Relative Signal Strength

An interesting question is why do we choose to image $^1$H? Of course, water is very important to humans, but there may be many other nuclei that give equally important physiological information.

• from last lecture and HW remember that the magnetization that we measure is proportional to
  $$\begin{eqnarray*} M_{0_{i}} \propto a_{i} s_{i}(s_{i}+1)\gamma_{i}^{2} \end{eqnarray*}$$
  
  
  
  
  
  where $a_{i}$ is the natural abundance of the nucleus

• plugging the above expression into one of our signal expressions, one finds that
  $$\begin{eqnarray*} {\rm signal} \propto \vert\gamma_i\vert^{3} a_{i}s_{i}(s_{i}+1) \end{eqnarray*}$$
  
  
  
  
  

• if you also consider that in a body, each nucleus has a relative abundance $r_{i}$ (for example $r_{13C} = number_{13C}/number_{13C\;and\;14c}$ we find
  $$\begin{eqnarray*} {\rm signal} \propto \vert\gamma_i\vert^{3} r_i a_{i}s_{i}(s_{i}+1) \end{eqnarray*}$$
  
  
  
  
  

• $^1$H has a high gyromagnetic ratio, overwhelming natural abundance, and effectively 100% relative abundance in our bodies. (IN-CLASS PROBLEM)

• in short, it's our best bet for imaging.

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