12.2. Electromagnetic Physics

Gamma interactions

In GATE, electromagnetic physics controls how charged particles and photons interact with matter as they travel through your geometry. For medical imaging and dosimetry, gamma interactions are especially important because they determine image contrast, detector response, and absorbed dose.

Gamma photons are electrically neutral, so they do not lose energy continuously like charged particles. Instead, they undergo discrete interactions. The most relevant processes at medical energies are the photoelectric effect, Compton scattering, and pair production. Each of these is handled by Geant4 physics models that are activated through the physics list you choose in GATE. Selecting an appropriate electromagnetic physics configuration is covered elsewhere in the Physics Lists chapter, so here we focus on what these processes do conceptually and how they affect your simulations.

At low and medium energies that are typical for SPECT and CT, the competition between the photoelectric effect and Compton scattering controls how far photons travel and whether they are fully absorbed or scattered. In PET, annihilation photons have fixed energy at 511 keV, so Compton scattering dominates in tissue and detector crystals, and photoelectric absorption is more important in dense, high atomic number detector materials such as LYSO or BGO. At higher energies used in radiotherapy, pair production becomes progressively more relevant, especially in high atomic number materials and at energies above a few MeV.

The photoelectric effect occurs when a gamma photon transfers almost all its energy to a bound electron, which is then ejected from an atom. The photon disappears. In Geant4 this is a single interaction step that deposits nearly the full photon energy in a small region. In detector crystals this process contributes to the photopeak in energy spectra, since the initial photon energy is converted locally into energy deposition that leads to scintillation light or charge. In tissue it contributes to local dose. The probability of photoelectric absorption increases quickly with atomic number and decreases with energy, so materials like bone or lead have strong photoelectric absorption at diagnostic energies, while soft tissue does not.

Compton scattering is an inelastic collision between a gamma photon and a loosely bound electron. The photon loses part of its energy and changes direction, and the electron is ejected with some kinetic energy. The energy and angle of the scattered photon are related by the Compton formula
$$
E'_\gamma = \frac{E_\gamma}{1 + \frac{E_\gamma}{m_e c^2} (1 - \cos \theta)},
$$
where $E_\gamma$ is the initial gamma energy, $E'_\gamma$ the scattered photon energy, $m_e c^2$ the electron rest energy, and $\theta$ the scattering angle. In simulations this process is essential for modeling scatter in patients and detectors. Scattered photons that are still detected produce a continuum below the photopeak. They degrade image quality in SPECT and PET, and they modify CT attenuation measurements. In dose simulations, Compton scattering spreads energy deposition over larger regions as scattered photons travel further before being absorbed.

Pair production becomes possible once the photon energy exceeds $2 m_e c^2 \approx 1.022 \text{ MeV}$. In this interaction, a gamma photon disappears in the electric field of a nucleus or an electron and produces an electron and a positron. The excess energy above the threshold is shared as kinetic energy between the two particles. In medical physics this process is important at megavoltage energies used in external beam radiotherapy and in shielding calculations for high energy accelerators. In PET, pair production is not the annihilation of positrons that you model in the patient, but a separate interaction of higher energy photons. In GATE, once an $e^-$ and $e^+$ are created, their subsequent transport is handled by the electron and positron electromagnetic models, which include their energy loss, scattering, and, for the positron, annihilation at the end of its range.

In all these gamma interactions, GATE uses Geant4 cross sections that depend on photon energy and material composition. The physics list determines which model implementation is used, for example a standard model or a low energy model optimized for medical imaging. Using realistic materials and selecting a physics list that covers your energy range are crucial because the balance between photoelectric effect, Compton scattering, and pair production directly affects scatter fractions, detector efficiency, and dose distributions.

Electron interactions

Electrons appear everywhere in GATE simulations. They are primary beams in electron radiotherapy, secondary particles from gamma interactions, and charged products of beta decay. Unlike photons, electrons are charged and continuously interact with matter through many small steps. Geant4 treats electron transport as a sequence of steps with continuous energy loss, multiple scattering, and occasional discrete interactions that create secondaries such as bremsstrahlung photons or delta electrons.

In GATE, the detailed choice of electron physics models is controlled in the physics list configuration, but the general mechanisms are always the same. The most important processes for medical physics are ionization energy loss, multiple scattering, and bremsstrahlung radiation.

Ionization and excitation represent the primary way electrons deposit energy in matter. As an electron travels, it interacts with atomic electrons, transferring small amounts of energy and either exciting or ionizing the atoms. The average rate of energy loss per unit path length is described by the stopping power, often written as $dE/dx$. In simulations this continuous slowing down leads to dense energy deposition along the electron track, which is a major contributor to absorbed dose, especially at the end of the electron range. In water and soft tissue, electron tracks are relatively short at typical beta energies, so electrons are responsible for local dose around radionuclide decays and around photon interaction sites.

The multiple scattering process describes the cumulative effect of many small angle elastic scatters of electrons from atomic nuclei. Instead of tracking every tiny scatter separately, Geant4 samples an effective deflection per step according to models that reproduce the overall angular distributions. Multiple scattering causes electrons to deviate from straight paths and spreads dose laterally. For example, in radiotherapy electron beams, multiple scattering broadens the beam as it penetrates a phantom. In diagnostic imaging simulations, electron scattering affects the precise locations of energy deposition within detector crystals and tissues, but because electrons travel short distances compared to photons, this effect is mainly local.

Bremsstrahlung is radiation emitted when an electron is accelerated in the Coulomb field of a nucleus. The electron loses part of its kinetic energy and emits a photon, often called a bremsstrahlung photon. The probability and spectrum of bremsstrahlung increase rapidly with electron energy and with the atomic number of the material. In water at diagnostic energies, bremsstrahlung is modest, but in high atomic number materials and at megavoltage energies, it becomes a major contributor to photon production. In external beam radiotherapy with photons, many of the treatment photons are themselves produced as bremsstrahlung in the accelerator target. Within GATE, bremsstrahlung is especially important in electron therapy beamlines and in high energy shielding calculations because it couples electron transport back into the gamma sector and so modifies both photon fields and dose patterns.

In addition to these main processes, electron electromagnetic physics includes discrete delta ray production, where a hard collision knocks out a secondary electron with sufficient energy to be tracked explicitly. When such secondaries are produced, total energy is conserved, and the simulation correctly represents local energy deposition patterns. Depending on the production cuts you specify, some of these secondaries may be tracked or may be treated as locally deposited energy.

Electron interactions in GATE are strongly influenced by material composition and density through cross sections and stopping powers. A small change in material definition, for example between lung and soft tissue, can produce noticeable differences in electron ranges and dose fall-off. Electron transport parameters, including step limits and production cuts, also affect how finely the code samples electron tracks. Tight cuts improve spatial accuracy of dose and energy deposition but increase computation time. The specific configuration of cuts and models is covered in the chapter on production cuts and transport parameters. Here it is essential to understand that electrons are the main carriers of energy from original photon interactions to the final absorbed dose, so realistic electron physics is central to any accurate dose simulation.

Positron interactions

Positrons are the antimatter partners of electrons. In GATE simulations they appear as primary particles from positron emitting radionuclides in PET, as secondaries from pair production, or as test beams in specific physics studies. Before annihilation, positrons behave in matter very similarly to electrons with the same kinetic energy. They lose energy by ionization and excitation, they can undergo multiple scattering, and they can emit bremsstrahlung. The main physical difference for medical simulation is what happens at the end of their track, where annihilation produces gamma photons that are often the actual signals in imaging.

As a positron travels through matter, it experiences ionization energy loss that is almost identical to that of an electron. It interacts with atomic electrons, transferring energy and gradually slowing down. The stopping power for positrons is very close to the electron stopping power at the same speed, with small differences that are usually negligible at the level of a basic medical physics simulation. Positrons also undergo multiple scattering, which causes their paths to deviate from straight lines and slightly broadens the region over which they deposit energy and where they eventually annihilate.

Because they have the same charge magnitude as electrons, positrons also produce bremsstrahlung photons in the electric field of nuclei. The probability and spectrum of this radiation are comparable to those for electrons at the same energy. In typical PET energies of a few hundred keV to a few MeV, bremsstrahlung from positrons in soft tissue is relatively small, but it becomes more relevant at higher energies and in dense high atomic number materials.

The characteristic process that distinguishes positrons is annihilation. Once a positron has lost enough energy, it can interact with an electron and annihilate. The most common channel in medical physics simulations is annihilation into two 511 keV photons emitted in nearly opposite directions. In the center of mass frame, the photons have exactly 180 degrees between them and equal energies of $m_e c^2 = 511 \text{ keV}$. In the laboratory frame, due to the small residual momentum of the positron electron system, there is a slight angular deviation and tiny energy imbalance, but for many applications these can be neglected.

In PET, the positron track from emission to annihilation has a finite range in tissue. The positron range is the distance between the emission point and the annihilation point. It is determined by the initial positron energy spectrum of the radionuclide and by the stopping power of the surrounding tissue. Higher energy positron emitters have longer ranges. When you simulate a PET tracer in GATE, the transport of positrons through tissue, including ionization, scattering, and annihilation, is handled by the positron electromagnetic physics. The 511 keV photons created at annihilation are then transported as gamma photons and can escape the patient and be detected by the scanner.

This finite positron range introduces an intrinsic blurring between the true location of the radionuclide and the line of response reconstructed from the detected annihilation photons. For common clinical PET radionuclides, this blurring is on the order of a millimeter to a few millimeters in soft tissue. In simulations, accurate modeling of positron transport ensures that the distribution of annihilation points, and therefore the spatial resolution and image quality, are realistic. Ignoring positron transport and placing annihilation at the emission point would underestimate this physical limit to PET resolution.

Besides the two photon annihilation, there is also a small probability of three photon annihilation, especially when orthopositronium states are formed. This produces a continuous spectrum of photon energies instead of two fixed 511 keV lines. In most medical applications this channel has a minor contribution and is often neglected, but the underlying physics models in Geant4 can account for these less common processes if enabled in specialized physics lists.

In GATE, the configuration of positron electromagnetic interactions is coupled to the general electromagnetic physics list you choose. For PET simulations aimed at realistic spatial resolution studies, it is important to use a physics option that includes detailed low energy electromagnetic processes and to define appropriate production cuts so that positron transport is modeled down to thermal energies where annihilation occurs. In dosimetry for radionuclide therapy, positron energy deposition is treated similarly to electron energy deposition. The local energy loss before annihilation contributes directly to absorbed dose, while the annihilation photons are part of the external photon field that can travel to other organs or escape the body.

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