Ionizing radiation transfers energy to tissue, knocking electrons from atoms and breaking chemical bonds. The most consequential target is DNA. Damage happens two ways. Direct damage: radiation breaks a DNA bond outright. This dominates for high-LET particles like protons at the Bragg peak. Indirect damage: radiation ionizes surrounding water, producing hydroxyl radicals that diffuse to the DNA and attack it. This dominates for the clinical X-rays produced by a linear accelerator. A standard 2 Gray fraction produces roughly 40 double-strand breaks per cell. Most are repaired. The unrepaired ones are the lethal events.
Oxygen reacts with DNA radicals to form stable, hard-to-repair peroxide lesions. Without it, the radical is fixed by a sulfhydryl donor instead and the damage is reversible.
The indirect damage mechanism has a dependency that shapes how tumors respond: it requires oxygen. Oxygen reacts with carbon-centered radicals on the DNA to form stable peroxide lesions that are difficult to repair. Without oxygen, a sulfhydryl donor fixes the radical instead, and the damage is reversible. The oxygen enhancement ratio — roughly 2.5 to 3 for clinical X-rays — means hypoxic tumor cells are two to three times more radioresistant. The chaotic vasculature that produces tumor hypoxia is not just a drug-delivery problem. It is a radiation-resistance problem too.
Large fractions activate disproportionately more quadratic kill — the survival curve steepens. That steepening is the whole biological story of hypofractionation.
The relationship between dose and cell survival is the linear-quadratic model. Surviving fraction equals e to the negative alpha D minus beta D squared. The alpha term captures cell kill from a single radiation track — proportional to dose. The beta term captures kill from two independent events that together become lethal — proportional to dose squared. At low doses the linear term dominates. At high doses per fraction, the quadratic term grows quickly and the survival curve steepens. This is why fraction size matters: large fractions activate more quadratic kill than small ones delivering the same total dose.
Five Rs explain why fractionation works. Repair: normal tissue fixes sublethal DNA damage more efficiently than tumor between fractions — the primary biological basis of the fractionation advantage. Repopulation: both tumor and normal tissue divide during a multi-week course; fast-growing tumors can regenerate between fractions, eroding cell kill. Redistribution: each fraction kills cells in sensitive phases, and survivors redistribute into more sensitive phases for the next fraction. Reoxygenation: killing well-oxygenated cells improves perfusion to hypoxic regions, making them vulnerable to the next fraction. Radiosensitivity: intrinsic differences — BRCA status, p53, cell type — underlie the population averages we use to plan treatment.
The five Rs translate into four strategies. Conventional fractionation — 2 Gray per day, five days per week — sits where the therapeutic ratio between high alpha-beta tumors and low alpha-beta late-responding tissues is most favorable. Hypofractionation uses fewer, larger fractions, justified when the tumor has a low alpha-beta, as in prostate cancer, making large fractions disproportionately effective. Accelerated fractionation maintains fraction size near 2 Gray but compresses total time, sometimes delivering two fractions per day, to starve tumor repopulation in fast-dividing cancers. Stereotactic body radiotherapy uses extreme hypofractionation — 10 to 25 Gray per fraction — made feasible by highly conformal geometry. At those fraction sizes, the linear-quadratic model's predictions become less reliable.
The biological amplification that makes SBRT efficient for the prostate tumor also makes it more demanding on adjacent normal tissue. Physics and radiobiology must both be right.
The same arithmetic that makes prostate SBRT biologically efficient also raises the biological dose to adjacent normal tissue. For the rectal wall — a late-responding tissue with alpha-beta of approximately 3 Gray — conventional prostate treatment delivers a BED of 100 Gray. SBRT delivers 124 Gray to that same wall. The biological amplification that makes SBRT efficient for the tumor also makes it more demanding on normal tissue in the field. This is why prostate SBRT requires precise, conformal targeting that minimizes rectal dose per fraction. The physics and the radiobiology must both be right, simultaneously.
Still open: does the LQ model break down at SBRT fraction sizes? Are vascular collapse and immune activation the real drivers at extreme doses?
The discipline of radiation oncology is the engineering of a gap. The linear-quadratic model and the alpha-beta ratio quantify it. The five Rs explain why it exists and what each fraction does to sustain it. The hard cases are where the ratio is narrow to begin with: head-and-neck cancers with multiple critical structures in close proximity, glioblastoma where the brain is the surrounding normal tissue. In those settings, every design decision — fraction size, total dose, treatment duration, beam arrangement — is a lever on the therapeutic ratio, and getting the lever wrong is exactly how 70 Gray in 35 fractions and 70 Gray in 10 fractions produce outcomes as different as controlled disease and permanent paralysis.
Cancer Research · Chapter 8 · Radiation Oncology
That's the chapter. Radiation is indiscriminate. Its selectivity is not an intrinsic property of the beam — it is produced by engineering a fractionation schedule that exploits the measurable biological difference between tumor and normal tissue. Alpha-beta encodes that difference. The five Rs explain it mechanistically. Biologically effective dose lets you compare schedules on the same scale. And the therapeutic ratio is what results when the engineering succeeds — and what collapses when the fraction size is wrong.