Oxygen Diffusion into a Polymer
Gel Dosimeter
Department of Physics
University of Surrey
Analysis
120
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 crosssection for interaction with incident X- or g-rays. The radiolysis of the water initiates freeradical 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.
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]:
100
d  t1/2
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.
2.5
0.5
0
0.0%
44.5 hrs
2
100 hrs
0.4%
0.6%
0.8%
1.0%
Figure 4: Dependence of R2 on concentration of
diffused oxygen.
143.5 hrs
187.5 hrs
•
1
0
0.2%
O2 concentration
•
69 hrs
1.5
40
20
0
200
400
600
800
1000
Square root of the diffusion time / s-1/2
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.
Conclusion
25 hrs
R2 / s -1
2.7
2.5
60
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.
1
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.
R2 / s–1
Oxygen sample
Air sample
1.5
R2 /s
-1
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 g photons.
Irradiating the PAG’s leads to an R2 distribution in the sample which reflects the degree of
penetration of the oxygen at the time of irradiation.
80
Figure 3: Penetration depth of oxygen front
vs. square root of exposure time
2
Experiment
'Air' diffusion
'100% O2' diffusion
0
The two lines show how, as expected, pure O2 spoils
the gel to a greater extent.
Problem
Depth / mm
Introduction
S. J. Hepworth
S. J. Doran
0.5
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
0
0
Figure 1: Typical T2-weighted raw image
data
20
40
60 / mm
Depth
80
100
120
Figure 2: R2 values in the region of interest
from the meniscus to a depth of 12 cm
Acknowledgements
References
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.
[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)