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### QUESTIONS» Basic Physics

Where does the MRI signal come from? This section explores the basic physics of magnetic resonance imaging.

# Spin Polarisation (QM)

## What is net spin polarisation?

The net magnetisation vector in the direction of the external magnetic field from an ensemble of spins, each of which are in a superposition of the Zeeman eigenstates.

The net magnetisation vector from an excess of spins in a higher Zeeman energy level.

Net polarisation with the field (the degree of polarisation is greatly exaggerated).

CORRECT. Net spin polarisation can occur in any direction in 3D space, and results in a net magnetisation in the sample. Instead of describing the magnetic direction of individual spins we describe the overall "polarisation" of a sample. This may seem like the same thing, but really we are trying to describe (or depict in a diagram) something which is only properly described by QM mathematics. Remember, in the QM perspective, spins do not occupy specific energy levels, or "point" in particular directions; depiction of such things in a QM diagram has a specific interpretation, which is that partial alignment of spins equates only to a spin polarisation density, not individual spin directions.

When spin polarisation occurs with or against the external magnetic field direction (i.e. there is a longitudinal magnetisation Mz), it produces an observable population difference between the two Zeeman energy eigenstates. When spin polarisation occurs perpendicular to the external magentic field direction (i.e. there is a transverse magnetisation Mx and/or My), it is as a result of quantum coherences between the two Zeeman energy eigenstates.

The introduction of energy into the system (e.g. an RF excitation pulse) causes a change in the net polarisation of the spins. A change in the Mz component of the net magnetisation vector is a change in the observable population difference between the two Zeeman energy eigenstates. Formation of Mx and My components of the net magnetisation vector are due to quantum coherences between the two Zeeman energy eigenstates.

INCORRECT. The spin up and spin down spin states are sometimes compared with the Zeeman energy levels. But this is a poor comparison, and may lead to confusion about which description is classical mechanics (CM) and which is quantum mechanics (QM). Even in the classical description, spins are not restricted to align with (parallel or spin up) or against (antiparallel or spin down) the external magnetic field direction. However, a simplification of the classical description of MRI does describe these spin states, assigning equivalent numbers of spins to the two states to produce the same net magnetisation vector. So this simplification can be helpful.

It is probably clearer to consider the Zeeman energy levels only as part of the QM description of MRI. They are named eigenstates for a reason: these energy levels only describe the states which are observable. Spins are not restricted to either state but exist in linear combinations of both states. This is certainly not a CM concept.