The Physics of MRI- Basic Spin Gymnastics

To understand MRI, it is first necessary to understand the physics of proton Nuclear Magnetic Resonance (NMR). The most important site of this resonance relevant to MRI is the nucleus of the hydrogen atom in water. While other protons occurs within biological molecules, water represents the most important site for MRI due to the concentration of protons in water and the dynamical properties of water. The proton is a fundamental nuclear particle which exhibits charge, mass and spin (FIGURE 1). While the first of these two concepts is familiar, the notion of spin is not as well appreciated. As the name suggests, it can be thought of as a rotation of the nucleus about its axis which in conjunction with the charge of the nucleus, gives the proton a magnetic property similar to a small bar magnet. However, in addition to the magnetic property of the nucleus, the spin together with the mass of the proton, gives it a property referred to as angular momentum. The combined effect of the spin, charge and mass are the three ingredients, which are responsible for NMR. Specifically, when a proton is placed in an applied magnetic field, it will precess or wobble. This precession is similar to that of a spinning gyroscope when placed in the earth’s gravitational field. In this case, the gyroscope appears to wobble about its axis at a specific frequency dictated by the strength of the gravitation field and the rotation characteristics of the gyroscope. In a similar manner, the proton’s precessional frequency, also known as the Larmor frequency, is dictated by the fundamental properties of the proton and is proportional to the strength of the magnetic field. For example, at a field strength of 1 Tesla (approximately 30,000 times stronger than the earth’s magnetic field), the Larmor frequency is 42.57 Mhz. Doubling the magnetic field strength to 2 Tesla would increase the Larmor frequency to 85.14 MHZ. The scaling factor between Larmor frequency and magnetic field is known as the gyromagnetic ratio ( and is tabulated in (FIGURE 2) along with the relative sensitivity of the NMR signal for various nuclei of biological interest. It is noteworthy, that not all nuclei can generate an NMR signal. Only isotopes with an odd number of protons or neutrons have a non-zero spin which permits the formation of an NMR signal. This figure shows that the nucleus of hydrogen, gives the biggest signal largely due to its gyromagnetic ratio and the fact that the most abundant isotope of hydrogen exhibits a spin. In comparison, the relevant isotopes of carbon, sodium or phosphorous are less abundant and therefore generate a much weaker NMR signal.