3.4 Beam Modifiers: Wedges, Compensators, Bolus & MLC Systems

Purpose and Classification of Beam Modifiers

\nUnmodified photon beams emerging from a linear accelerator target exhibit relatively uniform intensity across the flattened field. However, human anatomy presents sloping surface contours, heterogeneous tissue densities, and non-rectangular tumor volumes. Beam modifiers alter the physical beam profile to achieve homogenous dose within the target or protect adjacent normal tissues. \nBeam modifiers are categorized into attenuating modifiers (physical wedges, compensators), surface modifiers (bolus, spoiling screens), and dynamic mechanical modifiers (virtual/dynamic wedges, multileaf collimator systems).

---

Physical and Dynamic Wedges

Physical Wedges

\nA physical wedge is a slanted block of high-density material (lead, steel, or tungsten) placed in the accessory mount of the linac. The thick side of the wedge is termed the heel, and the thin side is termed the toe.

• Heel Effect: Radiation passing through the heel undergoes high attenuation, resulting in low dose delivery.
• Toe Effect: Radiation passing through the toe undergoes minimal attenuation, resulting in high dose delivery.

     Incident Unattenuated Photon Beam
             |||||||||||||||
             +-------------+  <-- Physical Wedge
             |            /| 
             |  Heel     / |  (High Attenuation)
             |          /  |
             |  Toe    /   |  (Low Attenuation)
             +--------+----+ 
             |||         |||||||
          Low Dose     High Dose  --> Tilted Isodose Gradient

Wedge Angle Definition

\nThe wedge angle ($\theta$) is not the physical slant angle of the lead block. It is defined as the angle through which an isodose curve is tilted relative to the perpendicular central axis at a reference depth of 10 cm in water. \nStandard physical wedge angles include 15\u00b0, 30\u00b0, 45\u00b0, and 60\u00b0.

Hinge Angle Formula

\nWhen two oblique beams intersect (such as in anterior-lateral head-and-neck fields or pelvic 3-field plans), hot spots develop near the junction of the shallow beam edges. Wedges are inserted with their heels facing each other to flatten the combined dose profile. The mathematical relationship between the hinge angle ($\phi$, the angle between the central axes of two converging beams) and the required wedge angle ($\theta$) is:

$\text{Hinge Angle } (\phi) = 180^\circ - 2(\theta)$ $\text{Wedge Angle } (\theta) = 90^\circ - \frac{\phi}{2}$

Wedge Factor (WF)

\nBecause physical wedges attenuate radiation, monitor units must be increased using the Wedge Factor (WF):

$\text{WF} = \frac{\text{Dose at reference depth with wedge}}{\text{Dose at reference depth without wedge}}$ \nPhysical wedge factors typically range from 0.30 to 0.80 and must be incorporated into the denominator of MU calculation formulas.

Enhanced Dynamic Wedges (EDW)

\nModern linear accelerators replace physical wedges with Enhanced Dynamic Wedges. EDW generates a wedged isodose profile by moving one independent collimator jaw (Y1 or Y2) smoothly across the field from open position to closed position while the beam is firing, dynamically modulating dose rate. EDW eliminates therapist lifting hazards, provides arbitrary wedge angles (10\u00b0 to 60\u00b0), and reduces beam hardening.

---

Tissue-Equivalent Bolus and Compensating Filters

Bolus

Bolus is a tissue-equivalent material placed directly on the patient's skin surface. It possesses an electron density and mass density identical to water ($\rho \approx 1.0\text{ g/cm}^3$, $Z_{\text{eff}} \approx 7.4$).

• Primary Purpose: To shift the build-up region and point of maximum dose ($d_{\max}$) closer to or directly onto the skin surface, eliminating skin sparing for superficial lesions (e.g., inflammatory breast cancer, skin carcinoma, surgical scar boost).
• Secondary Purpose: To fill anatomical deficits or cavities, evening out irregular surface topography.
• Commercial Types: Superflab, paraffin wax, wet towels, brass mesh bolus (used for post-mastectomy chest walls to maintain surface dose while avoiding high air gaps).

---

Multileaf Collimators (MLC) and QA Protocols

MLC Construction

Multileaf Collimators (MLCs) consist of motorized tungsten leaves (typically 40 to 120 individual leaves paired in opposing banks) integrated into the linac head. Individual leaf widths projected at isocenter range from 2.5 mm (High-Definition HD-MLC) to 5.0 mm - 10 mm (Standard MLC).

    Bank A Leaves                      Bank B Leaves
   +-------------+                    +-------------+
   |=============|------------------->|=============|
   |====================>             |=============|
   |===============>                  |=============|
   |=============|                    |=============|
   +-------------+                    +-------------+
                      Open Field
                      Aperture

Physical MLC Constraints

1. Inter-Leaf Leakage: Radiation leaking between adjacent moving tungsten leaves. Controlled via tongue-and-groove leaf edge construction (< 1.5% to 2.0% leakage).
2. Intra-Leaf Transmission: Radiation penetrating directly through the tungsten body of the leaf (< 1.0% to 1.5%).
3. Leaf Penumbra: Curved leaf ends maintain a constant penumbra width regardless of off-axis position.