# Accuracy of parameterized proton range models; a comparison

## TL;DR

This paper compares four parameterized models for calculating proton ranges, finding that spline interpolation offers the highest accuracy and the differentiated Bragg-Kleeman equation best reproduces the energy loss curve.

## Contribution

It provides a systematic comparison of different proton range models, highlighting the most accurate methods for clinical and imaging applications.

## Key findings

- Spline interpolation yields highest accuracy
- Differentiated Bragg-Kleeman best reproduces energy loss curve
- Analytical models from Bethe equation are less accurate

## Abstract

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy four different parameterizations models: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation.

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Source: https://tomesphere.com/paper/1704.08854