MOTION MANAGEMENT - Radiation Oncology: A Physicist's-Eye View - page 150

The question is, what should the margin, s , be? In a sophisticated
calculation, the normal tissue tolerance of each nearby normal tissue
would be taken into account separately. In the model whose results
are presented here, all normal tissues are lumped together and the

assumption is made that, as the irradiated volume increases, the

central axis dose must be decreased to keep morbidity at the same
level, using the volume dependence discussed in Chapter 5, namely
central axis dose = prescription dose ⋅ [( w +2 s )/ w ] f

where f is the volume dependence factor, here taken to be -0.1 and

the factor ( w +2 s ) is the beam width enlarged to allow for motion.
With these assumptions, for a 10 cm diameter tumor, one has the
result shown in Figure 7.7b in which the estimated EUD is plotted as
a function of the safety margin, s , given in units of √( p 2 + m 2 ).

Figure 7.7. Model of EUD as a function of beam margin. (a) schematic
illustration of the parameters involved. The dotted black curve is the

beam profile in the absence of motion. The solid red curve is the beam

profile after having added a safety margin, s. The dotted red curve is an
example of an offset beam profile due to motion. One sees the reduced

dose which it gives rise to on the left-hand side of the figure. (b) A plot

of EUD (based on an EUD parameter of -10) vs. the added safety

margin, s, in units of the sum in quadrature of p and m (see text).

In Figure 7.7b:
The dotted blue line shows what happens if one increases the beam
width (by increasing the safety margin, s) without lowering the
dose to keep the normal tissue reactions the same. The EUD
drops when too small a margin for motion is allowed, since the
target edge will then be underdosed, and rises to 100% of the

prescription dose as the field is enlarged, thus ensuring that

the prescription dose is given to the entire tumor.