MRI basic science

General

Concept

Net magnetization

All nuclei have protons that spin

Nuclei with unequal number of protons will have a net spin direction within that nuclei

The summation of all the spin of the nuclei within a unit space containing billions of hydrogen nuclei is called the NET MAGNETIC VECTOR (NMV).

The NMV has two components (Z (longitudinal magnetization) and XY vectors(transverse)) that changes based on the direction of the spin.

This spin direction is the clearest in the hydrogen atom as there are no other protons or neutrons to affect its spin. Hence it is used in MRI as the based detection method

Foundation

Since we are dealing with billions and billions of hydrogen nuclei, there is no need to use quantum mechanics methods.

FYI quantum mechanics only deal with a single nuclei and due to quantum uncertainty, the nuclei can have a spin that ranges between up and down spins. This ‘Range’ is due to quantum uncertainty, i.e. if you measure it at a certain time it can be up and it can be also down. Since we are dealing with large number of nuclei this does not matter.

In earths weak magnetization field, the NMV is in the direction of the magnetic field (B0).

T1 relaxation

Images here shows that you add an external magnetic field B0, it will take time for all the nuclei to point towards B0 direction. The time it takes to this measure as T1. At maximum T1 you have a large portion of the hydrogen nuclei pointing towards B0. T1 (aka Spin-lattice or thermal relaxation time) is time required for M to grow to (1 − 1/e) or about 63% of its final value (Mo)

When you introduce another external magnetic field at 90° to B0 it pushes the NMV away from B0 and this angulation allows for the NMR to precess around the B0. (If you look at each nuclei they will undergo a precession even with the very weak earth magnetic field and a local spin. Like a spinning top in motion, each nuclei has two spin. This precession is constant if the external magnetic field is constant and the nuclei being targeted is constant.) This precession speed/frequency is determined by the following larmor equation: precession frequency/(Larmor Fq) (MHz) = strength of the external magnetic field (Tesla) x gyromagnetic ratio (constant for each nuclei (MHz/T). It so happens that for protons when in a magnetic field used by MRIs (Tesla 1-7), the precession frequency is in the radio-frequency range. Hence we use pulses of magnetic fields that come on and off at radio-frequency rates (NOT FUCKING RADIOWAVES; RADIO WAVES ARE PART OF THE ELECTROMAGNETIC SPECTRUM, THIS IS JUST PULSES OF MAGNETIC WAVES PULSATING AT RADIOFREQUENCY RATES) to tip the NMV away from B0. Now that is tipped away the NMV is “resonating” at the larmor fq, think like a bridge that can sway in large amplitude if the fq of the wind or the footsteps are in the natural (i.e. larmor fq). If you turn off the B1 magnetic pulsation, over time the energy of the resonance will be spread into the surrounding and the NMR returns to pointing at B0 and there is no more secondary rotation about the B0. However, nuclei precession still occurs regardless. Time taken for NMR to return to B0= T1, time taken NMR to stop resonating = T2

When the protons is precessing, and a magnetic pulse given equal to the precession frequency of the hydrogen nuclei and at 90° to the direction of the MRI magnetic field will cause two things

Energy absorption by the nuclei to cause a larger portion of the nuclei to spin down (at a higher energy state) → causing the NET MAGNETIC VECTOR (NMV) to be in the transverse plane

When the proton is spinning it produces a magnetic force. the sum of the spin of all the protons in a cubic of space will produce a net magnetic force. The direction of this force can be longitudinal or transverse.

Longitudinal: parallel to the direction of magnetic field
Transverse: at 90° angle to the magnetic field.

If you give atoms just enough energy so that 1/2 of all the proton is in high energy state and the other half is in low energy state, then you will have maximum transverse magnetization

Magnetic relaxation vs stimulation

Feature	Stimulation, B1	Relaxation
In which plane	XY plane	XY plane
Area affected	All Nuclei in the plane	Only the local nuclei
Source	90° orientated RF Coils	Local protons and electrons
Occurs at	Larmor Fq	Larmor Fq

How Dipole dipole interactions causes T1 and T2 relaxation

Types of spins

Proton-proton

Proton-electron.

Due to its small size, an electron has a much larger gyromagnetic ratio (γ) than a proton and so a proton-electron dipolar interaction is much more powerful than a proton-proton interaction.
Paramagnetic substances like Gd+3 with multiple unpaired electrons are so effective at inducing magnetic relaxation.

Distance

Closer the better at causing relaxation

Angle

The strength of the dipolar interaction also depends on the quantity (3 cos²θ −1), where θ is the angle between the two spins.

At θ ≈ 54.7° (aka Magic angle) (3 cos²θ −1) = 0, since at 54.7° there is no positive and negative effect to the B0 field ( meaning there is no dipole dipole interactions) → the B0 field does not increase or decrease (i.e. no changes to the 1 Tesla B0 field: B0 field does not become 1.0001 tesla or 0. 9999 tesla) → there is no change to the larmor fq → the resonance of the NMR still persist and is not lost → therefore at the magic angle, portions of the tendons, nerves and cartilage can have paradoxically high T2 signal on MRI if they make an angle of 54.7° to the main magnetic field since the water molecules around the tendons, nerves, and cartilage are parallel to them.

At other angles (outside of 54.7°)

Angled dipole dipole reaction best seen in water held in fixed stable angles, i.e, water near large tissues such as tendon, cartilage and nerves:
Fixed angle dipole-dipole interactions will cause one dipole’s + or - field to overlap the B0 field. → this will add or subtract the uniform magnetic field B0 → giving local small variations in magnetic field BO’=B0 + Bmicro → these small variations changes the Larmor fq (=gyromagnetic ratio X magnetic field B) → now that the Larmor fq is different, the some nuclei will precess at a different frequency than the others → hence some nuclei’s precession will cancel out others → now the XY component of the new NMR will be shorter → T2 will be shortened very quickly

This is so quick that we cant detect it so tendon, nerve and cartilage tends to be dark in T2 (very short T2)
For T1 this wont be affected because it will take same amount of time for NMV to return to B0 since all nuclei are still precessing even though each nuclei might have a different precession frequency

Relative motion

All molecules are in motion.

The example above shows a water molecule in motion. Light red H is in B0, Dark red H is not in B0 → The dark red H is rotating relative to the light red H. → Light red H is a dipole and has its own weak magnetic field. If the rotation of the dark red H is going at a rate (not too fast or too slow just nice ) near the Larmor fq → dark red H can Take away the resonance in light red H → causing NMR to return to B0

If the rate of molecular tumbling, I. E. Dark red H is rotating too fast or too slow then relative to the larmor Fq, then no stealing of energy occurs → T1 remains long

The small dip in the T2 line at the middle of the graph is due to T1 effects on T2. When the above is happening energy can be stolen by the dark red H causing the precession to go out of phase.

How the spins move relative to one another is a strong determinant of the degree and type of relaxation (combined T1/T2 or T2 alone). If one of the spins resides on a molecule that is tumbling or rotating at frequency ω, its associated dipolar field will also fluctuate at the same frequency. If that frequency happens to closely match the Larmor frequency, then conditions are optimal to cause T1 relaxation in a nearby spin. Conversely, if the molecule on which the spin resides is hardly moving at all (as in large molecules fixed in cell membranes) the dipolar field will be relatively static, producing dephasing of nearby spins and predominantly T2 relaxation.

T1 and T2 relaxation time

T1 is always longer than T2

Tissue	T1 (msec)	T2 (msec)
Water/CSF	4000	2000
Gray matter	900	90
Muscle	900	50
Liver	500	40
Fat	250	70
Tendon	400	5
Proteins	250	0.1 - 1.0
Ice	5000	0.001

MRI with different TR and TE