KAHIBARO
35.4. Bragg Peak
Table of Contents
Depth-dose distribution
In proton therapy, the term Bragg peak refers to the sharp maximum in dose that appears near the end of the proton track. To see this feature clearly, you look at the depth-dose distribution in a medium such as water, which is a good approximation of soft tissue.
A depth-dose distribution is obtained by scoring absorbed dose as a function of depth along the proton beam axis. In practice, you define a phantom that is large enough to contain the entire proton track and attach a dose actor that records dose in thin slabs or voxels along the beam direction. After the simulation, you typically sum or average the dose over the transverse dimensions, so you obtain a one-dimensional curve: dose $D(z)$ versus depth $z$.
For a monoenergetic, narrow proton beam in water, this curve has a characteristic shape. Near the entrance surface, there is a relatively low, almost flat entrance region where the dose increases slowly with depth. As protons slow down, their stopping power increases and energy loss per unit path length becomes larger. This produces a rapid rise in dose and a pronounced maximum close to the point where most protons stop. That sharp maximum is the Bragg peak. Beyond the peak, dose falls off very steeply because few primary protons traverse further depth and only a small tail from secondary particles remains.
The rise and fall around the Bragg peak are governed by electromagnetic stopping power and by range straggling. Stopping power increases as protons decelerate, while range straggling causes a small spread in the depths where individual protons stop. Nuclear interactions also contribute, since some protons undergo nonelastic reactions and drop out of the primary beam before reaching the nominal peak, while secondaries create a low-dose tail beyond the peak.
In a GATE simulation, the depth-dose distribution is controlled by several choices. The proton energy determines the depth at which the peak appears. The phantom size and scoring resolution affect how clearly you can see the peak and how accurately you sample its position and shape. Proton physics models and production cuts influence the contribution from secondary particles and therefore the distal tail.
To extract a clean depth-dose curve from GATE, you usually proceed in three steps. First, configure a one-dimensional or three-dimensional dose actor covering the relevant part of the phantom, with voxel sizes small enough to resolve the narrow Bragg peak, often on the order of a millimeter or less in depth. Second, run a sufficient number of primary protons so that statistical fluctuations are small, particularly near the peak. Third, after the simulation, integrate or average the dose laterally to obtain $D(z)$ and normalize it, for example to the peak value or to entrance dose, so that curves from different energies or configurations can be compared.
The result is a depth-dose curve that clearly displays the Bragg peak and the rapid distal falloff, which are fundamental for understanding how proton beams deliver dose in radiotherapy.
The Bragg peak is the sharp maximum in the proton depth-dose curve that occurs near the end of the proton range, followed by a steep distal falloff in dose.
Proton range
The proton range is the average depth at which protons stop in a given material for a given initial energy. In water, range is often quoted in centimeters and is a key parameter in proton therapy planning. The Bragg peak appears close to the end of this range, so determining proton range from a simulated or measured depth-dose distribution is central to Bragg peak analysis.
There are several practical definitions of proton range. One common choice is the depth of the distal 80 percent point, often called $R_{80}$, which is the depth where the dose on the falling edge of the Bragg curve has dropped to 80 percent of the peak value. Another is the depth where the dose falls to 50 percent of the peak. The continuous slowing down approximation (CSDA) range is a theoretical quantity based on the integral of the inverse stopping power, but it is not measured directly. In a GATE simulation, you usually work with $R_{80}$ or a similar operational definition derived from the dose distribution.
To obtain the proton range in GATE, you first compute the depth-dose curve as described above. Then you determine the peak dose value, $D_{\text{max}}$, and search along the distal side of the peak for the depth where $D(z)$ reaches a chosen fraction of $D_{\text{max}}$, for example $0.8 D_{\text{max}}$ for $R_{80}$. Interpolation between depth points is usually necessary if your scoring voxels are thicker than a fraction of a millimeter. This procedure yields a numerical estimate of the range directly from the simulated data.
Analytical and tabulated data for proton range in water are available from reference sources like ICRU reports or stopping power tables. In validation studies, you compare the range obtained from your GATE simulation with these reference values. A good agreement, typically within a millimeter or better depending on beam energy and setup, indicates that your physics models, material definitions, and geometry configuration correctly reproduce proton transport.
The sensitivity of range to simulation parameters is a major reason to treat it carefully. Small changes in material density or composition can shift the range, as can inaccuracies in CT-to-material conversion when using patient geometries. Physics list choices and production cuts can also affect range slightly, particularly if they alter how nuclear interactions or low energy processes are handled.
In treatment applications, you seldom use a single pristine Bragg peak. Instead, you create a spread-out Bragg peak by combining several beams of different energies, each with its own Bragg peak at a different depth, in order to obtain a relatively uniform dose over a target volume. Nevertheless, the underlying concept remains the individual proton range for each energy. In GATE, simulating a set of monoenergetic beams and verifying the range for each is a standard step in validating a proton therapy model.
Proton range is therefore the quantitative link between the physical energy of the beam and the spatial position of the Bragg peak. By extracting it accurately from simulated depth-dose curves, you can assess how well your model reproduces proton transport and you can use that information to design and validate clinically relevant proton therapy simulations.
Proton range in a medium is defined from the depth-dose curve. A common definition is $R_{80}$, the depth on the distal side of the Bragg peak where the dose falls to 80% of the peak value.
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