And magnetization just prior to the n-th alpha pulse,

will have very similar shape to this equation, but

it can be presented as Mz(nTR) and Mz([n-1]TR cosine alpha,

e to -TR /T1, + M0(1- e to -TR /T1).

Okay this is going to n-th alpha pulse relative to n minus

1's magnetization, okay?

So eventually, this imaging is going to be in the steady

state which means there will be no signal difference

between Mz[n- 1] and Mz[nn], okay.

So these two will have the same equation or

the same signal intensity which is the deficient of a steady state.

So steady state in the steady state, so Mg[n.TR] and

Mg([n-1].TR) intensity will be the same.

And then we can solve this equation based on this relationship and

then that gives signal intensity of Mg, okay,

at the steady state to M0, 1- e to -TR/T1

divided by 1- cosine alpha e to -TR/T1.

Okay, this is going to be longitudinal magnetization, okay,

right before applying for excitation alpha pulse, okay, in the steady state.

And then the single intensity or gradient echo is going to be alpha pulse flipping,

the signal intensity is going to be the same as transverse

longitudinal magnetization multiplied by sine alpha.

So that is going to be the signal intensity flipped toward

the transverse plane, okay.

So that is going to be initial magnetization,

right after applying for this alpha pulse, okay?

And then that is going to decay during the time called echo time,

so we have to multiply e to the -TE/T2*, okay?

This is of a similar intensity of gradient echo imaging.

Okay, so I'm writing this equation again, okay as shown here.

You may not need to understand every detail of this procedure.

But you may just remember how this signal, gradient echo

imaging signal intensity can be affected by the time constant T1 as shown here,

and also T2*, and proton density, okay.