area under the phase encoding gradient in MRI I have a question about how I could compute the area (duration and amplitude) for the phase encoding gradient in a typical MRI gradient echo sequence. So, let us assume that my field of view in the phase-encode direction is 20 cms and I have a k-space matrix of size 256. From the tutorial here, I can see that the k-space spacing is $1/20e-3$ per meter. Let us also assume that the maximum gradient strength I can achieve is 10mT/m. 

I am now stuck and not sure how I can compute the area that I need under the phase encode area. I am aware that the area will change at each phase encoding step and at least from the pulse sequence diagrams that I see for a GE sequence, it seems that the amplitude is adjusted (going for negative max to positive max) and the gradient time is kept constant during each phase encode step.

However, I am at a loss as to how to compute this area?
Actually, it is as simple as the frequency encoding gradient. Both encoding gradients look terribly different, but in the end they work the very same way.


The outer $k$-space position $k_\textrm{max}$ is related to your resolution, e.g. $1\,\textrm{mm}$, or in terms of the FOV: $FOV/N$ where $N$ is the number of image pixels.
For the steps between two $k$-space lines, $\Delta k = 1/FOV$


With $k(t) = \frac{\gamma}{2\pi}\int_0^t G(t^\prime)\,\textrm{d}t^\prime$ you can find that for the largest gradient moment $M_\textrm{max} = \frac{\pi(N-1)}{\gamma FOV}$. The steps in between scale this down linearly. 

Pay attention to the line numbering, because the central line in $k$-space should be acquired with zero gradient moment.