N-D Imaging and Sequence Diagrams

• think of a 3D data set being made up of $N^{3}$ points $N_{x} \cdot N_{y} \cdot N_{z}$ where for now $N_x \equiv N_y \equiv N_z$
• due to transverse relaxation, historically have only had time to collect a single line of data ($N_x$ points) following each excitation. (IN-CLASS QUESTION)
• repeat the experiment $N_{y} \cdot N_{z}$ times to get all data.
• sequence diagram describes how we move about to collect these points
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  • area under each gradient determines location in $k$-space

  • if apply identical gradients again, will collect same line of $k$-space data.

  • in order to collect different $k$-space data need to vary the area of $G_{y}$ or $G_{z}$ gradients

  • gradients which are turned off before ADC comes on for sampling are generally referred to as ``phase encode'' gradients because they impart some phase that is constant during sampling

  • common name for phase encode gradient applied in the plane of the resulting image called phase encode, or primary phase encoding gradient

  • common name for phase encode gradient applied perpendicular to the plane of the displayed image called partition encode, or secondary phase encoding gradient

  • $k$-space step size in phase encode directions is conventionally determined by how much we change the PE gradient amplitude between repetitions of the experiment
    $$\begin{eqnarray*} \Delta k_y \equiv \Delta k_{PE} = \gamma \!\!\!\!\!-\Delta G_y \tau_y \equiv \gamma \!\!\!\!\!-\Delta G_{PE} \tau_{PE} \end{eqnarray*}$$
    
    
    
    
    

  • refer to gradient that is on during sampling as the read or frequency encoding gradient. Think of sampling in terms of time points we pick off at certain interval given by $\Delta t$, that relates to $k$-space spacing given by
    $$\begin{eqnarray*} \Delta k_x \equiv \Delta k_{R} = \gamma \!\!\!\!\!-G_x \Delta t \end{eqnarray*}$$
    
    
    
    
    

  • each time the experiment is repeated, the phase encode gradients are changed to cover different lines of $k$-space.

  • should always identify the PE and RD directions in images that you view

• under ideal conditions (no noise, no motion, no relaxation, no field issues, no frequency aliasing) phase encoding and frequency encoding are identical processes, but practically, this is not the case!

  
  
  
  
  
  
  
  

• shorthand for altering phase encode gradients is to draw them with many lines on a single sequence diagram(IN-CLASS QUESTION)

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• How long does experiment take??? (IN-CLASS QUESTION)
  $$\begin{eqnarray*} T_{T} &=& \mbox{Number of times experiment is performed} \cdot T_{R} \nonumber\\ &=& N_{y} \cdot N_{z} \cdot T_{R} \end{eqnarray*}$$