Flashcards on Linear Quadratic Model in Radiotherapy
Linear Quadratic Model in Radiotherapy: A Student's Guide
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Tumour radiotherapy radiobiology
12 cards
Card 1
Question: What is the main aim of tumour radiotherapy?
Answer: To achieve a high level of local tumour control (tumour control probability, TCP) at a low risk of normal tissue complications (normal tissue complica
Card 2
Question: How can exposure at a low dose rate be considered in terms of fractionation?
Answer: As exposure to an infinite number of infinitely small fractions.
Card 3
Question: Write the linear-quadratic (LQ) model equation for cell survival after a single fraction of dose d and after n fractions.
Answer: Single fraction: S = e^{-(α d + β d^2)}. After n fractions: S = e^{-n(α d + β d^2)}.
Card 4
Question: What assumption justifies using Poisson statistics for cell inactivation by radiation?
Answer: DSBs are rare, random events (produced by single tracks or by two close SSBs from independent tracks), so the number of lethal events per cell follows
Card 5
Question: How is the surviving fraction S related to the mean number of lethal hits per cell, m, under Poisson statistics?
Answer: S = exp(-m). For example, if m = 1 then S = exp(-1) ≈ 0.37 (37%).
Card 6
Question: What do the parameters α and β represent in the LQ model?
Answer: α is the average probability per unit dose of single-track lethal events (linear term). β is the average probability per unit dose squared of two-trac
Card 7
Question: At what dose D do the linear (αD) and quadratic (βD^2) contributions to log-survival become equal?
Answer: When αD = βD^2, i.e., at D = α/β.
Card 8
Question: What is a typical α/β value for tumour tissue and what does a large or small α/β indicate?
Answer: Typical tumour α/β ≈ 10 Gy. Large α/β (>6 Gy) indicates a relatively flat (near-exponential) survival curve; small α/β (1–4 Gy) indicates a wide shoul
Card 9
Question: Define the effect E in terms of surviving fraction S, and express E for a fractionated regimen with total dose D = n d.
Answer: E = -log S. For fractionation E = n(α d + β d^2) = (α + β d) D.
Card 10
Question: Provide the formula for biologically effective dose (BED) and explain its interpretation.
Answer: BED = E/α = [1 + d/(α/β)] D. It is the theoretical total dose required to produce the effect E if delivered with infinitely small dose per fraction (o