34.2. Radiation Dose Simulation

Table of Contents

Understanding Radiation Dose in Geant4

Radiation dose simulation is one of the most common and powerful uses of Geant4 in medical physics. In this chapter the focus is on how to represent dose in a Geant4 model, how it arises from the underlying tracking quantities, and what is specific to medical dose calculations compared with more general energy deposition studies.

Dose, Energy Deposition, and Mass

In Geant4 you never request “dose” directly from the tracking system. The toolkit transports particles and reports energy lost in matter. From this you compute dose by combining deposited energy with the mass of the region of interest.

The basic physical definition of absorbed dose $D$ is

$$
D = \frac{dE}{dm},
$$

where $dE$ is the energy deposited in a mass element $dm$. Geant4 provides you with $dE$ through step quantities, and you determine $dm$ from the geometry and material density.

Key rule: In Geant4, dose is not a built-in quantity. You must compute it from
$$D = \frac{E_{\text{dep}}}{m_{\text{volume}}}.$$

For medical applications, you typically integrate energy deposition over many events and normalize by the mass of a voxel, organ, or other target structure. The result can then be expressed in gray, where $1 \,\text{Gy} = 1 \,\text{J} / \text{kg}$.

From Steps to Dose

At the tracking level, Geant4 reports energy deposition per step through the step object. In a medical dose context, the usual workflow is to accumulate this per region or per voxel and then perform a mass normalization.

For each step, the tracking system provides the total energy deposited $E_{\text{dep, step}}$ in the material during that step, along with the volume in which the step occurred. You typically extract this in a stepping or sensitive detector class, then add it into an accumulator associated with a particular detector element, voxel, or organ label.

Over the course of an event, and then over many events, these accumulators store a sum of deposited energy $E_{\text{dep, total}}$ per region. Once the run finishes, you divide the accumulated energy in each region by its mass to obtain the mean dose in that region.

In medical physics simulations, it is common to choose detector or scoring elements so that they correspond to physically meaningful structures: water voxels in a water phantom, CT voxels in a patient geometry, or specific organs in a computational phantom.

Dose Scoring Concepts

Dose scoring in Geant4 is the process of collecting energy deposition in space and converting it into dose. Several different spatial organizations are used depending on the problem.

A typical medical dose scoring setup defines a 3D grid of small volumes, often called voxels, that cover the region of interest. Each voxel is a logical volume instance with known dimensions and material. During the simulation, you track in which voxel each step occurs, and accumulate the energy deposited into an array indexed by the voxel indices $(i, j, k)$. After the run, you normalize by the voxel masses to obtain a 3D dose distribution.

The most common scoring patterns in radiation dose simulations include scoring in a simple water phantom, scoring in a CT-derived voxel model, or scoring in macro regions such as organs or tumor targets. In all cases, the principle is identical: spatially associate steps with scoring elements, accumulate $E_{\text{dep}}$, and perform the mass division.

Using a Water Phantom for Dose

A water phantom is a standard reference object in medical physics because water approximates soft tissue and many clinical dosimetry protocols are based on water measurements. In Geant4, a water phantom is usually modeled as a box of water, possibly divided into thin slices or fine voxels.

For depth dose studies, for example for a photon or proton beam entering a water phantom, you can divide the phantom along the beam axis into slices. Each slice collects the total deposited energy in that region. Knowing the slice thickness, cross sectional area, and material density, you compute the mass, then obtain dose as a function of depth.

This type of simulation allows you to reproduce familiar physical curves, such as percentage depth dose curves for photon beams or the Bragg peak curve for protons. In a teaching context, the water phantom is a good place to start before moving to patient geometries.

Voxelized Patient and Phantom Geometries

To move closer to clinical situations, dose is frequently simulated in voxelized patient models or computational phantoms. Instead of a single homogeneous box, the geometry is discretized into a three dimensional matrix of small cells that may each have different materials and densities.

In such a geometry, each voxel has its own material derived for instance from CT data, and its own mass. In a Geant4 simulation, you still record energy deposition voxel by voxel, but the conversion to dose now must use the mass of each voxel individually, not a single bulk material approximation.

In patient or anthropomorphic phantoms, an additional layer of interpretation often assigns voxels to anatomical structures. After you have computed dose per voxel, you may further compute mean dose per organ or planning target volume by averaging dose over all voxels that belong to that structure.

Spatial Resolution and Statistical Uncertainty

In radiation dose simulation, there is always a balance between spatial resolution and statistical precision. Smaller voxels provide more detailed spatial dose information, but with a fixed number of primary histories, the energy deposited in each element becomes smaller and more variable, which increases the statistical uncertainties.

Because Geant4 uses Monte Carlo methods, the uncertainty in each dose bin decreases roughly as $1/\sqrt{N}$, where $N$ is the number of primary particles that contribute. To achieve clinically meaningful statistical precision at a fine voxel resolution, a very large number of simulated primary particles may be needed.

Important tradeoff: Finer dose voxel size gives better spatial detail, but increases the required number of simulated particles for acceptable statistical uncertainty.

In practice, medical physicists often choose a voxel size that matches or slightly refines the resolution of the planning CT, then run enough primary histories to reach a target relative uncertainty, for example a few percent in regions of interest.

Dose Normalization and Output Units

Once you have computed deposited energy per voxel, you must choose a normalization and unit system for presenting results. At the Geant4 level, energy is often in MeV and length in millimeters. To obtain dose in gray, you must convert both energy and mass to SI units.

The general conversion for a voxel is

$$
D_{\text{voxel}} \,[\text{Gy}] = \frac{E_{\text{dep}} \,[\text{MeV}] \times 1.6022 \times 10^{-13} \,\text{J/MeV}}{m_{\text{voxel}} \,[\text{kg}]}.
$$

You may also wish to normalize dose relative to a reference quantity. For example, for external beam therapy you may normalize to the dose at a reference depth or to the number of monitor units in a clinical beam. In radiopharmaceutical dosimetry, you often express dose per unit administered activity or per unit cumulated activity in an organ.

Whatever normalization you choose, it is essential to keep a clear record of the units and normalization factors, since misinterpretation at this step can invalidate a comparison with measurements or treatment planning data.

Clinical Context and Dose Quantities

Although Geant4 itself handles only physical dose, medical physics applications often require additional dose related quantities and interpretations. Examples include dose volume histograms for structures, mean and maximum organ doses, doses to planning target volumes, and indices such as homogeneity or conformity measures.

From a Geant4 perspective, these are post processing operations applied to the 3D dose data. For instance, a dose volume histogram is constructed by grouping voxels in an organ by their dose level and counting the corresponding volume. Similarly, a mean organ dose is computed by averaging the dose over all voxels that belong to that organ.

Radiation protection and diagnostic imaging may use effective dose or organ equivalent dose concepts, which introduce radiation weighting factors or tissue weighting factors. Geant4 itself does not apply these biological or protection factors, but supplies the basic physical dose that you can then transform according to the relevant standards.

Verification and Sanity Checks for Dose Calculations

Accurate radiation dose simulation requires not only correct physics and geometry, but also careful verification. Even simple mistakes in normalizing energy deposition to mass can lead to large dose errors.

Useful checks include verifying that the mean dose in a region scales linearly with the number of simulated primary particles, checking that calculated percentage depth dose curves or Bragg peaks agree qualitatively with textbook data, and confirming that doses in air or out of field regions are small and physically reasonable.

For patient or phantom geometries, it is advisable to compare Geant4 dose distributions, at least in simple setups, to an established treatment planning system or to published benchmark results. This kind of validation is extended in the Simulation Validation chapter, but in a medical context it is especially important because the ultimate goal is often related to patient safety and treatment quality.

By combining careful scoring, appropriate geometry, and suitable normalization, Geant4 provides a flexible and powerful framework for studying absorbed dose in a very wide range of medical physics scenarios.