05 Biology
Lea–Catcheside g-factor
Incomplete-repair factor for a continuous irradiation of duration T.
Listen
Listen · English
Simulation
Lea–Catcheside g-factor — Change the numbers; the scene follows.
Where it works
Linear accelerator
Isocenter
In the treated volume — tumour and OARs at isocenter, after the dose has been delivered.
Open this machineFormula
Variables
Results
g
g-factor
0.0861
μ
Repair constant
0.4621h⁻¹
BED
Biologically effective dose
55.831Gy
Curve
Explanation
What it means
The Lea–Catcheside g-factor reduces the quadratic dose term when irradiation is protracted, because some sublethal damage is repaired during the exposure. g → 1 for an acute dose and g → 0 for a very long LDR treatment. BED = D (1 + g D/(α/β)). This is a working relation in Radiobiology.
Where it is used
Clinically it sits on the Linear accelerator — Isocenter. In the treated volume — tumour and OARs at isocenter, after the dose has been delivered. Radiobiology sits between the prescription and the organ-at-risk: LQ, BED, EQD2, and why 2 Gy is not 2 Gy if the fraction size changed. Use it to compare regimens, not to invent one.
Linear accelerator · Open this machineHow to use it
Repair T½ often 0.5–1.5 h for early effects, longer for some late tissues. A 48 h LDR prostate implant has g ≪ 1, which is why 30 Gy LDR is not 30 Gy HDR. Change one input and watch the curve and the simulation follow.
Symbols
- TIrradiation time48 h
- T½Repair half-time1.5 h
- DDose30 Gy
- α/βAlpha/beta3 Gy
Worked example
A typical case from the default values: T = 48 h (Irradiation time); T½ = 1.5 h (Repair half-time); D = 30 Gy (Dose); α/β = 3 Gy (Alpha/beta). Substituting into the relation gives g = 0.0861; μ = 0.4621 h⁻¹; BED = 55.831 Gy. These are teaching numbers — align them with your machine.
Typical values give
- g = 0.0861
- μ = 0.4621h⁻¹
- BED = 55.831Gy
Where it comes from
The displayed formula is the working relation. Incomplete-repair factor for a continuous irradiation of duration T. Usual reference: Lea & Catcheside / Dale. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Lea & Catcheside / Dale
Assumptions & limits
Mono-exponential repair, constant dose rate, one session. Fractionated incomplete repair uses a different θ = e^{−μΔT} formula (not this g).
Pitfalls
α/β is a model parameter, not a measured organ. BED from incomplete repair or a changed overall time is not the simple n·d·(1+d/(α/β)). Never EQD2 a stereotactic dose with an α/β you did not state. Mono-exponential repair, constant dose rate, one session. Fractionated incomplete repair uses a different θ = e^{−μΔT} formula (not this g).
Keep this
BED = D (1 + g D / (α/β)) for a single continuous session (LDR, PDR pulse as approx.).
In this specialty