Harmonic Phase Images

One of the newest developments in tagged MRI processing leads to dense motion measurements obtained by extracting the phase of the underlying tag pattern. To illustrate, assume a SPAMM sequence with two 90° RF pulses has been applied, for which f0(p) = - cosgTp. Assuming the expression for the deformed tag profile (6) is accurate, the resulting image is

I(y, t) = I0(y, t) [-fi(t) cos(gTp(y, t)) + (1 - p(t))]

In this expression, the phase of the cosine, given by

is directly related to the desired motion map p{y, t). Furthermore, the spatial derivative of t) is related to the deformation gradient by t )=H lF -1g

2harp

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