Photon Beam Basics

Percent Depth Dose (%DD)

Percent depth dose (%DD) distributions give the dose, relative to maximum dose, as a function of depth. There are several key features of a %DD chart that should be noted.

Skin Sparing

MV photons do not reach maximum dose at the surface/skin but build-up to a maximum dose. This effect is referred to as skin sparing and is desirable for most photon treatments.

Depth of Maximum Dose (dmax)

The depth of maximum dose is closely connected to photon energy but also source-to-surface distance, field size and beam profile.

 Dose Fall Off

Dose fall off is gradual for photon beams. The slope of the fall off decreases with increasing photon energy.

Factors Influencing %DD

Inverse Square Law

The intensity of a photon point source will fall off as a function of the inverse of the square of the distance from the source .

The inverse square law occurs because photons from an anisotropic point source propagate spherically outward. As they do, the density of photons decreases as the surface area of the sphere increases.

Key Point: %dd increases slightly as SSD increases

This is because the ratio of inverse square from depth-of-interest to dmax approaches unity (1) as distance increases.

Attenuation

Photon attenuation is the process by which photons interact with matter and deposit some or all of their energy. Attenuation is influenced both by the material the beam is passing through and by the energy of the beam.

Attenuation is often measured using an attenuation coefficient, μ, normalized to the density of a material, ρ, referred to as a mass attenuation coefficient. The units of mass attenuation coefficients are cm2/g.

There are several attenuation coefficients to be aware of:

  • Mass Attenuation Coefficient
    • The fraction of primary photons removed from the beam per unit distance over medium density.
  • Mass Energy Transfer Coefficient
    • The fraction of primary beam energy transferred to charged particles in the medium per unit distance over medium density.
    • Mass energy transfer coefficient is related to KERMA (Kinetic Energy Released per unit MAss) as:
      • Ψ is the photon energy fluence

  • Mass Energy Absorption Coefficient
    • The fraction of primary beam energy by the medium per unit distance over medium density.
    • Dose is related to Mass Energy Absorption Coefficient as:
      • Ψ is the photon energy fluence

Key Point: KERMA and Dose are related by the relationship between Mass Energy Transfer Coefficient (which relates to energy transferred to charged particles that travel some distance) and Mass Energy Absorption Coefficient (which relates to local energy deposition).

Poly-energetic beams

Modern linac-generated photon beams consist of a spectrum of energies up to the maximum energy. Because attenuation is higher for the lower photon energies, the average energy of the photon beam becomes higher at deeper depths. This process, known as beam hardening, causes the average beam attenuation to decrease with depth.

Buildup

Buildup occurs because much of the energy transferred from the photon beam is initially absorbed by electrons which travel some distance. This energy is eventually deposited as dose at a deeper depth within the phantom.

The buildup region ends when the amount of energy taken downstream by liberated electrons is equal to the energy deposited at that location by electrons liberated upstream. This condition is known as charged particle equilibrium (CPE).

Depth of maximum dose (dmax) is found at the shallowest point where charged particle equilibrium is established. Prior to this point, more energy is carried away by liberated electrons than is deposited locally by electrons liberated upstream. Beyond dmax, attenuation and inverse square law reduce the intensity of the primary photon beam with increasing distance.

Isodose Charts

Isodose charts provide a 2D map of a dose distribution. Isodose charts are typically normalized to maximum dose but, especially in treatment planning, may be normalized to prescription dose.

Isodose charts illustrate several important aspects of MV photon dose distributions:

Central Axis

Dose is highest along the central axis of the beam.

Exception: For beams generated with a flattening filter there are often "horns" in the superficial isodose lines. The flattening filter overcompensates in this superficial region to produce a flatter dose distribution at treatment depths.

Field Edge 

Dose near field edge falls off rapidly. This is caused both by geometric penumbra and also loss of lateral scatter equilibrium.

Flattened field "horns"

The horns found in shallow depths of flattened fields are caused by differential attenuation within the flattening filter. Horns are most pronounced for lower MV fields and larger field sizes where the lateral photon energy is much lower (softer) than along the central axis.

Factors Influencing Dose Distributions

Photon Energy

Energy: Impact on %DD

Increased photon energy increases depth of maximum dose (dmax) because electrons liberated by the primary beam are of higher average energy. This means that the electrons travel farther and require more depth to reach charge particle equilibrium.

Increased photon energy decreases the slope of the dose fall off. This effect follows directly from the reduction of photon attenuation with increased energies.

MV Energy Spectrum

Linear accelerators create beams using Bremsstrahlung interaction. This means that they have a spectrum of energy rather than a single energy. Beam hardening, therefore, causes the slope of %DD to decrease at increasing depth.

Key Point: Energy of photon beams produced by linear accelerators are designated by their peak energy and MV (e.g. 6MV.) MV is used to distinguish these poly-energetic beams from mono-energetic beams which may use MeV.

Important Depth Dose Numbers to Remember

All data referenced to 10cm by 10cm fields. Dose fall-off beyond dmax calculated as average to a depth of 20cm using data from Kahn's The physics of Radiation Therapy, 4th edition or clinical data.

Photon Energy (MV)dmax (cm)%DD at 10cm depthTMR at 10cm depthDose Fall-off beyond dmax (%/cm)
Co-60
SSD/SAD = 80cm
0.5 cm56%0.683.7%/cm
6MV1.5 cm67%0.773.3%/cm
10MV2.5 cm73%0.843.1%/cm
18MV3.2 cm80%0.912.8%/cm

Energy: Impact on Scatter Angle

Higher energy photons will be scattered in a more forward direction than lower energy photons.

  • This effect is the result of conservation of energy and momentum during elastic collisions.
  • This effect is strongest for kV photons and has little impact on MV photons.

In the kV photon range, decreased energy causes the lower isodose lines to bulge out.

Beam Profile

Field Size

Percent depth dose increases with increasing field size.

Field size has the greatest impact on %DD for small fields.

Surface dose also increases with increased field size due to increased lateral scatter.

Equivalent Square Rule: A rectangular field has a %DD curve equivalent to a square field of the same Area to Perimeter ratio.

Although %DD curves are generally produced for square fields, many clinical fields are not square.

Key Point: Equivalent square is only valid for rectangular fields. Application to irregular fields will yield inaccurate results!

Field size designations

Geometric Field Size is defined as the projection of the primary collimator to the treatment difference. This is the field size defined by the light field.

Dosimetric/Physical Field Size is defined by the size of a given isodose line (typically 50%) at depth. This is often referred to as the full width at half maximum (FWHM).

Geometric field size may be bigger or smaller than physical field size. Measuring is the only way to tell!

Penumbra

A penumbra is the partially shaded region on the boarder of an open photon field and a block. Dose rapidly falls off in the penumbra region.

Geometric Penumbra

Geometric penumbra arises because the photon source has some finite size. As a result, the source is partially occluded near the field edge.

Geometric penumbra (GP) is dependent on source size (S), source-to-surface distance (SSD), depth (d), and source-to-collimator distance (SCD).

Geometric penumbra increases with:

    • Increasing source size
    • Increasing SSD
    • Decreasing field size, especially fields similar to the source size
    • Decreasing source of collimator distance

Transmission Penumbra

Transmission penumbra occurs as the result of incomplete attenuation of the beam at the edges of the collimator.

Transmission penumbra is dependent upon the construction of the collimator and, because of the changing collimator and beam angle, field size.

Physical penumbra

Typically defined as the lateral distance between the 80% and 20% isodose lines.

Physical penumbra includes the effects of geometric penumbra and transmission penumbra as well as a loss of CPE due to scattering near the field edges.

Key Point: Energy (in addition to collimator design, field size, and SAD) has an impact on penumbra. Lower energies tend to cause less transmission penumbra but have greater lateral scatter than higher energies. These competing effects yield the smallest physical penumbra at about 10MV in soft tissue.

Flatness and Symmetry

An unflattened MV photon beam will have its highest dose rate along the central axis of the beam. Dose rate falls off laterally resulting in a peaked isodose distribution.

Flattening Filters are cone-shaped pieces of metal commonly used to normalize the dose distribution laterally. These filters are designed to attenuate the central axis of the beam leaving a very uniform dose distribution at a given depth, usually 10cm. Shallower than this depth, the lateral region will have the highest dose rate which appear as "horns" on the dose distribution. Beyond 10cm depth, the dose distribution again becomes forward peaked.

Flatness

Flatness is defined in AAPM TG-45 as the ratio of the maximum to the minimum dose inside the central 80% of the field width at a given depth. Field width defined here as full width at half maximum (FWHM).

A flatness of +/-3% is acceptable.

Symmetry

Symmetry is defined in AAPM TG-45 as a maximum deviation of the left side dose from the right side dose of a beam over the central 80% of FWHM.

A flatness value of +/-2% is acceptable.

Key Point: Because linac photons are emitted in a continuous spectrum of energies, flattening filters cause differential beam hardening. As a result, flattening filters only achieve flatness at a limited depth range, usually 10cm.

Source-to-Surface Distance (SSD)

Dose rate decreases with increased SSD

Due to the impact of the inverse square law.

%DD increases with increased SSD

This is because percent depth dose is the ratio of dose-at-depth to dose at dmax. Ignoring attenuation, the dose difference at each of these points is determined by difference in inverse square law. This difference is greatest for short SSDs.

For example, take dmax = 1cm and d = 2cm. Evaluating at an SSD of 1cm and ignoring attenuation %DD = 44% while at an SSD of 10cm %DD = 84%.

Key Point: Converting %DD curves measured at one SSD to another SSD can be accomplished using the Mayneord F-factor.

Inhomogeneities

Inhomogeneities are regions of non-uniform electron density. These regions perturb the dose distribution and must be accurately modeled to determine local absorbed dose.

Electron Density

The Compton interaction is the dominant form of interaction between clinical photon beams and body tissues. Because the Compton interaction is the interaction of a photon with a single electron, knowledge of the electron density is important for determining beam attenuation.

For low Z atoms, such as those found in soft tissue, electron density is closely related to physical density. We can therefore convert CT number to physical density and use this for computing a dose distribution in the presence of non-uniform density.

Most elements in soft tissue have nearly the same Z/A ratio (0.5). Hydrogen is an important exception (Z/A=1).

The impact of pair production and photoelectric effect increases with increased atomic number. This becomes especially important for dose to bone.

Key Point: CTs are useful because the let us determine the number of electrons per unit volume.

Photons interactions in tissue are primarily Compton for clinical energy ranges.

Low Density (Air/Lung)

Lung tissue has a density of about 1/3 to 1/4 that of soft tissue. Because of this density difference, the interface of lung and soft tissue produces some of the strongest dose perturbations in the patient's body. Further, this perturbation has significant impact on the dose calculation accuracy for the lungs and targets within lungs.

Influence of low-density tissue inhomogeneities:

  • Dose is reduced at the upstream tissue/lung interface.
    • Within tissue, this is the result of loss of backscatter.
  • Within the lung, dose is initially depressed but will build up to exceed dose in a homogeneous medium.
    • The excess dose here is the result of decreased primary beam attenuation.
  • Penumbra within the lung will be greater because of increased electron range.
    • This effect is greatly increased for higher energy beams.
  • At the exiting lung/tissue interface, dose will again be depressed and need to build-up.
  • Beyond the low-density inhomogeneity, dose will be increased.

Key Point: Lung targets are usually treated with low MV photons because higher energies result in greater lung dose (increased scatter) and decreased target coverage (increased target buildup region).

High Density (Bone)

The impact of bone on a depth dose distribution arise both directly from the increased density of bone but also from the increased contributions of pair production and photoelectric effect caused by the higher atomic number constituents in bone.

Atomic numbers of bone constituents

Calcium: 20
Carbon: 6
Oxygen: 8

Influence of high-density tissue inhomogeneities:

  • Dose directly upstream of tissue/bone interface increases.
    • This is the result of increased backscatter.
    • 5-10% increase for MV fields.
  • Within bone, dose to bone decreases.
    • This is the result of lower electron density due to presence of high Z elements within bone.
  • For soft tissue embedded in bone, the dose will increase above dose in the absence of bone.
    • Result of two effects work together to increase the number of secondary electrons and increase their rate of energy deposition.
      1. The mass attenuation coefficient of bone is greater than for soft tissue, this causes an increase in secondary electrons liberated by the photon beam.
      2. The stopping power ratio for soft tissue is greater at all energies because the electron density of soft tissue is greater than bone. This means that more of the electron energy is imparted to the soft tissue.
  • Beyond the bone, dose will be reduced due to primary beam attenuation.

For high energy photon beams, pair production may become a significant source of interaction further complicating dosimetry.

Estimating Dose Beyond Inhomogeneity

Beyond the inhomogeneity, perturbations to the dose distribution is dominated by changes in attenuation to the primary beam. A simple way to estimate the magnitude of this effect is to use effective path length. Effective path length is the product of the density, relative to water, and the length the beam travels through the medium.

Example

If a beam travels through 5cm of soft tissue, 5cm of lung, and finally 5cm of soft tissue the effective path length would be 5x1 + 5x0.33 +5x1 = 11.65cm. Recalling that for a 6MV beam, dmax occurs at 1.5cm depth and loses approximately 4%/cm beyond this depth, we can compute that the %DD at this point is approximately 1 - (11.65 - 1.5)x0.04 = 59.4%

Generally, inhomogeneities have less impact on higher energy beams beyond the inhomogeneity. This is because higher energy beams are less attenuated in all mediums.

Tissue Properties to Remember

MaterialPhysical DensityCT Number Range
Air0.0012 g/cm3-1000
Lung0.33 g/cm3-500 to -900
Water1.0 g/cm30 (by definition)
Soft Tissue1.06 g/cm310-50
Bone1.8 g/cm3500-1000

Clinical Dose Distributions

Multi-Field Dose Distributions

Parallel Opposed Fields

Parallel opposed fields may be used for whole brain, mediastinal and other simple treatment sites.

Features of parallel opposed fields:

  • More homogeneous dose distribution than single field
  • Lower isodose levels spread laterally while higher isodose levels narrow in center to an "hour glass" shape
  • Minimum dose along beam axis is found at phantom mid-line
  • Depth of maximum dose increases with increased energy
  • Skin sparing increases with increased energy
  • Tissue homogeneity increases with increased energy

Tissue lateral effect (TLE) describes the situation in which, for parallel opposed beams, the dose near the surface becomes large relative to the dose at mid-plane for larger patients and for treatments with lower energies.

Energy Selection

Treatment energy selection is usually dictated by the ratio of maximum to minimum dose which is, in turn, determined by the patient's thickness. Generally, a higher energy will be selected if this ratio is greater than 1.1 - 1.15.

One common exception to this are targets embedded in lung where high energy beams (>10MV) require too much build-up to adequately cover the target.

Tissue lateral effect as a function of energy and patient thickness for various energies.

Field Junctions

Some target volumes are too large to be fully covered by a single beam. These targets are often treated with multiple fields. Because both fields have divergence, care must be taken in managing field overlap.

The point of field junction is typically at the point at which the geometric field boundaries (the 50% isodose line for a single field) come into contact.

This is convenient at the geometric field boundary nearly coincides with the light field, making setup simple.
Additionally the summation of the fields at the junction is 50% + 50% = 100%.

Match-at-Depth

The match-at-depth technique is used when two or more parallel fields are incident on a phantom adjacent to one another.

The depth of the match line typically corresponds to the most superficial aspect of the target or, for multiple opposed fields, the phantom/patient midline.

The surface separation (S) of two match-at-depth fields is determined by the source-to-axis distance (SAD) of each field, the field size (L) and the depth of the match line (d).

 

Non-Parallel Field Matching

Non-parallel field matching requires collimator and couch rotation to account for divergence of both beams.

Couch rotations are often referred to as couch kicks.

The most commonly cited example of such a beam arrangement is craniospinal fields. In this treatment Posterior-to-Anterior fields are used to irradiate the spine while opposed lateral fields are used to irradiate the whole brain.

Matching the collimator angle of the brain lateral fields to the spinal field divergence is achieved by:

Matching the opposed lateral brain fields is achieved via a couch kick with an angle determined by:

Field Modifiers

Wedges

Wedges are devices which adjust the angle of isodose line at a given depth via differential attenuation of the beam.

Wedge Angle is usually defined at 10cm depth in water.

Wedge Transmission Factor is defined as the ratio of the output with the wedge to the output without the wedge.

Types of Wedges

Physical (Individual) Wedges are made of metal and are attached to the treatment head prior to irradiation. The thin end of the wedge is known as the toe and the thick end is known as the heel. 

    • Physical wedges differentially harden the beam.
    • Physical wedges increase surface dose due to increased scatter.

Electronic (Dynamic) Wedges produce the appropriate angle by slowly moving the linac primary collimator or multi-leaf collimator across the field during delivery.

    • Electronic wedges do not harden the beam or significantly increase scatter (although there may be a small increase due to the effectively smaller field size).

Universal Wedges, such as those found on Elekta machines, house a single 60 degree physical wedge inside the treatment head. Wedge angles of less than 60 degrees may be produced by delivering part of the beam without a wedge (i.e. open field) and the rest using the universal wedge.

Common Wedge Applications

Dual Field Wedges

When two fields intersect at an angle other than 180 degrees, the resulting dose distribution will be heterogeneously weighted toward greatest overlap. Wedges may be used to improve the uniformity of such dose distributions.

The optimal wedge angle is determined by the angle of the incident beams (the hinge angle) as:

 

Breast Tangents

Traditional breast plans use two opposed fields positioned tangent to the chest wall. This approach minimizes dose to the heart and lungs. Because the beam path is thickest near the chest wall and becomes thinner superficially, open fields can result in significant dose heterogeneity. Wedges, with the toe toward the chest wall, may be used to produce a more uniform dose distribution.

Breast tangents often feature wedges or use field-in-field techniques to improve uniformity.

Blocking

Blocking is used to create fields of different shapes and sizes. The simplest blocking is accomplished using only the jaws located in the treatment head. Jaws, however, are only able to produce a rectangular field.

Custom Cutouts

The first method developed for producing irregular field shapes was the development of custom lead or Cerrobend cutouts and blocks. These blocks are typically mounted to a Lucite plate (tray) which could be affixed to the treatment head.

95% attenuation is considered clinically acceptable for a custom cutout or block.

Cerrobend is a brand name for Lipowitz metal which is used more often than lead to produce custom blocks because its lower melting point makes it easier to work with.

Cerrobend has a lower melting point than lead (70°C vs 327°C).

Cerrobend has a lower density than lead (9.4g/cc vs 11.34g/cc).

Beam QualityLead Block ThicknessCerrobend Block Thickness
Co-605.0 cm6.0 cm
6MV6.5 cm7.8 cm
10MV7.0 cm8.4 cm
25MV7.0 cm8.4 cm

Multileaf Collimation

The multileaf collimator (MLC) is a device made up of individually controlled leaves used to create complex field shapes.

Because MLC leaves have a finite width, the orientation of the leaves relative to the target is important. Generally, the collimator should be rotated to place the direction of leaf motion parallel to the shortest axis of the target.

Field-in-Field

Field-in-field (FIF) is an advanced field shaping technique utilizing the MLC. FIF is most often used to reduce the intensity of high dose regions by blocking those regions for some fraction of the beam.

Field-in-field is similar to intensity modulated radiation therapy (IMRT) in that it uses the MLC to produce multiple collimator openings with the goal of creating a conformal and uniform dose distribution. Unlike IMRT, which is planned using an inverse planning algorithm, FIF is forward planned.

Steps in Field-in-Field delivery

  1. The majority (typically 80-90%) of the dose at a given beam angle is delivered with the largest applicable MLC setting.
  2. The MLC is partially closed to occlude further dose to high dose regions and the remainder of the dose is delivered. This is the field within a field.
    • Between 1 and 5 MLC positions are typically used.

Key Point: Forward planning refers to the design of a radiation field by means of a user directly placing the field and calculating the resulting dose distribution. Inverse planning refers to a planning technique in which a user defines a set of end dose distribution goals (i.e. target dose, limiting dose to organs, etc.) and an algorithm attempts to produce a set of fields which achieve these goals.

Tissue Compensators

Bolus

Bolus refers to material placed on the patient’s skin surface with the intent of influencing dose distribution. The term may refer to either compensating bolus or buildup bolus depending upon the intent and construction of the bolus.

Buildup Bolus

Buildup bolus refers to material placed directly on the skin surface with the intent of increasing skin dose.

Buildup bolus is often used in treatment of skin lesions as well as to increase dose around an excision scar, especially in breast cancer treatment.

Buildup bolus is typically of uniform thickness between 5-10mm using superflab. Other materials such as brass may also be used for this purpose.

Compensating Bolus

Compensating bolus refers to material placed directly on the skin surface to even out irregular contours resulting in a more uniform dose distribution.

Compensating bolus is most commonly used in electron therapy where high and uniform superficial dose is desired.

Compensating bolus also reduces skin sparing which is undesirable in many applications. As a result, use of a tissue compensator may be preferred for photon treatments.

Compensating Filters

Compensating filters, commonly referred to as compensators, are attenuating material placed in the beam path to compensate for differences in patient thickness.

Compensators are distinguished from compensating bolus because they are not placed in direct contact with the patient. As a result, compensators allow greater skin sparing than compensating bolus. Additionally, compensating filters are typically used in photon treatments.

Compensator facts

  • Compensators are typically made of lead, copper or acrylic.
  • Compensators will harden photon beams and increase scatter dose.
  • Compensators can have finer resolution than an MLC.

The thickness of compensator material required may be estimated as in the below equation.

  • t is the thickness of the compensator material.
  • μ is the attenuation coefficient of the compensator material.
  • TPR is the tissue-phantom ratio at the point of interest.
A complex machined compensator used in IMRT
Illustration of compenator use in lateral field total body irratiation. Source: AAPM TG-29.

Knowledge Test

1. A delivery of 200MU with an open beam is known to deliver the correct dose to a target. How many monitor units are required to deliver the same dose to the same target using a wedge with a wedge factor of 0.85?

Question 1 of 3

2. Calculate the geometric penumbra of a 2mm source at a distant of 100cm from the source assuming a source-to-collimator distance of 30cm.

Question 2 of 3

3. What type of radiation has the greatest skin sparing effect?

Question 3 of 3


 

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