Magnetic Resonance Imaging

1. NMR occurs because certain atomic nuclei have a property known as spin


2. ‘Spin’ (I) is a quantum-mechanical property of the nucleus


3. Nuclei with even numbers of protons and neutrons have no spin


4. Nuclei with an odd number of protons and/or an odd number of neutrons have integer spin (I = 1, 2, 3…) or half-integer spin (I = 1/2, 3/2, 5/2…)


5. Only these nuclei with nonzero spin can be studied using NMR

There is no exact classical analogy for quantum-mechanical spin. A model that works well for many purposes is to picture the nucleus as a solid ball, and a nucleus with spin as rotating on an axis through its centre at a speed that is dependent on the quantum number.

 

Click on the Which nuclei? tab above to continue.

This table shows a range of nuclei of potential biomedical interest that have nonzero spin and hence can be used in NMR experiments.

Nucleus	Spin	Relative sensitivity	Natural abundance (%)
1H	1/2	1.00	99.98
13C	1/2	1.59 x 10-2	1.11
14N	1	1.01 x 10-3	99.63
15N	1/2	1.04 x 10-3	0.37
17O	5/2	2.91 x 10-2	0.04
19F	1/2	8.30 x 10-1	100.00
23Na	3/2	9.25 x 10-2	100.00
31P	1/2	6.63 x 10-2	100.00

 

The third column indicates sensitivity relative to the 1H nucleus, the most sensitive nucleus for NMR, and the fourth column indicates the abundance of the NMR-sensitive isotope of the nucleus. NMR experiments are very insensitive (see below) and so it is important to maximise these two values for good results.

From the table, 1H, 19F and perhaps 23Na and 31P look promising candidates for biological NMR experiments.

However, it is also important to consider the abundance of the elements in the body (unlike nuclear medicine, conventional MRI detects endogenous nuclei, rather than tracers). 1H is found in the body in huge abundance in the form of water, with about 10,000 times the concentration of other 1H-containing compounds or of 31P containing-compounds. There is very little 19F in the body, and 23Na is unsuitable for other reasons.

Therefore MRI is almost entirely restricted to detection of 1H nuclei (protons), almost entirely in water molecules. To a first approximation, and MR image is a map of the distribution of water in the body.

There are specialist applications, mostly in research, where 31P is detected or nuclei such as 19F or 13C are used for NMR tracer studies.

 

Click on the Spin tab above to continue.

• A nucleus with spin is pictured classically as a spinning ball of charge
• This spinning charge generates a magnetic field, denoted by the magnetic moment, µ
• In an applied magnetic field, B₀, according to quantum mechanics the magnetic moment of the ¹H nucleus (I=½) adopts one of two orientations (see diagram)
• According to classical electromagnetism, the nuclear magnetic moments experience a torque and precess about the z-axis (defined by B₀) at the Larmor frequency, ω₀ = γ B₀

Here γ is a gyromagnetic ratio, a constant for each nuclear species. For 1H, γ = 42. 57 MHzT^-1
The direction of the static field is usually taken to define the z-axis of a coordinate system, and the plane perpendicular to this direction is known as the xy-plane or transverse plane.

Also see: http://www.e-mri.org/nmr/precession.html

 

Click on the Magnetise patients.. tab above to continue.

• Nuclei aligned against the field have slightly more energy than those aligned with it, the difference being:
  

  

  Therefore the two orientations correspond to two quantum-mechanical energy levels.
• With a fixed amount of thermal energy available in the system, the lower energy level has a slightly greater population, which gives the sample as a whole a bulk magnetisation, M, lying along the z-axis.
• In the diagram the difference in population has been greatly exaggerated: at room temperature and typical MRI magnetic field strengths there is a excess of only about 5 or 6 nuclei oriented with the field as opposed to against it.
• M is therefore very small, which explains why NMR is such an insensitive experiment and also why manufacturers continually move towards higher field strength magnets (since the population difference depends on ΔΕ which is proportional to B₀.
• The orientation of precessing spins in the xy plane is random, so there is no net magnetisation along the x- or y-axes. (In a more strictly accurate quantum-mechanical description, this is a manifestation of Heisenberg’s uncertainty principle.)

 

Click on the ..then excite them! tab above to continue.

• 

  If an additional magnetic field, B₁, is applied which rotates in the xy plane at the same frequency as the bulk magnetisation – i.e. the Larmor frequency ω₀ – then a resonance condition occurs.
• At the magnetic field strengths used in MRI, ω₀ lies in the radiofrequency (RF) part of the electromagnetic spectrum. B₁ is therefore provided in the form of a radiowave  of the appropriate frequency.
• When this resonance condition is achieved, the bulk magnetisation precesses about the direction of B₁ as well as B₀, and so it tips (nutates) away from the z axis towards the xy plane.
• Nutation continues until B₁ is removed, so the amplitude and duration (t) of B₁ can be tailored to nutate M through specific angles α = γB₁t.

 

Click on the Building blocks tab above to continue.

• 

  The basic building blocks of simple NMR experiments are 90o and 180o  pulses, which are pulses of RF tailored to nutation M through these two angles.

 

Click on the Getting a signal tab above to continue.

• 

  Following a 90° pulse, magnetisation is entirely in the transverse (xy) plane
• This magnetisation is precessing in the plane about B₀ at the Larmor frequency, at ω₀.
•  According to Faraday’s law of induction, this changing magnetisation will induces a voltage, and hence a current, in a conductor placed adjacent to the sample.
• In NMR, this ‘conductor’ takes the form of a tuned coil (known as the ‘RF coil’).
• The induced signal, known as a free induction decay (FID), oscillates at ω₀ and decays exponentially.
• In practice, it is usual to collect a delayed signal, or ‘echo’, rather than the FID

 

Click on the Time to relax... tab above to continue.

• 

  The decay of the FID can be explained by considering what happens to the bulk magnetisation, M, when the RF pulse is switched off.
• Over time, M returns to its original orientation along B₀ (the z axis) as the transverse magnetisation decays away the end z-magnetisation recovers.
• Recovery of M_z is characterised by the longitudinal relaxation time, known as T₁.
• Decay of M_xy is characterised by the transverse relaxation time, known as T₂. It is this decay that is seen in the FID envelope.
• The T1 and T2 values of water protons vary between different tissues, and so spins in different tissues recover and decay and different rates. 

 

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