Radiobiology

BED

Biologically effective dose — a linear-quadratic model quantity that puts schedules with different doses per fraction on one scale, for a stated α/β.

RadiobiologyStudentFractionationSBRT

What is it?

Biologically effective dose (BED) is a way of comparing radiation schedules that use different doses per fraction. It comes from the linear-quadratic (LQ) model of cell survival and was introduced by Fowler in 1989.

The basic formula multiplies the total physical dose (n × d) by a "relative effectiveness" factor, 1 + d ÷ (α/β). The larger the dose per fraction, and the lower the tissue's α/β, the bigger that factor. Fowler's full formula also subtracts a term for repopulation over the overall treatment time; the version above leaves it out.

The result depends on the α/β you choose, so a BED is written with it as a subscript: Gy10 for an α/β of 10 Gy, Gy3 for 3 Gy. A BED quoted without its α/β is incomplete.

Why does it matter?

The same physical dose has a different effect when it is given in fewer, larger fractions. BED makes that visible. It is the basis for putting schedules such as conventional and hypofractionated courses side by side and — once converted to EQD2 — for adding doses from different parts of a treatment, such as external beam and brachytherapy.

Two cautions come with it:

  • BED is not an equivalent dose. Fowler notes that BED is sometimes mistaken for a "biologically equivalent dose", which it is not — the numbers differ by large factors. To get a dose you can compare with a familiar 2 Gy-per-fraction schedule, convert BED to EQD2.
  • The answer is only as good as α/β. A systematic review of published tumor α/β values (van Leeuwen 2018) found large variation between and within tumor sites, depending on histology, stage and the model used, and recommends exploring a range of values rather than relying on one. It also notes that whether the LQ model still holds at large fraction sizes is debated — relevant to SBRT and SRS.

How is it evaluated?

  1. Choose the α/β for the tissue and endpoint, from your protocol or the source you are following, and state it.
  2. Calculate n × d × [1 + d ÷ (α/β)] for each schedule or part of a treatment.
  3. Label each result with its α/β (e.g. Gy10) and compare only BEDs calculated with the same α/β.

BED is a modeling tool, not a constraint. Use the protocol's own dose limits, and any conversions it specifies, for clinical decisions.

The BED / EQD2 Calculator does this arithmetic and shows its working.

Example

BED = n × d × [1 + d ÷ (α/β)]
n = number of fractions, d = dose per fraction (Gy), α/β = tissue parameter (Gy)
30 × 2 GyPhysical dose60 GyBED, α/β = 10 Gy72 Gy10BED, α/β = 3 Gy100 Gy3EQD2, α/β = 10 Gy60 GyEQD2, α/β = 3 Gy60 Gy
Fowler's example. The two BEDs differ because they use different α/β values; converted to EQD2, both return to 60 Gy.

Fowler's own example: 30 fractions of 2 Gy (60 Gy).

  • With α/β = 10 Gy: 60 × (1 + 2 ÷ 10) = 72 Gy10
  • With α/β = 3 Gy: 60 × (1 + 2 ÷ 3) = 100 Gy3

The same treatment gives two different BEDs, one for each tissue. Converted to EQD2, both are 60 Gy.

Illustrative numbers only: the same 60 Gy given in 20 fractions of 3 Gy gives 60 × (1 + 3 ÷ 3) = 120 Gy3 — a higher BED for the late-responding tissue at the same physical dose.

Authoritative resources

Review articleSource Verified

Review by the originator of the term biologically effective dose (BED, introduced in Br J Radiol in 1989). Gives the BED formula — nd[1 + d/(α/β)], with an optional overall-time term — and the conversion to the equivalent dose in 2 Gy fractions by dividing BED by 1 + 2/(α/β) (1.2 for α/β = 10 Gy, 1.67 for 3 Gy, 2.0 for 2 Gy). Its worked example: 30 × 2 Gy = 60 Gy is 72 Gy10 to early-responding tissue and 100 Gy3 to late-responding tissue, but 60 Gy EQD2 to both. Full text read in Europe PMC (PMC3473681).

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Review articleSource Verified

Systematic review of 64 clinical studies reporting α, β and α/β for human tumors. It found large heterogeneity within and between studies; estimates for prostate and breast tumors generally indicated high fractionation sensitivity, those for head & neck, cervix, bladder and liver tumors low sensitivity, and others were mixed. It notes that whether the LQ model holds at large fraction sizes is debated, and recommends choosing parameters by site, histology and model and exploring a range of values. Full text read in Europe PMC (PMC5956964).

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AAPM reportSource Verified
AAPM TG-263: Standardizing Nomenclatures in Radiation Oncology
Mayo CS, Moran JM, Bosch W, et al. · AAPM · 2018

Recommendations for standardized naming of targets, organs at risk and dose-volume metrics. Section 9 sets out the DVH-metric nomenclature DoseLab follows: Vx (volume receiving at least dose x), Dx (minimum dose to the hottest sub-volume x), CVx and DCx (the "cold" complements), output units in square brackets (Gy or % of prescription; cc or % of the structure), and an EQD2Gy unit with the α/β written in parentheses — for example D90%(10)[EQD2Gy]. Section 10 asks that DVH metrics say whether a lower-dose PTV is segmented (excludes the higher-dose PTV) or not. Read in the AAPM report PDF.

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