FREE ESSAY ON RELIGION AND THE CHANGES THROUGH THE YEARS

RELIGION AND THE CHANGES THROUGH THE YEARS

Overview: Physics of Magnetic Resonance Microscopy
Magnetic resonance microscopy (MRM) is founded on the same physical principles as its
clinical cousin, magnetic resonance imaging (MRI). Two crucial discoveries have made MRI
possible. The 1952 Nobel Prize in Physics was awarded to Felix Bloch of Stanford and
Edward M. Purcell of Harvard for their discovery of nuclear induction. Nuclei with
unpaired nucleons (neutrons or protons) possess a magnetic moment arising from the
angular momentum of these spinning nucleons. The interested reader can find a thorough
quantum mechanical description in several excellent texts (e.g., A. Abragam, The
Principles of Nuclear Magnetism (1978), P.T. Callaghan, Principles of Nuclear Magnetic
Resonance Microscopy (1993)). 
Classical Interpretation
A classical treatment of nuclear magnetic resonance is frequently used to give an
intuitive understanding. Consider the unpaired protons of hydrogen in water. The proton
is a charged particle with angular momentum. When a collection of these protons are
placed in a strong magnetic field, the individual protons try to align with the external
field. The angular momentum causes all of the protons to precess about the magnetic field
much as the child's gyroscope precesses when placed on a pedestal. All the protons
precess at a very explicit frequency, the Larmor frequency , given by the equation 
where is a constant. Because the collection is precessing in synchrony at , the vector
components parallel to the magnetic field B0 add to each other to generate a net
magnetization M which also precesses at . Measuring the effect on a single proton would
be very difficult because the magnitude is so small. Because M is the sum of many protons
acting synchronously, it is large enough to measure. If an additional magnetic field B1
is applied at this same frequency, M can be forced away from the longitudinal (z) axis
into the transverse plane. But once in the transverse plane, M continues to precess. As
it does so, it will cause a time varying signal (at the Larmor frequency) in any loop of
wire (antenna) through which M passes. This is the nuclear induction, which forms the
basis for nuclear magnetic resonance. 
Spatial Encoding for MR Microscopy
Spatial encoding for MR microscopy is founded on the same fundamental principle as
MRI-the use of magnetic gradients to encode nuclear magnetic signals. In a typical
two-dimensional study, a gradient applied along the longitudinal (z) axis of the subject
defines a slice that is selectively excited by the simultaneous application of a resonant
radiofrequency (rf) pulse. Subsequent rf pulses and gradients are employed to generate
and encode the signal in the selected slice, typically yielding a 256 x 256 digital
array, with each element of the array representing the signal from an element of tissue
volume (voxel) within the slice. 
Resolution in MR Microscopy 
The resolution in an MR image must be defined on a volumetric basis. A standard clinical
study such as that shown in (A) of a human brain imaged at 1.5 Tesla employs a 5 mm-thick
slice with an in-plane field of view of ~ 250 x 250 mm. Each discrete picture element
(pixel) represents the signal from a 1 x 1 x 5 mm volume, i.e., a 5 mm3 voxel (volume
element) of tissue. 
Images B-D are derived from a 3D MRM acquisition of a formalin-fixed rat brain imaged at
9.4 Tesla by averaging adjacent pixels. The calculated images B & C demonstrate the
consequences of limited resolution on definition of brain architecture in the smaller rat
brain. 
The resolution in B is comparable to the clinical scan of the human brain. It is made by
averaging adjacent pixels from the original (high resolution) isotropic 3D array to
produce voxel dimensions the same as the clinical scan (A) in a rat brain image. Image C,
averaged to produce 64 times higher resolution than the human image (0.25 x 0.25 x 1.25
mm = 0.078 mm3), is still a poor depiction of the anatomy. The anatomy is seen more
clearly in D (.086 x.086 x .086 mm = .00064 mm3), which is ~ 8000 times higher resolution
than the images in A and B. Image D is one slice from the original 3D MR microscopy study
of 256 slices. MR microscopic techniques allow volume imaging at this resolution and
higher. 
Bibliography
Overview: Physics of Magnetic Resonance Microscopy
Magnetic resonance microscopy (MRM) is founded on the same physical principles as its
clinical cousin, magnetic resonance imaging (MRI). Two crucial discoveries have made MRI
possible. The 1952 Nobel Prize in Physics was awarded to Felix Bloch of Stanford and
Edward M. Purcell of Harvard for their discovery of nuclear induction. Nuclei with
unpaired nucleons (neutrons or protons) possess a magnetic moment arising from the
angular momentum of these spinning nucleons. The interested reader can find a thorough
quantum mechanical description in several excellent texts (e.g., A. Abragam, The
Principles of Nuclear Magnetism (1978), P.T. Callaghan, Principles of Nuclear Magnetic
Resonance Microscopy (1993)). 
Classical Interpretation
A classical treatment of nuclear magnetic resonance is frequently used to give an
intuitive understanding. Consider the unpaired protons of hydrogen in water. The proton
is a charged particle with angular momentum. When a collection of these protons are
placed in a strong magnetic field, the individual protons try to align with the external
field. The angular momentum causes all of the protons to precess about the magnetic field
much as the child's gyroscope precesses when placed on a pedestal. All the protons
precess at a very explicit frequency, the Larmor frequency , given by the equation 
where is a constant. Because the collection is precessing in synchrony at , the vector
components parallel to the magnetic field B0 add to each other to generate a net
magnetization M which also precesses at . Measuring the effect on a single proton would
be very difficult because the magnitude is so small. Because M is the sum of many protons
acting synchronously, it is large enough to measure. If an additional magnetic field B1
is applied at this same frequency, M can be forced away from the longitudinal (z) axis
into the transverse plane. But once in the transverse plane, M continues to precess. As
it does so, it will cause a time varying signal (at the Larmor frequency) in any loop of
wire (antenna) through which M passes. This is the nuclear induction, which forms the
basis for nuclear magnetic resonance. 
Spatial Encoding for MR Microscopy
Spatial encoding for MR microscopy is founded on the same fundamental principle as
MRI-the use of magnetic gradients to encode nuclear magnetic signals. In a typical
two-dimensional study, a gradient applied along the longitudinal (z) axis of the subject
defines a slice that is selectively excited by the simultaneous application of a resonant
radiofrequency (rf) pulse. Subsequent rf pulses and gradients are employed to generate
and encode the signal in the selected slice, typically yielding a 256 x 256 digital
array, with each element of the array representing the signal from an element of tissue
volume (voxel) within the slice. 
Resolution in MR Microscopy 
The resolution in an MR image must be defined on a volumetric basis. A standard clinical
study such as that shown in (A) of a human brain imaged at 1.5 Tesla employs a 5 mm-thick
slice with an in-plane field of view of ~ 250 x 250 mm. Each discrete picture element
(pixel) represents the signal from a 1 x 1 x 5 mm volume, i.e., a 5 mm3 voxel (volume
element) of tissue. 
Images B-D are derived from a 3D MRM acquisition of a formalin-fixed rat brain imaged at
9.4 Tesla by averaging adjacent pixels. The calculated images B & C demonstrate the
consequences of limited resolution on definition of brain architecture in the smaller rat
brain. 
The resolution in B is comparable to the clinical scan of the human brain. It is made by
averaging adjacent pixels from the original (high resolution) isotropic 3D array to
produce voxel dimensions the same as the clinical scan (A) in a rat brain image. Image C,
averaged to produce 64 times higher resolution than the human image (0.25 x 0.25 x 1.25
mm = 0.078 mm3), is still a poor depiction of the anatomy. The anatomy is seen more
clearly in D (.086 x.086 x .086 mm = .00064 mm3), which is ~ 8000 times higher resolution
than the images in A and B. Image D is one slice from the original 3D MR microscopy study
of 256 slices. MR microscopic techniques allow volume imaging at this resolution and
higher.