# Religion And The Changes Through The Years

Essay, Research Paper

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.

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.

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