KAHIBARO
35.5. Spread-Out Bragg Peak
Table of Contents
Multiple energies
A single monoenergetic proton beam deposits most of its energy in a narrow depth region, the Bragg peak. In clinical proton therapy this narrow peak is too sharp to cover a whole tumor volume that extends several centimeters in depth. To irradiate the entire target more uniformly, you combine several proton beams with different initial energies so that their individual Bragg peaks overlap in depth. This superposition creates a flat region of high dose, called the Spread-Out Bragg Peak, or SOBP.
In a GATE simulation, the basic idea is to simulate not one, but a set of proton beams with carefully chosen energies and relative weights. Each energy produces a Bragg peak at a slightly different depth in the phantom. When you sum the resulting depth dose curves, the individual peaks merge into a plateau that covers the desired depth range.
You can implement this in GATE in different ways. One straightforward way is to define several proton sources, each with a fixed energy. For example, you might define sources at 120 MeV, 130 MeV, 140 MeV, and 150 MeV, all entering a water phantom from the same position and direction. For each source you assign a relative activity or particle weight that reflects its contribution to the total beam. In the simulation you then run all these sources together, or in separate runs that you later sum during analysis.
Alternatively, you can use a single proton source with an energy distribution that mimics a clinical beam line, such as a set of discrete energy lines or a user defined energy spectrum. In this case, GATE samples the energy of each proton according to the chosen distribution, so the effective field at the phantom entrance is already a mixture of energies. The resulting depth dose distribution will show a built in SOBP if the spectrum is correctly designed.
To study the SOBP in a beginner friendly way, it is often helpful to first simulate a series of monoenergetic fields and record their depth dose curves with a dose actor in a water phantom. After you have these curves, you can export dose as a function of depth and combine them in Python. By choosing weighting factors for each energy and summing the curves, you can see directly how changing the weights makes the plateau flatter or broader. This post processing approach teaches how SOBPs are built and lets you experiment without modifying the beam line itself.
In clinical practice, instead of separate discrete beams, a physical range modulator or a dynamic energy scanning system produces a continuous SOBP. You can approximate this in GATE either with a sufficiently fine set of discrete energies or by modeling the actual modulator components in the geometry and letting the physics handle the resulting energy spectrum. For an introductory course, the multi energy source approach is usually easier to understand and implement.
The quality of the SOBP depends on the number of energies, their spacing, and the chosen weighting factors. More energy layers with finer spacing generally give a smoother and more uniform plateau but require longer computation times in Monte Carlo. In GATE, you can begin with a small set of energies, inspect the depth dose distribution, and then refine the set or weights to improve uniformity. Because you already know how to create a water phantom and add a dose actor from the previous chapter, you can focus here on changing only the proton beam configuration.
The final SOBP dose profile is simply the sum of the contributions from each energy. If $D_i(z)$ is the depth dose curve from energy $E_i$, and $w_i$ is its relative weight, the total SOBP dose as a function of depth $z$ is
$$
D_{\text{SOBP}}(z) = \sum_{i} w_i \, D_i(z)
$$
The choice of energies $E_i$ and weights $w_i$ determines the width, position, and flatness of the SOBP.
By computing and plotting $D_{\text{SOBP}}(z)$ from your GATE output, you can visually verify that you have produced a proper spread out peak rather than a set of separate Bragg peaks.
Treatment depth
In proton therapy, the aim of creating an SOBP is to cover the entire tumor volume throughout its depth while sparing as much healthy tissue as possible. The treatment depth is the depth range in the patient that needs to receive a prescribed, approximately uniform dose. In a simple water phantom model, you represent this as a depth interval, for example from 10 cm to 16 cm, that should be covered by the SOBP plateau.
To design an SOBP for a given treatment depth, you need to relate proton energy to range. The higher the initial energy, the deeper the Bragg peak appears in water or tissue. For a particular beam line and medium, this relationship can be expressed by a range curve, which can be obtained experimentally or from reference data. In a GATE context, you can approximate it by simulating monoenergetic protons in water and measuring the depth at which the dose falls to a specific fraction of the maximum, such as 80 percent. This depth is often taken as an operational definition of the proton range.
Once you know how range depends on energy, you can choose the highest proton energy so that its Bragg peak falls just beyond the distal edge of the tumor. This sets the distal end of the SOBP. You then add lower energy components whose Bragg peaks fall progressively closer to the entrance surface. The difference between the ranges of the highest and lowest energies gives the nominal width of the SOBP, which should at least match the tumor thickness.
In terms of simulation, you usually represent the patient by a water phantom when you first explore SOBPs. You attach a dose actor with a voxel size in the beam direction that is fine enough to resolve the plateau and the distal fall off. After running the SOBP configuration, you extract a one dimensional depth dose profile along the central axis. The clinically relevant part of this profile is the region where the dose remains within a given tolerance around the prescription, typically within a few percent. You compare this region to your intended treatment depth.
A simple way to quantify how well your SOBP covers the target is to compute the minimum and maximum dose within the target depth range, and normalize them to the prescription dose. If $z_{\text{prox}}$ and $z_{\text{dist}}$ define the proximal and distal edges of the target, you can evaluate
$$
D_{\text{min}} = \min_{z \in [z_{\text{prox}}, z_{\text{dist}}]} D_{\text{SOBP}}(z),
\quad
D_{\text{max}} = \max_{z \in [z_{\text{prox}}, z_{\text{dist}}]} D_{\text{SOBP}}(z).
$$
A well designed SOBP has $D_{\text{min}}$ and $D_{\text{max}}$ close to the prescribed dose throughout the treatment depth.
In GATE, once you have this profile, you can iteratively adjust beam energies and weights to shift or widen the SOBP until the plateau aligns with the desired depth interval. To move the SOBP deeper, you increase the highest energy and shift the whole energy set upward. To shift it shallower, you decrease the highest energy. To widen the SOBP to cover a thicker tumor, you add lower energy components that fill in dose at shallower depths, and tune their weights so that the resulting plateau remains flat.
While simple water phantoms are useful to understand the principle, real patient anatomy is more complex and inhomogeneous. In later chapters on voxelized geometry and patient CT dosimetry, you will see how the same ideas apply in the presence of different tissues and structures. For now, it is enough to recognize that in a homogeneous medium, there is a direct link between the choice of proton energies, their superposition into an SOBP, and the resulting treatment depth that receives uniform dose.
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