Radiosensitive polyacrylamide gels (PAG) provide a method of mapping dose distributions in 3D with sub-millimetre resolution [1]. Largely tissue equivalent, the dosimeter consists of a gelatin matrix infused with two co-monomers. A high percentage of

1
Oxygen Diffusion into a Polymer Gel Dosimeter
S. J. Hepworth S. J. Doran
Introduction Radiosensitive polyacrylamide gels
(PAG) provide a method of mapping dose
distributions in 3D with sub-millimetre
resolution 1. Largely tissue equivalent, the
dosimeter consists of a gelatin matrix infused
with two co-monomers. A high percentage of water
provides a high cross-section for interaction
with incident X- or g-rays. The radiolysis of the
water initiates free-radical polymerisation and
crosslinking 2, thus changing the local MRI
parameters of the gel. T2 variations are
inversely proportional to dose over a typical
range of 0.5 8 Gray. Dose mapping is performed
by acquiring an R2 (1/T2) parameter map and, on
a clinical scanner, one can achieve a resolution
of the order of 0.3 mm. Problem Oxygen impurities
consume the free radicals that have been created
by the radiation, thus inhibiting the desired
polymerisation. Although this problem is well
known, no quantitative studies have been
performed. This work aims to understand the
oxygen contamination problem by obtaining key
diffusion parameters. Experiment PAG samples
were prepared in test tubes filled to
approximately 1 cm below the opening. The tubes
were sealed under a nitrogen atmosphere. At time
zero, the tubes were opened to oxygen (either
100 O2 at atmospheric pressure or air).
Diffusion was allowed through the samples for
pre-prescribed times, after which all the tubes
received a dose of 3.2 gray from 60Co ? photons.
Irradiating the PAGs leads to an R2 distribution
in the sample which reflects the degree of
penetration of the oxygen at the time of
irradiation. Spatially resolved T2 values were
obtained using a standard multi-echo sequence on
a Siemens Vision 1.5 T scanner, acquiring 16
images with echo times regularly spaced between
50 and 800 ms. Clearly seen are light areas
corresponding to unpolymerised PAG, where oxygen
has inhibited the reaction, and dark areas
unaffected by oxygen diffusion, in which
radiation induced polymerisation has taken place.
Analysis For each tube, a profile of R2 is
created. Figure 2 demonstrates how, as oxygen
diffuses into the sample for varying lengths of
time, a polymerisation front is created. Figure
3 takes a single point on the front (in this case
the elbow at the bottom) and follows it as it
moves through the gel. We see typical Fickian
diffusion behaviour 3 d ? t1/2 The two lines
show how, as expected, pure O2 spoils the gel to
a greater extent.
Figure 3 Penetration depth of oxygen front vs.
square root of exposure time
These plots give us all the information that we
need to know in order to quantify the region of
the gel that will be affected by oxygen
contamination. Making the assumption that the
oxygen diffusion is independent of oxygen
concentration, we obtain D (8?2) ? 10-6 cm2
s-1 From this result, we can then work
backwards to estimate the shape of the relation
between the O2 and R2, as shown in Figure 4.
Figure 4 Dependence of R2 on concentration of
diffused oxygen.

• Conclusion
• These results demonstrate the first
  quantitative measurements of the diffusion of
  oxygen in polymer gel dosimeters
• We have made the first quantitative
  measurements of the relationship between oxygen
  concentration and the degree of inhibition
  of polymerisation

R2 / s -1
Depth / mm
Acknowledgements The authors are indebted to
Prof. M. O. Leach (Institute of Cancer Research,
Sutton) for use of imaging facilities and to
EPSRC for a studentship.
References 1 Maryanski et al. Magnetic
resonance imaging of radiation dose
distributions using a polymer-gel dosimeter
Phys.Med. Biol. 39 1437-1455(1994) 2 Collinson
et al.The polymerisation of acrylamide in
aqueous solution.Trans. Faraday Soc.53,
476-488 (1957) 3 Crank J. Mathematics of
Diffusion. Oxford Science Publications. (1975)
Figure 1 Typical T2-weighted raw image data
Figure 2 R2 values in the region of interest
from the meniscus to a depth of 12 cm