As the reader is aware, 3D CT images are obtained by collecting 2D slices and then stacking those slices. To determine if pCT is possible, we started by asking how many protons are needed to image a slice. Our calculations showed that, staying within dose limits similar to those received from X-ray CT, there are more than enough protons to image a slice. After stacking in pCT, protons that passed through multiple slices are used to refine the final image.
The calculation starts by considering that each slice contains a number of one millimeter (mm) cubic voxels. For example, a 200mm-by-200mm slice contains 40,000 voxels. We can think of each of these voxels as an unknown variable in a system of algebraic equations. We know that we need at least as many equations as unknowns to solve such a system. We ran the numbers and determined that one can use hundreds of protons, that is equations, for each unknown while limiting the dose absorbed by the patient. In short, with millions of proton trajectory histories there is enough “information”, in the information theory sense of the word, to assure us that pCT is possible.