When a single RIF (Radiation Induced Foci) is faced with multiple DSB's (Double Strand Break in DNA), it can end up rejoining the wrong ends, creating a possibly viable misrepair. A few of the viable mutations will escape our immune system, and a few of those could become cancerous.

If double DSB's are the real problem, then dose rate and repair time becomes all important. The probability that a hit will cause a DDSB is proportional to the inventory of still unrepaired DSB's at the time of the hit.3 To over-simplify, if the repair processes can keep up with the damage, and keep that inventory low, we are OK. If the damage rate is higher than the repair rate, the inventory of unrepaired DSB's will build up, and the probability of a DDSB and a misrepair will grow rapidly. //

If we conservatively assume 10 metabolic DSB's per cell-day, and 0.04 DSB's per millisievert then it would take 250 mSv per day to equal the number of DSB's produced by our metabolism. 250 mSv is about 25,000 times normal background radiation. If normal metabolic damage is equivalent to 250 mSv/d, then any damage associated with 2 mSv/d would almost certainly not be detectable. At the same time, it is not surprising that we start to detect harm at 20 or so mSv/d. At that point, the cell is forced to deal with a substantially higher than normal number of DSB's. ///

Nature has equipped us with a remarkably effective DNA repair system. She had to do this because our O2 based metabolism damages our DNA at a rate that is more than 25,000 times the damage rate from average background radiation.