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Basic Concept of MRI

Basic Concept of MRI. Chun Yuan. Proton. Electron. _. +. +. +. +. _. Neutron. Magnetic Moment. Magnetic dipole and magnetic moment Nuclei with an odd number of protons or neutrons have a net magnetic moment (spin) Most common nuclei which have magnetic moments are:

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Basic Concept of MRI

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  1. Basic Concept of MRI Chun Yuan

  2. Proton Electron _ + + + + _ Neutron Magnetic Moment • Magnetic dipole and magnetic moment • Nuclei with an odd number of protons or neutrons have a net magnetic moment (spin) • Most common nuclei which have magnetic moments are: • 1H, 2H, 7Li, 13C, 19F, 23Na, 31P, and 127I

  3. No External Magnetic Field • In the absence of an external magnetic field • The nuclei align randomly • The nuclei produce no net magnetization

  4. External Magnetic Field (B0) • The nuclei align in 1 of 2 positions depending on energy state • Low energy nuclei align with the field in parallel position • High energy nuclei alignagainst the field in antiparallelposition B0

  5. Increasing B0 • As B0 increases more nuclei align in the parallel low energy position B0

  6. Net Magnetization Vector • A net magnetization vector is formed • Pairs of parallel and antiparallel nuclei cancel • The magnetic moments of the unpaired nuclei create a sum effect called net magnetization vector • Only the unpaired nuclei participate in the MR signal B0

  7. Net Magnetization Vector • The net vector is the sum of all of the parallel, unpaired, low energy protons • The strength is the SUM of the magnetic strengths of the individual protons • The direction is the SUM of the polar directions of the individual protons • In the low energy state the net vector aligns along the longitudinal or Z axis and is called Mz B0 Mz

  8. Precession in B0 • They wobble like gyroscope • Thermal agitation prevents the nuclei from aligning perfectly with B0 so the nuclei actually align at an angle • As B0 attempts to pull the nuclei into perfect alignment the conflicting forces cause the nuclei to precess B0

  9. The LarmorEquation • The larmor equation calculates the frequency of precession • Precessionalfrequency depends on • The type of nucleus • The strength of the external magnetic field w = gBo Omega or Precessional Frequency Gamma or Gyromagnetic Ratio External Magnetic Field Strength

  10. Gyromagnetic Ratio g • The gyromagnetic ratio yields frequency at 1 Tesla • The GMR is unique for each type of nucleus Nucleus n 1H 2H 13C 14N 19F 23Na 27Al 31P GMR in MHz 29.16 42.58 06.53 10.70 03.08 40.05 11.26 11.09 17.24

  11. Example Most MR scanners operate at 1.5 T. What is the Larmor Frequency of protons at this field strength? f0 = 0 / 2 = B0 / 2 = (42.58 MHz/T)(1.5 T) = 63.84 MHz

  12. B0 Mz There’s No Signal Yet • Mz CANNOT BE MEASURED WHEN ALIGNED WITH B0 • Mz must be moved away from B0 in order to generate a signal • How do we move Mzaway from B0?

  13. RF Excitation • The frequency of the RF energy must match the frequency of the precessing nuclei in order to transfer energy • The magetic field exerted by the RF energy is called B1 • B1 must be transmitted perpendicular to B0 w = g Bo B0 = B1

  14. B0 B1 Resonance • In the presence of B1, low energy nuclei absorb energy and shift to high energy state B0 Mz B1

  15. B0 Mxy B1 Shift of the Net Magnetization • The direction of net vector shifts as the individual nuclei transition to high energy • The RF pulse is labelled according to shift it creates in the net magnetization • A 90 degree pulse moves the net magnetization 90 degrees • How far does a 180 degree pulse move the net magnetization? • When the net magnetization is in the transverse plane it is called Mxy

  16. Flip Angle • Magnetization is tipped using a radiofrequency pulse • Frequency of RF pulse is ω0 • Magnitude of RF pulse is B1(t) • Total tip angle is α=γ∫B1(t) dt • α=90º (π/2) maximizes signal • α=180º (π) called an inversion pulse • M essentially precesses around B1(t) with an instantaneous frequency of = B(t) z M M0 y B1(t) x

  17. Example • An RF field B1exp{-j 0t} is applied to a sample where B1= 50 milligauss. How long must it be applied to produce a tip of 90º? B1 t = /2 t = /(2B1) = /(2 (2 x 42.58 MHz/T)(0.05 Gauss x 10-4 T/Gauss)) = 1.17 milliseconds

  18. Relexation • WHEN B1 IS REMOVED THE NUCLEI EMIT ENERGY AND SHIFT BACK TO LOW ENERGY STATE • THE TRANSITION BACK TO LOW ENERGY STATE IS CALLED RELAXATION • AFTER EMITTING ENERGY THE NUCLEI RETURN TO PARALLEL ALIGNMENT B0 Mxy

  19. z M Mz y Mxy x Faraday’s Law of Induction • 3 CRITERIA MUST BE MET TO GENERATE A SIGNAL • A conductor • A magnetic field • Motion of the magnetic field in relation to the conductor • IN MR • The RF coil provides the conductor • And Mxy provides the movingmagnetic field because it precesses Antenna s(t) Mxy(t)

  20. Free Induction Decay (FID) • In the 90-FID pulse sequence, net magnetization is rotated down into the XY plane with a 90o pulse. • The net magnetization vector begins to precess about the +Z axis. • The magnitude of the vector also decays with time.

  21. Bloch Equation • The Block equation relate the time evolution of magnetization to • the external magnetic fields, • relaxation times (T1 and T2), • the molecular self-diffusion coefficient (D). • g is the gyromagnetic ratio • depends on nucleus • For proton g/2p = 42.58 MHz/Tesla

  22. Rotation Reference Frame x y x' y'

  23. External Magnetic Fields z • Static Magnetic Field B0 • RF Magnetic Field B1 y y' x x'

  24. T1 Relaxation • T1 relaxation is also known as thermal or spin-lattice relaxation • T1 relaxation involves an energy exchange--excited nuclei release energy and return to equilibrium • T1 relaxation causes recovery of the net magnetization to the longitudinal axis Mz M0 63% t Short T1 Long T1

  25. Example For a sample with T1 = 1 second, how long after a 180 degree pulse will the net magnetization be 0? z z z z M0 M M M Mz(t) = M0(1 - e -t/T1) + Mz(0) e -t/T1 0 = M0(1 - e -t/T1) - M0 e -t/T1 0 = 1 - 2e -t/T1 t = T1 ln2 = 0.69 seconds

  26. T2 Relaxation • T2 relaxation is also known as thermal or spin-spin relaxation • T2 relaxation involves the loss of phase coherence and is caused by the local magnetic field • T2 relaxation causes dephasing of the net magnetization in the transverse plane 37% T2

  27. T2* (Star) Relaxation • Two factors contribute to the decay of transverse magnetization. • molecular interactions (said to lead to a pure T2 molecular effect) • variations in Bo (said to lead to an inhomogeneous T2 effectThe combination of these two factors is what actually results in the decay of transverse magnetization. • The combined time constant is called T2 star and is given the symbol T2*. The relationship between the T2 from molecular processes and that from inhomogeneities in the magnetic field is as follows.

  28. Relaxation and contrast • Relaxation time T1, T2 and T2* vary with • Field strength • Temperature • Tissue types • In vitro vs. in vivo • Age • Fundamentally important for generating contrast At 1.5T: Gray matter White Matter CSF T1 (ms) 520 390 2000 T2 (ms) 100 90 300 proton density (relative) 10.5 11 10.8

  29. Images with Different Contrast

  30. Example Suppose an degree RF pulse is applied every TR seconds for a long time. What is the steady-state magnitude of Mxyimmediately after excitation assuming TR >> T2 Let M(n-) be the magnetization just before the nth RF pulse and M(n+) be the magnetization just after the pulse. Because TR >> T2, we know Mxy(n-) = 0. Therefore, Mxy(n+) = Mz(n-) sin and Mz(n+) = Mz(n-) cos T1 relaxation gives Mz([n+1]-) = M0(1 - e -TR/T1) + Mz(n+) e -TR/T1     RF ... TR

  31. Solution At steady state, M(n-) = M([n+1]-) Mz(n-) = M0(1 - e -TR/T1) + Mz(n+) e -TR/T1 Mz(n-) = M0(1 - e -TR/T1) + Mz(n-) cose -TR/T1 Thus, Mz(n-) = M0(1 - e -TR/T1) / (1- cose -TR/T1) and Mxy(n+) = Mz(n-) sin  = M0 sin  (1 - e -TR/T1) / (1- cose -TR/T1) (This equation comes in handy for analyzing MR imaging because images require multiple RF excitations and this equation is useful for optimizing )

  32. Spin Echo The basic MRI sequence is called “spin echo”. The RFexcitationfor spin echo is as follows: Sketch its response, where TE is on the order of several times T2* We know we get an FID in response to the 90 degree pulse: But, what does the 180 degree pulse do? 90º 180º RF TE/2 T2*

  33. Spin Echo y y faster slower 180º Recall dephasing gives: After the 180 degree pulse, the faster spins trail the slower ones: Thus, the spins “rephase”, then dephase again: (Note: Only dephasing due to T2* can be rephased. T2 relaxation is affected by random processes. Thus, the echo is lower in amplitude than the original FID) x x faster slower 90º 180º RF T2 T2* T2* s(t) T2* TE

  34. Spin Echo

  35. Spin echo signal for =90 From previous slide, with =90: Mxy(0) = M0 (1 - e -TR/T1) Adding T2 relaxation gives: Mxy(TE) = M0 (1 - e -TR/T1) e -TE/T2 “proton density (PD)” T1 weighting T2 weighting PD weighting T1 weighting T2 weighting T1 long short long T2 short short long

  36. MR Image Formation • Magnetic Field Gradient • Three key concepts in MRI formation: • slice selection • frequency encoding • phase encoding

  37. Slice Selection • Goal: Excite (Mz -> Mxy) in a well defined slice of tissue • Application of RF pulse and gradient field • Energy deposition at selective frequencies Excite this slice only RF Gz

  38. Diagram of Slice Selection • slice thickness depends on • RF pulse bandwidth • slice thickness depends on • Gradient strength wider slice B0 wider BW • RF bandwidth • Gz narrower slice steeper gradient BW = (/2)Gz z

  39. Pulse shape • Slice profile  Fourier Transform of the RF pulse shape • Square pulse: • Better choice: sinc pulse FT  RF Pulse Slice Profile FT  RF Pulse Slice Profile BW ~ 1/DT

  40. Slice Profile and RF Pulse

  41. Example What duration should an RF pulse be to excite a 1 mm slice of tissue using a gradient strength of 5 Gauss/cm (assume bandwidth (Hz)  1/duration (sec)). Required bandwidth is BW = (/2)Gz z = (42.58 MHz/T)(5 x 10-4 T/cm)(0.1 cm) = 2.1 kHz T = 1/BW = 0.47 msec

  42. Slice Dephasing Total dephasing roughly equivalent to half the area of the gradient Can be fixed with a negative gradient with half the area: Gz

  43. Phase Encoding • Phase encoding gradient is imposed before acquisition • While the gradient is on the nuclei precess at different frequencies • When the gradient is turned off the nuclei return to precessingat the same frequency but their phase has been shifted relative to their gradient position Gp Gp Gp

  44. Phase Encoding Equation

  45. Frequency Encoding Goal: Map Mxy(x,y) within the slice or “image plane” • Application of gradient field Gx after slice selection • Position along x axis encoded by frequency • applied during data acquisition • Centered at echo Gf

  46. Frequency Encoding Equation Note: Signal acquired in kx, ky space is a Fourier transform of M(x,y), so image M(x,y) can be reconstructed with inversed Fourier transform.

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