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PHYS 1110: MRI PHYSICS I TOPIC 2: BASIC PRINCIPLES IN MRI Lecture 1: Angular Momentum and Magnetic Moment States of Hydrogen What is the scientific principle behind MRI? How does it differ from other imaging “modalities”? As you know, MRI stands for “Magnetic Resonance Imaging”. MR imaging is a relatively new imaging technique, originating in the 1970’s. It is important to realize it is based on a phenomenon that was known before called “Nuclear Magnetic Resonance” (NMR). What is “Nuclear Magnetic Resonance”? In physics, resonance is the phenomenon in which an object or system begins to vibrate usually at a specific frequency due to a driving force or input. Objects can have a “resonant frequency”, which means if the input force oscillates with the same frequency, energy will be preferentially transferred to the object, resulting in a large vibration. In “NMR”, we have the words “Nuclear” and “Magnetic”. In this case, “Nuclear” refers to the nucleus of an atom. So it sounds like the nucleus of an atom has magnetic properties and that the nucleus can be made to vibrate or oscillate at a given “resonant” frequency. In fact, in NMR the input force or vibration is a rapid wave of a given frequency. If the rapid wave is transmitted into a sample, the nuclei in the atoms making up the sample may absorb energy from the wave and begin vibrating. As a result of their vibrations, the atoms will emit their own signals which can be recorded. The signals contain information about what elements are present in the sampe. So NMR, discovered in 1937, was first used to analyze the chemical makeup of samples. Dr. Paul Laterbur working in the 1960’s and 70’s, figured out a way to use NMR principles to create images of the inside of the body. Thus, MRI was born. Notice that the word “nuclear” was left out of “MRI”. THis was done to avoid the negative connotation that exists with nuclear power and radiation. In fact, MRI does not use radiation that is normally considered harmful such as x-rays or products of radioactive decay. The only radiation encountered in an MRI procedure is a radio wave transmitter. MRI “works” because subatomic particles (protons, neutrons, electrons) have magnetic properties. That is to say, surrounding protons, neutrons and electrons is a tiny magnetic field that can be manipulated by the MRI process. Where does this field come from? The answer is different depending on whether you use “classical” physics or the currently accepted “Quantum Mechanics”. Prior to the 20th century, “classical” physics was used to explain natural phenomena. Classical physics is built on the three laws of motion proposed by Issac Newton, and the equations of James Maxwell which explained electromagnetic phenomena. The origin of the magnetic properties of subatomic particles would be fairly easy to visualize using classical physics. Classically we would regard a subatomic particle such as a proton as a tiny sphere. We know a proton was a positive electric charge, so we would imagine the charge to be distributed over its surface. In order to create the associated magnetic field, the proton would have to be rotating about an Axis:

A rotating object possesses angular momentum. Angular momentum is a vector quantity. For a rotating sphere, it points along the axis rotation.

The danish physicist Orsted established that magnetic fields are created by moving charged particles. Thus, the rotating proton will generate a magnetic field. The magnetic field is similar in appearance to the field around a bar magnet.

The generated magnetic field is described by a vector called the magnetic moment.

So classically, it is fairly easy to understand nuclear magnetism. Unfortunately, if we look more closely at the observed behaviors of subatomic particles, they can be explained by the modern theory of quantum mechanics. Classical physics breaks down when you try to apply it in general to the behaviour of the subatomic world. The solution was to propose a new theory based on some fairly radical ideas about the nature of matter. This theory is called “Quantum Mechanics”. The postulates (basic given assumptions) of quantum mechanics are quite different from classical physics:

A pair of physicists named Stern and Gerlach performed experiments in the early 20th century that suggested that

subatomic particles had a property that mimicked that of a spinning particle. But according to the quantum mechanics, these particles were more like waves, so there was nothing in reality (whatever reality is!) that was spinning. Stern and Gerlach called this property “Spin”. So “spin” is an intrinsic (essential) property of a subatomic particle. “Spin” is angular momentum. So a subatomic particle (proton, neutron, electron) appears to possess angular momentum just like a spinning object would, but in this case, the “spin” is a quantum mechanical property that has no classical equivalent. So like before, because the proton is charged, the presence of spin will lead to the proton possessing a magnetic moment:

Spin States of Hydrogen A hydrogen atom consists of a nucleus made up of a single proton and a single orbiting electron. So if we consider the behaviour of a single proton it is equivalent to discussing a nucleus of hydrogen. What was important about the experiments of Stern and Gerlach is that spin, like energy, is quantized. That is, it is only available in certain fixed amounts. What does that mean? It means a proton can only exist in certain fixed energy states. But to talk about the energy state of a proton, we need a reference. Since the proton is behaving like a tiny magnet, the reference will be its orientation to an external magnetic field. This is why an MRI machine must create a large, external magnetic field, to create a reference and force the protons into these quantized energy states. Let’s use a pair of large magnets to create a uniform magnetic field in space, and imagine we could place a proton between the poles:

The magnetic field around the proton is similar to that around a bar magnet. So, we could imagine that the arrowhead of the vector is the “north” pole of the magnet, and the tail is the “south” pole. If the proton obeyed the laws of classical physics, the proton could have any orientation relative to the external magnetic field, the difference just being that different orientations would represent different energies.

This is not what the results of the Stern-Gerlach experiment produced. The spin of the proton can only take on certain fixed orientations relative to the external field. Spin is quantized. A proton is called a “Spin-½” particle. This means the component of the spin vector parallel to the external field direction must be numerically equal to

, where the constant

is “Planck’s Constant”....