Fourier?
      • Phase symmetry?
      • Read symmetry?
      • Why not use both?
      • ZIP?
    • Rapid Imaging (FSE &EPI) >
      • What is FSE/TSE?
      • FSE parameters?
      • Bright Fat?
      • Other FSE differences?
      • Dual-echo FSE?
      • Driven equilibrium?
      • Reduced flip angle FSE?
      • Hyperechoes?
      • SPACE/CUBE/VISTA?
      • Echo-planar imaging?
      • HASTE/SS-FSE?
    • Parallel Imaging (PI) >
      • What is PI?
      • How is PI different?
      • PI coils and sequences?
      • Why and when to use?
      • Two types of PI?
      • SENSE/ASSET?
      • GRAPPA/ARC?
      • CAIPIRINHA?
      • Compressed sensing?
      • Noise in PI?
      • Artifacts in PI?
  • …Contrast Agents
    • Contrast Agents: Physics >
      • Why Gadolinium?
      • Paramagnetic relaxation?
      • What is relaxivity?
      • Why does Gd shorten T1?
      • Does Gd affect T2?
      • Gd & field strength?
      • Best T1-pulse sequence?
      • Triple dose and MT?
      • Dynamic CE imaging?
      • Gadolinium on CT?
    • Contrast Agents: Clinical >
      • So many Gd agents!
      • Important properties?
      • Ionic v non-ionic?
      • Intra-articular/thecal Gd?
      • Gd liver agents (Eovist)?
      • Mn agents (Teslascan)?
      • Feridex & Liver Agents?
      • Lymph node agents?
      • Ferumoxytol?
      • Blood pool (Ablavar)?
      • Bowel contrast agents?
    • Contrast Agents: Safety >
      • Gadolinium safety?
      • Allergic reactions?
      • Renal toxicity?
      • What is NSF?
      • NSF by agent?
      • Informed consent for Gd?
      • Gd protocol?
      • Is Gd safe in infants?
      • Reduced dose in infants?
      • Gd in breast milk?
      • Gd in pregnancy?
      • Gd accumulation?
      • Gd deposition disease?
  • …Cardiovascular and MRA
    • Flow effects in MRI >
      • Defining flow?
      • Expected velocities?
      • Laminar v turbulent?
      • Predicting MR of flow?
      • Time-of-flight effects?
      • Spin phase effects?
      • Flow void?
      • Why GRE ↑ flow signal?
      • Slow flow v thrombus?
      • Even-echo rephasing?
      • Flow-compensation?
      • Flow misregistration?
    • MR Angiography - I >
      • MRA methods?
      • Dark vs bright blood?
      • Time-of-Flight (TOF) MRA?
      • 2D vs 3D MRA?
      • MRA parameters?
      • Magnetization Transfer?
      • Ramped flip angle?
      • MOTSA?
      • Fat-suppressed MRA?
      • TOF MRA Artifacts?
      • Phase-contrast MRA?
      • What is VENC?
      • Measuring flow?
      • 4D Flow Imaging?
      • How accurate?
    • MR Angiography - II >
      • Gated 3D FSE MRA?
      • 3D FSE MRA parameters?
      • SSFP MRA?
      • Inflow-enhanced SSFP?
      • MRA with ASL?
      • Other MRA methods?
      • Contrast-enhanced MRA?
      • Timing the bolus?
      • View ordering in MRA?
      • Bolus chasing?
      • TRICKS or TWIST?
      • CE-MRA artifacts?
    • Cardiac I - Intro/Anatomy >
      • Cardiac protocols?
      • Patient prep?
      • EKG problems?
      • Magnet changes EKG?
      • Gating v triggering?
      • Gating parameters?
      • Heart navigators?
      • Dark blood/Double IR?
      • Why not single IR?
      • Triple IR?
      • Polar plots?
      • Coronary artery MRA?
    • Cardiac II - Function >
      • Beating heart movies?
      • Cine parameters?
      • Real-time cine?
      • Ventricular function?
      • Tagging/SPAMM?
      • Perfusion: why and how?
      • 1st pass perfusion?
      • Quantifying perfusion?
      • Dark rim artifact
    • Cardiac III - Viability >
      • Gd enhancement?
      • TI to null myocardium?
      • PS (phase-sensitive) IR?
      • Wideband LGE?
      • T1 mapping?
      • Iron/T2*-mapping?
      • Edema/T2-mapping?
      • Why/how stress test?
      • Stess drugs/agents?
      • Stress consent form?
  • …MR Artifacts
    • Tissue-related artifacts >
      • Chemical shift artifact?
      • Chemical shift in phase?
      • Reducing chemical shift?
      • Chemical Shift 2nd Kind?
      • In-phase/out-of phase?
      • IR bounce point?
      • Susceptibility artifact?
      • Metal suppression?
      • Dielectric effect?
      • Dielectric Pads?
    • Motion-related artifacts >
      • Why discrete ghosts?
      • Motion artifact direction?
      • Reducing motion artifacts?
      • Saturation pulses?
      • Gating methods?
      • Respiratory comp?
      • Navigator echoes?
      • PROPELLER/BLADE?
    • Technique-related artifacts >
      • Partial volume effects?
      • Slice overlap?
      • Aliasing?
      • Wrap-around artifact?
      • Eliminate wrap-around?
      • Phase oversampling?
      • Frequency wrap-around?
      • Spiral/radial artifacts?
      • Gibbs artifact?
      • Nyquist (N/2) ghosts?
      • Zipper artifact?
      • Data artifacts?
      • Surface coil flare?
      • MRA Artifacts (TOF)?
      • MRA artifacts (CE)?
  • …Functional Imaging
    • Perfusion I: Intro & DSC >
      • Measuring perfusion?
      • Meaning of CBF, MTT etc?
      • DSC v DCE v ASL?
      • How to perform DSC?
      • Bolus Gd effect?
      • T1 effects on DSC?
      • DSC recirculation?
      • DSC curve analysis?
      • DSC signal v [Gd]
      • Arterial input (AIF)?
      • Quantitative DSC?
    • Perfusion II: DCE >
      • What is DCE?
      • How is DCE performed?
      • How is DCE analyzed?
      • Breast DCE?
      • DCE signal v [Gd]
      • DCE tissue parmeters?
      • Parameters to images?
      • K-trans = permeability?
      • Utility of DCE?
    • Perfusion III: ASL >
      • What is ASL?
      • ASL methods overview?
      • CASL?
      • PASL?
      • pCASL?
      • ASL parameters?
      • ASL artifacts?
      • Gadolinium and ASL?
      • Vascular color maps?
      • Quantifying flow?
    • Functional MRI/BOLD - I >
      • Who invented fMRI?
      • How does fMRI work?
      • BOLD contrast?
      • Why does BOLD ↑ signal?
      • Does BOLD=brain activity?
      • BOLD pulse sequences?
      • fMRI Paradigm design?
      • Why "on-off" comparison?
      • Motor paradigms?
      • Visual?
      • Language?
    • Functional MRI/BOLD - II >
      • Process/analyze fMRI?
      • Best fMRI software?
      • Data pre-processing?
      • Registration/normalization?
      • fMRI statistical analysis?
      • General Linear Model?
      • Activation "blobs"?
      • False activation?
      • Resting state fMRI?
      • Analyze RS-fMRI?
      • Network/Graphs?
      • fMRI at 7T?
      • Mind reading/Lie detector?
      • fMRI critique?
  • …MR Spectroscopy
    • MRS I - Basics >
      • MRI vs MRS?
      • Spectra vs images?
      • Chemical shift (δ)?
      • Measuring δ?
      • Backward δ scale?
      • Predicting δ?
      • Size/shapes of peaks?
      • Splitting of peaks?
      • Localization methods?
      • Single v multi-voxel?
      • PRESS?
      • STEAM?
      • ISIS?
      • CSI?
    • MRS II - Clinical ¹H MRS >
      • How-to: brain MRS?
      • Water suppression?
      • Fat suppression?
      • Normal brain spectra?
      • Choice of TR/TE/etc?
      • Hunter's angle?
      • Lactate inversion?
      • Metabolite mapping?
      • Metabolite quantitation?
      • Breast MRS?
      • Gd effect on MRS?
      • How-to: prostate MRS?
      • Prostate spectra?
      • Muscle ¹H-MRS?
      • Liver ¹H-MRS?
      • MRS artifacts?
    • MRS III - Multi-nuclear >
      • Other nuclei?
      • Why phosphorus?
      • How-to: ³¹P MRS
      • Normal ³¹P spectra?
      • Organ differences?
      • ³¹P measurements?
      • Decoupling?
      • NOE?
      • Carbon MRS?
      • Sodium imaging?
      • Xenon imaging?
  • ...Artificial Intelligence
    • AI Part I: Basics >
      • Artificial Intelligence (AI)?
      • What is a neural network?
      • Machine Learning (ML)?
      • Shallow v Deep ML?
      • Shallow networks?
      • Deep network types?
      • Data prep and fitting?
      • Back-Propagation?
      • DL 'Playground'?
    • AI Part 2: Advanced >
      • What is convolution?
      • Convolutional Network?
      • Softmax?
      • Upsampling?
      • Limitations/Problems of AI?
      • Is the Singularity near?
    • AI Part 3: Image processing >
      • AI in clinical MRI?
      • Super-resolution?
  • ...Tissue Properties Imaging
    • MRI of Hemorrhage >
      • Hematoma overview?
      • Types of Hemoglobin?
      • Hyperacute/Oxy-Hb?
      • Acute/Deoxy-Hb?
      • Subacute/Met-Hb?
      • Deoxy-Hb v Met-Hb?
      • Extracellular met-Hb?
      • Chronic hematomas?
      • Hemichromes?
      • Ferritin/Hemosiderin?
      • Subarachnoid blood?
      • Blood at lower fields?
    • T2 cartilage mapping
    • MR Elastography?
    • Synthetic MRI?
    • Amide Proton Transfer?
    • MR thermography?
    • Electric Properties Imaging?
  • Copyright/Legal
    • Copyright Issues
    • Legal Disclaimers
  • Forums/Blogs/Links
  • What's New
  • Self-test Quizzes - NEW!
    • Magnets & Scanners Quiz
    • Safety & Screening Quiz
    • NMR Phenomenon Quiz
    • Pulse Sequences Quiz
    • Making an Image Quiz
    • K-space & Rapid Quiz
    • Contrast & Blood Quiz
    • Cardiovascular & MRA Quiz

Flow-compensation

Please explain how flow compensation (gradient-moment nulling) software works.  
Gradient-moment nulling or flow-compensation
The idea of adjusting the waveforms of imaging gradients to correct for flow-related dephasing was first implemented by Picker scientist Fred Pattany working at Wake Forest in the late 1980's. The original technique was known as MAST (Motion Artifact Suppression Technique) proved immediately useful for suppressing artifacts and improving quality of MR images.
Other vendors quickly followed suit, creating similar pulse sequences that became generically known as "flow compensation" or "gradient-moment nulling". Today these methods are known by various trade names: Siemens (GMR = "Gradient-Moment Rephasing"), GE ("Flow Comp"), Philips (FLAG = "FLow Adjusted gradients"), Hitachi (GR - "Gradient Rephasing"), and Canon (FC = "Flow Compensation").
Gradient-moment nulling or flow-compensation
Without gradient-moment nulling (GMN)
Gradient-moment nulling or flow-compensation
With GMN: Note clearer delineation of vessels
In gradient-moment nulling, additional gradient lobes are added prior to signal readout to compensate in advance for motion-induced dephasing at the time of the echo.  As a simple example, let us analyze the velocity-compensated GRE sequence shown right.  Note that the readout gradient has a more complex appearance than in the usual GRE sequence, with the addition of the two orange lobes.  These additional gradient lobes give this sequence its flow-compensation properties.
Gradient-moment nulling or flow-compensation
For stationary spins, the additional orange gradient lobes have no net effect, each adding or subtracting a constant amount of phase. Since there are two positive-going and two negatively-going lobes before the center of the echo, their net effect is zero. 
The net phase changes for spins moving at constant velocity are shown in the lower portion of the diagram. Using the standard GRE readout gradient, moving spins accumulate phase that is nonzero at the center of the echo (blue circle). This non-zero phase at mid-echo results in signal loss.

These two extra GMN lobes play a clever little game with the phase. The first orange lobe creates a phase gain, but the second orange lobe during the next time interval, when added to the phase changes from the first blue lobe, create a strongly negative phase loss. By the middle of readout, however, the net phase of the moving spins using GMN has returned to zero (orange circle).
This is a very simple illustration using a GRE sequence, but the same method may be applied to other pulse sequences and imaging axes. For example, GMN can be performed along the slice-select direction as well as along the readout direction. It can also be extended to correct for higher orders of motion, such as constant acceleration.  
The principal limitations of GMN techniques are: (1) they correct only for motion at constant velocity or acceleration; (2) the minimum TE is lengthened because time is needed to fit in the extra gradient lobes; (3) stresses on the imaging gradients are increased, potentially limiting field-of-view or slice thickness for a given TR; and (4) artifacts caused by eddy currents may be induced by the rapid gradient switching required.
For a more quantitative description of how GMN works, click on the Advanced Discussion tab or check one of the references below.

Advanced Discussion (show/hide)»

To explain how gradient-moment nulling works, it is necessary to make use of a fact developed in the Advanced Discussion section of the prior Q&A on Even-Echo Rephasing. Here we showed that for constant velocity flow (v) through a constant gradient (G), total phase shift (Φ) increases quadratically with time (T).  In other words 
Φ =  KT² 
where K = ½ γ G v is a constant when velocity and readout gradient strength are also constant.  
This quadratic dependence of total phase gain upon time is shown in the figure below.  Note that after 1, 2, 3, and 4 gradient intervals each of duration T, the phase has increased quadratically to KT², 4KT², 9KT², and 16KT² respectively.  The incremental phase contributions of the 1st, 2nd, 3rd, and 4th gradient intervals are therefore  KT², 3KT², 5KT², and 7KT², respectively.
Picture
Let us now consider in a more quantitative way the first-order gradient-moment nulling pulse sequence previously diagrammed..
Picture
To analyze what happens to a spin moving at constant velocity, we will do an incremental phase calculation similar to that performed for the even-echo rephasing case.  After the first block, the phase should again be  KT².  The incremental phase contribution from the two blocks that compose the second lobe is 2 x (−3KT² = −6KT².  The net phase of the moving spins immediately after the double block is therefore KT²  −5KT² = .−5KT². Finally, the first readout block contributes its incremental +5KT², yielding a net phase of zero at t = TE. By adding these extra gradient blocks, we have compensated or corrected for phase dispersions attributable to constant velocity.

The above example describes first-order (velocity) gradient-moment nulling. The method can be easily extended by to compensate for phase dispersions due to second-order (acceleration), third-order ("jerk"), and even higher degrees of motion. These higher order corrections require more gradient lobes (specifically, n+1 additional lobes, where n = motion order to be compensated). These extra lobes take time to play out, so using higher order GMN even further lengthens minimum TE and reduces number of slices for a given TR. Also, the effectiveness of the method decreases as the order increases. In practice, therefore, velocity-compensated GMN is nearly exclusively used, with acceleration-compensated GMN performed only occasionally.


References
     Elster AD. Motion artifact suppression technique (MAST) for cranial MR imaging: superiority over cardiac gating for reducing phase shift artifacts. AJNR Am J Neuroradiol 1988; 9:671-674. 
     Haacke EM, Lenz GW. Improving MR image quality in the presence of motion by using rephasing gradients.  AJR Am J Roentgenol 1987; 148:1251-1258.
     Pattany PM, Phillips JJ, Chiu LC, et al.  Motion artifact suppression technique (MAST) for MR imaging.  J Comput Assist Tomogr 1987; 11:369-377. 
     Richardson DN, Elster AD, Williams DW III. Gd-DTPA-enhanced MR images: accentuation of vascular pulsation artifacts and correction using gradient-moment nulling (MAST). AJNR Am J Neuroradiol 1990; 11:209-210. 

Related Questions
     Can you explain even-echo rephasing?

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