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).
EQD2
The total dose in 2 Gy fractions that the linear-quadratic model predicts would have the same effect as a given schedule, for a stated α/β.
What is it?
EQD2 is the total dose that, given in 2 Gy fractions, the linear-quadratic model predicts would have the same biological effect as the schedule you are looking at — for a stated α/β. It has also been called the normalized total dose (NTD).
It is calculated from BED: divide the BED by the relative effectiveness of a 2 Gy fraction, 1 + 2 ÷ (α/β). Fowler gives the divisors: 1.2 for an α/β of 10 Gy, 1.67 for 3 Gy, and 2.0 for 2 Gy.
Like BED, EQD2 needs its α/β stated. AAPM TG-263 writes it into the metric name: D90%(10)[EQD2Gy] is the EQD2 covering 90% of a target calculated with α/β = 10 Gy.
Why does it matter?
EQD2 turns any schedule into a number on the familiar 2 Gy-per-fraction scale, so doses from different fractionations can be compared and added. A common use is in cervix cancer, where external beam and brachytherapy doses are summed: EMBRACE II adds them as EQD2, using α/β = 10 Gy for tumor effects and 3 Gy for late normal-tissue damage, and expresses its planning aims and limits as EQD2 totals.
Unlike BED, EQD2 values for the same 2 Gy-per-fraction treatment are the same whatever α/β is used — 30 × 2 Gy is 60 Gy EQD2 for any tissue. The α/β only changes the answer when the dose per fraction is not 2 Gy.
The same cautions apply as for BED: the result depends on the α/β chosen, published tumor α/β values vary widely, and the LQ model's accuracy at large fraction sizes is debated.
How is it evaluated?
- Use the α/β your protocol specifies for the tissue and endpoint (EMBRACE II, for example, specifies 10 Gy for targets and 3 Gy for organs at risk).
- Calculate EQD2 = n × d × (d + α/β) ÷ (2 + α/β) for each part of the treatment.
- Add the parts only if they use the same α/β.
- Label the result with its α/β — e.g. EQD210 or D90%(10)[EQD2Gy].
Low-dose-rate and pulsed brachytherapy need an extra correction for repair during delivery (EMBRACE II assumes a repair half-time of 1.5 hours), which this simple formula does not include.
The BED / EQD2 Calculator does this arithmetic, adds the parts for each α/β and shows its working. The example below is one of its worked examples.
Example
= n × d × (d + α/β) ÷ (2 + α/β)
The NRG cervix protocol template tabulates the total point A EQD2 (α/β = 10 Gy) for combinations of external beam and HDR brachytherapy. Its first row, 45 Gy external beam plus 4 × 7 Gy HDR, totals 83.9 Gy. Assuming the external beam is given in 1.8 Gy fractions (25 × 1.8 Gy), the arithmetic is:
- External beam: 45 × (1.8 + 10) ÷ (2 + 10) = 44.25 Gy
- HDR: 28 × (7 + 10) ÷ (2 + 10) = 39.67 Gy
- Total: 83.9 Gy EQD210
The GYN Brachytherapy page shows where this sum fits into cervix planning.
Authoritative resources
The overview of the EMBRACE II study of image-guided IMRT with chemotherapy followed by MRI-based adaptive brachytherapy for locally advanced cervical cancer. It sets out the study's external beam dose constraints (hard and soft, with separate bowel limits when the para-aortic nodes are treated), the brachytherapy planning aims and limits for the high-risk CTV, GTV, point A, bladder, rectum, sigmoid and bowel in total EQD2, and the vaginal dose points. Open access.
The template NRG Oncology gives investigators for writing the radiation therapy section of a cervical cancer trial, covering external beam (photon, MR-linac and proton) and brachytherapy. It describes supine or prone setup, full- and empty-bladder simulation scans fused to build an internal target volume, diagnostic MRI and PET/CT fusion, standard structure names (including Spc_Bowel and BoneMarrow), example prescriptions, HDR point A and volume-directed (CTV_HR) brachytherapy, and per-protocol and variation-acceptable compliance criteria for both the external beam plan and the combined EBRT + brachytherapy dose. Its values are examples meant to be edited for each trial. DoseLab's cervix tables quote its per-protocol levels.
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.
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).
TPS guidance
Step-by-step guidance planned. Added only once verified.
Step-by-step guidance planned. Added only once verified.