How to calculate Gy2 (Gray2) EQD2 (Equivalent Dose in 2 Gy fractions) for a patient with a history of head and neck cancer undergoing reirradiation?

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Calculating EQD2 (Equivalent Dose in 2 Gy Fractions) for Head and Neck Reirradiation

EQD2 is calculated using the linear-quadratic (LQ) formula: EQD2 = D × [(d + α/β) / (2 + α/β)], where D is the total dose, d is the dose per fraction, and α/β is the tissue-specific ratio. 1

The Linear-Quadratic Formula

The calculation converts any fractionation scheme to its biological equivalent if delivered in 2 Gy fractions:

  • D = total physical dose delivered (in Gy)
  • d = dose per fraction (in Gy)
  • α/β = tissue-specific radiosensitivity ratio (in Gy)

For example, if a patient received 60 Gy in 30 fractions (2 Gy per fraction), the EQD2 equals 60 Gy. However, if they received 45 Gy in 15 fractions (3 Gy per fraction) with α/β = 3 Gy, the EQD2 = 45 × [(3 + 3) / (2 + 3)] = 54 Gy. 1

Tissue-Specific α/β Values for Head and Neck Organs at Risk

Critical normal tissue α/β values derived from clinical data are essential for accurate EQD2 calculations in reirradiation planning. 1

Recommended α/β Values Using the LQ-L Model:

  • Spinal cord: α/β = 2.72 Gy, with EQD2 constraint of 55.91 Gy 1
  • Brainstem: α/β = 2.82 Gy, with EQD2 constraint of 57.54 Gy 1
  • Optic pathway: α/β = 0.55 Gy, with EQD2 constraint of 57.35 Gy 1
  • Brachial plexus: α/β = 6.57 Gy, with EQD2 constraint of 60.13 Gy 1
  • Esophagus: α/β = 5.38 Gy, with EQD2 constraint of 65.66 Gy 1

The linear-quadratic-linear (LQ-L) model provides better fit than the standard LQ model across conventional fractionation through SBRT regimens. 1

Calculating Cumulative EQD2 for Reirradiation

When planning reirradiation, sum the EQD2 from the initial treatment and the planned reirradiation course for each organ at risk. 2, 3

Step-by-Step Algorithm:

  1. Reconstruct the previous radiation dose distribution accurately, identifying the maximum doses to each critical structure from the initial treatment 2

  2. Calculate EQD2 from the initial treatment using the formula above with tissue-specific α/β values 1

  3. Calculate EQD2 for the planned reirradiation using the same formula and α/β values 1

  4. Sum both EQD2 values to determine cumulative biological dose: Cumulative EQD2 = EQD2(initial) + EQD2(reirradiation) 2, 3

  5. Compare cumulative EQD2 to established constraints to assess feasibility and toxicity risk 2, 1

Critical Considerations for Head and Neck Reirradiation

The degree of tissue recovery from initial radiation is uncertain and varies by organ, making cumulative dose calculations inherently imprecise. 2

  • The spinal cord maximum cumulative EQD2 should be limited to approximately 50 Gy with conventional fractionation, though this represents initial treatment constraints 2
  • In reirradiation series, median maximum cumulative EQD2 values have reached 56.8 Gy for brainstem, 63.6 Gy for optic nerve, and 28.8 Gy for spinal cord, though these exceeded traditional constraints 3
  • The time interval between radiation courses affects tissue recovery and toxicity risk, but no validated recovery formula exists 2

Practical Example for Reirradiation Planning

If a patient previously received 66 Gy in 33 fractions (2 Gy/fraction) to a head and neck tumor with spinal cord maximum dose of 45 Gy:

  • Initial spinal cord EQD2 = 45 × [(2 + 2.72) / (2 + 2.72)] = 45 Gy 1
  • If planning reirradiation with 60 Gy in 30 fractions (2 Gy/fraction) with spinal cord maximum of 20 Gy:
  • Reirradiation spinal cord EQD2 = 20 × [(2 + 2.72) / (2 + 2.72)] = 20 Gy 1
  • Cumulative spinal cord EQD2 = 45 + 20 = 65 Gy, which exceeds the 55.91 Gy constraint and requires plan modification 1

Common Pitfalls to Avoid

Do not assume complete tissue recovery from initial radiation when calculating cumulative doses, as this leads to underestimation of toxicity risk. 2

  • Avoid proceeding with reirradiation without accurate reconstruction of the previous dose distribution, as estimates are unreliable 2
  • Do not use a single α/β value for all tissues; organ-specific values are essential for accurate biological dose calculations 1
  • The carotid artery requires particular caution in reirradiation due to risk of carotid blowout syndrome, though specific EQD2 constraints are not well-established 2

References

2
Guideline

Dose Constraints in Head and Neck Reirradiation

Praxis Medical Insights: Practical Summaries of Clinical Guidelines, 2026

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Professional Medical Disclaimer

This information is intended for healthcare professionals. Any medical decision-making should rely on clinical judgment and independently verified information. The content provided herein does not replace professional discretion and should be considered supplementary to established clinical guidelines. Healthcare providers should verify all information against primary literature and current practice standards before application in patient care. Dr.Oracle assumes no liability for clinical decisions based on this content.

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