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

Effect of B1 on M

How does B1 tip the net magnetization (M)?  
NMR, radiofrequency B1
Before diving into the details of how RF stimulation affects M, let us quickly review what M is and where the B1 field comes from.
NMR, radiofrequency B1
Net magnetization (M), the averaged sum of many individual quantum spins, can be treated as a regular vector in classical physics.
For the purposes of the next several Q&A's, it is probably better to forget completely about individual nuclear spins and consider only the net magnetization (M), the sum of many spins averaged together.  The bizarre aspects of quantum mechanics can then be disregarded and the motion of M analyzed using classical physics.  Think of M as a big spinning bar magnet, if you must.
The radiofrequency field (B1) is applied perpendicular to the main magnetic field (Bo). The B1 field is produced either by a local coil (as shown in the picture) or more commonly, from windings in the walls of the scanner itself. Initially, M is aligned with Bo but will be tipped out of alignment during application by the rotating/oscillating B1 field.  Like pushing a child on a swing, the B1 field must be applied near the Larmor frequency for this to occur.
NMR, radiofrequency B1, flip angle
With continued application of the B1 field, M precesses at continually larger angles away from Bo.
NMR, radiofrequency B1
Vertical bore scanner showing main (Bo) and RF (B1) fields. M is initially aligned with Bo but will be tipped away by the action of B1, precessing at the resonance frequency.
Continued application of the B1 field results in progressive tipping of the net magnetization away from its initial alignment with Bo. M can be rotated 10°, 90°, 180°, 270°, 836°, or any amount. After every 360° rotation M returns to its initial alignment with Bo.  Some progressive arbitrary rotations of M are shown below.

The ambitious diagram below tries to represent what is happening to individual spins at the quantum level as well. Remember that in addition to M, each proton is also precessing around the Bo field individually.  From the Heisenberg uncertainty principle we cannot know the exact direction any particular proton magnetic moment is pointing at any given time.  However, it can be shown that a homogenous B1 field does not change the relative orientation of individual spins. The entire ensemble, like M, is merely rotated by the RF field.  This is why the magnitude of the net magnetization (M) after an RF-pulse is the same as before an RF-pulse, although it is changed in direction.
NMR, radiofrequency B1
As long as the B1 field is left on, M can be rotated to any angle. However, neither the magnitude of M nor the relative orientation of spins changes during this rotation.

Advanced Discussion (show/hide)»

In the my original Q&A textbook, I posed the following question to physics experts just to test their knowledge of quantum mechanics...

Does flipping the magnetization in an NMR experiment by a full 360° return the system to its original state (i.e., like it was at 0°)? How about two full rotations (720°)?

The answer depends upon one’s definition of “the system” used in the question. If one describes the NMR system by a single wavefunction, the answer is NO for a 360° rotation, but YES for 720°! This unexpected result derives from the spinor property of protons. The spinor property is well known in group theory and is also occurs in solid-state physics where it is referred to as a "crystal double group." In fact the state vectors (|+½> and |-½>) are actually spinors and not simple vectors.

After a rotation of 360° the wave function (Ψ) describing the system can be shown to be identical to that existing at 0°, but with a reversal in its sign. In terms of the wave-function analysis previously presented, this is equivalent to saying that after a 360° rotation, a = -a(0) and b = -b(0), where a(0) and b(0) were the values of a and b before the rotation. An additional 360° rotation (720° total) is required to return a and b (and hence Ψ) to their original values. The fact that two complete rotations are required to return the system to its starting point can be likened to a Möbius strip, where one must travel along the strip twice to return to its origin.

In practical MR imaging applications, however, the single wavefunction description of the NMR system is inadequate because the statistical mechanical nature of the NMR system is not taken into account. The system is more properly described by the mixed state density operator which, being composed of the ensemble averaged outer product of the wavefunction corresponding to the system, does not change sign under a 360° rotation. Thus the magnetization of an ensemble of protons (which is the expectation value of a spin operator) will not change sign under a 360° rotation, and will not be directly observable in a conventional MR imaging experiment.

I introduced this curious spinor property to remind everyone of the beauty and complexity of the NMR phenomenon; it also provides stimulating conversation at physics cocktail parties and baffles residents at radiology rounds. The spinor phenomenon plays no role in routine MR imaging, but it can be physically observable, having been demonstrated in several laboratory NMR experiments in which the spin-up and spin-down portions of the wave function have been ingeniously separated.


References
     Elster AD, Burdette JH. Questions and Answers in MRI, 2nd ed. St. Louis: Mosby, 2001, p 28.
     Hanson L. Is quantum mechanics necessary for understanding magnetic resonance?  Concepts Mag Reson Part A 2008;32A(5):329-340.

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