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Category Medicine & Tests

Presets:

Total Dose (Gy) Range: 0.1 – 200 Gy

Number of Fractions Range: 1 – 60

Dose per Fraction (Gy) Auto-computed from Total Dose ÷ Fractions

α/β Ratio (Gy) Typical: 10 (tumors), 3 (late tissues), 1.5 (prostate)

Enter values or select a preset, then press Calculate.

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About

Errors in radiotherapy dose fractionation directly risk tumor underdosage or catastrophic normal tissue toxicity. The Biologically Effective Dose (BED) quantifies the true biological impact of a fractionation scheme using the linear-quadratic (LQ) model, parameterized by the tissue-specific α/β ratio. A typical late-responding tissue uses α/β = 3 Gy, while most tumors and acute-responding tissues use 10 Gy. This tool computes BED and the Equivalent Dose in 2 Gy fractions (EQD2) for any arbitrary scheme. It assumes complete sublethal damage repair between fractions and does not account for repopulation, reoxygenation, or redistribution (the remaining 3 of the 4 Rs of radiobiology). For hypofractionated regimens exceeding 8 - 10 Gy per fraction, the LQ model may overestimate biological effect; the universal survival curve or modified LQ models are more appropriate in that domain.

Formulas

The Biologically Effective Dose is derived from the linear-quadratic model of cell survival. For a treatment delivering n fractions of dose d each:

BED = n ⋅ d ⋅ (1 + dα/β)

The Equivalent Dose in 2 Gy fractions converts any scheme to its radiobiological equivalent at the standard 2 Gy per fraction reference:

EQD2 = BED × α/β2 + α/β

Where: n = number of fractions. d = dose per fraction in Gy. α/β = tissue-specific ratio in Gy characterizing repair capacity. BED = Biologically Effective Dose in Gy. EQD2 = Equivalent Dose in 2 Gy fractions. The product n ⋅ d equals the total physical dose D. Thus BED = D ⋅ (1 + d/(α/β)).

Reference Data

Clinical Scenario	Total Dose (Gy)	Fractions	Dose/Fraction (Gy)	α/β (Gy)	BED (Gy)	EQD2 (Gy)
Breast (whole, conventional)	50	25	2.0	10	60.0	50.0
Breast (hypofractionated, UK)	40.05	15	2.67	10	50.7	42.3
Prostate (conventional)	78	39	2.0	1.5	182.0	78.0
Prostate (moderate hypo)	60	20	3.0	1.5	180.0	77.1
Prostate (SBRT)	36.25	5	7.25	1.5	211.4	90.6
Lung SBRT (peripheral)	54	3	18.0	10	151.2	126.0
Lung SBRT (central)	50	5	10.0	10	100.0	83.3
Brain metastases (WBRT)	30	10	3.0	10	39.0	32.5
Brain metastases (SRS single)	20	1	20.0	10	60.0	50.0
Head & Neck (standard)	70	35	2.0	10	84.0	70.0
Cervix (EBRT component)	45	25	1.8	10	53.1	44.3
Rectal (short course)	25	5	5.0	10	37.5	31.3
Rectal (long course)	50.4	28	1.8	10	59.5	49.6
Palliative bone (single)	8	1	8.0	10	14.4	12.0
Palliative bone (fractionated)	30	10	3.0	10	39.0	32.5
Palliative bone (short)	20	5	4.0	10	28.0	23.3
Spinal cord tolerance	50	25	2.0	2	100.0	50.0
Hodgkin lymphoma (ISRT)	20	10	2.0	10	24.0	20.0
Skin (keloid prevention)	12	3	4.0	10	16.8	14.0
Esophagus (definitive)	50.4	28	1.8	10	59.5	49.6

Frequently Asked Questions

The LQ model increasingly overestimates cell kill at doses per fraction above approximately 8 - 10 Gy. For SBRT regimens using 15 - 20 Gy per fraction, the computed BED should be interpreted cautiously. Alternative models such as the Universal Survival Curve (USC) or the modified LQ model with a linear tail (LQL) better approximate high-dose-per-fraction radiobiology. Clinical outcome data rather than pure LQ extrapolation should guide decisions in the SBRT domain.

A low α/β (e.g., 1.5 - 3 Gy for prostate adenocarcinoma, late-responding normal tissues like spinal cord) means the tissue is highly sensitive to changes in fraction size. Small increases in dose per fraction cause disproportionately large BED increases. A high α/β (e.g., 10 Gy for most carcinomas and acute-responding tissues) makes BED relatively insensitive to fractionation. Consensus values: late normal tissue 3 Gy, most tumors 10 Gy, prostate 1.5 Gy, melanoma 2.5 Gy, breast 4 Gy (some data).

Yes. Compute BED separately for each component using the appropriate dose per fraction and number of fractions, then sum the BED values. For HDR brachytherapy, each insertion is treated as a fraction. For LDR brachytherapy (e.g., permanent prostate implants), a different formulation incorporating dose rate and repair half-time is needed - the standard formula shown here does not apply to continuous low-dose-rate delivery.

Most published dose-response and tolerance data in radiation oncology were established using 2 Gy per fraction schedules. EQD2 converts any scheme to this reference, enabling direct comparison with historical benchmarks. For example, spinal cord tolerance is often quoted as 50 Gy in 2 Gy fractions (EQD2). BED is more fundamental but less intuitive clinically because its numeric scale varies with α/β.

No. The basic LQ-BED formula used here assumes negligible repopulation and complete inter-fraction repair. For rapidly proliferating tumors (e.g., head and neck squamous cell carcinoma), extended treatment breaks increase effective tumor repopulation. A time-corrected BED subtracts a repopulation term: BED_corrected = BED − 0.693 ⋅ (T − T_k) / (α ⋅ T_p), where T is overall treatment time, T_k is the kick-off time for accelerated repopulation, and T_p is the potential doubling time.

Clinical prescriptions must use practical dose-per-fraction values (typically rounded to 0.05 or 0.1 Gy increments) and whole-number fractions. After computing the theoretically equivalent scheme, round the dose per fraction to the nearest clinically deliverable increment, then recalculate the true BED of the rounded prescription to verify it remains within acceptable bounds. A BED difference of less than 2 - 3% from the target is generally considered clinically insignificant.