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Magnetic Resonance in Medicine 963

of Lauterbur’s original suggestions were made. In 1977, some of the details of the internal structure of the nucleus.
W. S. Hinshaw and his colleagues published a high-quality The spin of the nucleus is characterized by a spin quan-
wrist image. Their technique used time-dependent gra- tum number I. The quantum theory of angular momentum
dient fields to localize signal generation to a “sensitive shows that the value of I is fixed for a given nucleus
point,” which could be scanned through the patient. In and can have only integer or half-integer values (i.e.,
1
3
1978, Damadian and associates published an axial cross I = 0, , 1, ,.. .). The magnitude of the nuclear angular
2 2 √
section of the human chest using a “field focusing” tech- momentum J is I(I + 1) h (h = 1.055 × 10 −34 J sec is
nique that has not been widely utilized in subsequent in- Planck’s constant divided by 2π). The angular momentum
vestigations. By 1980, W. A. Edelstein and co-workers had in a given direction can only assume the 2I + 1 discrete
produced cross-sectional images of the human head and values −Ih, −(I − 1)h, up to Ih. Note that these results
body by the spin-warp technique they had developed. This display one of the peculiar features of the quantum theory;
was a modification of the two-dimensional Fourier trans- although the total magnitude of the magnetic moment is
√
form method proposed in 1975 by A. Kumar and others. I(I + 1)γ h, the maximum projection in the direction
The spin-warp technique has become widely standardized of the applied field, which is the only portion that can be
in modern NMR scanners. The 1980s witnessed a rapid physically observed, is the somewhat smaller value I γ h.
proliferation of manufacturers and users of MR scanners. Protons, electrons, and neutrons have been found to
1
These scanners are almost certainly the most significant eachhave I = .Nucleiwithevennumbersofbothprotons
2
new diagnostic equipment introduced into medicine dur- and neutrons all have I = 0. The nuclei with I = 0 have no
ing this time. angular momentum and no magnetic moment and, there-
Thus, in the 70-year period from 1911 to 1981, NMR fore,cannotproducenuclearmagnetism.Thisaccountsfor
went through the stages of being an unsuspected property the large number of chemical elements that cannot be stud-
of unknown subatomic structures, through a period of im- ied by NMR. Odd–odd nuclei all have integral values for
portance only to basic physics, followed by a period during I while even–odd and odd–even types have half-integral
which it was developed as a tool for specialized chemical values for I. Table I is a listing of the spin and magnetic
applications, and finally becoming a crucial medical tool
useful to millions of patients and employing thousands of
workers. TABLE I Magnetic Properties of Nuclei of Current or Poten-
tial Medical Interest a
Resonant Magnetic
C. Nuclear Magnetism
frequency Nuclear moment Natural
2
Nuclear magnetism is an aggregate property of enormous Nucleus at 1 T (MHz) spin, I (10 −26 A m ) abundance (%)
numbers of identical nuclei responding in step to exter- 1 H 42.57 1 2.44 99.985
nally imposed magnetic fields. All magnetic phenomena 2 H 6.54 2 1 0.61 0.015
occurring within matter, in the final analysis, can be ex- 3 H 45.41 1 2.61 0.0
plained only by quantum mechanical methods: analyses 13 2 1
C 10.71 0.61 1.10
based on strictly classical methods are known to lead 14 2
N 3.08 1 0.29 99.63
to significantly erroneous conclusions. The most useful 15 N 4.31 1 −0.25 0.37
method of characterizing phenomena of nuclear mag- 17 O 5.77 2 5 −1.13 0.038
netism, however, involves the use of macroscopic magne- 19 F 40.05 2 1 2.30 100.0
tization vector M. The behavior of M is governed by the 23 Na 11.26 2 3 1.45 100.0
Bloch equations, which are classical in form, but which 25 Mg 2.61 2 5 −0.51 10.0
incorporate, in an empirical fashion, the more fundamen- 2
31 P 17.23 1 0.99 100.0
tal principles of quantum theory. The quantum theory of 2
33 S 3.27 3 0.42 0.75
nuclei in a magnetic field, and in thermal equilibrium with 2
35 Cl 4.17 3 0.54 75.7
their surroundings, is presented now as a prelude to dis- 2
39 K 1.99 3 0.26 93.258
cussing the Bloch equations. 2
41 K 1.09 3 0.14 6.73
Each different atomic nucleus is viewed as consisting 2
43 Ca 2.86 7 −0.75 0.135
of protons and neutrons. The properties of the nucleus in- 2
57 Fe 1.36 1 0.079 2.2
clude its charge, mass, and size, as well as its spin. The spin 2
127 I 8.51 5 1.68 100.0
endows the nucleus with an angular momentum J and a 2
magnetic moment m. The vectors m and J are proportional a
Adapted from data in Walker, F. W., et al. (1984). “Chart of the
to one another m = γJ, where γ , the gyromagnetic ratio, Nuclides,” General Electric, San Jose, CA; Lederer, C. M., and Shirley,
varies from one nucleus to another and presumably reflects V. S. (1978). “Table of Isotopes,” 7th ed., Wiley, New York.