3.6.3 Magnetic Resonance Imaging (MRI)
Paul C. Lauterbur and Peter Mansfield received Nobel Prize in Physiology or
Medicine for discoveries concerning magnetic resonance imaging in 2003, which
shows that physics contributes fields of biology and medical science, and a good
example of contribution of biophysics to human welfare. MRI method is based on
following principle. Water molecules occupy more than 60 % in total weight of the
body, and each tissue contains water molecules, i.e. hydrogen atoms. Differences of
hydrogen concentration (spin density, ρ), spin–lattice relaxation time (T1) and spin–
spin relaxation time (T2) among tissues of human body. In addition to the differences
of these values among the tissues, there is difference of these values between normal
tissues and abnormal tissues. MRI uses the differences appeared in the NMR signal
and makes image of the NMR signal by use of gradient magnetic field of Lauterbur’s
idea. Bottomley and his colleagues improved NMR image exceeding X-ray CT
image in 1983, and NMR becomes practically realized in clinical application. The
difference of relaxation times and positional information obtained from gradient of
magnetic field are used for information of imaging in MRI. Gradient of magnetic
fields are formed by gradient coils along directions of x-axis, y-axis and z-axis.
Frequency of applied pulse of radio wave, ν 0 is made resonance under condition
ofΔE ¼ hν 0 ¼ g N β N H 0 and the resonance occurs at position of external magnetic
field intensity, H 0 . And so NMR signal and positional information are obtained
simultaneously, where g N and β N are g-value and nuclear magneton of atomic
nucleus, respectively. On the other hand, values of spin-lattice relaxation time (T1)
and spin-spin relaxation time (T2) in relaxation process are used for imaging
information. These relaxation times are defined by Bloch’s equation as follows.
Temporal change of magnetization along z-axis, i.e. spin-lattice relaxation, T1 is
relaxation process of spin system to equilibrium magnetization M 0 and diagonal
elements of density matrix transfer to Boltzmann distribution, which is shown as
following equation.
dM x
dt ¼ À
M z ÀM 0
T 1
.
Temporal change along x-axis and temporal change along y-axis (spin-spin
relaxation time (T2) is process of off-diagonal elements of density matrix transferring to zero which is shown as following equations.
dM x
dt ¼ À
dM x
T 2
, À
dM y
T 2
Schematic illustration of MRI is shown in Fig. 3.14.
Spin is degree of freedom and atomic nucleus with electric charge generates
magnetic moment. Therefore, each spin takes precession around magnetic field H 0 at
frequency under condition ofν o ¼
γ H 0
2π . Magnetic field pulse of Larmor frequency is
applied from lateral direction in pulse method. And magnetic field pulse H1 of same
phase is applied duration time t from x-axis direction in rotating reference frame (
ν o ¼
γ H 0
2π , rotating around z-axis). Direction of magnetic field pulse H1 is constant in
the rotating reference frame, and spin takes precession at angular velocity of γ H1
3.6 Magnetic Resonance
43
Paul C. Lauterbur and Peter Mansfield received Nobel Prize in Physiology or
Medicine for discoveries concerning magnetic resonance imaging in 2003, which
shows that physics contributes fields of biology and medical science, and a good
example of contribution of biophysics to human welfare. MRI method is based on
following principle. Water molecules occupy more than 60 % in total weight of the
body, and each tissue contains water molecules, i.e. hydrogen atoms. Differences of
hydrogen concentration (spin density, ρ), spin–lattice relaxation time (T1) and spin–
spin relaxation time (T2) among tissues of human body. In addition to the differences
of these values among the tissues, there is difference of these values between normal
tissues and abnormal tissues. MRI uses the differences appeared in the NMR signal
and makes image of the NMR signal by use of gradient magnetic field of Lauterbur’s
idea. Bottomley and his colleagues improved NMR image exceeding X-ray CT
image in 1983, and NMR becomes practically realized in clinical application. The
difference of relaxation times and positional information obtained from gradient of
magnetic field are used for information of imaging in MRI. Gradient of magnetic
fields are formed by gradient coils along directions of x-axis, y-axis and z-axis.
Frequency of applied pulse of radio wave, ν 0 is made resonance under condition
ofΔE ¼ hν 0 ¼ g N β N H 0 and the resonance occurs at position of external magnetic
field intensity, H 0 . And so NMR signal and positional information are obtained
simultaneously, where g N and β N are g-value and nuclear magneton of atomic
nucleus, respectively. On the other hand, values of spin-lattice relaxation time (T1)
and spin-spin relaxation time (T2) in relaxation process are used for imaging
information. These relaxation times are defined by Bloch’s equation as follows.
Temporal change of magnetization along z-axis, i.e. spin-lattice relaxation, T1 is
relaxation process of spin system to equilibrium magnetization M 0 and diagonal
elements of density matrix transfer to Boltzmann distribution, which is shown as
following equation.
dM x
dt ¼ À
M z ÀM 0
T 1
.
Temporal change along x-axis and temporal change along y-axis (spin-spin
relaxation time (T2) is process of off-diagonal elements of density matrix transferring to zero which is shown as following equations.
dM x
dt ¼ À
dM x
T 2
, À
dM y
T 2
Schematic illustration of MRI is shown in Fig. 3.14.
Spin is degree of freedom and atomic nucleus with electric charge generates
magnetic moment. Therefore, each spin takes precession around magnetic field H 0 at
frequency under condition ofν o ¼
γ H 0
2π . Magnetic field pulse of Larmor frequency is
applied from lateral direction in pulse method. And magnetic field pulse H1 of same
phase is applied duration time t from x-axis direction in rotating reference frame (
ν o ¼
γ H 0
2π , rotating around z-axis). Direction of magnetic field pulse H1 is constant in
the rotating reference frame, and spin takes precession at angular velocity of γ H1
3.6 Magnetic Resonance
43