Rad 226b/BioE 326b In Vivo MR: Relaxation Theory and Contrast Mechanisms

Transcription

1 Rad 226b/BioE 326b In Vivo MR: Relaxation Theory and Contrast Mechanisms Daniel Spielman, Ph.D., Dept. of Radiology Lucas Center for MR Spectroscopy and Imaging (corner of Welch Rd and Pasteur Dr) office: x

2 Topics Administrative details Course Overview Motivational examples Lecture #1 Introduction 2

3 Course Administration Lectures Tues, Thurs 4:30-5:50 pm, Lucas Learning Center P units TA Keshav Datta, Office: Lucas Center, keshavd@stanford.edu Office Hours Tues/Thurs 3:30-4:30 pm, Office: Lucas Center PS061 or by arrangement with instructor ( spielman@stanford.edu) Web site Lecture notes, homework assignments, other handouts (pdf files) 3

4 Sacred text of NMR Course Materials Textbooks J. Kowalewski and L. Mäler, Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications, Taylor & Francis, Boca Raton, FL Available on-line at searchworks.stanford.edu. F. van de Ven, Multidimensional NMR in Liquids, Wiley- VCH, New York, (optional) R. de Graaf, In Vivo NMR Spectroscopy, 2 nd Edition, Wiley & Sons, Chichester, UK, Available on-line at searchworks.stanford.edu (optional) M. Levitt, Spin Dynamics, Wiley, Chichester. UK, 2001 (optional) Additional reference (not required, but very useful!) A. Abragam, Principles of Nuclear Magnetism, Clarendon Press, Oxford,

5 Assignments and Grading Weekly problem sets (75%) Final project (25%) Oral presentation on student selected topic from current in vivo MR literature 5

6 Overview Main Themes: Although T 1 and T 2 can be included as phenomenological constants, the physics behind these NMR relaxation rates provides new insights connecting observed data to underlying anatomy and physiology. Relaxation theory explains many of the contrast mechanisms used in current MRI techniques and is useful for developing new hypothesis and research questions. Prerequisites RAD226A/BIOE326A or familiarity with the NMR spin density operator and MRI. 6

7 Roadmap Applications MR Physics and Math Relaxation basics Redfield Theory TRE CEST? Cross relaxation? Does Gd- DTPA shorten T 2 or just T 1? Spin density operator, coherences, MRI, MRS large break (prerequisites) Intuition What about the magic angle effect? Topics 1. Review (1.5 wks) 2. Basics of NMR relaxation (2 wks) 3. Redfield theory (1.5 wks) 4. Contrast agents (1.5 wk) 5. Advanced topics (2 wks) 6. Total relaxation and enlightenment 7

8 Nuclear Magnetic Resonance Spectroscopy study of materials via interactions with electromagnetic fields. Energies associated with NMR are orders of magnitude smaller than those of typically thermal processes. EM radiation Spectroscopy γ-rays x-rays ultraviolet visible infrared microwave Energy RF 10 6 Hz Mössbauer electronic vibrational rotational NMR energy of chemical bonds thermal NMR Nuclei are very sensitive to local magnetic fields. Interact extremely weakly with their environment. The process by which nuclear spins evolve towards statistical equilibrium with their macroscopic environment is called relaxation. 8

9 NMR: A Short History Discovery of NMR 1937 r B = B 0 z ˆ NMR in liquids and solids 1945 FT-NMR s µ z θ r µ θ = 54.7!, I = 1, m = µ z = 1 γ!, " µ = 3 γ! 2 2 1D Spectrum 2D Spectrum I.I. Rabi F. Bloch E. Purcell R. Ernst Nobel Prize Physics 1944 Nobel Prize Physics 1952 Nobel Prize Chemistry

10 NMR: A Short History Determining 3D structures of biological macromolecules K. Wüthrich 1980s Nobel Prize Chemistry D Spectrum Imaging 1980s-1990s P. Lauterbur P. Mansfield NMRI Nobel Prize: Medicine

11 NMR versus MRI Chemistry lab: NMR spectroscopy experiments High resolution studies of liquids Solid state NMR (e.g. magic angle spinning) most relevant for in vivo studies Studies of substances (or nuclei) with broad resonance lines In vivo MRI pure liquid tissue crystalline solid Complex mixture of stuff undergoing physiological processes Types of questions: Where is it? How much? Dynamics (e.g. flow, relaxation, chemical exchange)? 11

12 MRI Standard analysis based on a water signal made up of many independent (non-interacting) nuclei + phenomenological T 1 and T 2 relaxation times. Leads to very powerful approaches (e.g. k-space) that adequately explain the bulk of MRI techniques and applications. A. Macovksi MRI relaxation: Where did the water go? 12

13 Equations of MRI!! Bloch equations: ( B = B 0ˆ z ), magnetization M given by d! M dt With gradients, signal is & γ s e (t) = M ( ' 2π = γ M! B 0ˆ z M ˆ xx + M y y ˆ t 0 G x ( t $ )d t $, γ 2π ( M M z 0)ˆ z T 2! B = ( B 0 + G x (t)x + G y (t)y + G z (t)z)ẑ t 0 γ G y ( t $ )d t $, 2π k x k y k z t 0 T 1, the received Linear gradients ) G z ( t $ )d t $ + * Gradients trace a trajectory through k-space G x G y t FT 13

14 Limitations Why do different tissues have different relaxation times? How is image contrast affected by dynamic processes such as Molecular tumbling? Chemical exchange? Inter- and intra-molecular interactions? Flow, perfusion, and diffusion? Not currently covered in this class Are there relaxation mechanisms that can be exploited to generate new types of contrast or new contrast agents? 14

15 Example: Conventional MRI Brain Hemorrhage T1 T1+Gad T2 Why does water from different tissues appear different on MRI? What is the implication for a tissue being dark on a T1-weighted scan? Or bright on a T2-weighted scan? How do MR contrast agents work? 15

16 Example: Tendon Imaging T 2 of tendons is strongly dependent on the angular orientation with respect to B 0 : magic angle = 54.7 o Tendon parallel to B 0 Tendon angle = 55 o B 0 B 0 acute Achilles tendon rupture: 3D GRE, TR/TE=21/7 ms What about T 1? 16

17 Example: Blood In a CPMG sequence, the T 2 of blood depends on the refocusing rate. τ 180 =6 ms What happened to the veins? CPMG MRI pulse sequence τ 180 =48 ms 17

18 Example: Myelin Myelin is an important component of brain white matter. Why are there such a wide range of T 2 components? Why do some go away when the sample is placed in D 2 O? Kim Butts-Pauly: How does the water peak shift with temperature when the myelin melts? 18

19 Example: Cartilage imaging In the presence of a long-duration low-power RF pulse, transverse magnetization relaxes with a time constant known as T 1ρ. Unlike T 2 or T 2*, data suggest T 1ρ is strongly correlated with cartilage damage due to osteoarthritis. M xy Spin-lock Rf pulse T 2 * decay w/o spin-lock T 1ρ decay with spin-lock Borthakur, et al., NMR Biomed. 2006; 19:

20 Example: Spins > ½ If I m only interested in MRI why should I care about the NMR physics of particles with spins > ½? What is the spin of Gd +3 or Fe +2? 20

21 Example: Contrast agents Why does the T 1 relaxivity of Gd-DTPA increase 10 fold when bound to albumin (Gd-DTPA-albumin)? Magnevist MS-325 MS-325 is used as a blood pool agent. 21

22 Example: Contrast agents Gd-DTPA is a widely used MR contrast agent used to shorten T 1 Why does Dy-DTPA exhibits almost no T 1 shortening and is just used as a T 2 * (or T 2 ) shortening agent? What about Europium? SPIOs? Gd +3 : 7 unpaired e - s Dy +3 : 5 unpaired e - s 22

23 Example: MT in Tissue Two pools of protons Bound pool of macromolecules (very short T 2 ) Unbound pool of free water (long T 2 ) Selectively saturation short-t 2 (bound protons) Magnetization exchanged between saturated bound protons and unsaturated mobile protons Observe reduced magnetization of longer T 2 (mobile) water protons Why do macromolecules have a short T 2? What about T 1? 23

24 Example: Magnetization Transfer no MT Imaging Myelin? RF saturate macromolecules off-resonance Rf 90 o with MT G z signal 1 H Spectrum f no MT with MT 24

25 Example: Magnetization Transfer Previous MT example: RF G z signal 31 P example: RF G z saturate macromolecules off-resonance RF saturate 1 H nuclei off-resonance RF 90 o 31 P 90 o no saturation with saturation 1 H Spectrum f with saturation no saturation signal 31 P Spectrum f 25

26 Example: Magnetization Transfer Dynamic Nuclear Polarization 5 T and 0.8 K 13 C magnetization increases ~100,000 fold!

27 Next lecture: Review of the spin density operator and coherence 27