## Magnetization or magnetic polarization

The sum of the spins generates the net magnetization. Magnetization or magnetic polarization M is the vector that describes the density of magnetic dipole moments and therefore spins in this case. It is usually defined as the quantity of magnetic moment per unit volume.

Magnetization is a fundamental notion for magnetic resonance. It is calculated using a set of equations termed the Bloch equations. For simplicity, we could mention that according to the Bloch equations, magnetization M will precess around a B field at the Larmor frequency ω = γ*B.

## Introduction

A detaild description of Magnetic Resonance Imaging is provided below and on the linked pages. We could distinguish two main phases. The first is the polarization phase which consists of the alignment of the spins and the growth of a net magnetization. The second is the detection phase which consists of the tipping (flipping) of the magnetization (by a magnetic field component) with the simultaneous absorption of energy, followed by the emission of a signal during relaxation.

## Polarization: Magnetic field Bo induces growth of longitudinal magnetization

Let us consider a subject (or sample) which is found in the magnetic field of the Earth (50μΤ). In general, upon the influence of a magnetic field, spins will tend to preferentially align themselves with the direction of the field, thereby adopting a low energy state while precessing around the direction of the field, or will align themselves opposite to the direction of the field, thereby adopting a high energy state, while precessing accordingly. The influence of the magnetic field is counteracted by thermal collisions. Due to combined influence of the magnetic field and the thermal collisions, an equilibrium will be established for the population, termed thermal equilibrium which is described by the Boltzmann distribution. In the magnetic field of the Earth and at room/body temperature, the amount of spins in the lower energy state is almost equal to that of spins in the higher energy state with a very small excess of spins ~3 x 10-6 in the lower energy orientation.

Let us consider that a subject is placed in a strong magnetic field Bo such as that of an MRI scanner (1.5-3 Tesla). Conventionally, the magnetic field is said to be applied on the z axis (longitudinally). In MRI, we are imaging the hydrogen nuclei or protons as they are very abundant (cf. presence in water molecules).

Figure 1: Growth of net magnetization towards a maximum value Mo. Image: Allen D. Elster, MRIquestions.com (ref).

The magnetic field Bo will exert a torque on the spins of the sample, causing them to align themselves with the direction of the magnetic field Bo. As a result, they will be adopting the lowest energy configuration which is termed "spin-up" or “aligned” or "parallel" to the magnetic field. It is noted that this is a spontaneous process and that any other configuration requires supplying energy to the system. For instance, the “spin-down” or “anti-aligned” or “anti-parallel” configuration is considered a higher energy configuration. This is similar to a compass whose needle points spontaneously to the North Pole under the effect of the magnetic field of the Earth. In order to make the needle point to the South Pole, we need to rotate the needle with our hand and thereby do work and provide energy to the system. (It is noted that the stronger the magnetic field, the more energy we have to supply).

The progressive alignment of an increasing number of spins results in the growth of a net longitudinal magnetization of the system along the z axis, termed Mz, which represents the sum of the magnetic properties of the spins and which grows progressively towards a maximal value termed Mo (Figure 2). Simultaneously, the spin system transitions to a lower energy configuration and energy is transferred as heat (thermal energy) away from it. This procedure is termed "T1 thermal relaxation”. Due to original studies performed in solids, which are characterized by a crystalline lattice, it is also termed "spin-lattice relaxation". Different tissues have different T1: CSF 4-5 seconds, gray matter approximately 1 second and white matter slightly shorter.

The process was modelled by Felix Bloch in his 1946 paper on “Nuclear Induction” (term used instead of NMR) as a simple exponential function with T1 as a first-order time constant:

Mz = Mo (1-e-t/T1)

T1 represents the time required for Mz to reach (1 − 1/e) or approximately 63% of its maximum value Mo.

Figure 2: Growth of Mz magnetization component towards a maximum value Mo. Image: Allen D. Elster, MRIquestions.com (ref).