Polyvinyl alcohol-Fricke hydrogel and cryogel: two new gel dosimetry systems with low Fe3+

diffusion

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Phys. Med. Biol.45 (2000) 955–969. Printed in the UK PII: S0031-9155(00)08696-6

Polyvinyl alcohol–Fricke hydrogel and cryogel: two new geldosimetry systems with low Fe3+ diffusion

K C Chu†‡, K J Jordan†§, J J Battista†§, J Van Dyk†§ and B K Rutt‡§† London Regional Cancer Centre, London, Ontario, Canada‡ The John P Robarts Research Institute, London, Ontario, Canada§ The University of Western Ontario, London, Ontario, Canada

Received 13 October 1999, in final form 12 January 2000

Abstract. Two new Fricke dosimeter gel systems with low diffusion rates have been developed for3D radiation dosimetry purposes. Both systems consist of a solution of 20% (by weight) polyvinylalcohol (PVA) in a 50 mM H2SO4 solution with 0.4 mM ferrous ammonium sulphate and xylenolorange (FX). The difference in the two gels is the way that the gelation process was initiated: eitherby bringing the temperature to (a) +5◦C or (b)−20◦C before returning them to room temperature.These gels are termed ‘hydrogel’ and ‘cryogel’, respectively. The hydrogel is optically transparent,and can be used with either optical or MRI detection methods for dosimetric imaging. The cryogelis rubbery in texture but opaque, so its internal Fe3+ concentration can only be measured with MRI.The hydrogel’s optical attenuation coefficient is linear (r2 = 0.99) with dose from 0 to 20 Gy witha sensitivity of 0.106 cm−1 Gy−1 (at 543 nm). In terms of MR relaxation rate, the dose responsefor both the hydrogel and cryogel was linear (r2 = 0.99) with a sensitivity of 0.020 s−1 Gy−1

(at 1.5 T). The Fe3+ diffusion coefficient (at 20◦C) was measured to be 0.14 mm2 h−1, which issignificantly lower than similar preparations reported for porcine gelatin or agarose. The PVA–FXgels can be stored for long periods of time before exposure to radiation, since the auto-oxidationrate was 10 times less than that of gelatin–Fricke recipes. The new gels developed in this work area significant improvement on previous Fricke gel systems.

1. Introduction

Recent developments in three dimensional (3D) conformal radiation therapy can be efficientlyvalidated using gel dosimetry. The two main types of gel dosimeter used to date are based onpolymer–acrylamide–gelatin (PAG), Fricke–gelatin or Fricke–agarose gels. Numerous papershave been published describing the mechanism, applications and measurements of the PAGgels (Maryanskiet al 1993, 1994, 1996, 1998, Ibbottet al 1997, Oldhamet al 1998, Baldocket al 1998) and Fricke gels (Goreet al 1984, Applebyet al 1988, Olssonet al 1989, 1991,Duzenliet al 1994, Gambariniet al 1994, Olsen and Hellesnes 1994, Bengtssonet al 1996,Lucianiet al 1996, Di Capuaet al 1997). In this work, we limited our attention to Fricke typegels, which are non-toxic and which are easily prepared in the presence of oxygen, comparedwith PAG gels.

The traditional Fricke gels consist of Fe2+ ions (in 1 to 5% agarose and/or gelatin) whichupon irradiation oxidize to Fe3+. The concentration of the Fe3+ ion is linearly proportional to thedose absorbed and its concentration can be measured using optical spectroscopy (Appleby andLeghrouz 1991), optical computed tomography (CT) (Kellyet al1998a) or magnetic resonance(MR) T1 relaxation imaging (Goreet al 1984, Olssonet al 1990, Audet and Schreiner 1997).Unfortunately, the Fe3+ ion is known to diffuse and by the time the dose distribution is imaged,

0031-9155/00/040955+15$30.00 © 2000 IOP Publishing Ltd 955

956 K C Chu et al

its spatial integrity may have substantially degraded (Day 1990, Balcomet al 1995). Theblurring of the measured dose distribution (Olssonet al1992, Harriset al1996, Kronet al1997)may be as much as 1.5 mm within the first hour and this is a serious disadvantage comparedwith PAG gels (Schreineret al1994, Pedersenet al1997). Although it is possible to minimizethe effects of diffusion by performing measurements immediately after irradiation and as fastas possible at a reduced temperature of 10◦C (Raeet al 1996), this introduces a practicalinconvenience. Alternatively, the diffusion coefficient can also be lowered using chelatingagents that anchor the Fe3+ species (Raeet al 1996). One such chelating agent is xylenolorange, which not only lowers the diffusion coefficient in Fricke gel systems but also producesa visible colour change as a function of dose (Gupta and Narayan 1985, Appleby and Leghrouz1991, Kellyet al 1998a). This optical change can be measured with a spectrophotometer forpoint dosimetry or an optical CT scanner for 3D dosimetry. However, diffusion remains as adisadvantage of traditional Fricke–xylenol orange gel dosimeters.

In the pursuit of an improved Fricke gel recipe with even less diffusion, we present initialresults from two new tissue-equivalent gel systems (Chuet al1999a,b). The gel matrix is basedon the polyvinyl alcohol (PVA) molecule. PVA is a common water-soluble polymer that is usedin the film and adhesive industries, and it is obtainable with tight manufacturing tolerancesand with low impurity levels, which is an advantage over organically based gel materials.Since the PVA material is also non-toxic and it can be prepared in the presence of oxygen, itoffers advantages over the PAG gel preparations. When mixed with Fricke chemicals, PVAis a versatile radiochemical gel matrix for either optical CT or MRI detection methods. PVAsolution can be transformed into an opaque rubbery cryogel by freezing at−20◦C and thenreturning it slowly to room temperature (Manoet al 1986, Chu and Rutt 1997). However, wehave discovered that by simply lowering the temperature of the PVA solution to +5◦C andreturning it to 20◦C, an optically clear hydrogel forms which can be used withboth opticaland MR detection methods.

Our PVA gel system differs from previous attempts to use PVA solutions to measure highdoses of irradiation (103 to 105 Gy). It has been shown that irradiation causes scission andcrosslinking of the polymer chain in PVA solutions and this changes the molecular weightand viscosity of PVA solutions (Berkowitchet al 1957, Sakurada and Ikada 1964). Themechanism for this phenomena has been described (Grishina 1963, Hirano 1964). By usingcertain additives, it was possible to crosslink PVA films using ionizing irradiation (Bernsteinet al 1965) or UV light (Tsunoda and Yamaoka 1964). In these studies, along with others(Peppas 1973), the high levels of irradiation used fell outside the range deemed useful forradiation therapy purposes, and will not be discussed further. The PVA gel system describedhere is suitable in the range of medical therapeutic applications (0 Gy to 20 Gy).

2. Materials and methods

2.1. PVA gel preparation

An acid solution of 50 mM H2SO4 (ACS897-02, BDH, Toronto, Canada) in de-ionized waterwas first prepared. The acid solution was used to make four solutions containing ferrousammonium sulphate (F-1543 Sigma, St Louis, MO) and xylenol orange (22 785-4, Aldrich,Milwaukee, WI) in a molar ratio of 1:1. Each solution had a ferrous ion concentration of 1.2,2.4, 3.6 or 4.8 mM and was labelled as ‘FX concentrate’. Then three different amounts ofPVA (98.4% hydrolysed, 22 000 molecular weight: 30573, BDH, Poole, UK) were dissolvedin the acid solution at 120◦C for 3 hours. The PVA concentrations were set to 18, 24 or30% by weight. The hot PVA solutions were then cooled to 45◦C, at which time five parts

PVA–Fricke hydrogel and cryogel 957

of PVA solution were then thoroughly mixed with one part of our premade FX concentrate.Hence, there were 12 final recipes containing 15, 20 or 25% PVA, with 0.2, 0.4, 0.6 or 0.8 mMFX, all dissolved in 50 mM H2SO4 solution. These blends were poured into 4.5 ml cuvettes(58017-875, VWR Canlab, Mississauga, Canada), covered with paraffin wax (to minimizeevaporation), centrifuged (to remove air bubbles) and subsequently stored at either +5 or−20◦C. Samples were returned to room temperature over a time period of 2 or 6 hours priorto irradiation, respectively.

To compare our results with a gelatin–Fricke recipe, we dissolved 4.8% by weight gelatin(G-2500, Sigma, St Louis, MO) in 37.5 g of 65◦C water. This solution was allowed to coolto 40◦C at which time 7.5 g of 2.4 mM FX concentrate was added. The final blend (whichcontained 4% gelatin and 0.4 mM FX) was cooled to 5◦C to allow it to set. The gel wasreturned to 20◦C for irradiation and detection.

2.2. Dose calibration

Calibration samples were obtained by irradiating cuvettes submersed in the centre of a waterbath using lateral parallel-opposed-pair (POP) cobalt-60 beams to a total central dose of 0, 2.5,5, 7.5, 10, 15 or 20 Gy. The optical densities (ODs) of the PVA–FX hydrogels were measured ata wavelength of 543 nm using a 1 mWgreen helium–neon laser (167 4P, Uniphase, Manteca,CA) with a silicon diode optical detector and power meter (models 818-UV and 1830-C,Newport, Irvine, CA). All OD values were obtained through the 1 cm path length defined bythe cuvette dimensions.

For both the PVA–FX hydrogels and cryogels, the MR relaxation rate (R1 = 1/T1) wasalso measured using a fast 2D inversion recovery spin echo (f-IRSE) method on a clinical 1.5 TSIGNA MR scanner (General Electric Medical Systems, Milwaukee, WI). All of the cuvetteswere placed upright and centred in the head coil. A single 20 mm thick coronal slice was takenthrough the centre of all of the cuvettes. Other MR parameters include echo train length= 4,RBW = ±15.6 kHz, TE= 15 ms, TR= 5000 ms, 0.5 pFOV, 1 NEX, 256×256 pixels, 22 cmFOV; TI = 50, 100, 200, 300, 400, 600, 800, 1600 or 4000 ms. The time to acquire one imagewas 3.0 minutes, and hence, all nine images were acquired within 27 minutes. Although thisimaging time was excessive, this MR imaging method for measuringT1 can be considered asa gold standard technique.

These same samples were also MR imaged using a fast 3D Look-Locker (f3DLL) pulsesequence (Hendersonet al 1999) that generated three-dimensionalR1 (= 1/T1) maps with0.7 mm3 voxels. This pulse sequence produced 192 images, which were subsequentlyprocessed to produce a 12 sliceR1 volume. The total imaging time of this multi-slice 3Dpulse sequence was 3.65 minutes.

2.3. Diffusion measurements

Diffusion measurements were performed on cuvettes filled with either PVA–FX hydrogels orcryogels, by applying POP irradiation only to the top half of a cuvette (with a 9 mmacrylicbuild-up and a backscatter layer) while the bottom half was shielded using a 10 cm lead alloy(Cerrobend®) block. A total of 40 Gy was delivered to the unblocked region. OD measurementsthrough the 1 cm pathlength of the cuvette were collected every 0.5 mm along the length ofthe cuvette to sample the step-shaped profile. Six OD profiles were collected from 0.82 to72 hours after irradiation in order to determine the diffusion coefficient.

These same samples were also MR imaged using the f3DLL pulse sequence to producea 12 sliceR1 volume map. SixR1 volume maps were acquired at various times from 6.25 to

958 K C Chu et al

96.1 hours after irradiation. The signal to noise ratio (SNR) from images produced from thef3DLL pulse sequence was lower than that of a standard f-IRSE pulse sequence. However,because of f3DLL’s exceptional speed, it was preferred since it could obtain a ‘pseudo-snapshot’of the diffusing edge within 3.65 minutes. Three cuvettes could be imaged at the same timeby centring the cuvettes horizontally inside the horizontally mounted surface coil.

3. Results

3.1. Reaction rates

Figure 1 shows the OD of 20% PVA with 0.2 to 0.8 mM FX as a function of time afterirradiation to 20 Gy, all at room temperature. We note that the PVA gel with FX concentrationof 0.2 mM shows an increase as a function of time during the first 50 minutes of reaction.At concentrations above 0.2 mM FX, the OD remained fairly constant with a slow baselineupward drift. This slow increase in OD as a function of time is independent of dose and iscaused by auto-oxidation. The rate of baseline drift is mainly a function of FX concentration(table 1). However, the PVA concentration also has a small influence on the rate of baselinedrift.

Time after irradiation, minutes

0 20 40 60 80 100 120

Opt

ical

Den

sity

1.45

1.50

1.55

1.60

1.65

1.70 20% PVA hydrogel

0.8 mM FX

0.6 mM FX

0.4 mM FX

0.2 mM FX

Figure 1. OD of 20% PVA–FX hydrogels in cuvettes as a function of time after irradiation to20 Gy.

In table 1, it is shown that for an FX concentration of 0.4 mM, the change in OD at roomtemperature was 0.0015 per hour. By storing the samples at 5◦C, the auto-oxidation wasreduced by a factor of ten. We note that the refrigerated samples were allowed to reach toroom temperature for OD measurement in order to prevent condensation from forming on thecuvette surface.

3.2. Dose sensitivity

The optical dose sensitivities of 20% PVA with different FX levels are plotted in figure 2. Allof the PVA–FX gel samples show a linear response as a function dose to 20 Gy. The slopesand linearity quality (r2) are summarized in table 2 along with data collected from the 15%PVA–FX gels.

PVA–Fricke hydrogel and cryogel 959

Table 1. The average rate of auto-oxidation in un-irradiated PVA–FX hydrogels in cuvettes storedat either 5 or 20◦C. The values were obtained over a 31 day period.

OD change per hour(through a 1 cm cuvette)

% PVA mM FX Stored at 20◦C Stored at 5◦C

15 0.2 0.0007 0.000 1115 0.4 0.0014 0.000 1615 0.6 0.0022 0.000 2115 0.8 0.0031 0.000 3220 0.2 0.0007 0.000 0720 0.4 0.0016 0.000 1320 0.6 0.0027 0.000 2420 0.8 0.0040 0.000 514% gelatin 0.4 0.0201 0.002 40

Delivered Dose, Gy

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

Opt

ical

Den

sity

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.2 mM FX

0.4

0.8 mM FX

0.6

20% PVA hydrogel

Figure 2. The response in OD of 20% PVA–FX hydrogels in cuvettes to various levels of dose.The symbol size encompasses one standard deviation in the measured data.

Since our OD measurements were through a 1 cmpathlength, all the OD values reportedhere can be converted to optical attenuation coefficients (in units of cm−1) by multiplying theOD number by 2.303. For example, 20% PVA with 0.4 mM FX has an OD dose sensitivity of0.046 Gy−1, which converts to an optical attenuation coefficient of 0.106 cm−1 Gy−1.

The MRR1 response of the PVA–FX hydrogels to dose shows a similar trend as the opticaldata. Figure 3(a) shows that the hydrogel has a linearR1 response to dose to 20 Gy. Table 3reports the corresponding slopes and linearity along with data collected from the 15% PVA–FXgels.

In terms of the PVA cryogel, the dose response (R1 against dose) is shown in figure 3(b).These graphs are similar to that of the PVA hydrogel, except for a vertical shift in the data.This vertical shift is a result of an increase in the baselineR1 value of the cryogel comparedwith the hydrogel. The last two columns in table 3 summarize the dose response properties ofthe PVA–FX cryogels.

960 K C Chu et al

Table 2. The response in OD of PVA–FX hydrogels in cuvettes to dose extracted from figure 2 issummarized. The linearity (r2) of the dose response from 0 to 20 Gy is also reported for variouscombinations of PVA–FX.

OD sensitivity(through 1 cm cuvette) Linearity

% PVA mM FX (Gy−1) r2

15 0.2 0.060 0.998015 0.4 0.050 0.999715 0.6 0.044 0.999015 0.8 0.039 0.999820 0.2 0.053 0.997720 0.4 0.046 0.997920 0.6 0.042 0.997920 0.8 0.036 0.9953

Table 3. MR relaxation rateR1 sensitivity and linearity of PVA–FX hydrogel and cryogel to dosefrom 0 to 20 Gy is tabulated from figure 3.

Hydrogel CryogelR1 sensitivity Hydrogel R1 sensitivity Cryogel

% PVA mM FX (s−1 Gy−1) linearity r2 (s−1 Gy−1) linearity r2

15 0.2 0.021 0.9945 0.022 0.997215 0.4 0.017 0.9984 0.019 0.992215 0.6 0.017 0.9986 0.017 0.987415 0.8 0.015 0.9984 0.016 0.9941

20 0.2 0.020 0.9939 0.022 0.995720 0.4 0.019 0.9984 0.020 0.998820 0.6 0.017 0.9977 0.018 0.996320 0.8 0.015 0.9958 0.016 0.9973

3.3. Diffusion rates

A typical OD profile along the length of a half irradiated cuvette filled with PVA–FX hydrogelis shown in figure 4 (top, acquired at 0.82 hours). Figure 4 (middle) shows the correspondingR1 profile obtained from the f3DLL MR imaging sequence at 6.25 hours after irradiation. Thesolid line is the least squares fits to data using the equation (Kronet al 1997):

Y = Y0 +1

2(Y1− Y0)

{1 +

(X −X0)√(X −X0)2 + n

}(1)

whereY is the measuredR1 or OD value at the positionX; Y0 andY1 are the minimum andmaximum values ofY , respectively;X0 is the amount of horizontal shift necessary to placethe location of the inflection point at the zero distance value andn is a curvature parameter thatvaries inversely with the slope of the inflection point.Y0, Y1, X0 andn are fitted parametersobtained from our multi-variate fitting program (Grace 1992).

Kron et al (1997) showed that a plot ofn versus time after the start of irradiation is linearand its slope (in units of mm2 h−1) when multiplied by the factor 0.212 is equal to the diffusioncoefficient (D). Figure 5 shows several plots of the averagen versus time for the different gellevels. The diffusion coefficients determined by both optical and MR methods for PVA–FXgels are shown in figure 6 as a function of gel concentration.

PVA–Fricke hydrogel and cryogel 961

Delivered Dose, Gy

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

Rel

axat

ion

rate

R1,

s-1

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.2 mM FX

0.4

0.8 mM FX

0.6

20% PVA hydrogel

(a)

Delivered Dose, Gy

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

Rel

axat

ion

rate

R1,

s-1

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0.2 mM FX

0.4

0.8 mM FX0.6

20% PVA cryogel

(b)

Figure 3. The inversion recovery spin echoR1 dose response of 20% PVA–FX hydrogels (a)and cryogels (b) in cuvettes to various levels of dose. The symbol size encompasses one standarddeviation in the measured data.

4. Discussion

4.1. Auto-oxidation rate

An unexpected benefit of using PVA as the matrix for the Fricke ingredients is that the rateof auto-oxidation was significantly less than that of previously published Fricke gels. Wefound that at room temperature, the auto-oxidization caused the OD of PVA with 0.4 mMFX to increase by a rate of 0.0015 h−1. At +5 ◦C this value dropped to 0.000 14 h−1. Hence,samples kept in the refrigerator could be used several days later, which is a practical advantage.Even after 6 months, refrigerated samples can still be used, although the background OD mayhave increased by 0.5. However, we do not propose to researchers to wait longer than 2 weeksbetween gel production and irradiation (Gupta and Gomathy 1974) since the detection dynamicrange may be reduced.

Table 1 clearly shows that the auto-oxidation rates of the PVA–FX gels are ten times lessthan those of 4% gelatin–FX samples (whose OD change was 0.02 h−1 at room temperatureor 0.002 h−1 at 5◦C).

962 K C Chu et al

0

2

4

0.82 hours

-10 -5 0 mm 5 10

-10 -5 0 mm 5 10 R

1, s

-1

1.6

2.2

2.8

6.25 hours

O.D

.

Figure 4. The bottom figure shows a half irradiated cuvette filled with 20% PVA and 0.4 mMFX. A typical line profile from an optical scan through the hydrogel 0.82 hours after irradiationis shown at the top. The middle plot is a plot of a single line of pixels from the central slice of a12 slice 3D volume set ofR1 maps generated from the f3DLL pulse sequence. The solid lines arethe lines of best fit to equation (1).

4.2. Dose sensitivity

The optical and MRR1 dose sensitivities of the PVA gels are approximately the same as thatreported for agarose and gelatin systems withsimilar FX concentrations(Tarteet al 1996,Zahmatkeshet al 1998, Kellyet al 1998b). Hence, the use of PVA does not significantly alterthe Fricke–gel mechanism.

In terms of the optical properties, there is a small decrease in sensitivity with increasingPVA concentration (table 2). Table 2 reveals that the optical dose sensitivity is reducedsignificantly when there is a larger initial Fe2+ concentration in the original gel. This inverserelationship is expected from the postulated mechanism of the chain reaction responsiblefor Fe3+ production (Applebyet al 1988). The optical dose sensitivity was highest with acombination of 15% PVA and 0.2 mM FX. However, figure 1 shows that samples with 0.2 mMFX require 50 minutes after irradiation to reach an equilibrium concentration. Similar findingsin gelatin and agarose gels were reported by Kellyet al (1998a) and Appleby (1999). At higherconcentrations of 0.4 to 0.8 mM FX, equilibrium is established in less than 20 minutes. Hence,a good compromise between obtaining a fast response time and high dose sensitivity is achievedby using a FX level of 0.4 mM. Data reported by Appleby (1999) suggest FX levels of 0.3 mMreach equilibrium in 12 minutes while having a dose sensitivity value between samples with 0.2and 0.4 mM FX. For example, preliminary unpublished data by Shortt (1999) shows that theoptical dose sensitivity of 20% PVA is approximately doubled by lowering the FX concentrationto 0.3 mM FX. Shortt measured an OD dose sensitivity of 0.073 Gy−1 which is comparableto agarose based gels withsimilar FX concentrations(Appleby and Leghrouz 1991).

PVA–Fricke hydrogel and cryogel 963

Time, hours

0 25 50 75 100

Cur

vatu

re p

aram

eter

n, m

m2

0

20

40

60

80

100

120

15% PVA

20% PVA

25% PVA

4% gelatin

Figure 5. Plots of the curvature parametern as a function of time for various gels are shown. Then

from the PVA gels were averaged from gels with 0.2 to 0.8 mM FX. The gelatin sample containedonly 0.4 mM FX. Equation (1) was used to extractn from several line profiles collected at varioustimes.

Gel Concentration, %

0 5 10 15 20 25 30

Diff

usio

n C

oeffi

cien

t D, m

m2 hr

-1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

PVA by MRI

PVA by OD

gelatin

Figure 6. The average diffusion coefficientD plotted as a function of gel concentration. Allmeasurements were averaged using samples with various FX levels. The MRI data were averagedfrom both hydrogel and cryogel results.

Other recipe modifications such as varying the xylenol orange levels, using other additivesor increasing the oxygenation level may also improve the dose sensitivity (Zahmatkeshet al1998). However, some of these improvements in sensitivity could cause undesirable effectssuch as longer response times and lower linearity at high doses levels. Although we made noattempts to optimize the sensitivity of our gels for either optical or MRI detection, it is clearfrom the literature (Back and Olsson 1999) that the optical (Appleby and Leghrouz 1991) andMRI (Schulzet al 1990, Olssonet al 1990) dose sensitivity are maximized at two completelydifferent concentrations of ferrous ions (i.e. 0.1–0.3 mM and 1.0–10 mM, respectively). Thusthe recommended FX levels in this paper are adequate for both optical and MRI detection,but not optimized for maximum sensitivity using either detection method. In terms of MRI

964 K C Chu et al

sensitivity, it can be increased by several factors by (i) using a ferrous ion concentration of1.0–1.5 mM (Olssonet al1989, 1990; Schulz 1990) and (ii) not using xylenol orange (Back andOlsson 1999). At these levels of Fe2+ ions and no xylenol orange, the MR dose sensitivity rangesfrom 0.031 to 0.12 s−1 Gy−1 depending on the agarose or gelatin concentration. However, thedrawback of these gels is their high Fe3+ diffusion coefficients of 1.0 to 1.8 mm2 h−1. BothRaeet al (1996) and Kronet al (1997) reported that by adding xylenol orange concentrationsof 0.1 to 0.2 mM, the diffusion coefficient can be reduced by an average of 2.5 times to 0.3 to0.82 mm2 h−1. However, this was at the sacrifice of MR dose sensitivity, which now rangedfrom 0.0093 to 0.014 s−1 Gy−1. By using FX with 20% PVA instead of 4% gelatin (Raeet al1996) or 4% gelatin plus 1% agarose (Kronet al 1997), there is a small gain in MR dosesensitivity to 0.015 to 0.020 s−1 Gy−1 as shown in table 3. Even with this modest increase inMR dose sensitivity by using PVA, it is clear that the use of xylenol orange with Fe2+ in anygel matrix causes the MRI dose sensitivity to decrease by an average of 6.6 times (agarose orgelatin) or 4.3 times (PVA).

4.3. Diffusion coefficients

Figure 6 shows that the diffusion coefficient is an inverse function of PVA concentration. The20% PVA has an average Fe3+ diffusion coefficient of 0.14 mm2 h−1, which is considerablylower than all previously published values ranging from 0.3 to 2.2 mm2 h−1 (summarized byKron et al 1997). The mechanism governing this substantially lower diffusion coefficient inPVA compared to agarose or gelatin could be attributed to (i) the higher gel content or (ii) thehigher viscosity of the PVA–FX blends. Both of these diffusion mechanisms are consistentwith those found in other gels and viscous liquids (Geankoplis 1978). Although xylenol orangehas been shown to lower the Fe3+ diffusion coefficient in gelatin and agarose gels, it is notknown if this is also true in PVA. Further research is recommended to understand the actualphenomena in PVA.

Figure 6 reveals that the Fe3+ diffusion coefficient can be even further reduced by increasingthe PVA concentration above 20%. However, there are practical reasons for keeping the PVAlevel close to 20% since at higher concentrations the viscosity increases dramatically, and makesmixing of the FX concentrate difficult. Even if sophisticated mixing equipment were used,tissue equivalency and dose sensitivity would be poorer at higher PVA concentrations. The CTnumber of both 20% PVA–FX cryogel and hydrogel was determined to be approximately 44 HU(measured using 120 kVp, 100 mA on a AcQSim PQ5000 CT scanner, Picker International,Highland Heights, OH), and hence, it can be considered as tissue-equivalent (Wegener 1992).

4.4. Hydrogel considerations

One problem with using PVA hydrogels is that the viscosity of these gels increases overlong periods of time (e.g., days) at room temperature (Finch 1973). Solutions with highconcentrations of PVA (i.e. above 7% by weight) will slowly partially crosslink and this causesthe increase in viscosity and turbidity (i.e., optical scatter coefficient). This phenomenon hasbeen studied thoroughly and summarized by Peppas (1973, 1975), but we unexpectedly foundthat as long as the hydrogels are stored at +5◦C, and then used within 7 days of manufacturing,our hydrogels remained optically clear. Peppas (1973) states that it is necessary to followexactly the same procedure every time a PVA solution is prepared. The time–temperaturehistory of the preparation affects the rate of spontaneous crosslinking of PVA solutions. Thus,it is recommended that the turbidity issue be examined more carefully to fully characterizethe PVA–FX hydrogels. In the extreme limit, PVA cryogels can be considered as a form of

PVA–Fricke hydrogel and cryogel 965

hydrogel that has a large amount of crosslinking, which explains their greater opacity. Thefreezing and thawing cycles accelerate the crosslinking mechanism.

4.5. Cryogel considerations

The diffusion coefficients of Fe3+ in PVA cryogels (measured from MRR1 maps) were foundto be within 10% of the values reported for PVA hydrogels (measured from OD profiles).The cryogels have the distinct advantage of no auto-oxidation during storage at−20◦C.Although the cryogels are rubbery and tough as a material, there are two potential complicationsin manufacturing this gel. First, upon freezing, the gel will expand similarly to ice andcould crack the mould container. Plastic containers such as polyethylene, polypropyleneor polycarbonate were found to be good container materials. Secondly, we found that rapidcooling by submersing the sample in liquid nitrogen produces the most homogenous cryogelswith the smallest crystal structures. Hence, the rate of cooling affects the cryogel homogeneity.

Because PVA cryogel is flexible and stable at 37◦C, one application for PVA–FX cryogelis its use as a radiosensitive bolus material during radiation treatment. As a bolus material, theskin dose can be determined directly since the surface colour adjacent to the skin will changefrom an orange colour to a dark brown colour when exposed to radiation. Since the Frickemechanism is slightly temperature sensitive (Gupta 1973), the dose calibrations and readoutfor in vivostudies would require that the cryogel be calibrated at similar conditions mimickingthat of when it was usedin vivo.

Although the material is non-toxic, it should not be in direct contact with skin but ratherseparated with a thin layer of plastic film. This prevents the cryogel from dehydrating andbeing contaminated, which will affect the dose measurements.

4.6. MR techniques

For MR imaging to be a practical detection method in Fricke gel dosimetry, it must rapidlyacquire images which can be converted to accurateT1 maps. Kronet al (1997) recognizedthis, and reported the use of a 2D Look-Locker pulse sequence on a small bore NMR scannerfor gel dosimetry in less than 15 minutes. Hendersonet al (1999) improved the Look-Lockerpulse sequence by (i) accelerating the data collection, (ii) applying its concept to 3Dk-spacedata collection and (iii) implementing it on a clinical MR scanner. By using Henderson’sf3DLL pulse sequence to measureT1 in our Fricke gels, our total MR acquisition time was3.65 minutes. Although we only required a single slice for the work presented in this paper,the f3DLL provided a true 3D volume set which is useful for future 3D Fricke gel dosimetry.

This is the first report of a MRI pulse sequence that is capable of providing 3DR1 maps (ordose distributions) with sub-millimetre slice thicknesses and pixel sizes of irradiated phantons.Most researchers use a stack of 2D MRI images to generate a 3D image; however, 2D MRI onclinical scanners is inherently limited to a minimum slice thickness of 2 or 3 mm. Hence, it isrecommended that true 3D pulse sequences be used for high resolution gel dosimetry.

The f3DLL sequence samples the magnetization repeatedly during recovery after aninversion pulse. It uses 144 or more small tip-angle (‘alpha’) pulses following the inversionpulse, grouped into 8 groups, and thereby producing 8 ‘effective’ inversion time images. Usingthe Look-Locker signal equation, these 8 time points can be fitted, and theT1 relaxation timeat each voxel determined by non-linear regression.

TheT1 values of our samples obtained by using the f3DLL compared to the nine pointf-IRSE was nearly unity (figure 7: slope= 0.92, r2 = 0.99). However, the increase inspeed of the f3DLL comes at the sacrifice of SNR in ourT1 results compared to the data

966 K C Chu et al

T1 from inversion recovery spin echo, seconds

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

T1

from

f3D

LL,

seco

nds

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Figure 7. The comparison of theR1 determined by the f3DLL pulse sequence (with 0.66 mm3

voxels) and the fast inversion recovery spin echo method (with 17.2 mm3 voxels). The error barsrepresent± one standard deviation.

obtained using the f-IRSE technique. This compromise in SNR was necessary to minimizeintra-imaging diffusion effects in our profiles which would occur in long inversion recoveryimaging sequences typically used to measureT1 dose mapping. Since theT1 accuracy wasa function of the SNR in our images, we maximized the SNR in two ways: (1) by using asmall receive-only RF coil with a homogeneous region that matched our sample size, and (2) byadjusting the MR parameters so that (a) after the last ‘alpha’ pulse, the equilibrium longitudinalmagnetization has a maximum value rather than being saturated, and (b) the 8 time points areplaced around the longitudinal magnetization’s null point. If necessary the SNR can also beincreased by using larger voxel sizes or by averaging several data sets.

In this work, theT1 standard deviation in the f3DLL versus the IRSE was 9% and 0.16%respectively. However, these values cannot be directly compared to each other since the voxelsizes (0.66 mm3 versus 17.2 mm3) and detection coils (3 in receive only surface coil versus atransmit/receive head coil) were completely different. A future study properly comparing theSNR from each pulse sequence is recommended.

5. Summary

We have discovered two gelation methods for PVA solutions which allows it to replace organicgelatin or agarose in traditional Fricke gel systems. Gelation is initiated into a hydrogel orcryogel by refrigeration or freezing, respectively.

These initial experiments suggest that one recipe with a reasonable compromise in reactionrate, dose sensitivity, diffusion coefficient and tissue equivalence contains 20% (by weight)of PVA with 0.4 mM ferrous ammonium sulfate and 0.4 mM xylenol orange, all in a 50 mMH2SO4 aqueous solution. However, further FX adjustments may be necessary for increasedoptimization of the desired qualities of individual researchers. The optical density andR1

response were both found to be linear (r2 = 0.99) from 0 to 20 Gy with a sensitivity of0.046 Gy−1 and 0.020 s−1 Gy−1, respectively. These values are similar to those found withgelatin or agarose recipes at the same FX concentrations. Diffusion coefficient of the Fe3+ ionwas determined both by using an optical scanning method and a fastT1 MR pulse sequence.

PVA–Fricke hydrogel and cryogel 967

D was found to be 0.14 mm2 h−1 which is significantly lower any previously publishedpreparations in gelatin or agarose. The PVA–FX cryogel system has a rubbery consistency sothat it could be used as a bolus material and surface dosimeter in radiation therapy. However,its internal dose distribution can only be determined by using MRI since it is opaque.

Four key advantages of the PVA–FX cryogel and hydrogel are that (1) its diffusion rateis low even at room temperature, (2) it can be pre-made and kept refrigerated or frozen untilrequired for use, (3) it has a low rate of auto-oxidation of the ferrous ions and (4) it is non-toxic.Further research is required to fully optimize and characterize this new gel matrix.

Acknowledgments

We would like to acknowledge the financial support from the LHSC University Hospital–Centre for the Advancement of Medical Device Technology and the National Cancer Instituteof Canada. The author (KC) is funded through the Medical Physics Residency Program at theLondon Regional Cancer Centre.

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