Principles of (N)MR Imaging Peder Larson, Ph.D. University of California – San Francisco, Department of Radiology and Biomedical Imaging Experimental NMR Conference, Educational Presentation, Asilomar, Pacific Grove, CA March 28, 2017 https://radiology.ucsf.edu/research/labs/larson/educational-materials (Google: Peder Larson Lab, Educational Materials link on sidebar)
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Principles of (N)MR Imaging - UCSF Radiology · From NMR to MRI •1946: NMR phenomenon first discovered by Felix Bloch and Edward Purcell (Physics Nobel Prize in 1952) •1973: First
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The key factors were the development of fast imagingtechniques, particularly gradient echo, and phasedarray coil technology. The 1990s also saw the coming ofage of earlier developments, namely cardiac MRI andEcho Planar Imaging (EPI). EPI, which is the fastest and
one of the most cutting edge methods, was actually oneof the first imaging methods to be proposed, by Sir PeterMansfield. EPI is now extensively used in neurologicalimaging through functional MRI (fMRI) and diffusionimaging.
1.3 How to use this book
Everyone starts MRI with the same basic problem: it’slike nothing else they’ve learnt in the past. All thatknowledge you have about radioactive isotopes and
MR: What’s the attraction?
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Figure 1.3 First ever human head image using MRI at 0.1 T
from EMI Central Research Laboratories. For this image CT
type “back projection” was used. Courtesy of Ian Young.
The early history of NMR‘Nuclear induction’, as it was first described, was dis-covered in 1945, soon after the close of World War II,by Bloch and independently by Purcell and Pound. Itis said that the development of radio communica-tions in the war effort, to which Purcell had con-tributed scientifically, was one of the factorsunderpinning this important scientific discovery.Another important factor, as in the development ofatomic physics, was the expulsion or fleeing ofEuropean physicists from the Nazi regime, an exodusthat included Bloch and Bloembergen. What didthese MR pioneers discover? That you can detect asignal (a voltage in a coil) when you place a sample ina magnetic field and irradiate it with radiofrequency(RF) energy of a certain frequency, the resonant orLarmor frequency. The signal is produced by theinteraction of the sample nuclei with the magneticfield. The spin echo was ‘stumbled upon’ by Hahn in1949. He discovered that you could get a repeat of theNMR signal at a delayed time by adding a secondburst of RF energy. That’s all you need to know fornow. So what were NMR researchers doing betweenthe forties and the seventies – that’s a long time incultural and scientific terms. The answer: they weredoing chemistry, including Lauterbur, a professor ofchemistry at the same institution as Damadian,albeit on different campuses. NMR developed into alaboratory spectroscopic technique capable ofexamining the molecular structure of compounds,until Damadian’s ground-breaking discovery in 1971.
Figure 1.4 0.15T resistive magnet used by Philips in the
early development of MRI. Courtesy of Philips Medical
Received signal is the spatial Fourier Transform of the transverse (xy) net magnetization! Evaluated at k-space location that depends on gradients
Example : consider signal from three locations - x= 0, x1, x2 - with magnetic field gradient on
Signal is sum of different locations, which have different frequencies with gradient
Or we can model our object with delta functions and use the Fourier transform
( ) ( ) ttpg dGtk
t
ò=0
2
K-space
kx
ky
Frequency space(k-space), M(kx,ky)
x
y
FourierTransform
Image space, m(x,y)
GX
GY
periodic variation in signal spatial distribution or imagebrightness, measured not as line-pairs per centimetrebut as ‘cycles per centimetre’ (which are very similar).
Applying the theory of Fourier, any image (not justMRI) may be decomposed into a spectrum of periodic(sinusoidal) brightness variations or spatial frequen-cies. In a digital image with a matrix of 256!256 pixelsthere are 256!256 possible spatial frequencies, allow-ing for positive and negative values. If we know thespatial frequencies we can calculate an image of theobject that formed them. The purpose of MR localiza-tion by gradients is to manipulate the MR signal so thatit gives all the spatial frequencies necessary to form animage. Each point of data or k-space is a spatial fre-quency component.
Figure 7.10 shows an image and its constituent spatialfrequencies (k-space). If we remove the high spatial fre-quencies we are left with an image which has the rightbrightness but no detail. Removing the low spatial fre-quencies leaves the image with details of edges andsharp features but low intensity elsewhere. So bigobjects have low spatial frequencies. Small objects orsharp edges have high spatial frequencies.
7.5.2 Totally fazed: phase encoding
Most people find phase encoding the hardest part ofMR image formation to understand, but gaining a con-ceptual grasp of it will pay dividends in terms of youroverall understanding. Consider the following in
Spaced out: spatial encoding
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Figure 7.10 Images and their 2D spectra (k-space) showing: (a) reconstruction from all spatial frequencies, (b) low spatial
frequencies, i.e. the centre of k-space only and (c) high spatial frequencies, i.e. the edges of k-space only.