Those pictures are fabulous! They tell it all

Dose deposition with Superposition algorithm |
Dose deposition with Convolution algorithm |

Superposition dosimetry |
Convolution dosimetry |

Here is the answer I received:

At the risk of over simplification:

Superposition and convolution are closely related. However not necessarily identical. There are several algorithms out there in commercial planning systems. Some of them are best described as superposition and others best described as convolution. Adoption of the particular terms for calculation options in commercial RTP products probably does not help the situation – the terms may be used by a particular vendor to describe a particular algorithm that mathematically may have elements of one or the other or both.

The way I would think about it is as follows.

The basic group of algorithms are “superposition” algorithms, meaning that they calculate the dose throughout a medium by combining the dose contributions to each point by summing the dose contributed from multiple dose point kernels or pencil beam kernels. Now if the phantom (or patient) is homogeneous and the beam spectrum and angular distribution is assumed to be spatially invariant then this superposition can be achieved mathematically by convolution (where the term is used in the strict mathematical sense). This is typically implemented using FFT.

However in most real life cases there are inhomogeneities and the kernel is also spatially variant – in this case convolution cannot be used to calculate the superposition. Therefore the 3D superposition calculation (which is effectively a 3D integration) is performed “long hand”.

This is probably the origin of the advice your correspondent received from the RTs they spoke to.

A very good reference for this is Ch 26 of “Handbook of Radiotherapy Physics: Theory and Practice.” (2007) Edited by Mayles, Nahum and Rosenwald and published by Taylor and Francis.

I’m sure there are others who may be better at explaining this more succinctly and clearly than I but I hope this helps.

The verbal explanation that followed this was very mathematically oriented and mentioned matrices and Fourier Transformations! So be warned, it is way off the 'need to know' track!

The 'pure' convolution seemed to be a simple homogeneous assessment of dose deposition which was quite analogous to manual planning - that is, the dose in the pixel 5cm in, will be 88%. While the 'pure' superposition was a more comprehensive assessment of dose production based on the density of the pixel.

There are also 'impure' variants which start from one end and add additional features.

Bottom line is - difficult and NOT need to know. Superposition more accurate because tissue density accounted for in dose calculation.

W.r.t Monte Carlo algorithm, that is much easier to understand, and it is essentially a modelling problem. The basis is a probability scenario into which you pump millions of individual trials, the summation of which is a dose deposition pattern. For example the photon exits the target. The first air molecule in the area has a 1x10-6 probability of interaction. The interaction has a 0.5 chance of ionisation and a 0.5 chance of no ionisation. If there is an ionisation, there is a 0.1 chance of a 1MeV photon and a 5MeV ejected electron, a 0.2 chance of a 2MeV photon and a 6MeV electron, etc etc. If all the interaction probabilities are accurately identified and modelled, then predicted dose deposition will be exact. Ifsomething like the scattering from the jaws is left out then the surface dose will be too low and the depth dose will be too high.

Does this make sense?