Hosaka-Cohen Transformation
Encyclopedia
Hosaka-Cohen Transformation (also called H-C transformation) is a mathematical method of converting a particular two-dimensional scalar magnetic field map to a particular two-dimensional vector map. The scalar field map is of the component of magnetic field which is normal to a two-dimensional surface of a volume conductor; this volume conductor contains the currents producing the magnetic field. The resulting vector map, sometimes called “an arrowmap” roughly mimics those currents under the surface which are parallel to the surface, which produced the field. Therefore, the purpose in performing the transformation is to allow a rough visualization of the underlying, parallel currents.
The transformation was proposed by Cohen and Hosaka of the Biomagnetism
group at MIT, then was used by Hosaka and Cohen to visualize the current sources of the magnetocardiogram.
Each arrow is defined as
where z of the local x, y, z coordinate system is normal to the volume conductor surface, x-circumflex and y-circumflex are unit vectors, and Bz is the normal component of magnetic field. This is a form of 2-dimensional gradient of the scalar quantity Bz and is rotated by 90 degrees from the conventional gradient.
Almost any scalar field, magnetic or otherwise, can be displayed in this way, if desired, as an aid to the eye, to help see the underlying sources of the field.
The transformation was proposed by Cohen and Hosaka of the Biomagnetism
Biomagnetism
Biomagnetism is the phenomenon of magnetic fields produced by living organisms; it is a subset of bioelectromagnetism. The study of the biological effects of magnetic fields is magnetobiology...
group at MIT, then was used by Hosaka and Cohen to visualize the current sources of the magnetocardiogram.
Each arrow is defined as
where z of the local x, y, z coordinate system is normal to the volume conductor surface, x-circumflex and y-circumflex are unit vectors, and Bz is the normal component of magnetic field. This is a form of 2-dimensional gradient of the scalar quantity Bz and is rotated by 90 degrees from the conventional gradient.
Almost any scalar field, magnetic or otherwise, can be displayed in this way, if desired, as an aid to the eye, to help see the underlying sources of the field.
Further reading
- Koch, H. (2004) Recent advances in magnetocardiography. Journal of Electrocardiology 37: 117-122.
See also
- BiomagnetismBiomagnetismBiomagnetism is the phenomenon of magnetic fields produced by living organisms; it is a subset of bioelectromagnetism. The study of the biological effects of magnetic fields is magnetobiology...
- BioelectromagnetismBioelectromagnetismBioelectromagnetism refers to the electrical, magnetic or electromagnetic fields produced by living cells, tissues or organisms. Examples include the cell membrane potential and the electric currents that flow in nerves and muscles, as a result of action potentials...
- David Cohen (physicist)David Cohen (physicist)David Cohen is known mostly for his pioneering work in the area of Biomagnetism , where he made many of the first measurements....
- ElectrophysiologyElectrophysiologyElectrophysiology is the study of the electrical properties of biological cells and tissues. It involves measurements of voltage change or electric current on a wide variety of scales from single ion channel proteins to whole organs like the heart...
- Magnetic fieldMagnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
- MagnetocardiographyMagnetocardiographyMagnetocardiography is a technique to measure the magnetic fields produced by electrical activity in the heart using extremely sensitive devices such as the Superconducting Quantum Interference Device...
- MagnetometerMagnetometerA magnetometer is a measuring instrument used to measure the strength or direction of a magnetic field either produced in the laboratory or existing in nature...