Selecting a Slice or Slab of Spins

• have established that doing 3D imaging can take a long time, want to determine if we can select a single 2D slice of data, or at least a smaller 3D volume to work on

• again apply the concept of applying a linear gradient to ``spread'' the Larmor frequency of the spins being imaged

• Design an input rf pulse, that has a finite frequency spread, or $BW_{rf}$. Only those spins whose Larmor frequency of the input rf should be excited by the transmit pulse

• Goal is to produce uniform spin-density, i.e., would like a pulse that uniformly excites the slice or slab. Uniform excitation in frequencies corresponds to a sinc shaped pulse in the time domain.

• Finally find relationship between $BW_{rf}$ and the thickness of the excited region $TH$
  $$\begin{eqnarray*} BW_{rf} &\equiv& \Delta f \nonumber\\ &=& (\gamma \!\!\!\!\!... ...\!\!-G_z TH/2) \nonumber\\ &\equiv& \gamma \!\!\!\!\!-G_{ss} TH \end{eqnarray*}$$
  
  
  
  
  

• Understand the distribution of frequencies desired, what does this imply about the excitation pulse
  $$\begin{eqnarray*} B_1(t) \propto \mbox{sinc} (\pi\Delta f \; t) \end{eqnarray*}$$
  
  
  
  
  
  need to get reasonably good representation of the sinc function. Effectively, response improves as the number of cycles in the pulse increases
  $$\begin{eqnarray*} n_{zc} = [\tau_{rf}/t_1] = [\Delta f\; \tau_{rf}] \end{eqnarray*}$$
  
  
  
  
  
  (IN-CLASS QUESTION)

• to select subsequent slices change the demodulation frequency
  
  

  
  
  
  
  
  
  
  

• through this process, can select a slab of spins out of a 3D volume. Generally treat thin slab of spins as a 2D slice. Should not forget that 2D image is made of spins from slice with thickness $TH$. By convention in the book, $TH$ refers to the thickness of the excited slab, and $\Delta z$ refers to the thickness of a smaller partition out of a 3D data set.

• practical slice select process looks like
  
  

• think of bulk of spins as being tipped at $t=0$. therefore, they are tipped into the transverse plane while gradient is still being applied, and they begin to dephase before the end of the rf pulse

• therefore, need to refocus them, similar to making a gradient echo along the slice select direction, get all spins back to $\phi = \phi_{0}$ independent of $z$-position

• by applying different gradients during slice-select process can re-orient the slab arbitrarily