Ice instead of water: how to calculate proton range more accurately express
A proton beam aimed at a tumor cuts through soft tissue like a knife through butter, but its range depends on the subtle properties of water, the stuff we're mostly made of. Water is the body's main component, and how quickly protons slow down in it determines exactly where they deposit their energy.
Long-standing debates have hampered efforts to pin down the key number — the mean excitation energy (I): for liquid water, it's hard to measure directly because water evaporates. But amorphous ice (the same water, just frozen into a disordered structure) has a stopping power per unit density that matches liquid water at all proton energies. It's like comparing two recipes for the same dough: same flour, but in one case the batter is runny and in the other it's set, yet it bakes the same.
The authors used two computational methods: one accurate at high energies, the other at low energies, down to the peak of energy loss. Combining them, they obtained reliable stopping-power values and fed them into a program that simulates proton range in tissues. Comparison with precise depth-dose measurements showed that a value of I = 79.4 eV fits best.
Now doctors will have a firmer physical foundation for planning proton therapy. Water, which had always been a nuisance in measurements, has, through ice, shown us how to treat more precisely.
Original abstract
as written by the authors arXiv:2608.15368v1
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.
Amorphous ice is water frozen so quickly that the molecules don't have time to arrange into a crystal lattice. Essentially, it's 'liquid water in a solid state,' and its properties are closer to water than those of the regular ice from your freezer.