In a normal MR image, the image intensity is obtained by measuring the NMR signal corresponding to each tissue location. In the presence of an external magnetic field, the local nuclear spins sum to provide the tissue magnetization. Application of an RF pulse of a specific power and frequency content leads to absorption of energy by the spin system, and the magnetization is rotated by 90 degrees, into the transverse plane, where it precesses and induces a signal in a coil around the sample. In the process of returning to the original orientation (this process is known as relaxation), a coil measures the local generated signal for spin-echo images. The detected signal is a function of tissue relaxation parameters, as well as the local proton density, and may be described analytically as:
where is the system gain, and
is the equilibrium
magnetization.
and
are the tissue relaxation parameters, and
and
are imaging parameters.
In a tagged MR image, a series of selective RF pulses are applied prior to the conventional imaging protocol decribed above, rotating the tissue magnetization. The aggregate effect of the pulse sequences gives the following expression for the tag intensity:
In (2) , is the flip-angle, and
is the time between application of
the tag and the imaging pulse sequence.
As in Guttman [6],
we simulate the Bloch equations for
the MR imaging process, and
obtain a sequence of tag profiles as a function
of time.
The tag profiles approximate
inverted Gaussian functions which undergo
tissue relaxation,
becoming less visible in later phases of
the heart cycle (fig. 1). In these simulations the following
parameters were used: duration of tag pulse was
msec, Gyromagnetic Ratio was
HZ/G,
gradient strength was
G/mm,
sec,
and
sec.
The RF pulse had the following form:
where is a sinc pulse,
is the Hamming window, and
G.