Pre-treatment patient-specific stopping power by combining list-mode proton radiography and x-ray CT

The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining (1) pre-treatment x-ray CT and (2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin( ##IMG## [http://ift.tt/2woE9a6] {$\Vert {\bf A}{\bf x}-{\bf b}\Vert _2^2$} )). The parameter A represents the cumulative path-length crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness/physical thickness) are denoted by x . The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linear-solver with ##IMG## [http://ej.io...] {${\bf x}\geqslant0$}

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