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Docteur de l'université Automatic Segmentation and Shape Analysis ...

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Chapter 1 Introduction 11<br />

B0. The rotation of the transverse magnetization induces voltage in the receiving<br />

coil which turns into electric signal.<br />

Because of the spin-lattice interaction, the rf signal <strong>de</strong>cays as the magnetization<br />

tend to re-align to the direction of the static field B0. The <strong>de</strong>cay is characterized<br />

by the spin-lattice relaxation time T1. The interacting nuclei of different spin state<br />

lead to the spin-spin relaxation, in which the individual spins fan out, or <strong>de</strong>phase,<br />

<strong>and</strong> the net transverse component of magnetization <strong>de</strong>creases at a rate controlled<br />

by the spin-spin relaxation time T2. In practice the magnetization un<strong>de</strong>rgoes T ′ 2<br />

relaxation due to the inhomogeneities in the external magnetic field. The overall<br />

T ∗ 2 <strong>de</strong>cay is combined effect of T2 <strong>and</strong> T ′ 2. The values of T1 <strong>and</strong> T2 <strong>de</strong>pend on the<br />

physical property of the material, which varies among the population according<br />

to the tissue type <strong>and</strong> condition.<br />

The suppression caused by field inhomogeneities can be avoi<strong>de</strong>d by an additional<br />

flip of spins by π using rf pulses, creating an ‘echo’ of the signal. By tuning the<br />

interval TR over which the recovered longitudinal magnetization is periodically<br />

tipped to the transverse plane by the rf pulse, <strong>and</strong> the echo time TE when the<br />

echo is <strong>de</strong>tected, the result images displays different forms of contrast. A T1<br />

weighted image acquired with TR ≤ T1, <strong>and</strong> TE relatively short to T2 highlights<br />

the differences in T1 within the sample, while the T2 weighted image produced by a<br />

setting of relatively long T1 <strong>and</strong> TE T2 enhances the contrasts between materials<br />

with different T2. With relatively long TR <strong>and</strong> short TE, the spin <strong>de</strong>nsity or proton<br />

<strong>de</strong>nsity weighted image displays only the <strong>de</strong>nsity of spin without contrast in T1 or<br />

T2.<br />

In imaging experiments, a spatial gradient in the magnetic field is used to enco<strong>de</strong><br />

the spins in the sample with varying frequency <strong>and</strong> phase at different location.<br />

The signal acquired is thus in the k-space of wave vector, which is a Fourier<br />

transform of the spatial information. An inverse Fourier transform can be applied<br />

to reconstruct the spatial content from the reciprocal domain of k-space, forming<br />

the image of the sample. A thourough treatment of the subject from its physical

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