Magnetic Resonance
Imaging
Maurice Goldman
Member Académie des sciences
History of MRI
• MRI was born in 1973.
The parents:
• Paul Lauterbur (then at Stony Brooks),
• Sir Peter Mansfield (Nottingham, not yet
Sir at the time)
were awarded the Nobel Prize in Physiology
or Medicine in 2003.
The principle
• The imaging is that of liquid samples,
essentially water protons in living
organisms (for medical MRI).
• If the (supposedly linear) sample is
subjected to a field gradient, the position is
coded by it is resonance frequency, and
that’s all!
• If the sample is not linear, the problem
gets more involved.
Paul Lauterbur
(Gordon Conference, spring 1973)
1- Excite a 2D slice by a rf pulse in a field gradient
along Oz,
2-Apply a gradient along a perpendicular direction
and look at the frequency dependence of the
NMR signal,
3- Repeat at various orientations of the gradient,
4- Deduce the 2D image by Back-Projection.
5- Iterate as many times as necessary.
Dubbed “Zeugmatography”
Strips selected by a given gradient
direction
G

• The signal amplitude
at each frequency is
due to the cumulative
contribution of the
spins in adjacent
sample strips
Back Projection
-Assume uniform
contribution along each
strip.
Superposing these strip
amplitudes for different
orientations, yields the
amplitudes for each pixel.
These are used for iteration.
Same approach as in
CT scanner
Peter Mansfield
(Ampere summer school, Cracow, fall 1973)
Gives a lecture on
“NMR diffraction from static spins”, based
essentially on the same idea of using field
gradients, but initially thought to be able to
resolve structures at the atomic level.
Recognizes that a more modest ambition on
liquid samples might be easier to reach.
Most common practice:
Phase encoding
Kumar, Welti and Ernst (1975):
same as 2D spectroscopy
• Slice selection with gradient Gz,
• Blind phase encoding with gradient Gy during
time t,
• Sampling with gradient Gx during time t
• Repeat for various durations t.
Drawback: relaxation during t.
Better sequence
Edelstein, Hutchison et al (1980):
Use always the same duration t, but vary
the amplitude of the gradient Gy.
Schematic sequence
Rationale of imaging
The gospel of MRI
The strategy for imaging:
Perform an adequate filling of the
reciprocal space and Fouriertransform it.
That’s all, folks!
Filtered Back-Projection
Fourier transform in polar coordinates
Phase encoding
Fourier transform in normal coordinates (FFT)
Contrast production
Contrast agents
•Superparamagnetic particles
•Gadolinium chelates
Improvements
• Selective excitation by sinc pulse:
Sinc(x)=sin(x)/x
• Produce gradient echo to observe signal,
• Refocus magnetization to increase S/N,
• Series of specialized sequences for
specific applications,
• Improved gradients, etc.
Ex : True FISP sequence
Ex : MARYSE Sequence
Other measurements
• Flow :
phase imaging or presaturation of fov.
• Diffusion tensor:
bouncing on cell walls modifies apparent
diffusion coefficient
Single-shot sequences for fast imaging
Ex: Echo Planar Imaging (30 to 50 ms)
(P. Mansfield 1978)
Various codings of reciprocal space
Functional MRI (fMRI)
• Hemoglobin is
diamagnetic
• Deoxyhemoglobin is
paramagnetic. It
decreases locally the
relaxation times
• Images are obtained
by difference
Lauterbur (1973)
two capillaries of water
Mansfield, Maudsley (1977)
cross section of finger
Edelstein, Hutchison et al. (1980)
chest (slice thickness 18.5 mm)
My radiologist (2008)
head and brain (slice thickness sub mm )