1. Spatial Encoding: Sub mm from meter sized RFy x y . . z x
Excitation: rotating frame y x
To Receiver
Detection: . RF
detection coils z .
To Receiver
Problem:
RF coils are sensitive to transverse component of How do we localize to a spatial location when RF field is sensitive to entire volume?

2. Field diagram Simplified Drawing of Basic Instrumentation.
Body lies on table encompassed by
coils for static field Bo,
gradient fields (two of three shown),
and radiofrequency field B1.
Image, caption: copyright Nishimura, Fig. 3.15

3. Gradient Fields
The gradient field is the last magnetic field we have to discuss.
- key for imaging
- Paul Lauterbur
Gradient coils are designed to create an additional B field that varies linearly across the scanner as shown below when current is driven into the coil. The slope of linear change is known as the gradient field and is directly proportional to the current driven into the coil.
The value of Bz varies in x linearly. Bz
slope = Gz Bo
Whole Body Scanners:
|G| = 1-4 G/cm
(10-40 mT/m)
Gz can be considered as the magnitude of the gradient field, or, if you
like, as the current level being driven into the coil. z

4. Putting it all together: The Bloch equation
Sums of the phenomena
precession,
RF excitation
transverse
magnetization
longitudinal
magnetization
Changes the direction
of , but not the length.
These change the length of
only, not the direction.
includes Bo, B1, and

5. Review: Cosine Theorem (What is a mixer? )
- Consider a pulse A(t) that is multiplied by cos(ot). This is called modulation .
A(t) is called the envelope function.
o is the carrier frequency.
Mixer
A(t) cos(ot)
A(t)
cos(ot)
B1(f)
Frequency response of RF pulse
o = 2fo fo f
-fo

6. Selective Slice Excitation
Lets consider 2D imaging
Slice excitation or selective excitation
We first spoke of B1(t) as a rectangle, an on/off pulse,
a) Now modulate the carrier cos(ot) by B1(t) where B1(t) is a sinc .
F.T.
B1(t)
Mixer
B1(t) cos(ot)
B1(t)
cos(ot)
B1(f)
-fo fo f
Create a circularly polarized field

7. Slice Selection
Simultaneously, we apply a gradient Gz. This creates a mapping along z such that only a subset of spins will be within the bandwidth of the RF pulse. z  z 
slope = Gz
F.T.
B1(t) cos(ot) o
Set amplitude of Gz such that bandwidth of
where is the desired slice thickness.

9. Gradient Fields: In Plane Encoding
Apply Gx during a FID
Frequency is proportional to Bz
slope = Gx Bo x

10. Gradient Fields: In Plane Encoding
Signal(t) Sr f t fo
The Fourier transform of the signal gives us the projection of the object. The signal detected by the coil, a function of time (t),has spatial information encoded into it. Bz
so,
slope = Gx Bo x

11. Gradient Fields: Example
Assume a 20 cm wide head.
Let Gx = 2 G/cm
What is the frequency range across the head?

12. Gradient Fields: Example
Assume a 40 cm wide object.
Gx = 0.5 G/cm
At 1 T,
Bandwidth of interest is small compared to MHz.

13. Gradient Fields: Matlab example
sr(t) x
m(x) t
sr(t) t
s(t)
m(x) x

14. Gradient Fields
Gy changes field strength of B field in z direction as a function of y
Gz changes field strength of B field in z direction as a function of z

15. Generalized Gradient Fields
We can write this all together by looking at G as a vector. Each element refers to the gradient field present at any time ( current in the coil at that time).

16. Basic Procedure 1) Selectively excite a slice (z)
- time? .4 ms to 4 ms
- thickness? 2 mm to 1 cm
2) Record FID, control Gx and Gy
- time? 1 ms to 50 ms
3) Wait for recovery
- time? 5 ms to 3s
4) Repeat for next measurement.
- measurements? 128 to 512
- in just 1 flip
5) Next: More on spatial encoding