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See more information about the problems in Class Notes Lecture 5 |
Problem 0 - Imaging on Cylinder
Flow is along y-axis
What are the acquired image and the velocity, position, diffusion signatures?
Problem 1 - Periodic
- Show that for average over φ, we get pure absorptive line-shape, and for a particular isochromat, average over φ in general has dispersive line-shape (Show the response in cylindrical coordinate)
- Normal shim: x,y (first order spherical harmonic). Show that if there are terms x^2-y^2, xy, then the sideband will show up at twice Ω
- Calculate the FID and the spectrum for rotary vs non-rotary, then plot them on top of each other
Problem 2 - Chemical Shift
- Show that chemical shift tensor
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see [Class Notes Lecture 5] for now h4. Problem 0 - Imaging on Cylinder Flow is along y-axis !p01.jpg! !p02.jpg! What are the acquired image and the velocity, position, diffusion signatures? \\ h4. Problem 1 - Show that for average over φ, we get pure absorptive line-shape, and for a particular isochromat, average over φ in general has dispersive line-shape (Show the response in cylindrical coordinate) - Normal shim: x,y (first order spherical harmonic). If there are terms x^2-y^2, xy, then the sideband will show up at twice Ω - Calculate the FID and the spectrum for rotary vs non-rotary, then plot them on top of each other \\ h4. Problem 2 - Show that chemical shift tensor \\ {latex} $\sigma = \sigma_{iso} + (\frac{\sigma}{2})(3 cos^{2}\theta -1)- \frac{\delta^{eta}}{4}sin^{2}\theta(e^{i2\phi}+e^{-i2\phi})$ {latex} \\ {latex} |
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$\sigma_{iso}=(\sigma_{xx}+\sigma_{yy}+\sigma_{zz})/3$
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{latex} \\ {latex} $\delta=\frac{2}{3}\sigma_{zz}-\frac{1}{3}(\sigma_{xx}+\sigma_{yy})$ { |
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} \\ {latex} $\eta=3(\sigma_{yy}-\sigma_{xx})/2(\sigma_{zz}-\sigma_{xx}-\sigma_{yy})$ {latex} \\ - Show that under random rapid motion spins \\ {latex |
- Show that under random rapid motion spins
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}$< \sigma > = \sigma _{iso}${latex} \\ It average out any |
It average out any non-isometric
...
parts,
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so
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we
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have
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a
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homogeneous
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sample.
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So
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the
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does
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not
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the
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orientation
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of
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When
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- ;
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- calculate
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- the
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- for
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- Find σ(θ,φ),
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- (when
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Problem 3 - Decoherence
- What is the contribution of the chemical shift anisotropy to T2?
Problem 4 - Carl-Purcell Sequence
- Look at diffusive attenuation of water rotating in magnetic field gradient. Show that the faster you rotate it, the effective T2 is approaching T2.
Problem 5 - Chemical Exchange
- Show the plot of the chemical exchange (when τ|ΔωA-ΔωB| approaching 1, the 2 peaks merge at the center) [Hint: check out appendix F]
Problem 6 - Slow Exchange
- Show that by collect this terms in slow exchange
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\\
h4. Problem 3
- What is the contribution of the chemical shift anisotropy to T2?
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h4. Problem 4
- Look at diffusive attenuation of water rotating in magnetic field gradient. (The faster you rotate it, the effective T2 is approaching T2)
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h4. Problem 5
- Show the plot of the chemical exchange (when τ\|ΔωA-ΔωB\| approaching 1, the 2 peaks merge at the center) \[Hint: check out appendix F\]
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h4. Problem 6
- Show that by collect this terms in slow exchange
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$e^{i\omega_{A}t_{1}}e^{i\omega_{A}t_{2}} , e^{i\omega_{A}t_{1}}e^{i\omega_{B}t_{2}} , e^{i\omega_{B}t_{1}}e^{i\omega_{A}t_{2}} , e^{i\omega_{B}t_{1}}e^{i\omega_{B}t_{2}}$
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then do phase cycle and collect data set
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{latex} \\ then do phase cycle and collect data set \\ {latex} $cos(\omega_{A/D}T_{1})e^{i\omega_{A/D}t_{2}} , sin(\omega_{A/D}T_{1})e^{i\omega_{A/D}t_{2}}$ {latex} \\ Then we get pure absorptive |
Then we get pure absorptive line-shape