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 -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 PAG’s 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.

Figure 1: Typical T2-weighted raw image data

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.

S. J. HepworthS. J. Doran

Department of PhysicsUniversity of Surrey

Oxygen Diffusion into a Polymer Gel Dosimeter

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

Figure 2: R2 values in the region of interest

from the meniscus to a depth of 12 cm

Figure 3: Penetration depth of oxygen front vs. square root of exposure time

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)

AcknowledgementsThe authors are indebted to Prof. M. O. Leach (Institute of Cancer Research, Sutton) for use of imaging facilities and to EPSRC for a studentship.

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 = (82) 106 cm2 s1

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.

R2 / s

1

R2 / s–1

0

2.7

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120

25 hrs

44.5 hrs

69 hrs

100 hrs

143.5 hrs

187.5 hrs

Depth / mm

0

20

40

60

80

100

120

0 200 400 600 800 1000

Square root of the diffusion time / s-1/2

Dep

th /

mm

'Air' diffusion

'100% O2' diffusion

0

0.5

1

1.5

2

2.5

0.0% 0.2% 0.4% 0.6% 0.8% 1.0%

O2 concentration

R2

/s-1

Oxygen sample

Air sample