Table 1.

Definition of terms used in this paper.

Symbol	Dimensions	Explanation
$L(\overrightarrow{r})$	Dimensionless	Local energy enhancement, i.e. the ratio of the energy deposited due to the nanoparticles to that which would be deposited if no nanoparticles were present, both considered at a point in space $\overrightarrow{r}$
〈L〉	Dimensionless	average local energy enhancement, i.e. the average of $L(\overrightarrow{r})$ taken over a sphere of radius r centred on the centre of the cluster
S1(r)Δr	nm3	Average energy deposited in a thin spherical shell of radius r and thickness Δr for a 1 Gy dose applied uniformly (i.e. in the absence of nanoparticles) or equivalently the volume of this shell multiplied by 〈L〉.
S1(r)Δr	nm3	Average of the square of the energy deposited in a thin spherical shell of radius r and thickness Δr for a 1 Gy2 applied uniformly (i.e. in the absence of nanoparticles).
I 1	nm3	The total additional dose deposited in the sensitive volume due to a single cluster embedded in a 1 Gy background dose.
I 2	nm3	The total additional dose-squared deposited in the sensitive volume due to a single cluster embedded in a 1 Gy background dose.