1-14-99 Notes

Protons want to align to preferred opposite axis from field. Spin-up and Spin-down are labels, and do not have an exact relationship with North/South

Put protons in magnetic field -> want to go to lowest energy state. But they experience local fields from each other.

To change from down to up -> requires energy from environment, in quanta.

It takes a while for protons to equilibrate because it needs exactly the right energy. This time is the T1. It is an exponential process, that equilibrates quickly at first but slower over time. It is a phenomenon similar to cooling. Hot coffee cools exponentially.

Question? What determines T1? Not electromagnetic energy, but nonlinear effects do exist with temperature.

Note inverse relationship:

Short T1 = fat, long T1 = CSF.

Long T2 = CSf, short T2=fat.

Rate of precession depends on rate of spinning particle: (same for all protons)

Also, depends on strength of magnetic (or gravitational for a top) field.

Torque= force against angular momentum ?

To convert precession to signal => apply radio pulse at right freq gamma=42.58/tesla*B0

Note: We can selectively excite protons by making B field vary from one position to the next.

Protons will precess around that pulse.

Take ensemble at equilibrium. The protons are all out of phase so only net z magnetization exists.

The radio pulse couples only to the z-component of magnetization, turning the z-component into xy => MR signal

Mxy (after pulse)= Mz (before pulse)

Mz does not precess, but Mxy does.

Keep in mind, we change between lab and rotating frame of reference. Use the rotating from to understand the RF pulse.

How fast does precession occur around B1? Remember B0 is in tesla, B1 is in millitesla. Hence, precession for B1 1-3 kHz.

Question: Orientation of wires: Remember, EMF = k dB/dt. We need to have the wire sense a changing field (that is, be perpendicular).

Choice of antenna: choose antenna that is closest as possible to pick up as much signal as possible.

Equations from last time:

Mz = Mo (1- exp(-tr/T1))

tr = repetition time, ie time between RF pulses

Longer time between pulses, get more signal back.

Signal = Mxy = Ms exp(-te/T2)

te = time from excitation to sampling

T1 and T2 tissue specific and are on different time scales

Why does dephasing occur? Inhomogeneity in the magnetic field. We can vary down to 1/10 part per million, 12.8 Hz at 3 tesla. In one hundred milliseconds, protons can completely dephase.

1950 Hahn spin echo. Discovered it graphically (analogy of Newton w/ calculus)

Decay happens at T2*. Apply 180 pulse. Protons that were precessing slower and lagging beforehand are now ahead, but still precessing closer. Faster protons are still precessing faster, but now are behind. At te, the spin echo, they catch up again. We have cancelled out the inhomogeneity effects! (Spin around the room!)

The rate of spin will vary with space. But, it will not vary before/after the 180 pulse, it will just be in the opposite direction.

T2* = field inhomogeneity.

T2 = tissue specific, interaction of protons with one another.

T1 and T2 are reasonably independent. We can control them separately by varying TR and TE, respectively.

Let us say tr = 1 sec. (short) CSF will reach less than half of recovery. Fat will recover much faster. Gray matter is in between. => T1 weighted image.

Let us say, te = 50 msec. (long). Get t2 contrast (fat decays faster and will be darker, CSF will be bright).

In general:

Short te, lose T2 contrast.

Long tr, lose T1 contrast.

So:

1. Short tr, short te => T1 contrast

2. Long tr, long te => T2 contrast

3. Long tr, short te => Proton density: no T1, no T2. But, no protons outside head, so you do get attractive images and high signal.

4. Short tr, long te = get T1 and T2 contrast => useless. Given tissue has long T1 > short T2. Not only no contrast, no signal! Only get contrast by reducing signal: T1, reduce signal from CSF. T2, reduce fat. In order to get any contrast, signal goes down to zilch.

3 unknowns, 2 variables. Need more than one experiment to solve for t1 and t2. Can acquire more than one image.

2 images w/ long TR, one w/ short TR (short and long echo time - double).

Question? Doesn't this depend on sensitivity of antenna? Yes, but antenna sensitivity has limits. Signal is in tens of microvolts. Also, black body radiation (EM energy emitted by temperatures greater than 0 kelvin) only 2 orders of magnitude lower than our signal.

Caltech people can take pictures of cells! They use really small antenna.

T1 depends on field strength

T1r - approach to equilibrium along radio pulse (B1). Much shorter than T1 (Mark please verify this). Contrast much different.

Question? T2

1/T2 (obs) = 1/T2 (intermolecular interactions) + 1/T2 (field inhomogeneity) + 1/T2 (diffusion)

T2D - diffusion weighted images

T2 - intermolecular important clinically