{"entity":{"id":"linear-quadratic-model","kind":"technology","name":"The linear-quadratic model and fractionation","aka":[],"tldr":"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.","summary":"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.","status":"established","asOf":"2026-09-16","links":[{"label":"Wikipedia","url":"https://en.wikipedia.org/wiki/Linear-quadratic_model"}],"tags":["radiation-wave1"],"related":[],"cancers":[],"sections":["radiation"],"technologies":["hypofractionated-radiotherapy","sbrt","imrt-igrt"],"targets":[],"drugs":[],"companies":[],"institutions":[],"pathways":[],"terms":["alpha-beta-ratio","biologically-effective-dose","hypofractionation","gray-unit"],"trials":[],"people":[],"bottlenecks":[],"keyPapers":[],"journals":[],"notes":[],"principle":"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.","strengths":["Simple and predictive within the clinical range","Explains why hypofractionation works in breast and prostate cancer","Basis for dose summation"],"limitations":["Overestimates kill at very large fractions","Ignores time, hypoxia and immune effects unless extended","Alpha/beta values carry wide uncertainty"],"since":1980},"route":"/technologies/linear-quadratic-model/","neighbours":{"section":[{"id":"radiation","kind":"section","name":"Radiation Therapy","route":"/fronts/radiation/"}],"technology":[{"id":"hypofractionated-radiotherapy","kind":"technology","name":"Hypofractionated radiotherapy","route":"/technologies/hypofractionated-radiotherapy/"},{"id":"imrt-igrt","kind":"technology","name":"IMRT / IGRT (modern external beam)","route":"/technologies/imrt-igrt/"},{"id":"sbrt","kind":"technology","name":"SBRT / SABR (stereotactic radiotherapy)","route":"/technologies/sbrt/"}],"term":[{"id":"alpha-beta-ratio","kind":"term","name":"Alpha/beta ratio","route":"/terms/alpha-beta-ratio/"},{"id":"biologically-effective-dose","kind":"term","name":"Biologically effective dose (BED) and EQD2","route":"/terms/biologically-effective-dose/"},{"id":"gray-unit","kind":"term","name":"Gray unit (Gy)","route":"/terms/gray-unit/"},{"id":"hypofractionation","kind":"term","name":"Hypofractionation (fewer, larger radiotherapy doses)","route":"/terms/hypofractionation/"}]}}