Concept of proton radiography using energy resolved dose measurement

Energy resolved dosimetry offers a potential path to single detector based proton imaging using scanned proton beams. This is because energy resolved dose functions encrypt the radiological depth at which the measurements are made. When a set of predetermined proton beams 'proton imaging field' are used to deliver a well determined dose distribution in a specific volume, then, at any given depth x of this volume, the behavior of the dose against the energies of the proton imaging field is unique and characterizes the depth x. This concept applies directly to proton therapy scanning delivery methods (pencil beam scanning and uniform scanning) and it can be extended to the proton therapy passive delivery methods (single and double scattering) if the delivery of the irradiation is time-controlled with a known time-energy relationship. To derive the water equivalent path length (WEPL) from the energy resolved dose measurement, one may proceed in two different ways. A first method is by matching the measured energy resolved dose function to a pre-established calibration database of the behavior of the energy resolved dose in water, measured over the entire range of radiological depths with at least 1 mm spatial resolution. This calibration database can also be made specific to the patient if computed using the patient x-CT data. A second method to determine the WEPL is by using the empirical relationships between the WEPL and the integral dose or the depth at 80% of the proximal fall off of the energy resolved dose functions in water. In this note, we establish the evidence of the fundamental relationship between the energy resolved dose and the WEPL at the depth of the measurement. Then, we illustrate this relationship with experimental data and discuss its imaging dynamic range for 230 MeV protons.