Full dosimetry modules

Quick reference

Dosimetry cheat sheet

Fast-lookup formulas and tables for common radiation therapy treatment-planning calculations.

Formulas

General physics

Inverse square law

I₂ = I₁ · (d₁/d₂)²

Dose rate vs distance from a point source.

Equivalent square

eq = 4 · A / P

Field size for dosimetry-table lookups.

Output factor

OF = Sc · Sp

Collimator (Sc) × phantom (Sp) scatter for a field size.

Dose — convolution/superposition

D(r) = ∫ TERMA(x)·K(x→r) d³x

Heterogeneity-corrected photon dose.

TERMA

TERMA = μ · Ψ

Energy released per unit mass = attenuation × fluence.

PDD → TMR

TMR(d) ≈ PDD(d) · [(SSD + d) / (SSD + dmax)]²

Convert %DD (fixed SSD) to TMR (fixed SAD); the Mayneord F factor is the same correction when changing SSD.

MU & dose calc

Monitor units (SAD)

MU = D / (K · Sc · Sp · TMR · TF)

MU for an isocentric (SAD) setup.

Monitor units (SSD)

MU = D / (K · Sc · Sp · PDD · TF) × (SCD / SSD)²

MU for a fixed SSD setup; the (SCD/SSD)² factor corrects from the calibration distance (SCD) to the treatment SSD.

Inverse-square factor

f = (d₁ / d₂)²

Dose-rate factor when the source distance changes from d₁ to d₂.

Wedge transmission

TW = D_wedge / D_open

Wedge factor / transmission to apply.

Tray / accessory factor

TF = 1 / transmission

Accounts for tray/block attenuation in MU.

Radiobiology

Linear-quadratic survival

S = exp[−(α·D + β·D²)]

Cell survival vs single fraction dose D.

Biologically effective dose

BED = n·d · (1 + d / (α/β))

Biological effect for n fractions of size d.

EQD2

EQD2 = D · (d + α/β) / (2 + α/β)

Convert a regimen to 2-Gy equivalent dose.

OER

OER = D_hypoxic / D_oxygenated

Dose ratio for equal effect, hypoxic vs oxic.

Plan evaluation

Conformity index (Paddick)

CI = (TV_PIV)² / (TV · PIV)

TV_PIV = target volume inside the prescription isodose; ideal = 1.

Conformity index (RTOG)

CI = PIV / TV

Prescription isodose volume ÷ target volume; ideal = 1, >1 means normal-tissue irradiation.

Homogeneity index (ICRU 83)

HI = (D2% − D98%) / D50%

HI → 0 means uniform target dose.

Gradient index

GI = V_50% / V_100%

Dose fall-off outside the target (lower = sharper).

Gamma analysis

γ = √((ΔD/ΔD_crit)² + (Δr/Δr_crit)²)

ΔD = dose difference, Δr = distance-to-agreement; pass when γ ≤ 1 (e.g., 3% / 3 mm).

Radioactive decay

Activity

A = A₀ · e^(−λt)

Activity remaining after time t.

Half-life

T½ = ln(2) / λ

Relates decay constant to half-life.

Air-kerma strength

Sk = Γδ · A (unit U = cGy·cm²/h)

Source strength is distance-independent; the air-kerma rate at distance r is Sk / r².

Quick lookups

Equivalent square (4·A/P)

Field (cm)
Eq. square (cm)
6 × 8
6.86
8 × 10
8.89
10 × 10
10.00
10 × 15
12.00
15 × 20
17.14
20 × 20
20.00

Common OAR constraints (QUANTEC-style)

OAR
Constraint
Limit
Lung
V20
< 30–35%
Lung
Mean dose
< 20 Gy
Spinal cord
Dmax
< 45–50 Gy
Heart (breast/chest RT)
Mean dose
< 4–5 Gy
Heart (pericarditis)
Mean dose
< 26 Gy
Heart
V30
< 46%
Rectum
V70
< 20%
Bladder
Dmax
< 65–80 Gy
Parotid (contra)
Mean
< 26 Gy
Kidney (mean)
Mean
< 18 Gy
Brainstem
Dmax
< 54 Gy
Optic chiasm
Dmax
< 55 Gy
Lens
Dmax
< 6 Gy

Common prescriptions

Site
Regimen
Fractionation
Breast (whole) — conventional
50 Gy
25 fx (2 Gy/fx); used when hypofractionation is unsuitable
Breast (post-mastectomy + nodes)
50 Gy
25 fx (2 Gy/fx)
Prostate (definitive) — conventional
78–79.2 Gy
39–44 fx (1.8–2 Gy/fx); moderate hypo now preferred
Lung NSCLC stage III (definitive CRT)
60 Gy
30 fx (2 Gy/fx); 74 Gy was inferior (RTOG 0617)
SCLC limited stage (CRT)
45 Gy
30 fx BID (1.5 Gy/fx)
Rectal (long-course neoadjuvant CRT)
50.4 Gy
28 fx (1.8 Gy/fx)
Head & neck (definitive IMRT)
70 Gy
35 fx (2 Gy/fx)
Glioblastoma (Stupp)
60 Gy
30 fx (2 Gy/fx)
Glioblastoma (elderly/unfit)
40 Gy
15 fx (2.67 Gy/fx)
Cervical (pelvic EBRT + brachy)
45 Gy
25 fx (1.8 Gy/fx), then brachytherapy boost
Endometrial (pelvic EBRT)
45 Gy
25 fx (1.8 Gy/fx)
Bladder (bladder-preserving CRT)
64 Gy
32 fx (2 Gy/fx; BC2001); 64.8 Gy/36 in older RTOG
Esophageal (definitive CRT)
50.4 Gy
28 fx (1.8 Gy/fx)
Pancreatic (conventional CRT)
50.4 Gy
28 fx (1.8 Gy/fx)
Anal (definitive CRT)
50.4 Gy
28 fx (1.8 Gy/fx), boost to 54–59.4 Gy
Hodgkin lymphoma (ISRT)
20–30 Gy
10–15 fx (2 Gy/fx)
Melanoma (adjuvant nodal)
50 Gy
25 fx (2 Gy/fx)
Breast (whole) — preferred
40 Gy
15 fx (2.67 Gy/fx, START-B)
Breast (whole)
42.5 Gy
16 fx (2.66 Gy/fx, Canadian)
Breast (whole) — 5-fraction
26 Gy
5 fx (5.2 Gy/fx, FAST-Forward)
Prostate (moderate hypo) — preferred
60 Gy
20 fx (3 Gy/fx, CHHiP)
Prostate (moderate hypo)
70 Gy
28 fx (2.5 Gy/fx, RTOG 0415)
Rectal (short-course neoadjuvant)
25 Gy
5 fx (5 Gy/fx)
Esophageal (pre-op CROSS)
41.4 Gy
23 fx (1.8 Gy/fx, neoadjuvant)
Prostate SBRT
36.25 Gy
5 fx (7.25 Gy/fx)
Lung SBRT (early NSCLC)
54 Gy
3 fx (18 Gy/fx)
Lung SBRT (alternate)
48 Gy
4 fx (12 Gy/fx)
Pancreatic SBRT
33–40 Gy
5 fx (SBRT)
Melanoma brain metastases (SRS)
18–24 Gy
1 fx (SRS)
Palliative bone
8 Gy
1 fx
Palliative bone
20 Gy
5 fx
Palliative (bleeding/obstruction)
30 Gy
10 fx

Common radionuclides

Source
Avg energy
Half-life
Co-60
1.25 MeV
5.27 y
Cs-137
0.662 MeV
30.0 y
Ir-192
~0.38 MeV
73.8 d
I-125
28 keV
59.4 d
Pd-103
21 keV
17.0 d
Ra-223
5.0–7.5 MeV (α)
11.4 d

Organ tolerance — Emami TD5/5 & TD50/5 (2 Gy/fx)

Organ
Endpoint
TD5/5 (Gy)
TD50/5 (Gy)
Bladder
Severe contracture/ulceration
65
80
Brain (whole)
Necrosis / infarction
45
60
Brainstem
Necrosis
50
65
Colon
Obstruction / perforation
45
55
Cornea
Keratitis
50
90
Ear (middle)
Severe conductive hearing loss
55
65
Esophagus
Stricture / perforation
55
68
Eye (lens)
Cataract
10
18
Eye (retina)
Blindness
45
65
Heart
Pericarditis / cardiomyopathy
40
50
Kidney (whole)
Clinically significant nephritis
23
28
Larynx
Necrosis / cartilage damage
70
80
Liver (whole)
Liver failure
30
40
Lung (whole)
Radiation pneumonitis
17.5
24.5
Optic nerve / chiasm
Optic neuropathy
50
65
Ovary
Permanent sterilization
2
6
Parotid
Xerostomia (severe)
32
46
Pituitary
Hypopituitarism
45
60
Rectum
Severe proctitis / necrosis
60
80
Salivary glands
Xerostomia
50
70
Skin
Necrosis / ulceration
55
65
Small bowel
Obstruction / perforation
40
55
Spinal cord
Myelopathy / necrosis
47
70
Stomach
Ulceration / perforation
50
65
Testis
Permanent sterilization
1
2
Thyroid
Hypothyroidism
45
80
Ureter
Stricture
75
95
Vagina
Ulcer / necrosis
90
100