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Fundamental Physics of MRI

Fundamental Physics of MRI. Introduction to Cardiovascular Engineering Michael Jay Schillaci, PhD Managing Director, Physicist Thursday, September 11 th , 2008. Overview. Theoretical Background Magnetism and Matter MR Safety and Brain Physiology MR Fields and Coils

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Fundamental Physics of MRI

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  1. Fundamental Physics of MRI Introduction to Cardiovascular Engineering Michael Jay Schillaci, PhD Managing Director, Physicist Thursday, September 11th, 2008

  2. Overview • Theoretical Background • Magnetism and Matter • MR Safety and Brain Physiology • MR Fields and Coils • Main and Gradient Fields • Spatial Encoding • Radio Frequency Coils • RF Field Mechanics • Image Formation • Basic Pulse Sequences • RF Fields and Timing • Growing (T1) and Decaying (T2) • Repeating (TR) and Listening (TE) M R I

  3. The Siemens Magnetom Trio Total Body Imaging System Magnetic Resonance Imaging Magnetic Resonance Imaging (MRI) technology allows total body imaging using many modalities and advanced analysis techniques.

  4. Theoretical Background

  5. The Causes of Magnetism • Macroscopic View • Current in wire • Field is “around” wire • Depends on current • Depends on distance • Microscopic View • Moment of atom • Field is “about” nucleus • Depends on material • Depends on angle

  6. Magnetism in Matter • Field Effects • Electric field is “out” • Magnetic field is “around” • Forces are “orthogonal” • Material Effects • Insulators – charges “stuck” • Fields are very weak • Conductors – charges “free” • Fields may be very strong

  7. Material Dependence • Net Magnetization • varies with field, temperature and material • Local Field • Susceptibility alters the local field Conductivity Susceptibility In Absence of External Field Moments Align Randomly

  8. The Effects of Magnetism • Two ways to assess effects of magnetic fields: • Determine Magnetic Force • Forces move objects • Field is a covariate of force • Determine Magnetic Energy Density • Energy heats objects • Field is correlated with energy

  9. Lower Higher State Transitions • RF Waves are Absorbed • Energy increases • RF Waves are Emitted • Energy decreases Lower Higher

  10. Electromagnetic Energy • Quantum Mechanics governs state transitions • Energy of transition • Planck’s constant • Energy values X-Ray, CT Excites Electrons MRI Excites Protons

  11. MRI Safety Food and Drug Administration (FDA) International Electrotechnical Commission (IEC) • The FDA and IEC place limits on SAR and How a Scanner Estimates SAR Determines energy for 90 and 180 degree flip Adds up energy of all RF pulses divides by TR Divides by patient weight to get whole body SAR Peak SAR estimated as 2.5 times higher on most scanners IEC/FDA Limits for Whole Body Heating Normal mode limit (suitable for all patients): 2 W/kg First level controlled mode (medical supervision): 4 W/kg Second level controlled mode (requires IRB approval): 4 W/kg IEC/FDA Limits for Localized Heating Head normal mode limit (averaged over head): 3.2 W/kg Torso normal mode limit: 10 W/kg No first level for head, torso or extremities

  12. Brain Physiology • Energy Density • Conductivity • Relationship

  13. Empirical Methods • Brain Conductivity • Conductivity of 20 brains • 10 hours after death • Results • Conductivity depends on frequency: • 1.39 S/m (0.14 S/m) at 900 MHz • 1.84 S/m (0.16 S/m) at 1,800 MHz

  14. MR Fields and Coils

  15. Magnetization Directions +z Bc Longitudinal(Z Axis) Bo Bo +y +x Transverse (XY Plane) B0 is Total Static Field BC is Dynamic RF Field

  16. Magnetic Precession • Static Field “splits” states • Zeeman splits high/low energy states • RF Field “rotates” moments • Precession Frequency M= net (bulk) magnetization M B0 m ~ 1 ppm excess in spin-up state creates the net Magnetization… B0 m NMR Parameters B0=1T* B0 m = gJ dJ / dt = m × Bo dm/dt =g (m× Bo) * For comparison: In the Earth’s magnetic field ( 0.00005 T ), hydrogen precesses at ~2100 Hz.

  17. Magnetic Precession In the absence of a strong magnetic field, the spins are oriented randomly. Thus, there is no net magnetization (M). NO FIELD HIGH FIELD The difference between the number of protons in the high-energy and low-energystates results in a net magnetization (M) and gives rise to the Larmor Equation.

  18. The Larmor Frequency • Energy Difference • Frequency B0 m • E = Eup – Edown = mz Bo - (-mz Bo ) • = 2 mz Bo B0 m Larmor Equation • E = hv0 = 2 mz Bo = 2(1/2 h /2p g) B0

  19. B M Main Field • Field Characteristics • Generated by Helmholtz Coils • Currents are parallel (same direction) • Field along MRI axis a a Coil 2 Coil 1

  20. BG Gradient Field • Field Characteristics • Created by Maxwell Pair • currents are anti-parallel (opposite direction) • Field along MRI axis b b Coil 2 Coil 1

  21. Total (Static) Field B0 • Main Field • Helmholtz Coils (Currents in same direction) • Gradient Field • Maxwell Pair (Currents in opposite direction) B0=BM+ BG

  22. Spatial Encoding • The Magnetic Field varies • Frequency depends on position (z) • Field depends on the material (tissue) DB0= 0.018 T Dz = 0.16 m By choosing a frequency we can select a “slice” of the brain.

  23. Slice Selection Gradients • Slope of gradient slice thickness • Field strength limits minimum slice thickness • Position of gradient determines slice selection • Change currents to move zero point of field Field Strength Field Strength Field Strength Field Strength Z Position Z Position Z Position Z Position

  24. BC Head Coil is Transmitter and Receiver +y BC +z wo +x wo Dw = 1/ t t Radio Frequency (RF) Coils • Galois Coils • RF Transmitter sends frequency • RF Receiver encodes signal Fourier Transform

  25. Origin of the MR Signal During Excitation (to) Before Excitation After Excitation During Excitation (t1) Excitation tips the net magnetization (M) down into the transverse plane, where it can generate current in detector coils (i.e., via induction). The amount of current oscillates at the (Larmor) frequency of the net magnetization.

  26. Rotation and Excitation Net Magnetization M0 Naturally Rotates Around Applied Field B0 An RF Pulse Causes the Net Magnetization M0 to Rotate Away From B0

  27. +z B0 M M0 BC MZ +x MXY RF Field - Mechanics • An RF pulse (excitation) rotates the total magnetization M away from axis • The torque depends on the total field • In the laboratory frame the total field is • In the rotating frame the total field is +y

  28. +z B0 M M0 +y +x T1 - Definition • Spin-Lattice Relaxation Time (T1) • Net magnetization M0 is sum along external field, B0 • T1 measures amount of M0 aligned with field • T1 is time for ~63% of M0 to realign with B0

  29. +z B0 M0 MZ BC +y MXY +x T2 - Definition • Spin-Spin Relaxation Time (T2) • Transverse magnetization MXY is perpendicular to B0 • T2 measures amount of MXY perpendicular to field • T2 is time for ~39% of MXY to remain in transverse plane

  30. Simulated MRI Click here to view web content.

  31. Image Formation

  32. Image Formation • Integrate Magnetization to get the MRI signal • Select a z “slice”; tissue differences in slice give contrast • Scanner acquires K-Space weights • Image at several times; reconstruct and average slices 

  33. Gradient Echo Imaging • Assume perfect “spoiling” -transverse magnetization is zero before each excitation: • Spin-Lattice (T1) Relaxation occurs between excitations: • Assume steady state is reached during repeat time (TR): • Spoiled gradient rephases the FID signal at echo time (TE):

  34. T1 and T2 Recovery Times • Determine Mz at half-multiples of T1 • Determine Mxy at half-multiples of T2

  35. T1 and T2 Values • Equilibrium or Net Magnetization Values • Depends directly (linearly) on field strength • Depends (roughly) on percentage of H20 content in tissue 1Table Adapted from: http://members.lycos.nl/mri/Nieuw/T1eng.htm 2White/Grey Matter: http://www.fmrib.ox.ac.uk/~stuart/lectures/lecture4/sld004.htm 3CSF Value: http://www.ivis.org/special_books/Braund/tipold/chapter_frm.asp?LA=1 4Values From: Huettel Chapter 5 and http://members.lycos.nl/mri/Nieuw/T1eng.htm

  36. T1 - Characteristics • A Greater value for T1 • Means a lesser amount of M0 has “recovered” at a given time B0 = 1.5 T White Matter Gray Matter CSF B0 = 0.5 T

  37. CSF B0 = 1.5 T White Matter Gray Matter B0 = 0.5 T T2 - Characteristics • A greater value for T2 • Means a greater amount of M0 has recovered at a given time

  38. T1 and T2 Weighted Images • Measuring Magnetization • Send RF at TR (repeat) • Listen for signal at TE (echo) • T1 WEIGHTED IMAGE • Echo at T2 min • Repeat at T1 max • T2 WEIGHTED IMAGE • Echo at T2 max • Repeat at T1 min TR TE Max T1 Contrast Min T2 Contrast TR TE Min T1 Contrast Max T2 Contrast

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