Principle of Magnetic Resonance Imaging

Principle

Modern 3 tesla clinical MRI scanner.

Magnetism

Elementary subatomic particles such as protons have the quantum mechanical property of spin. Nuclei such as ¹H or ³¹P, with an odd number of nucleons, always have a non–zero spin and therefore a magnetic moment. Some other isotopes such as C have no unpaired neutrons or protons, and no net spin.

When these spins are placed in an external magnetic field they start to precess around the direction of that field. The magnetic field also creates two energy states that the protons can occupy which are separated by a quantum of energy. The thermal energy of the sample causes the molecules to tumble leaving only a very small excess of protons to cause magnetic polarization.

Resonance

The energy difference between the proton energy states corresponds to electromagnetic radiation at radio frequency wavelengths. Resonant absorption of energy by the protons due to an external oscillating magnetic field (radio wave) will occur at the Larmor frequency.

The net magnetization vector has two components. The longitudinal magnetization is due to an excess of protons in the lower energy state. This gives a net polarization parallel to the external field. The transverse magnetization is due to coherences forming between the two proton energy states. This gives a net polarization perpendicular to external field in the transverse plane. The recovery of longitudinal magnetization is called T1 relaxation and the loss of phase coherence in the transverse plane is called T2 relaxation.

When the radio frequency pulse is turned off, the transverse vector component produces an oscillating magnetic field which induces a small current in the receiver coil. This free induction decay (FID) lasts only a few milliseconds before the thermal equilibrium of the spins is restored. The actual signal that is measured by the scanner is formed by a refocusing gradient or radio wave to create a gradient or spin-echo.

Imaging

Slice selection is achieved by applying a magnetic gradient in addition to the external magnetic field during the radio frequency pulse. Only one plane within the object will have protons that are on–resonance and contribute to the signal.

A real image can be considered as being composed of a number of spatial frequencies at different orientations. A two–dimensional Fourier transformation of a real image will express these waves as a matrix of spatial frequencies known as k–space. Low spatial frequencies are represented at the center of k–space and high spatial frequencies at the periphery. Frequency and phase encoding are used to measure the amplitudes of a range of spatial frequencies within the object being imaged. The frequency encoding gradient is applied during readout of the signal and is orthogonal to the slice selection gradient. During application of the gradient the frequency differences in the readout direction progressively change. At the midpoint of the readout these differences are small and the low spatial frequencies in the image are sampled filling the center of k-space. Higher spatial frequencies will be sampled towards the beginning and end of the readout filling the periphery of k-space.

Phase encoding is applied in the remaining orthogonal plane and uses the same principle of sampling the object for different spatial frequencies. However, it is applied for a brief period before the readout and the strength of the gradient is changed incrementally between each radio frequency pulse. For each phase encoding step a line of k–space is filled