Computed tomography dose index
The computed tomography dose index (CTDI) is a commonly used radiation exposure index in X-ray computed tomography (CT), first defined in 1981. The unit of CTDI is the gray (Gy) and it can be used in conjunction with patient size to estimate the absorbed dose. The CTDI and absorbed dose may differ by more than a factor of two for small patients such as children. Definitions. Because CT scanners typically acquire multiple slices during a single rotation with a single beam, the CTDI is calculated by integrating over the dose profile for a single axial  rotation, then dividing by the nominal beam width: formula_1 where formula_2 is the number of slices acquired per single axial rotation, formula_3 is the width of a single acquired slice (and thus formula_2formula_3 is the nominal beam width) and formula_6 is the radiation dose measured at position formula_7 along the scanner's main axis - the dose profile. This measurement is most often made using a 100-mm standard pencil dose chamber as this is representative of a typical scan length: formula_8. The absorbed dose to water formula_9 (used to refer back to patient dose) is typically measured in a cylindrical  head (16 cm diameter) or body (32 cm diameter) phantom of length approximately 14–15 cm. The dose distribution imparted by a CT scan is much more homogeneous than that imparted by radiography, but is still somewhat larger near the skin than in the centre of the body. The "weighted" CTDI was introduced to account for this: formula_10 using measurements acquired at central and peripheral positions in the head or body phantoms described above. CTDI in helical CT. In helical CT, the pitch of the machine - a factor of the speed at which the couch travels through the gantry and the  tube rotation frequency - also impacts on patient dose. The pitch factor, P, is defined as formula_11 where formula_12 is the distance travelled by the couch during one full gantry rotation and formula_13 is the beam collimation (single-slice CT) or the total thickness of all simultaneously acquired slices (multislice CT). The following quantity is therefore used to take account of pitch: formula_14 Similar measures with yet wider chambers are useful for CT systems with large numbers of detector rows. CTDI can also be measured with polymer gel dosimetry. Relation to DLP. The dose-length product (DLP) is a quantity defined  for use in CT as formula_15 for formula_2 and formula_3 as described above (formula_18 is therefore the total scan length). This quantity is analogous to the dose-area product (DAP) used in planar radiography.