# Calculating Voxel Size

x = FOV_{x}/N_{x}

y = FOV_{y}/N_{y}

z = the slice thickness (for 2D imaging) or z = FOV_{z}/N_{z} (for 3D imaging)

where FOV is field-of-view and N is the acquisition matrix size in a particular direction.

You have to be a little careful if a scan percentage (aka *phase resolution*) of less than 100% is applied. In this case, fewer lines of *k*-space are acquired in the phase encoding direction. Lines furthest away from the centre of *k*-space are not acquired and are "zero-filled" instead. (This is performed so that *k*-space is symmetrical. See the *k*-space Q&A.) This leaves us in a dilemma: do we quote the *acquired* pixel size, as per the equations stated above, or the *reconstructed* pixel size, which is smaller in the phase-encoding direction, because of the zero-filling? The acquired pixel size (sometimes called the Fourier pixel size) is more informative because it communicates the true limitations of the pulse sequence.

If you are describing a pulse sequence, make sure all relevant data is quoted so that there is no confusion: FOV, acquisition matrix, scan percentage, reconstruction matrix, whether partial Fourier is used, and maybe even the actual number of *k*-space lines acquired.

Here are two helpful rules to get your head around problems like these:

- The
*line spacing*in k-space is inversely proportional to the*FOV*in real space. - How "
*far out*" we acquire data in k-space is inversely proportional to the*resolution*in real space.

### A Worked Example (on a Philips scanner):

These data parameters are entered at the console:

FOV: 380mm, RFOV†: 90%, scan matrix: 240, scan percentage: 70%.

- FOV
_{frequency}= 380mm. - Scan matrix
_{frequency}= 240. - Pixel size
_{frequency}= FOV_{frequency}/Scan matrix_{frequency}= 380/240 = 1.58mm.

- FOV
_{phase}= FOV*RFOV = 380*0.9 = 342mm. - Scan matrix
_{phase}= scan matrix*RFOV*scan percentage ‡ = 240*0.9*0.7 = 151. - Pixel size
_{phase}= FOV_{phase}/Scan matrix_{phase}= 342/151 = 2.26mm

†Note that RFOV affects both FOV and matrix in the phase encoding direction, and so has no net effect on the pixel size. It simply saves time because fewer lines are acquired. RFOV is also known as phase FOV (pFOV).

‡Partial Fourier (aka 0.5 NEX, or halfscan) has no effect on acquired resolution.

Further reading on this topic:

Books: MRI From Picture to Proton p55, Q&A in MRI p92-95