Radiation protection maze / labyrinth - what they do & how they work widget

Radiation protection maze / labyrinth - what they do & how they work widget

Maze radiation protection calculations

In this Ionactive resource we do not intend to consider maze calculations in any detail - there is plenty of that on the internet. However, to make best use of the widget we will provide an outline of what the calculations involve. For the avoidance of doubt, nothing in the widget uses monte carlo techniques (such as MCNP). MCNP (and other similar tools) have their place, particularly in complicated geometry applications. However, for the mazes considered in this widget the standard calculation techniques are well understood, and importantly are proved to work. [Ionactive comment:  We have nothing against MCNP and have our own licensed version, although do not use it often. However, we have come across situations in work life where a client might be told by a contractor they need MCNP in order to evaluate the safety of their proposed simple maze (in hospitals and industry). The use of such transport code if often not needed, and is therefore an expensive project addition, where a more standard and less expensive approach to the maze evaluation would suffice.]

The calculation approach in the widget is compatible with the following literature based on medical facilities:

• NCRP Report No. 151, Structural Shielding Design and Evaluation from Megavoltage X- and Gamma-Ray Radiotherapy Facilities.
• IAEA  Report 47 Radiation Protection in the Design of Radiotherapy Facilities.
• IPEM Report 75 Design and Shielding of Radiotherapy Treatment Facilities

The widget does not specifically represent a medical (e.g. radiotherapy linac) situation, and it's aim (interactively explaining maze concepts) will apply far outside the medical sector. It is worth reminding you that:

• Only photons are considered in the widget (i.e. not neutrons).
• Neutrons may be added later (or in a different widget).
• If neutrons were present in the maze (they are not in this widget) they can yield neutron capture gamma rays which may need to be shielded by a door.
• In this widget the collimated source case assumes no leakage from the sides or back of the collimator (whereas typically in a linear accelerator medical application, 0.1% - of the primary beam dose rate - is often assumed).
• In this widget the source geometry is fixed (e.g. does not rotate). 

The maze calculations

Chris Robbins (of Grallator) would tell you (quite correctly) that there is a lot of maths / programming going on 'under the hood' of the widget. This is what makes this widget so useful and interactive! However, if you put aside the widget engine, the physics and maths are not that complicated. There are several things to consider, and not all will be in this first version of the widget. 

• Scatter off the the primary wall next to the inner maze exit (considered).
• Direct ray path (from unshielded) source through the shielding (considered).
• Leakage from a collimated source its scatter off walls (not considered, although for the unshielded source 'leakage' is effectively 100% in all directions and is accounted for).
• Scatter off an object that the radiation is directed towards, other than the primary wall (not considered). This first version of the widget does not consider an object in the radiation beam (e.g. a patient, radiographic object, product for irradiation). An object adds another level of calculation since it will attenuate the beam (to some extent) and scatter it (to some extent).

Essentially the maze calculation is based on the following aspects:

• Inverse square law calculations, at each stage of the maze, relative to the dose rate at 1m from the source.
• An effective dose reduction at each stage of the maze (at the turn) due to a combination of some photons being absorbed in the shielding material, whilst others are scattered from it. The scatter is dependent on the energy of the radiation, the angle of radiation incident on the shielding wall in the maze,  the shielding wall material and the area of the wall available for scatter. Scatter coefficients are tabulated in the above referenced reports.
• Some reasonable assumptions are made. For example, it is assumed that after the first scatter the 10MV photons are reduced in energy to no more than 0.5 MeV (therefore the above mentioned scatter coefficients will also change). 

The calculation will then look something like the following (the collimated source is used in this example and for one dog-leg). 

\[ D_{e}=D\frac{\alpha_{o}A_{o}\alpha _{z}A_{z}}{(d_{h}d_{r}d_{z})^{2}}\]

The terms above are as follows:

D_e  = Dose rate at the maze entrance.

D   = Dose rate 1m from source.

α_o   = Scatter coefficient for the primary wall.

A_o   = Area of scatter on the primary wall.

α_z   = Scatter coefficient for the first section of the maze wall.

A_z   = Area of scatter off the maze wall.

d_h   = Distance between the source and primary wall.

d_r  = Distance between primary wall and centre point of first leg of maze.

d_z  = Distance from centre point of first leg of maze, down to the entrance. 

The intention of this widget resource was not to provide a written maze design lesson (!) so we will leave it here - but for those interested, the above expression and variables are placed onto a widget snapshot  below to provide context. The mathematics under the hood of the widget are significantly more sophisticated than our illustrated example.  

Maze / labyrinth investigations

In this final section we will explore some interesting findings which are illustrated by the widget. 

Missing shielding?

Set the widget up as shown in the picture below and move in and out of the first part of the maze. What do you notice?

Did you see the peak dose rate which then drops off (until you venture further down the maze)? Take a look at the following position. 

Try a little further in still ...

You will notice the radiation dose rate in the maze is in all cases dominated by direct radiation from the unshielded source. You find that :

• Dose rate at entrance is 1.23 relative units (RU).
• Dose rate a little way in is 107000 RU.
• Dose rate a little further still is 20.3 RU.

Can you see what is going on here? Take a look at the following diagram.

If you assume you cannot enter the maze (i.e. door is interlocked when the unshielded source is exposed), then there is no issue - and your assumption is reasonable in many workplace situations. 

However, consider the following:

• What if the maze was shorter or configured slightly differently (see example below).
• What if the maze backs on to another maze (i.e a mirror image). In this case what might the dose rate be in the maze of the facility NOT being used? (see example below). 

Is the maze too generous?

The maze is probably too generous in many cases, especially where you have a collimated source. 

Take a look at the following collimated source example. For this we have opened the collimator as wide as possible (i.e. primary scattering wall area is maximised). Note the dose rate at the maze entrance and a little further down the maze (see diagrams below). 

Note that the dose rates at the two positions are as follows:

• Maze entrance  - dose rate of 36 relative units (RU)
• A little way down the maze - dose rate of 156 RU.

Suppose we are aiming for 1 RU (perhaps think of this as 1 micro Sv/h if you wish), then the maze might appear less than generous- i.e. should it be longer still? 

What we need here is not maze length but a turn. Consider this in the diagrams below. In the first we have added a dog-leg maze extension, and in the second we have moved just around the corner- what do you notice? 

If you play further with the widget you will notice (for the scenario being presented) that we don't need the rest of the maze - it is now too generous. We need the turn but not the further maze extension, so let's remove it as shown in the diagram below. 

The above maze is a classic shape often used in the medical and industrial sector. An even more compact (shorter) version of this configuration might need a 'light' shielded door, but it will be nothing like the shielding required for a direct shielded (no maze) facility. 

Reduce the maze area!

The lower the cross-sectional area of the maze, the less scatter (and better radiation protection performance for a given situation). Often there is a trade-off between optimising radiation protection and maintaining a practical work area.  In the medical sector (i.e. radiotherapy) the maze dimensions may be influenced by getting a hospital bed around it (including each corner!). In the industrial radiography sector the maze may need dimensions sufficient to bring items in and out for NDT (non destructive testing). In industrial irradiation the product being irradiated is often conveyored into and out of the irradiator via a maze, and so maze dimensions will need to accommodate the maximum likely product size. 

For the widget, the standard internal floor to ceiling shielding dimension has been set at 3m. One way to reduce scatter into (and around) the maze is to add one or more down-lintels - as shown in the diagram below.  

Recall that some photons are scattered from the maze wall, and the area of scatter is multiplied by a scatter coefficient (the value is dependent on angle of incident, energy and shielding material). Reducing the scattering area will reduce the total photon load scattered down the maze. By moving the lintel drop down slider fully to the right (1m), the cross-sectional area of the maze exit is reduced from 6m² to 4 m². Try this using the widget!  As shown in the snapshots below, the dose rate can be seen to reduce to 2/3 of the non-lintel case (i.e. '4m²/6m²' of the dose rate). 

The widget reports the following dose rates:

• No down lintel in place - 36 relative units (RU)
• 1m down lintel in place - 24 RU (as expected)