Optimal beam width and spacing scaling law
In plain words
Choosing stripe width and gap is currently trial and error. A rule connecting them to tissue type and depth is missing.
Precise statement
Derive a scaling relation for the therapeutic ratio as a function of beam width w, centre-to-centre spacing s, and depth, including beam broadening by multiple scattering for protons and by scattered photons for x-rays, so that the pattern merges into a uniform field at the target while staying fractionated in normal tissue. An answer is a design rule for w and s with the physical quantities that set them.
What would settle it
Measured dose profiles at depth combined with tolerance data across several geometries, showing a single relation that predicts the optimum.
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