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Abstract
This paper is devoted to a theory of the NMR signal behavior in biological tissues
in the presence of static magnetic field inhomogeneities. We have developed an approach
that analytically describes the NMR signal in the static dephasing regime where diffusion
phenomena may be ignored. This approach has been applied to evaluate the NMR signal
in the presence of a blood vessel network (with an application to functional imaging),
bone marrow (for two specific trabecular structures, asymmetrical and columnar) and
a ferrite contrast agent. All investigated systems have some common behavior. If the
echo time TE is less than a known characteristic time tc for a given system, then
the signal decays exponentially with an argument which depends quadratically on TE.
This is equivalent to an R2* relaxation rate which is a linear function of TE. In
the opposite case, when TE is greater than tc, the NMR signal follows a simple exponential
decay and the relaxation rate does not depend on the echo time. For this time interval,
R2* is a linear function of a) volume fraction sigma occupied by the field-creating
objects, b) magnetic field Bo or just the objects' magnetic moment for ferrite particles,
and c) susceptibility difference delta chi between the objects and the medium.