The linear-quadratic model and fractionation
The equation radiotherapy uses to compare schedules: cell kill has a part proportional to dose and a part proportional to dose squared, and the ratio between them (alpha over beta) tells you how much a tissue cares about the size of each fraction.
Overview
The linear-quadratic model describes the surviving fraction of cells after a dose d as exp(minus alpha d minus beta d squared). Tissues and tumours with a high alpha/beta ratio (around 10 Gy, most tumours and acutely reacting tissues) are little affected by fraction size; those with a low ratio (around 3 Gy for late-reacting normal tissue, and perhaps 1.5 Gy for prostate cancer) are very sensitive to it. Jack Fowler and others turned this into the biologically effective dose, which lets clinicians compare a 25-fraction course with a five-fraction one and underpins hypofractionation, stereotactic dosing and re-irradiation sums. The model breaks down at very large fractions and ignores repopulation unless extended.
How it works
Radiation cell kill has a linear component from single lethal events and a quadratic component from pairs of sublethal events that combine; their ratio sets each tissue's sensitivity to fraction size.
- Simple and predictive within the clinical range
- Explains why hypofractionation works in breast and prostate cancer
- Basis for dose summation
- Overestimates kill at very large fractions
- Ignores time, hypoxia and immune effects unless extended
- Alpha/beta values carry wide uncertainty
Latest papers
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