Basic Principles of Magnetic ResonanceJorge JovicichSeptember 4, 2001Contents1 Introduction 22 MRI: a brief historical background 23 A MR Experiment 33.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Can we scan the subject? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.3 The subject goes into the magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3.1 Equilibrium magnetization M0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3.2 Dynamics of the magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3.3 Rotating coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.4 Brief radio-frequency pulses are applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.4.1 M0is excited with an RF pulse: MR signal . . . . . . . . . . . . . . . . . . . . . . . . 73.4.2 Relaxation of the MR signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.4.3 Bloch equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Bibliography 101Basic Principles of Magnetic Resonance1 IntroductionThe primary purpose of this lecture is to provide an overview of the basic principles involved in the processof obtaining a nuclear magnetic resonance signal. The following lectures will discuss how this signal can beused to generate images that carry information about brain function.The lecture begins with a short and incomplete history of the developments that led to the discoveryof key imaging concepts. The third and largest section covers the basic physics that explain the origin andsome of the properties of the nuclear magnetic resonance signal. Finally, some relevant reference texts andarticles are listed.These lecture notes are not complete and should be taken as a guide. It is expected that students willcomplete the suggested reading for a a more complex coverage of the topics discussed.2 MRI: a brief historical backgroundMagnetic Resonance Imaging, or MRI, stems from the application of nuclear magnetic resonance (NMR)to radiological imaging. The adjective ’magnetic’ refers to the use of an assortment of magnetic fieldsand ’resonance’ refers to the need to match the (radio)frequency of an oscillating magnetic field to the’precessional’ frequency of the spins of some atomic nucleus (hence the ’nuclear’) in a tissue molecule.The concept of nuclear magnetic resonance started with the discovery of the spin nature of the protonfollowed by the study of the interaction of this spin with a magetic field. The phenomenon of mageticresonance was first applied for studying the chemistry and structure of solids and liquids. The possibilityof using MR for the study of living tissue sparked interest in the development of bio-medical applications,particularly when it was proved that abnormal and normal tissues could be distinguished using MR. Nearlyfour decades passed before MR was successfully employed in medical imaging.Below is a brief and incomplete list of some of the milestones in the development of MRI as we use ittoday.• 1922, Otto Stern & Walter GerlachExperimental observation of spin quantization in electrons: Stern and Gerlach passed a beam of silveratoms through an inhomogeneous magnetic field to study the magnetic properties of the electron. Thesilver atoms were in their ground or equilibrium state, which means that the net electric charge waszero and that they had a single unpaired electron in the outer electron orbit. At that time the expectedresult was that the beam of silver atoms should have a smooth distribution around the center becausethe magnetic moment of the atom (due only to the unpaired electron) should feel a net force in theinhomogeneous magnetic field and because all possible orientations of the magnetic moment shouldbe in principle possible. However, the result was that the beam was split into two clearly separatecomponents of equal intensity. This result was later explained by Uhlenbeck and Goudsmit (1925,1926), who proposed that the electron had an intrinsic magnetic moment, or spin, with only twopossible orientations, thereby introducing the concept of spin quantization.• 1937, Isidor I. Rabi (Nobel Prize in Physics, 1944)NMR phenomenon in molecular beams: Radio-Frequency (RF) energy is absorbed by atomic nucleiwithin samples placed in a strong magnetic field. For the absorption to be efficient the RF must havea special frequency called resonance frequency or Larmor frequency. The Larmor frequency is definedby the magnetic field strength and the atomic nuclei.• 1945, Felix Bloch & Edward M. Purcell (Nobel Prize in Physics, 1952)NMR phenomenon in solids: Bloch & Purcell, independently, where the first to demonstrate the NMRphenomenon in bulk materials.• 1949, Norman F. Ramsey (Nobel Prize in chemistry, 1989)Chemical shift theory: atomic nuclei in different chemical environments can be identified as a result ofa small change in resonance frequency caused by the electron cloud of the molecule. A molecular systemcan be thus described by its absorption spectrum: continuous wave magnetic resonance spectroscopy2Basic Principles of Magnetic Resonancewas born. The sensitivity of the experiment was low: each resonance frequency (i.e., each nuclei species)was separately excited. To achieve enough signal-to-noise ratio many excitations were necessary foraveraging, making the experiments extremely slow.• 1971, Raymond V. DamadianTumor detection is possible using NMR: Cancerous tissue in rats exhibited dramatically prolongedNMR relaxation times. Relaxation times of normal tissues also vary significantly, though less dramat-ically than cancer tissue. With these findings Damadian conceived and originated the application ofmagnetic resonance technology to medical uses, including whole-body scanning and diagnostic imaging.• 1972, Paul C. LauterburMR image principle: the shift in resonance frequency resulting from the imposition of a magnetic fieldgradient can be used to generate a two-dimensional spatial distribution of protons in a water sample.• 1976, Peter MansfieldEcho Planar Imaging (EPI): …
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