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A new dosimeter based on ferrous sulphate solution and agarose gel
Appl. Radiar. Isor. Vol. 42, No. 11, pp. 1081-1086, Int. J. Radia:. Appl. Instrum. Part A Printed in Great Britain. All rights reserved
1991 Copyright
0883-2889/91 $3.00 + 0.00 0 1991 Pergamon Press plc
A New Dosimeter Based on Ferrous Sulphate Solution and Agarose Gel L. E. OLSSON’*,
A. APPLEBY*
and J. SOMMER3
‘Department of Radiation Physics, Malmii, Lund University, Malmij University Hospital, 21401 Malmii, Sweden, 2Radiation Science Program, Rutgers, The State University of New Jersey, Bldg 4087, Kilmer Campus, New Brunswick, NJ 08903, U.S.A. and 3FMC Corporation, Litex A/S, 2665 Vallensbaek Strand, Denmark
(Received 30 January 1991) A new dosimeter made of ferrous sulphate solution and agarose gel has been developed. Due to a chain reaction in the agarose gel the sensitivity of the ferrous sulphate dosimeter is increased substantially. A G(Fer+)-value up to almost 180 (100 eV)-’ can be achieved. The G(Fe3+)-value and the linear dose response are dependent on the initial ferrous ion concentration. This dosimeter also has a uniform sensitivity over large volumes. The concentration of sulphuric acid has only minor influence on the sensitivity.
1. Introduction 1. I. Background
A dosimeter gel in which the absorbed dose is measured by magnetic resonance imaging (MRI) is a dosimetry system able to measure the absorbed dose distributions in volumes of several litres simultaneously at all points. The gel dosimetry system also has the advantage that no measuring instrument that might distort the radiation distribution has to be inserted. The resolution depends on the MRI equipment used and is typically in the order of cubic millimetres. The gel can be formed into a phantom of any shape. This technique has earlier been demonstrated by Olsson et al. (1990) and Appleby et al. (1987). To enable these measurements the dosimeter gel should ideally fulfill the following requirements: (1) linear dose response, (2) high and uniform sensitivity over the volume, (3) physical stability for a sufficiently long time period (days), (4) image stability for a sufficient time for MRmeasurements to be made.
for correspondence.
1.2. The agarose gel Agarose is a polysaccharide, [C,2H,405(OH)& isolated from agar, which is obtained from certain marine red algae and forms a gel of stable, long chains. Such a gel is a relatively transparent anti-convection medium of extremely high strength and containing relatively large pores (FMC BioProducts Source Book, 1988).
The dosimeter gel consists of agarose gel and acidic ferrous ammonium sulphate solution. Ferric ions are produced when the gel is exposed to ionization radiation in proportion to the absorbed dose (Appleby et al., 1987, 1988; Olsson et al., 1989; Schulz et al., 1990). The absorbed dose to the gel is measured *Author
by nuclear magnetic resonance. The inverse of the spin-lattice relaxation time (ljrl) is proportional to the concentration of the paramagnetic ion. Since ferric ions are paramagnetic, l/T1 is proportional to the absorbed dose. A calculated l/T 1 image from an MR-scanner of a slice through the phantom will actually show the absorbed dose to that part of the phantom (Olsson et al., 1990). Recently, this item has been the subject of an introductory review (Day, 1990).
The main difficulty of making a dosimeter gel of ferrous sulphate solution and agarose is the necessity to have an acidic medium, since the ferrous ions are not soluble in neutral solutions. Sulphuric acid which we have used in our experiments, causes breakdown of the chain structure of the agarose gel. This effect increases with temperature. At room temperature the process is very slow. It should be stressed that agarose gels are rather resistant to sulphuric acid compared to other gelling substances e.g. agar and gelatin, which, from our experience, do not make up stable gels at corresponding conditions. The agarose powder has to be boiled in water to form a gel. The ferrous solution is then added,
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OLSON
II Fig. 1. The experimental set-up for analysis of the cooling rate dependence. One set of vials is located inside the gel and a water phantom, which initially are of the same temperature as the vials (representing slow cooling rate). Another set is located free in air (representing rapid cooling rate). The room temperature is approx. 21°C.
preferably at a lower temperature than the boiling point. By this procedure the destructive ability of the sulphuric acid is reduced. In practice, the optimum time for adding the sulphuric acid is when the gel is near to stiffening. When a dosimeter gel phantom is formed the volume is typically at least 1 litre. This means that the cooling rate at the edge of such a phantom will be significantly faster than at its centre. Since the breakdown of the agarose gel is temperature dependent, the result will be a non-uniform gel, especially when large volumes are prepared. We discovered that this non-uniformity influences the sensitivity of the gel. The two kinds of agarose dosimeter gel described by Appleby et al. (1987, 1988) and by Olsson et al. (1989) did not show a uniform sensitivity over large volumes. A uniform sensitivity within the gel phantom is essential for dose distribution studies. The purpose of this study was to develop an agarose based dosimeter gel which best fulfils the four requirements stated above. The type of dosimeter gels described here can also be evaluated using a spectrophotometer, whereby the ferric production is monitored by its optical absorption of 304nm. This study concerns, however, only applications in connection with magnetic resonance imaging.
et al.
earlier been used by Olsson et al. (1989). The second gel, SeaPlaqueR has an even lower gelling temperature ( Q 30°C) but it has a lower gel strength. Appleby et a/. (1987, 1988) have used this gel. Another kind of polysaccharide, SeaGel’ (FMC Marine Colloids Division, U.S.A.), has also been used as an additive. SeaGel’” is a linear non-gelling polysaccharide purified from locust beam gum. The SeaGel” was heat-degraded to obtain lower viscosity of the polysaccharide solutions. The irradiation method and the Tl-measurement of the dosimeter gel in the vials have been described elsewhere (Olsson et al., 1989). The absorbed doses were in the range @40 Gy. By comparing the slopes of the dose-response curves for the gels to the slope for standard Fricke solution the G-values (sensitivities) were calculated. The slope of Fricke solution was 0.018 ss’Gy_’ (Olsson et al., 1989) and the G-value for 6 MV was taken as 15.6 (100 eV) ’ (ICRU, 1969). 2.1.
General
preparation
procedure
To make a final volume of 2000mL, agarose powder (plain or mixed with SeaGel was added to a glass beaker containing 1500 mL triple distilled water. The mixture was allowed to stand for at least 30 min. It was then boiled until a clear solution was obtained (typically less than 10 min). In order to cool the gel, the beaker was immediately positioned in a water bath of circulating cold tap water. The gel was also purged with oxygen in order to replace the oxygen that was lost during the boiling. Ferrous ammonium sulphate solution (500 mL) containing 4.0 mM sodium chloride heated to the mixing temperature was added when the gel was near its stiffening point, 42 and 32’C for LSL and SeaPlaque”, respectively. Compensation (by adding water) for the evaporated water was also made. The gel was then poured into vials (dia = 23 mm) as well as into larger containers to be used as phantoms. The agarose powder contains a certain amount of water. approx. 5%. The amount of gel added in this
5
4
3
2
2. Materials
and Methods
To minimize the cooling rate dependence, gels with fairly low gelling temperature were selected, Agarose/LSL (FMC, Litex A/S, Denmark) and Agarose/SeaPlaque’” (FMC BioProducts, U.S.A.). The first gel, LSL, is a low temperature (approx. 36°C) gelling type with high gel strength. This gel has
1
0
30
20
10 Absorbed
dose
40
(Gy)
Fig. 2. The dose response for two agarose gels, LSL gel (1% by weight, 1.0 mM ferrous ions) and SeaPlaqueE gel (1.25%, 1.5 mM ferrous ions) for different cooling rates. The slope of the lines represents the sensitivity. 0, SeaPlaque, slow cooling rate; W, SeaPlaque, rapid cooling rate; 0, LSL, slow cooling rate; 0. LSL. rapid cooling rate.
A new dosimeter gel
0
0.2
0.4
Concentration
I 0.8
0.6
0
Seagel (SC by weight)
Fig. 3. The sensitivity ratio (slow/rapid cooling rate) for LSL gel (0) (1% by weight, 1.0mM ferrous ions) and SeaPlaque@ gel (B) (1.25% by weight, 1.5 mM ferrous ions) at different SeaGelE concentrations. The error bars indicate 1 SD.
study is given in percent by weight, including water content.
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I
10
Aboorl#d d-
I
30
20
40
(GY)
Fig. 5. The dose-response curves for SeaPlaque” gel (1.25% by weight) with SeaGel@ (0.25%) for three different ferrous ion concentrations. The sulphuric acid concentration is 50mM. W, OSmM, r =0.998 (0-10Gy); 0, l.OmM, r = 0.9993 (O-30 Gy); A, 1.5 mM ammonium ferrous sulphate, r = 0.9998 (O-40 Gy).
the
2.2. Cooling rate dependence
To examine the dependence of the cooling rate the vials, during their cooling period, were located outside (corresponding to rapid cooling rate) as well as at the centre of a filled phantom containing gel at the mixing temperature (corresponding to slow cooling rate). The phantom was a cylinder 170 mm in both diameter and height. This phantom was surrounded by a basin filled with water also at the same temperature as the gel. This experimental set-up was designed to simulate the cooling rate at the edge and at the centre of a large gel phantom (Fig. 1). The proportions of the different gelling substances were varied to optimize the sensitivity of the gels according to the criteria that the sensitivity should be high, and equal at the two extremes of cooling rate. 2.3. Sulphuric acid and ferrous concentrations
For SeaPlaque@ gel the different mixtures with and without SeaGel@ were also studied for various sulphuric acid concentrations (0.05-0.4 M). The ferrous _.._
ammonium sulphate and sodium chloride concentrations were 1.5 and 1.OmM, respectively. One composition of SeaPlaque@ with SeaGel@ (1.25 and 0.25% by weight, respectively, and 0.05 M sulphuric acid) was further investigated with respect to the ferrous ion concentration, 0.25-2mM. 3. Results 3.1. The cooling rate dependence A stiff and stable LSL-agarose gel is achieved at a concentration of 1% by weight. For pure LSL gel the sensitivity ratio between slow and rapid cooling rate is high, approx. 1.7 (Fig. 2). When SeaGel@ is added the ratio decreases as a function of the concentration (Fig. 3). The sensitivity ratio for LSL with 0.75% by weight SeaGel@ is better than for pure LSL. Even so, the ratio (1.06) is too large to make the LSL a useful gel for phantom dosimetry. Adding more SeaGels will increase the gelling temperature. Since SeaPlaque@ is a gel with less gel strength than LSL the concentration was increased to 1.25% by weight to obtain a stiff and stable gel. For pure 0.25
0.11 $ :=
I
0.10 -
0.09 -
0.081 0
0.1 Sulphuric
0.2
0.3
acid ooncentrtiion
0.4
I
0.5
(M)
Fig. 4. The sensitivity of SeaPlaque@ (1.25% by weight) and SeaPlaque@ gel (1.25%) and SeaGel@ added (0.25%) at different sulphuric acid concentrations. The ferrous ion concentration is 1.5 mM. 0, SeaGel@ added, slow cooling rate; n , SeaGel@ added, rapid cooling rate; 0, no SeaGel@ added, slow cooling rate; 0, no SeaGelE added, rapid cooling rate.
0
0.5 Fwmw
1
1.5
km coma&Mm
2
2.5
(mM)
Fig. 6. The sensitivity for SeaPlaque” gel (1.25% by weight) with SeaGel@ (0.25%) added at different initial ferrous ion concentrations. The sulphuric acid concentration is 50 mM. The sensitivity decreases with increasing ferrous sulphate concentration. Note the right-hand scale where the sensitivity is expressed as multiples of the sensitivity of standard Fricke solution [G(Fe’+)= 15.6 (100 eV)-‘1.
L. E. OLSON et al.
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II0
20
10 Absorbed
dose
30
J
40
(Gy)
curves for SeaPlaqueR gel (1.25% Fig. 7 The doseeresponse . by weight, 1.5 mM ferrous ions) with 0.25% by weight or 0.25% galactose added. q (dotted line), SeaGel* SeaGel” added, slow cooling rate; n (solid line), SeaGel’” added, rapid cooling rate; 0 (dotted line) galactose added, slow cooling rate; l (solid line), galactose added. rapid cooling rate.
SeaPlaque” the sensitivity ratio is not as high as for LSL, being approx. 1.05 (Figs 2 and 3). At added SeaGels’ concentrations of 0.12% or more, the difference in sensitivity is negligible or less than 1% (Fig. 3). The sensitivity is also higher for SeaPlaque” than LSL. 3.2. Sulphuric acid concentration At higher sulphuric acid concentrations, for SeaPlaque” both with and without SeaGel” added, the sensitivity is somewhat greater but the difference in sensitivity between slow and rapid cooling rate is also enhanced (Fig. 4). The increase in sensitivity is rather moderate, so the disadvantages of the cooling rate dependence and a poorer gel strength at higher acid concentrations are greater than the advantage of improved sensitivity. 3.3. The ferrous
ion concentration
The ferrous ion concentration significantly influences the sensitivity of the gel (Fig. 5) which decreases with increasing ferrous ion concentration. For the 1.5 mM concentration the sensitivity is six times higher than for standard ferrous sulphate (“Fricke”) solution (Fig. 6). The G(Fe3+)-value is 94 + 2 (100 eV)-’ The dose interval in which the dose response is linear decreases as the ferrous concentration decreases. For a dosimeter gel prepared with 1.O mM ferrous ions the linear dose response reaches approx. 30 Gy. In these agarose gels, which are bubbled with oxygen, the depletion of oxygen occurs much later than the depletion of the ferrous ions.
4. Discussion For pure agarose (i.e. without addition of SeaGelg), it is evident that the sensitivity of the dosimeter gel is dependent on the cooling rate of the gel. The sensitivity increases with increasing breakdown (acid hydrolysis) of the agarose gel. It may be that this increase in sensitivity is due to a more
uniform distribution of agarose throughout the gel, as the acid hydrolysis of agarose will probably not only create “loose ends”, that are able to “sweep” into the otherwise carbohydrate free pores, but also produce short oligosaccharide chains that participate in the chain reaction described in the Appendix. This increased presence of carbohydrate in the gel cavities could increase the sensitivity by decreasing steric hindrance to the propagation of reaction (9). (The reaction number refers to the mechanism in the Appendix.) An effective increase in the rate constant of this reaction would decrease k, , thereby increasing G(Fe’+ ). This means that the increased hydrolysis of agarose in the centre of a large phantom due to a slower cooling rate will also increase the sensitivity of the gel in the centre of the phantom. It is also evident from our results that the addition of SeaGel” to the agarose diminishes the effect of the cooling rate. For SeaPlaque” the cooling rate dependence is negligible when substantial amounts of SeaGel” are added. This will probably not, however. occur for LSL since adding more than 0.75% by weight of SeaGelR to the mixture will increase the gelling temperature of the mixture resulting in a poorer gelling due to the increased break-down of the gel, caused by the acid at higher temperatures. The difference between SeaPlaque” and LSL may be that the SeaPlaque” gel can be mixed with ferrous solution at a temperature about 1O’C less than can LSL. We believe that the SeaGel% effect is due to the distribution of carbohydrate throughout the gel. Therefore the addition of SeaGel” not only increases the general sensitivity of the gel system, but also diminishes the above-mentioned effect of the acid degradation of the gel, as the presence of SeaGel” throughout the pores of the gel outweighs the extra carbohydrate released by the acid hydrolysis. That the diminishing of the cooling rate effect is due to the extra available carbohydrate throughout the gel structure is rendered probable by experiments performed with the addition of the monosaccharide galactose to the agarose gels. These experiments gave results similar to the results obtained with the addition of SeaGel” (Fig. 7). The sensitivity and the linearity are, however, not as good as for gels with SeaGel”. The sensitivity increases slowly with increasing sulphuric acid concentration. At a high sulphuric acid concentration, however, it is harder to mould a stable gel and it also affects the homogeneity of the dose response. We prefer 50 mM sulphuric acid, since that gives us both reproducible and linear dose-response curves. Actually this is also valid for the standard Fricke system (Fricke and Hart, 1966). The low sulphuric acid concentration recommended by Schulz et al. (1990) (625 mM) may contribute to the nonlinear shape of their dose-response curves. The sensitivity increases with decreasing ferrous ion concentration. At high ferrous concentrations the probability decreases for the radicals to react with
A new dosimeter
agarose molecules. Then the ferric yield will decrease, since fewer radicals will be formed that eventually can oxidize ferrous ions. This is consistent with the proposed reaction mechanism, since reactions (2) and (15) represent competition for OH radicals between Fe’+ and agarose. At very low ferrous concentrations the possibility for reacting with ferrous ions is constant and small, because there is large possibility for reacting with agarose. The initial G-value will therefore be nearly constant when the ferrous concentrations are small. On the other hand, at high ferrous concentrations the G-value will be low and slowly decreasing with that concentration. This is due to the large likelihood that OH will react with ferrous ions instead of agarose. This qualitative discussion is supported by the shape of the line in Fig. 6. We have earlier used 1.5 mM ferrous concentration to measure absorbed dose distributions (Olsson et al., 1990). We preferred that concentration in spite of the lower sensitivity when compared to a concentration of, for example, 0.5 mM. There are two reasons for this. The dose response shows a better linearity and the chemical reactions are completed immediately after irradiation. According to Appleby et al. (1988) the reactions for a gel of 0.4mM ferrous concentration will not be completed until after approx. 20min and this may cause a delay in the MR measurement, which should be started as soon as possible to minimize the effect of the diffusion. In this paper we have addressed the properties of dosimeter gels of agarose/Fe3+-type as they pertain to radiation dosimetric applications. The applicability of this system to imaging of non-uniform dose distributions depends also on the rate of diffusion of the ferric ions responsible for the dosimetric image (Olsson et al., 1990). Recently, this question has also been quantitatively addressed by Schulz et al. (1990), who predicted that diffusion of ferric ions can be expected at a rate of about 1.9 mm/h. If this prediction is verified, accurate radiation dose distributions measured by these systems should be performed as soon as possible post-irradiation, or the measured distributions corrected for this effect.
5.
Conclusions and Composition of the New Dosimeter Gel
The new dosimeter gel has suitable qualifications for measurement of absorbed dose distributions using the magnetic resonance imaging technique. The sensitivity is high compared to ferrous sulphate solution and uniform over a large volume, the dose response is linear over a wide absorbed dose range. It is mechanically stable for several days and is rather easy to prepare. This dosimeter gel in use together with magnetic resonance imaging, MRI, could have a number of applications in radiation therapy, since it is possible to mould the gel to arbitrary configurations and to integrate the absorbed doses from different kinds of fields and radiation qualities.
gel
The new dosimeter
1085
gel consists
of:
1.25% by weight SeaPlaque”, 0.25% SeaGels, 0.05 M sulphuric acid, 1 .O mM sodium chloride and ferrous ammonium sulphate in a concentration that gives the desired linear dose range depending upon the application (preferably between 0.5-1.5 mM). Acknowledgements-This project was supported by the Swedish Cancer Society (project 2349-B90-OlXA) and the Cancer Foundation of Malmo University Hospital. The valuable discussions with Jan-Ove Christoffersson, Ph.D. are also acknowledged. New Jersey Agricultural Experiment States Publication No. D-07124-1-90, supported by state funds.
References Appleby A., Christman E. and Leghrousz A. (1987) Imaging of spatial radiation dose distribution in agarose gels using magnetic resonance. Med. Phys. 14, 382. Appleby A., Leghrousz A. and Christman E. (1988) Radiation chemical and magnetic resonance studies of aqueous agarose gels containing ferrous ions. Radiat. Chem. 32, 241. Day M. J. (1990) Radiation dosimetry using nuclear magnetic resonance: an introductory review. Phys. Med. Biol. 35, 1605. FMC BioProducts Source Book (1988) p. 53. FMC Corporation. Fricke H. and Hart E. J. (1969) Radiation Dosimetry (Eds Attix F. H. and Roesch W. C.), Vol. 2, p. 193. Academic Press, New York. Hart E. J. (1952) Mechanism of the gamma-ray-induced oxidation of aqueous ferrous sulfate-formic acidoxygen solutions. J. Am. Chem. Sot. 74, 4174. ICRU (1969) Radiation Dosimetry: X-rays und Gamma Rays with Maximum Photon Energies Between 0.6 and 50 Me V. ICRU, Washington, DC. Olsson L. E., Petersson S., Ahlgren L. and Mattsson S. (1989) Ferrous sulphate gels for determination of absorbed dose distributions using MRI technique: basic studies. Phys. Med. Biol. 34, 43. Olsson L. E., Fransson A., Ericsson A. and Mattsson S. (1990) MR-Imaging of absorbed dose distributions for radiotherapy using ferrous sulphate gels. Phys. Med. Biol. 35, 1623. Schulz R. J., deGuzman A. F., Nguyen D. B. and Gore J. C. (1990) Dose-response curves for Fricke-infused agarose gels as obtained by nuclear magnetic resonance. Phys. Med. Biol. 35, 1611. Spinks J. W. T. and Woods R. J. (1976) An Introduction to Radiation Chemistry, p. 299. Wiley, New York. APPENDIX The Radiation Chemistry of the Dosimeter Gel The agarose dosimeter gels have a high sensitivity. It is well known that organic additives can increase the G(Fe)+ )value of ferrous sulphate solutions or “Fricke solution” (Spinks and Woods. 1976). To exnlain the hiah sensitivitv ofthis kind of dosimeter gel a chain reaction within the gel is needed. A reaction scheme, adapted from Hart (1952) for ferrous solutions containing formic acid, has been nrooosed for agarose gels containing ferrous ions (Appleby it al., 1988). The chain is initiated by the radicals H, e.q and OH and the hydrogen peroxide generated by radiolytic decomposition of water. Using RH to represent the agarose molecule, and RX and ROH to represent reduced and oxidized forms of agarose respectively, the following reactions are postulated:
L. E. OLSON et al.
1086
*HO, + H+ + Fe2+ +H,O,
‘RO
‘do,
Fig. Al. The dynamics of the agarose-dependent chain propagation reactions in the agarose dosimeter gel. The chain starts with an agarose radical, *R which, in presence of oxygen, gives rise to another radical, *RO,. An oxidation of ferrous to ferric ions takes place and the product RO,H continues the oxidation and produces another radical, *RO. What makes the chain complete is the latter radical’s capability to react with agarose again. As a result a new *R is formed, which can then start a second chain. Initiation H,O+H,
OH, eaq, H,O,
e,+H++H OH + RH-i*R
(1) + H,O
H+RH+*R+H>.
(2) (3)
When the gel is exposed to radiation the radicals H, OH, ea; and hydrogen peroxide, H,O, are generated. These products react with the agarose molecule, RH, and induce the agarose radical, *R (2) and (3). which starts the chain reactions. Propagation *R + 0r+*R02
(4)
Fe2+ + *RO 2-t Fe3+ + RO- z RO;
+ H+ +RO,H
RO,H
+ lRO + OH-
+ Fe2+ +Fe’+
*RO + RH +*R
+ ROH
H + 0, -+*HO*
(5) (6)
Fe*++H,O,-+Fe-‘++OH+OH-
(11)
+ Fe3+.
The most important steps for the chain mechanisms are reactions (4) and (9). In (4) a radical, lRO, is formed that both oxidizes ferrous ions, (5), (6) and (8) and results in a new radical, *RO. This can re-react with agarose (9) and as a result a new *R is formed and the reactions can start from the beginning again. This process is dependent on the gel being well oxygenated. The chain propagation steps that depend on agarose are illustrated schematically in Fig. Al. Reactions that could terminate the chain are (12t(l6). Reactions (12)(16) will dominate at high doses as Fe’+ builds up.
(7) (8) (9) (10)
Termination Fe’+ + *R-+Fe’+
+ H+ + RX
(12)
Fe’+ + *R -+Fe3+ + RH+ + Fe2+ + *RO+Fe’+ Fe’+ + OH +Fe3+ Fe’+ + *ROr +Fe2+
(13)
+ ROH
(14)
+ OH-
(15)
+ H+ + 0: + RX.
(16)
The reaction products from reactions (12)-(16) will not contribute further to continual chain reactions. There is a finite possibility that ferric ions will be reduced, (12) and (16). Normally this possibility would be small, but it would increase when the fraction of ferric ions grows. There are also two reactions, (I 3) and (15) that although they produce ferric ions still terminate the chain reaction. From the reaction scheme it can be shown that:
G(Fe’t)‘i [Fe’+] ‘[o,l
2(G, + Go,) [Fe*+],
+k z
P,l
k [Fe’+] + k [Fe’+]
‘IRH]
4F]
From the above it is evident that, if the reaction scheme is correct the sensitivity would be dependent on the ferrous, oxygen and agarose concentrations. Since we observe an inverse relationship between G(Fe3+) and [Fe”], the term k4[Fe3+]/[Fe2+] must be less significant than the terms k2[Fe2’]/[0,] and k,[Fe’+]/[RH], especially since [Fe’+] will be much smaller than [Fe2+] at low doses. The dependence on oxygen concentration is predicted by the above reaction scheme to be such that G(Fe3+) increases as [Or] increases. We have previously reported this effect of oxygen concentration (Appleby et al., 1988; Olsson et a/., 1989). Work is in progress to evaluate the constants k,-k,.
1991 Copyright
0883-2889/91 $3.00 + 0.00 0 1991 Pergamon Press plc
A New Dosimeter Based on Ferrous Sulphate Solution and Agarose Gel L. E. OLSSON’*,
A. APPLEBY*
and J. SOMMER3
‘Department of Radiation Physics, Malmii, Lund University, Malmij University Hospital, 21401 Malmii, Sweden, 2Radiation Science Program, Rutgers, The State University of New Jersey, Bldg 4087, Kilmer Campus, New Brunswick, NJ 08903, U.S.A. and 3FMC Corporation, Litex A/S, 2665 Vallensbaek Strand, Denmark
(Received 30 January 1991) A new dosimeter made of ferrous sulphate solution and agarose gel has been developed. Due to a chain reaction in the agarose gel the sensitivity of the ferrous sulphate dosimeter is increased substantially. A G(Fer+)-value up to almost 180 (100 eV)-’ can be achieved. The G(Fe3+)-value and the linear dose response are dependent on the initial ferrous ion concentration. This dosimeter also has a uniform sensitivity over large volumes. The concentration of sulphuric acid has only minor influence on the sensitivity.
1. Introduction 1. I. Background
A dosimeter gel in which the absorbed dose is measured by magnetic resonance imaging (MRI) is a dosimetry system able to measure the absorbed dose distributions in volumes of several litres simultaneously at all points. The gel dosimetry system also has the advantage that no measuring instrument that might distort the radiation distribution has to be inserted. The resolution depends on the MRI equipment used and is typically in the order of cubic millimetres. The gel can be formed into a phantom of any shape. This technique has earlier been demonstrated by Olsson et al. (1990) and Appleby et al. (1987). To enable these measurements the dosimeter gel should ideally fulfill the following requirements: (1) linear dose response, (2) high and uniform sensitivity over the volume, (3) physical stability for a sufficiently long time period (days), (4) image stability for a sufficient time for MRmeasurements to be made.
for correspondence.
1.2. The agarose gel Agarose is a polysaccharide, [C,2H,405(OH)& isolated from agar, which is obtained from certain marine red algae and forms a gel of stable, long chains. Such a gel is a relatively transparent anti-convection medium of extremely high strength and containing relatively large pores (FMC BioProducts Source Book, 1988).
The dosimeter gel consists of agarose gel and acidic ferrous ammonium sulphate solution. Ferric ions are produced when the gel is exposed to ionization radiation in proportion to the absorbed dose (Appleby et al., 1987, 1988; Olsson et al., 1989; Schulz et al., 1990). The absorbed dose to the gel is measured *Author
by nuclear magnetic resonance. The inverse of the spin-lattice relaxation time (ljrl) is proportional to the concentration of the paramagnetic ion. Since ferric ions are paramagnetic, l/T1 is proportional to the absorbed dose. A calculated l/T 1 image from an MR-scanner of a slice through the phantom will actually show the absorbed dose to that part of the phantom (Olsson et al., 1990). Recently, this item has been the subject of an introductory review (Day, 1990).
The main difficulty of making a dosimeter gel of ferrous sulphate solution and agarose is the necessity to have an acidic medium, since the ferrous ions are not soluble in neutral solutions. Sulphuric acid which we have used in our experiments, causes breakdown of the chain structure of the agarose gel. This effect increases with temperature. At room temperature the process is very slow. It should be stressed that agarose gels are rather resistant to sulphuric acid compared to other gelling substances e.g. agar and gelatin, which, from our experience, do not make up stable gels at corresponding conditions. The agarose powder has to be boiled in water to form a gel. The ferrous solution is then added,
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OLSON
II Fig. 1. The experimental set-up for analysis of the cooling rate dependence. One set of vials is located inside the gel and a water phantom, which initially are of the same temperature as the vials (representing slow cooling rate). Another set is located free in air (representing rapid cooling rate). The room temperature is approx. 21°C.
preferably at a lower temperature than the boiling point. By this procedure the destructive ability of the sulphuric acid is reduced. In practice, the optimum time for adding the sulphuric acid is when the gel is near to stiffening. When a dosimeter gel phantom is formed the volume is typically at least 1 litre. This means that the cooling rate at the edge of such a phantom will be significantly faster than at its centre. Since the breakdown of the agarose gel is temperature dependent, the result will be a non-uniform gel, especially when large volumes are prepared. We discovered that this non-uniformity influences the sensitivity of the gel. The two kinds of agarose dosimeter gel described by Appleby et al. (1987, 1988) and by Olsson et al. (1989) did not show a uniform sensitivity over large volumes. A uniform sensitivity within the gel phantom is essential for dose distribution studies. The purpose of this study was to develop an agarose based dosimeter gel which best fulfils the four requirements stated above. The type of dosimeter gels described here can also be evaluated using a spectrophotometer, whereby the ferric production is monitored by its optical absorption of 304nm. This study concerns, however, only applications in connection with magnetic resonance imaging.
et al.
earlier been used by Olsson et al. (1989). The second gel, SeaPlaqueR has an even lower gelling temperature ( Q 30°C) but it has a lower gel strength. Appleby et a/. (1987, 1988) have used this gel. Another kind of polysaccharide, SeaGel’ (FMC Marine Colloids Division, U.S.A.), has also been used as an additive. SeaGel’” is a linear non-gelling polysaccharide purified from locust beam gum. The SeaGel” was heat-degraded to obtain lower viscosity of the polysaccharide solutions. The irradiation method and the Tl-measurement of the dosimeter gel in the vials have been described elsewhere (Olsson et al., 1989). The absorbed doses were in the range @40 Gy. By comparing the slopes of the dose-response curves for the gels to the slope for standard Fricke solution the G-values (sensitivities) were calculated. The slope of Fricke solution was 0.018 ss’Gy_’ (Olsson et al., 1989) and the G-value for 6 MV was taken as 15.6 (100 eV) ’ (ICRU, 1969). 2.1.
General
preparation
procedure
To make a final volume of 2000mL, agarose powder (plain or mixed with SeaGel was added to a glass beaker containing 1500 mL triple distilled water. The mixture was allowed to stand for at least 30 min. It was then boiled until a clear solution was obtained (typically less than 10 min). In order to cool the gel, the beaker was immediately positioned in a water bath of circulating cold tap water. The gel was also purged with oxygen in order to replace the oxygen that was lost during the boiling. Ferrous ammonium sulphate solution (500 mL) containing 4.0 mM sodium chloride heated to the mixing temperature was added when the gel was near its stiffening point, 42 and 32’C for LSL and SeaPlaque”, respectively. Compensation (by adding water) for the evaporated water was also made. The gel was then poured into vials (dia = 23 mm) as well as into larger containers to be used as phantoms. The agarose powder contains a certain amount of water. approx. 5%. The amount of gel added in this
5
4
3
2
2. Materials
and Methods
To minimize the cooling rate dependence, gels with fairly low gelling temperature were selected, Agarose/LSL (FMC, Litex A/S, Denmark) and Agarose/SeaPlaque’” (FMC BioProducts, U.S.A.). The first gel, LSL, is a low temperature (approx. 36°C) gelling type with high gel strength. This gel has
1
0
30
20
10 Absorbed
dose
40
(Gy)
Fig. 2. The dose response for two agarose gels, LSL gel (1% by weight, 1.0 mM ferrous ions) and SeaPlaqueE gel (1.25%, 1.5 mM ferrous ions) for different cooling rates. The slope of the lines represents the sensitivity. 0, SeaPlaque, slow cooling rate; W, SeaPlaque, rapid cooling rate; 0, LSL, slow cooling rate; 0. LSL. rapid cooling rate.
A new dosimeter gel
0
0.2
0.4
Concentration
I 0.8
0.6
0
Seagel (SC by weight)
Fig. 3. The sensitivity ratio (slow/rapid cooling rate) for LSL gel (0) (1% by weight, 1.0mM ferrous ions) and SeaPlaque@ gel (B) (1.25% by weight, 1.5 mM ferrous ions) at different SeaGelE concentrations. The error bars indicate 1 SD.
study is given in percent by weight, including water content.
1083
I
10
Aboorl#d d-
I
30
20
40
(GY)
Fig. 5. The dose-response curves for SeaPlaque” gel (1.25% by weight) with SeaGel@ (0.25%) for three different ferrous ion concentrations. The sulphuric acid concentration is 50mM. W, OSmM, r =0.998 (0-10Gy); 0, l.OmM, r = 0.9993 (O-30 Gy); A, 1.5 mM ammonium ferrous sulphate, r = 0.9998 (O-40 Gy).
the
2.2. Cooling rate dependence
To examine the dependence of the cooling rate the vials, during their cooling period, were located outside (corresponding to rapid cooling rate) as well as at the centre of a filled phantom containing gel at the mixing temperature (corresponding to slow cooling rate). The phantom was a cylinder 170 mm in both diameter and height. This phantom was surrounded by a basin filled with water also at the same temperature as the gel. This experimental set-up was designed to simulate the cooling rate at the edge and at the centre of a large gel phantom (Fig. 1). The proportions of the different gelling substances were varied to optimize the sensitivity of the gels according to the criteria that the sensitivity should be high, and equal at the two extremes of cooling rate. 2.3. Sulphuric acid and ferrous concentrations
For SeaPlaque@ gel the different mixtures with and without SeaGel@ were also studied for various sulphuric acid concentrations (0.05-0.4 M). The ferrous _.._
ammonium sulphate and sodium chloride concentrations were 1.5 and 1.OmM, respectively. One composition of SeaPlaque@ with SeaGel@ (1.25 and 0.25% by weight, respectively, and 0.05 M sulphuric acid) was further investigated with respect to the ferrous ion concentration, 0.25-2mM. 3. Results 3.1. The cooling rate dependence A stiff and stable LSL-agarose gel is achieved at a concentration of 1% by weight. For pure LSL gel the sensitivity ratio between slow and rapid cooling rate is high, approx. 1.7 (Fig. 2). When SeaGel@ is added the ratio decreases as a function of the concentration (Fig. 3). The sensitivity ratio for LSL with 0.75% by weight SeaGel@ is better than for pure LSL. Even so, the ratio (1.06) is too large to make the LSL a useful gel for phantom dosimetry. Adding more SeaGels will increase the gelling temperature. Since SeaPlaque@ is a gel with less gel strength than LSL the concentration was increased to 1.25% by weight to obtain a stiff and stable gel. For pure 0.25
0.11 $ :=
I
0.10 -
0.09 -
0.081 0
0.1 Sulphuric
0.2
0.3
acid ooncentrtiion
0.4
I
0.5
(M)
Fig. 4. The sensitivity of SeaPlaque@ (1.25% by weight) and SeaPlaque@ gel (1.25%) and SeaGel@ added (0.25%) at different sulphuric acid concentrations. The ferrous ion concentration is 1.5 mM. 0, SeaGel@ added, slow cooling rate; n , SeaGel@ added, rapid cooling rate; 0, no SeaGel@ added, slow cooling rate; 0, no SeaGelE added, rapid cooling rate.
0
0.5 Fwmw
1
1.5
km coma&Mm
2
2.5
(mM)
Fig. 6. The sensitivity for SeaPlaque” gel (1.25% by weight) with SeaGel@ (0.25%) added at different initial ferrous ion concentrations. The sulphuric acid concentration is 50 mM. The sensitivity decreases with increasing ferrous sulphate concentration. Note the right-hand scale where the sensitivity is expressed as multiples of the sensitivity of standard Fricke solution [G(Fe’+)= 15.6 (100 eV)-‘1.
L. E. OLSON et al.
1084
II0
20
10 Absorbed
dose
30
J
40
(Gy)
curves for SeaPlaqueR gel (1.25% Fig. 7 The doseeresponse . by weight, 1.5 mM ferrous ions) with 0.25% by weight or 0.25% galactose added. q (dotted line), SeaGel* SeaGel” added, slow cooling rate; n (solid line), SeaGel’” added, rapid cooling rate; 0 (dotted line) galactose added, slow cooling rate; l (solid line), galactose added. rapid cooling rate.
SeaPlaque” the sensitivity ratio is not as high as for LSL, being approx. 1.05 (Figs 2 and 3). At added SeaGels’ concentrations of 0.12% or more, the difference in sensitivity is negligible or less than 1% (Fig. 3). The sensitivity is also higher for SeaPlaque” than LSL. 3.2. Sulphuric acid concentration At higher sulphuric acid concentrations, for SeaPlaque” both with and without SeaGel” added, the sensitivity is somewhat greater but the difference in sensitivity between slow and rapid cooling rate is also enhanced (Fig. 4). The increase in sensitivity is rather moderate, so the disadvantages of the cooling rate dependence and a poorer gel strength at higher acid concentrations are greater than the advantage of improved sensitivity. 3.3. The ferrous
ion concentration
The ferrous ion concentration significantly influences the sensitivity of the gel (Fig. 5) which decreases with increasing ferrous ion concentration. For the 1.5 mM concentration the sensitivity is six times higher than for standard ferrous sulphate (“Fricke”) solution (Fig. 6). The G(Fe3+)-value is 94 + 2 (100 eV)-’ The dose interval in which the dose response is linear decreases as the ferrous concentration decreases. For a dosimeter gel prepared with 1.O mM ferrous ions the linear dose response reaches approx. 30 Gy. In these agarose gels, which are bubbled with oxygen, the depletion of oxygen occurs much later than the depletion of the ferrous ions.
4. Discussion For pure agarose (i.e. without addition of SeaGelg), it is evident that the sensitivity of the dosimeter gel is dependent on the cooling rate of the gel. The sensitivity increases with increasing breakdown (acid hydrolysis) of the agarose gel. It may be that this increase in sensitivity is due to a more
uniform distribution of agarose throughout the gel, as the acid hydrolysis of agarose will probably not only create “loose ends”, that are able to “sweep” into the otherwise carbohydrate free pores, but also produce short oligosaccharide chains that participate in the chain reaction described in the Appendix. This increased presence of carbohydrate in the gel cavities could increase the sensitivity by decreasing steric hindrance to the propagation of reaction (9). (The reaction number refers to the mechanism in the Appendix.) An effective increase in the rate constant of this reaction would decrease k, , thereby increasing G(Fe’+ ). This means that the increased hydrolysis of agarose in the centre of a large phantom due to a slower cooling rate will also increase the sensitivity of the gel in the centre of the phantom. It is also evident from our results that the addition of SeaGel” to the agarose diminishes the effect of the cooling rate. For SeaPlaque” the cooling rate dependence is negligible when substantial amounts of SeaGel” are added. This will probably not, however. occur for LSL since adding more than 0.75% by weight of SeaGelR to the mixture will increase the gelling temperature of the mixture resulting in a poorer gelling due to the increased break-down of the gel, caused by the acid at higher temperatures. The difference between SeaPlaque” and LSL may be that the SeaPlaque” gel can be mixed with ferrous solution at a temperature about 1O’C less than can LSL. We believe that the SeaGel% effect is due to the distribution of carbohydrate throughout the gel. Therefore the addition of SeaGel” not only increases the general sensitivity of the gel system, but also diminishes the above-mentioned effect of the acid degradation of the gel, as the presence of SeaGel” throughout the pores of the gel outweighs the extra carbohydrate released by the acid hydrolysis. That the diminishing of the cooling rate effect is due to the extra available carbohydrate throughout the gel structure is rendered probable by experiments performed with the addition of the monosaccharide galactose to the agarose gels. These experiments gave results similar to the results obtained with the addition of SeaGel” (Fig. 7). The sensitivity and the linearity are, however, not as good as for gels with SeaGel”. The sensitivity increases slowly with increasing sulphuric acid concentration. At a high sulphuric acid concentration, however, it is harder to mould a stable gel and it also affects the homogeneity of the dose response. We prefer 50 mM sulphuric acid, since that gives us both reproducible and linear dose-response curves. Actually this is also valid for the standard Fricke system (Fricke and Hart, 1966). The low sulphuric acid concentration recommended by Schulz et al. (1990) (625 mM) may contribute to the nonlinear shape of their dose-response curves. The sensitivity increases with decreasing ferrous ion concentration. At high ferrous concentrations the probability decreases for the radicals to react with
A new dosimeter
agarose molecules. Then the ferric yield will decrease, since fewer radicals will be formed that eventually can oxidize ferrous ions. This is consistent with the proposed reaction mechanism, since reactions (2) and (15) represent competition for OH radicals between Fe’+ and agarose. At very low ferrous concentrations the possibility for reacting with ferrous ions is constant and small, because there is large possibility for reacting with agarose. The initial G-value will therefore be nearly constant when the ferrous concentrations are small. On the other hand, at high ferrous concentrations the G-value will be low and slowly decreasing with that concentration. This is due to the large likelihood that OH will react with ferrous ions instead of agarose. This qualitative discussion is supported by the shape of the line in Fig. 6. We have earlier used 1.5 mM ferrous concentration to measure absorbed dose distributions (Olsson et al., 1990). We preferred that concentration in spite of the lower sensitivity when compared to a concentration of, for example, 0.5 mM. There are two reasons for this. The dose response shows a better linearity and the chemical reactions are completed immediately after irradiation. According to Appleby et al. (1988) the reactions for a gel of 0.4mM ferrous concentration will not be completed until after approx. 20min and this may cause a delay in the MR measurement, which should be started as soon as possible to minimize the effect of the diffusion. In this paper we have addressed the properties of dosimeter gels of agarose/Fe3+-type as they pertain to radiation dosimetric applications. The applicability of this system to imaging of non-uniform dose distributions depends also on the rate of diffusion of the ferric ions responsible for the dosimetric image (Olsson et al., 1990). Recently, this question has also been quantitatively addressed by Schulz et al. (1990), who predicted that diffusion of ferric ions can be expected at a rate of about 1.9 mm/h. If this prediction is verified, accurate radiation dose distributions measured by these systems should be performed as soon as possible post-irradiation, or the measured distributions corrected for this effect.
5.
Conclusions and Composition of the New Dosimeter Gel
The new dosimeter gel has suitable qualifications for measurement of absorbed dose distributions using the magnetic resonance imaging technique. The sensitivity is high compared to ferrous sulphate solution and uniform over a large volume, the dose response is linear over a wide absorbed dose range. It is mechanically stable for several days and is rather easy to prepare. This dosimeter gel in use together with magnetic resonance imaging, MRI, could have a number of applications in radiation therapy, since it is possible to mould the gel to arbitrary configurations and to integrate the absorbed doses from different kinds of fields and radiation qualities.
gel
The new dosimeter
1085
gel consists
of:
1.25% by weight SeaPlaque”, 0.25% SeaGels, 0.05 M sulphuric acid, 1 .O mM sodium chloride and ferrous ammonium sulphate in a concentration that gives the desired linear dose range depending upon the application (preferably between 0.5-1.5 mM). Acknowledgements-This project was supported by the Swedish Cancer Society (project 2349-B90-OlXA) and the Cancer Foundation of Malmo University Hospital. The valuable discussions with Jan-Ove Christoffersson, Ph.D. are also acknowledged. New Jersey Agricultural Experiment States Publication No. D-07124-1-90, supported by state funds.
References Appleby A., Christman E. and Leghrousz A. (1987) Imaging of spatial radiation dose distribution in agarose gels using magnetic resonance. Med. Phys. 14, 382. Appleby A., Leghrousz A. and Christman E. (1988) Radiation chemical and magnetic resonance studies of aqueous agarose gels containing ferrous ions. Radiat. Chem. 32, 241. Day M. J. (1990) Radiation dosimetry using nuclear magnetic resonance: an introductory review. Phys. Med. Biol. 35, 1605. FMC BioProducts Source Book (1988) p. 53. FMC Corporation. Fricke H. and Hart E. J. (1969) Radiation Dosimetry (Eds Attix F. H. and Roesch W. C.), Vol. 2, p. 193. Academic Press, New York. Hart E. J. (1952) Mechanism of the gamma-ray-induced oxidation of aqueous ferrous sulfate-formic acidoxygen solutions. J. Am. Chem. Sot. 74, 4174. ICRU (1969) Radiation Dosimetry: X-rays und Gamma Rays with Maximum Photon Energies Between 0.6 and 50 Me V. ICRU, Washington, DC. Olsson L. E., Petersson S., Ahlgren L. and Mattsson S. (1989) Ferrous sulphate gels for determination of absorbed dose distributions using MRI technique: basic studies. Phys. Med. Biol. 34, 43. Olsson L. E., Fransson A., Ericsson A. and Mattsson S. (1990) MR-Imaging of absorbed dose distributions for radiotherapy using ferrous sulphate gels. Phys. Med. Biol. 35, 1623. Schulz R. J., deGuzman A. F., Nguyen D. B. and Gore J. C. (1990) Dose-response curves for Fricke-infused agarose gels as obtained by nuclear magnetic resonance. Phys. Med. Biol. 35, 1611. Spinks J. W. T. and Woods R. J. (1976) An Introduction to Radiation Chemistry, p. 299. Wiley, New York. APPENDIX The Radiation Chemistry of the Dosimeter Gel The agarose dosimeter gels have a high sensitivity. It is well known that organic additives can increase the G(Fe)+ )value of ferrous sulphate solutions or “Fricke solution” (Spinks and Woods. 1976). To exnlain the hiah sensitivitv ofthis kind of dosimeter gel a chain reaction within the gel is needed. A reaction scheme, adapted from Hart (1952) for ferrous solutions containing formic acid, has been nrooosed for agarose gels containing ferrous ions (Appleby it al., 1988). The chain is initiated by the radicals H, e.q and OH and the hydrogen peroxide generated by radiolytic decomposition of water. Using RH to represent the agarose molecule, and RX and ROH to represent reduced and oxidized forms of agarose respectively, the following reactions are postulated:
L. E. OLSON et al.
1086
*HO, + H+ + Fe2+ +H,O,
‘RO
‘do,
Fig. Al. The dynamics of the agarose-dependent chain propagation reactions in the agarose dosimeter gel. The chain starts with an agarose radical, *R which, in presence of oxygen, gives rise to another radical, *RO,. An oxidation of ferrous to ferric ions takes place and the product RO,H continues the oxidation and produces another radical, *RO. What makes the chain complete is the latter radical’s capability to react with agarose again. As a result a new *R is formed, which can then start a second chain. Initiation H,O+H,
OH, eaq, H,O,
e,+H++H OH + RH-i*R
(1) + H,O
H+RH+*R+H>.
(2) (3)
When the gel is exposed to radiation the radicals H, OH, ea; and hydrogen peroxide, H,O, are generated. These products react with the agarose molecule, RH, and induce the agarose radical, *R (2) and (3). which starts the chain reactions. Propagation *R + 0r+*R02
(4)
Fe2+ + *RO 2-t Fe3+ + RO- z RO;
+ H+ +RO,H
RO,H
+ lRO + OH-
+ Fe2+ +Fe’+
*RO + RH +*R
+ ROH
H + 0, -+*HO*
(5) (6)
Fe*++H,O,-+Fe-‘++OH+OH-
(11)
+ Fe3+.
The most important steps for the chain mechanisms are reactions (4) and (9). In (4) a radical, lRO, is formed that both oxidizes ferrous ions, (5), (6) and (8) and results in a new radical, *RO. This can re-react with agarose (9) and as a result a new *R is formed and the reactions can start from the beginning again. This process is dependent on the gel being well oxygenated. The chain propagation steps that depend on agarose are illustrated schematically in Fig. Al. Reactions that could terminate the chain are (12t(l6). Reactions (12)(16) will dominate at high doses as Fe’+ builds up.
(7) (8) (9) (10)
Termination Fe’+ + *R-+Fe’+
+ H+ + RX
(12)
Fe’+ + *R -+Fe3+ + RH+ + Fe2+ + *RO+Fe’+ Fe’+ + OH +Fe3+ Fe’+ + *ROr +Fe2+
(13)
+ ROH
(14)
+ OH-
(15)
+ H+ + 0: + RX.
(16)
The reaction products from reactions (12)-(16) will not contribute further to continual chain reactions. There is a finite possibility that ferric ions will be reduced, (12) and (16). Normally this possibility would be small, but it would increase when the fraction of ferric ions grows. There are also two reactions, (I 3) and (15) that although they produce ferric ions still terminate the chain reaction. From the reaction scheme it can be shown that:
G(Fe’t)‘i [Fe’+] ‘[o,l
2(G, + Go,) [Fe*+],
+k z
P,l
k [Fe’+] + k [Fe’+]
‘IRH]
4F]
From the above it is evident that, if the reaction scheme is correct the sensitivity would be dependent on the ferrous, oxygen and agarose concentrations. Since we observe an inverse relationship between G(Fe3+) and [Fe”], the term k4[Fe3+]/[Fe2+] must be less significant than the terms k2[Fe2’]/[0,] and k,[Fe’+]/[RH], especially since [Fe’+] will be much smaller than [Fe2+] at low doses. The dependence on oxygen concentration is predicted by the above reaction scheme to be such that G(Fe3+) increases as [Or] increases. We have previously reported this effect of oxygen concentration (Appleby et al., 1988; Olsson et a/., 1989). Work is in progress to evaluate the constants k,-k,.