Proposal of a consistent value for the mean excitation energy of liquid water using advanced modeling, detailed simulations and precission proton Bragg curves

Abstract

Protontherapy precision depends on accurately knowing the stopping power of liquid water, as it is the most abundant component of soft body tissues. Difficulties when working with volatile liquids have led to a long-standing debate regarding the values of the stopping power and the mean excitation energy $I$ of liquid water. The equivalence between the stopping power of liquid water and amorphous ice per unit mass density across all clinically relevant proton energies opens the possibility to obtain a reliable estimation of the $I$-value of liquid water. In this work, we employ two complementary theoretical methodologies to assess the proton stopping power of water. The MELF-GOS (Mermin Energy Loss Function - Generalized Oscillator Strengths) approach, based on the perturbative dielectric formalism, serves as an accurate reference for sufficiently high energies, while the novel non-perturbative TDDFT-Penn (time-dependent density functional theory - Penn) method ensures accuracy for energies even below the stopping maximum. These stopping-power values were incorporated into the simulation code SEICS (Simulation of Energetic Ions and Clusters through Solids) to evaluate proton Bragg curves from $1$ to $230$ MeV. Comparisons with available precise depth-dose measurements provide critical insights that help establish the consistent value $I = 79.4$ eV for liquid water, providing robust physical grounds for improving range prediction for treatment planning.