Radiotherapy

Physical foundations of ionizing-dose deposition, attenuation, and distribution in tissue.

Conceptual context

Radiotherapy uses ionizing radiation to deposit energy in tissue with a carefully controlled spatial distribution. The central physical question is not only how much energy the beam carries, but where that energy remains. As the beam enters the body, it interacts with matter, creates secondary particles, and loses intensity. Therefore $D$ is not usually greatest exactly at the surface. It may rise through a buildup region, reach $D_max$ at $z_max$, and then decrease. Understanding this shape separates three different ideas: local deposition, attenuation in tissue, and geometric dilution of the beam.

🟢 Essential level

$D$ measures how much $E_d$ is received by each unit of tissue mass.

It is not the same as beam intensity: dose describes energy retained locally, whereas intensity describes energy still crossing an area. As $z$ increases, primary radiation is attenuated, but secondary electrons also carry energy into slightly deeper regions. This competition creates a buildup zone, a $z_max$, and a later decrease in $D$. The exact profile depends on beam energy, tissue, field size, and geometry. $PDD$ compares points in the profile with the maximum reference dose. The key idea is to read the curve as a spatial balance among secondary-particle production, energy transport, and progressive loss of the primary beam. A graph must therefore be read by regions rather than as one uniform decay process, and that regional reading is exactly what decides where treatment is most effective and where surrounding healthy tissue stays best protected from unnecessary harm, which is why clinical planning always treats the depth-dose curve as a map of physical trade-offs rather than a single number to memorize.

🔵 Formal level

Basic formulas

The basic definition relates $D$, $E_d$, and $m$:

Absorbed dose

Delivery speed is described through $\dot{D}$, $\delta_{D}$, and $\delta_{t}$:

Average dose rate

Both relations are strictly local: they describe what happens at one specific tissue point, not the total dose received by the entire treated volume.

Real student questions

What is the physical difference between the linear attenuation coefficient and the effective coefficient? The linear attenuation coefficient describes the interaction probability of primary photons per unit length, whereas the effective coefficient empirically summarizes the combined decrease of absorbed dose due to primary beam attenuation, Compton scattering, and geometric beam divergence beyond the peak depth.

Why is the maximum dose not located at the skin surface? This is due to the build-up effect. High-energy incident photons transfer energy to secondary electrons through ionization. These electrons travel a certain distance before depositing their kinetic energy, accumulating the dose until electronic equilibrium is reached at the peak depth.

How does the source-to-surface distance affect the delivered dose? The dose decreases with distance due to the geometric expansion of the beam, which is quantitatively modeled using the inverse square law of distance.

Why is it useful to work with percentage depth dose? Because it simplifies the comparison of different beam profiles and treatment fields independently of the absolute machine calibration.

Final synthesis

External beam radiotherapy is a spatially and temporally controlled process of energy transfer. The dose profile in tissue, characterized by the build-up region, the maximum dose, and the post-maximum exponential decay, is the result of the physical balance between primary attenuated photons and energy-depositing secondary electrons. Its precise modeling ensures the effectiveness of cancer treatments and the safety of surrounding healthy tissues.