An exact form for the magnetic field density of states for a dipole

Magn Reson Imaging. 2001 Sep;19(7):1017-23. doi: 10.1016/s0730-725x(01)00422-2.


We present an analytical form for the density of states for a magnetic dipole in the center of a spherical voxel. This analytic form is then used to evaluate the signal decay as a function of echo time for different volume fractions and susceptibilities. The decay can be considered exponential only in a limited interval of time. Otherwise, it has a quadratic dependence on time for short echo times and an oscillatory decaying behavior for long echo times.

Publication types

  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Humans
  • Magnetic Resonance Imaging / methods*
  • Magnetics
  • Physical Phenomena
  • Physics