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Copy file name to clipboardExpand all lines: teaching-sequence-sims.html
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<xmptheme=spacelabstyle=display:none;>
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# RF pulse design and simulations: supplementary animations
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### Steady state calculations
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In lectures we derived a steady-state relationship for an SSFP sequence, which can be illustrated as below for a particular set of tissue and sequence parameters:
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<imgsrc="images/ssfp_plot.png" width="70%">
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We can pick out some of these and animate the motion of a magnetization isochromat depending on the off-resonance dephasing angle (per TR) \\(\psi\\):
In the diagram above the isochromats are spead out in the direction of the applied gradient - this is a physically realistic picture. We may also draw the vectors on top of one another so that we can directly compare their directions:
You see that there are **spurious echoes** when all the magnetisation vectors are aligned. This is unphysical, and these disappear when the number of isochromats is increased. For example, using 100 isochromats:
Magnetisation as a function of space (gradient induced phase offset) and then also as a function of k - the Fourier conjugate variable. This is a simple sequence of RF pulses and gradients
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Magnetisation as a function of space (gradient induced phase offset) and then also as a function of k - the Fourier conjugate variable. This is a simple sequence of RF pulses and gradients. We can see that RF pulses have the effect of rotating all isochromats, while gradients add a rotation that varies over the voxel.
As time goes by, the number of non-zero Fourier terms needed to describe the magnetisation increases. This is because each successive gradient period adds new k-space terms to the mix.
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Here again we see that the RF pulse mixes Mx, My, Mz but doesn't change the spatial modulation while the gradients do. In the Fourier domain we see that RF pulses mix up coefficients *of a given spatial order*, whereas gradients shift to higher order coefficients.
# RF pulse design and simulations: supplementary animations
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### Steady state calculations
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+
In lectures we derived a steady-state relationship for an SSFP sequence, which can be illustrated as below for a particular set of tissue and sequence parameters:
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+
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<imgsrc="images/ssfp_plot.png"width="70%">
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+
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We can pick out some of these and animate the motion of a magnetization isochromat depending on the off-resonance dephasing angle (per TR) \\(\psi\\):
In the diagram above the isochromats are spead out in the direction of the applied gradient - this is a physically realistic picture. We may also draw the vectors on top of one another so that we can directly compare their directions:
You see that there are **spurious echoes** when all the magnetisation vectors are aligned. This is unphysical, and these disappear when the number of isochromats is increased. For example, using 100 isochromats:
Magnetisation as a function of space (gradient induced phase offset) and then also as a function of k - the Fourier conjugate variable. This is a simple sequence of RF pulses and gradients
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Magnetisation as a function of space (gradient induced phase offset) and then also as a function of k - the Fourier conjugate variable. This is a simple sequence of RF pulses and gradients. We can see that RF pulses have the effect of rotating all isochromats, while gradients add a rotation that varies over the voxel.
As time goes by, the number of non-zero Fourier terms needed to describe the magnetisation increases. This is because each successive gradient period adds new k-space terms to the mix.
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+
Here again we see that the RF pulse mixes Mx, My, Mz but doesn't change the spatial modulation while the gradients do. In the Fourier domain we see that RF pulses mix up coefficients *of a given spatial order*, whereas gradients shift to higher order coefficients.
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