1. February 20, 2003Francisco M. Martinez Magnetic Resonance for BME 458 Francisco (Paco) Martinez

2. February 20, 2003Francisco M. Martinez MR Principle Magnetic resonance is based on the absorption and emission of energy in the radio frequency range of the electromagnetic spectrum.

3. February 20, 2003Francisco M. Martinez Historical Notes Discovered independently by Felix Bloch (Stanford) and Edward Purcell (Harvard) Initially used in chemistry and physics for studying molecular structure (spectrometry) and diffusion In 1973 Paul Lauterbur obtained the 1 st MR image using linear gradients 1970’s MRI mainly in academia 1980’s Industry joined forces

4. February 20, 2003Francisco M. Martinez MRI Timeline 1946 MR phenomenon - Bloch & Purcell 1950 Spin echo signal discovered - Erwin Hahn 1952 Nobel Prize - Bloch & Purcell 1950 - 1970 NMR developed as analytical tool 1972 Computerized Tomography 1973 Backprojection MRI - Lauterbur 1975 Fourier Imaging - Ernst (phase and frequency encoding) 1977 MRI of the whole body - Raymond Damadian Echo-planar imaging (EPI) technique - Peter Mansfield 1980 MRI demonstrated - Edelstein 1986 Gradient Echo Imaging NMR Microscope 1988 Angiography - Dumoulin 1989 Echo-Planar Imaging (images at video rates = 30 ms / image) 1991 Nobel Prize - Ernst 1993 Functional MRI (fMRI) 1994 Hyperpolarized 129 Xe Imaging 2000? Interventional MRI

5. February 20, 2003Francisco M. Martinez MR Physics Based on the quantum mechanical properties of nuclear spins Q. What is SPIN? A. Spin is a fundamental property of nature like electrical charge or mass. Spin comes in multiples of 1/2 and can be + or -. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2

6. February 20, 2003Francisco M. Martinez Properties of Spin Nuclei with: Odd number of Protons Odd number of Neutrons Odd number of both exhibit a MAGNETIC MOMENT (e.g. 1 H, 2 H, 3 He, 31 P, 23 Na, 17 O, 13 C, 19 F )

7. February 20, 2003Francisco M. Martinez Properties of Spin Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin. (e.g. 4 He, 16 O, 12 C) In nuclear magnetic resonance, it is unpaired nuclear spins that are of importance.

8. February 20, 2003Francisco M. Martinez Spins and Magnetic Fields When placed in a magnetic field of strength B, a particle with a net spin can absorb a photon, of frequency . The frequency depends on the gyromagnetic ratio , of the particle Larmor relationship  =  B  = Resonant Frequency (rad/s)  = Gyromagnetic ratio B = magnitude of applied magnetic field

9. February 20, 2003Francisco M. Martinez  / (2  ) Nucleus MHz / T 1 H -42.575 13 C-10.705 19 F - 40.054 23 Na-11.262 31 P-17.235

10. February 20, 2003Francisco M. Martinez Biological abundances Hydrogen (H)63% Sodium (Na) 0.041% Phosphorus (P) 0.24% Carbon (C) 9.4% Oxygen (O) 26% Calcium (Ca) 0.22% Nitrogen (N)1.5% Calculated from: M.A. Foster, Magnetic Resonance in Medicine and Biology Pergamon Press, New York, 1984.

11. February 20, 2003Francisco M. Martinez Spins and Magnetic Fields The AVERAGE behavior of many spins (many magnetic moments) results in a NET MAGNETIZATION of a sample (substance/tissue) Randomly oriented Oriented parallel or antiparallel Net magnetization (Up/Down  0.999993) Bo

12. February 20, 2003Francisco M. Martinez Bloch Equation Says that the magnetization M will precess around a B field at frequency  =  B Vs.

13. February 20, 2003Francisco M. Martinez Nomenclature B 0 = External magnetic field normally on the “z” direction Magnetization Longitudinal magnetization Transverse magnetization Magnetic Field M 0 = Initial magnetization B 0 = Magnitude of main magnetic field B 1 = Magnitude of RF field Detected signal

14. February 20, 2003Francisco M. Martinez Solution to Bloch Eq. Jump to Matlab simulations that solve the Bloch Equation - Observe “Rotating Frame of Reference”

15. February 20, 2003Francisco M. Martinez Excitation Recall that the net magnetization (M) is aligned to the applied magnetic field (B 0 ). Q. How can we rotate M so that it becomes perpendicular to B 0 ? A. RF Excitation Rotating magnetic fields (B 1 ) applied in the plane transverse to B 0

16. February 20, 2003Francisco M. Martinez Tip angle Tip angle =

17. February 20, 2003Francisco M. Martinez Resonance If  RF =  0 Resonance Excitation is effective If  RF   0 Excitation occurs but it is not optimal Matlab simulation

18. February 20, 2003Francisco M. Martinez Relaxation There are thermal processes that will tend to bring M back to its equilibrium state T 1 recovery = Spin-lattice relaxation T 2 relaxation = Spin-Spin relaxation

19. February 20, 2003Francisco M. Martinez T 1 - relaxation Longitudinal magnetization (M z ) returns to steady state (M 0 ) with time constant T 1 Spin gives up energy into the surrounding molecular matrix as heat Factors Viscosity Temperature State (solid, liquid, gas) Ionic content Bo Diffusion etc.

20. February 20, 2003Francisco M. Martinez T 2 - relaxation Transverse magnetization (M xy ) decay towards 0 with time constant T 2 Factors T 1 (T 2  T 1 ) Phase incoherence Random field fluctuations Magnetic susceptibility Magnetic field inhomogeneities (RF, B 0, Gradients) Chemical shift Etc. Matlab simulations of T 1 and T 2

21. February 20, 2003Francisco M. Martinez Typical T 1 ’s, T 2 ’s, and Relative Density for brain tissue T 1 (sec) T 2 (sec)  R Distilled Water 3 3 1 CSF 3 0.3 1 Gray matter 1.2 0.06 - 0.080.98 White matter 0.80.045 0.8 Fat0.150.035 1

22. February 20, 2003Francisco M. Martinez Bloch Eq. Revised Solution on the rotating frame of reference

23. February 20, 2003Francisco M. Martinez Pulse Sequences 90° - 90° - 90° - …  -  -  -  -  - … 180° - 90° - 180° - 90° … (Inversion recovery) 90° - 180° - 180° - 180° - 180° … 90° - 180° - 90° - 180° … (Spin echo)

24. February 20, 2003Francisco M. Martinez Hardware For the BME458 laboratory PERMANENT Pulse Programmer RF Synthesized Oscillator Recei ver Mixer RF Amplifier Detector MAGNET RF Amp. Oscilloscope Sync. CH1 CH2 RF Transmitting coil Sample RF Receiving coil

25. February 20, 2003Francisco M. Martinez Receiver High gain Linear Low noise Centered at 15 MHz

26. February 20, 2003Francisco M. Martinez Pulse programmer Pulse generator that creates the pulse sequences. Pulses can be varied in: Duration (1 – 30  s) Spacing (10  s – 9.99 s) Number of “B” pulses (0 – 99) Repetition time (1 ms – 10 s)

27. February 20, 2003Francisco M. Martinez 15 MHz Osc/Amp/Mixer Tunable oscillator Display Coarse/fine adjustment Power amplifier Amplifies pulses to produce 12 gauss (Max 150W) Mixer Multiplies CW-RF with received signal

28. February 20, 2003Francisco M. Martinez 15 MHz Osc/Amp/Mixer Mixer Multiplies CW-RF with received signal CW FID Mix

29. February 20, 2003Francisco M. Martinez Imaging Requires magnetic fields as a function of position Therefore frequency of oscillation is a function of position

30. February 20, 2003Francisco M. Martinez Gradients

31. February 20, 2003Francisco M. Martinez Gradients Recall that: Now:

32. February 20, 2003Francisco M. Martinez Hardware

33. February 20, 2003Francisco M. Martinez Pulse sequences Spin echo Gradient echo EPI Spiral … 100’s

34. February 20, 2003Francisco M. Martinez References http://www.cis.rit.edu/htbooks/mri/ Principles of magnetic resonance imaging. Dwight G. Nishimura, 1996