Mo= net alignment when all protons are parallel/antiparellel
Mz equation= calculate how much relaxation has occured
given tissue and given repetition time we can calucluate longitudinal magnetization 
Mz decreases over time

TE= echo time
time between 90degree pulse and when echo appears
Second diagram
red curve - no inhomogeneities (dictated by Time constand T2)
Blue curve = not a perfect magnet, it decays faster, and that curve is characterized by t2*
When you apply the 180 degree pulse we get the echo to occur on the T2 curve
We look at the magnetization on the T2 curve at the echo time. 


You apply the 180 degree pulse halfway between echo time and 90 degree pulse

MEMORIZE MRI SIGNAL EQUATION FOR EXAM
MRI Singnal = (Longitudinal magnetization before 90 degree pulse) times the decay or the ratio of the echo time to the time constant

Description

Purposely create an inhomogenous field (gradient field. 
With gradient field, there is different spinning speeds at different parts of the body.
Protons in the strongest part of the field spin faster, the protons in the lower end spin slower. 
Using larmor equation we can calculate how fast the protons are spinning with the gradient field turned on.

Description

For exam we should be able to write out signals using fourier transformations. 
Given B1 field and gradient field you should get mri signal or given two factors should be able to find the thrid. 

Yes if you flip the orientation of the magnet

Notice for MRI signal the amplitude gets smaller and smaller
The flip is caused by the 180 degree flip
Also certain times when the gradient is on and when it is off
straight lines from 10-20 before the 180 pulse because we are looking at this in the rotating frame and so it looks like there is no magnetic field.
Bo is still on though
we don't see the spin because we are in the rotating frame

If the isocenter is the rotating frame, the gradient looks like 
\
 |\    isocenter
    \|
      \

How to pick out individual signals

Second position has higher frequency. Further away from isocenter than proton 1

Also means that they are not from the same tissue. proton 2 could be from a different density

As you get farther from the isocenter the protons are spining faster 

You need to know what direction the pulse was applied

To pick out individual signals for each tissue from the bulk signal

Separate colors based on wavelength; similarly mathematical process that takes the cumulative signal and breaks it down into individual signals

Use a gradient magnetic field too get a beat frequency (because protons are spinning at different magnitudes sometimes they cancel each other out and sometimes they add to each other)

With fourier transformations, we change the beat frequency based on time that tapers off into a frequency that shows the wavelength size. 

Takes the spin-echo signal and fourier transforms to give a graph with lines going up and down

left to right - slowest to fastest

height of lines - amplitude of waves

isocenter near the slower end of the graph and higher side of the gradient near the faster side