Despite their superficially disparate nature, there is a striking formal similarity between air traffic control, and the processes studied in radiobiology.
In air traffic control, the objects of attention are the aircraft flight paths across a bounded region of airspace, called a sector. In radiobiology, the objects of attention are the energetic particle tracks across the bounded region of space occupied by a biological cell.
In air traffic control, there is a relationship between the number of flights passing through a sector, and the workload of an air traffic controller, and this relationship is given by a linear-quadratic function. In radiobiology, there is a dose-response relationship between the dose of radiation inflicted on a cell, and the biological response of interest, which may be the number of chromosome aberrations, DNA mutations, or the probability of cell death. For radiation of a fixed type and energy, the dose inflicted on a cell essentially corresponds to the number of particle tracks crossing the cell. Hence, the dose-response relationship is a relationship between the number of particle tracks crossing a cell, and the biological consequences. In the case of so-called chromosome translocations, a response crucially related to the probability of subsequent carcinogenesis, the dose-response relationship is given by a linear-quadratic function.
Let us elaborate on these linear-quadratic relationships a little in order to understand the reasons for such formal similarity. In the case of air traffic, the linear component of controller workload is due to (i) the number of routine flight level and airspeed instructions issued per aircraft, and (ii) the communication required with other controllers, when an aircraft is received from, or transferred to another sector. This component of controller workload is independent of the flow-rate, the number of aircraft passing through the sector per hour.
The quadratic component of controller workload is that associated with aircraft conflict-prediction and resolution; there are regulatory separation minima between aircraft, which must not be infringed. Each aircraft could be in potential conflict with any other aircraft in that same sector in the same time-window, hence this component of workload squares with the number of flights. This component of workload is clearly flow-rate dependent; at times of very low flow-rate, it will vanish.
In radiobiology, it is generally acknowledged that in those circumstances where there is a linear-quadratic dose-response relationship, the linear component arises from intra-track mechanisms, whilst the quadratic component arises from inter-track mechanisms. For example, chromosome translocations occur when genetic material is exchanged between two different chromosomes. It is generally thought that such chromosome aberrations occur because the two separate chromosomes both suffer double-strand breaks; i.e., the double-helix of DNA is thought to be broken in two separate chromosomes. The fragments from the two broken chromosomes are then exchanged, rather than spliced back to the correct chromosomes from which they originated.
There is a linear-quadratic relationship between radiation dose and the number of chromosome translocations in an irradiated cell. The linear component is due to individual particle tracks breaking two separate chromosomes. In contrast, the quadratic component is thought to be due to independent particle tracks breaking two separate chromosomes. This component squares with the dose because a break caused by one particle has a chance of interacting with a break caused by any other particle which passes through the cell within the same time-frame, (a period determined by the cycle of cellular repair processes). This component of the dose-response relationship is therefore dose-rate dependent; at low dose-rates it vanishes.
As yet, however, there appear to be no textbooks for those wishing to jointly specialise in air traffic control and radiobiology.