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Year : 2019  |  Volume : 15  |  Issue : 3  |  Page : 498-503

Analysis of induced error by susceptibility effect in low-density gel dosimeters

1 Department of Radiation Science, The School of Allied Medical Sciences, Tehran University of Medical Sciences, Tehran, Iran
2 Department of Radiotherapy Oncology, Cancer Research Centre, Cancer Institute, Tehran University of Medical Sciences, Tehran, Iran
3 Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Iran; WAVES Research Group, Department of Information Technology, Ghent University, Ghent, Belgium
4 Department of Food Science and the Rutgers Center for Lipid Research, New Jersey Institute for Food, Nutrition, and Health, Rutgers University, New Brunswick, New Jersey 08901, USA

Date of Web Publication29-May-2019

Correspondence Address:
Dr. Farideh Pak
Department of Radiation Science, The School of Allied Medical Sciences, Tehran University of Medical Sciences, West Taleghani Avenue, Poursina Street, Tehran 14174
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jcrt.JCRT_407_17

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 > Abstract 

Purpose: In low-density (LD) gel dosimeter, diffusive spin–spin relaxation rate (R2)-dispersion caused by susceptibility-induced internal gradient leads to a significant deviation in the measured R2 from the real value. In this study, the effect of induced internal gradient on R2 was visualized and quantified algebraically as an important cause of inaccuracy in LD gel dosimeters.
Materials and Methods: In this method, two sets of LD and unit-density (UD) gel dosimeters were prepared. The LD gel was made by mixing the UD gel with expanded polystyrene spheres. The R2 was used to determine the spatially resolved decay rates due to diffusion in internal magnetic field. The internal gradient was calculated for a multiple spin–echo sequence.
Results: It is shown that in a LD gel, the internal gradient leads to overestimation of mean R2 value (R2mean). Pixel-by-pixel R2 measurements inside a LD gel showed significant deviation from R2 mapping in UD gel.
Conclusion: It appears that significant differences between R2mean in a selected region of interest and pixel-by-pixel R2 values are the main source of inaccuracy in dose mapping of a LD gel.

Keywords: Dose mapping, inaccuracy, low-density gel dosimeter, mathematical analysis, susceptibility effect

How to cite this article:
Pak F, Vaezzadeh V, Eqlimi E, Mirheydari M. Analysis of induced error by susceptibility effect in low-density gel dosimeters. J Can Res Ther 2019;15:498-503

How to cite this URL:
Pak F, Vaezzadeh V, Eqlimi E, Mirheydari M. Analysis of induced error by susceptibility effect in low-density gel dosimeters. J Can Res Ther [serial online] 2019 [cited 2021 Nov 28];15:498-503. Available from: https://www.cancerjournal.net/text.asp?2019/15/3/498/244214

 > Introduction Top

Complicated three-dimensional dose distributions created by conformal radiotherapy techniques need a dosimeter with the capability of measuring in three dimensions continuously. Polymer gel dosimeters have been considered as promising dosimetry systems, which record three-dimensional dose distribution in conformal radiotherapy.

The polymer gel dosimeters have been used extensively for dose verification in water-equivalent tissues (unit-density [UD] tissues) and in homogeneous media. For adequate dose verification in different dosimetry situations and tissues, however, a gel with the possibility of simulating different electron densities is of great interest.[1] In the treatment of mediastinal tumors, the most commonly encountered heterogeneity is lung tissue. The lower electron density of lung tissue makes the induced radiation interactions occur at different spatial scales compared to water density-equivalent tissue. To verify the dose distribution in low-density (LD) tissues, the polymer gel density was reduced by either beating the gel solution into a foam-like consistency or embedding expanded polystyrene spheres in the gel solution.[1],[2],[3] Haraldson et al. attempted to make a lung-equivalent gel dosimeter using styrofoam beads expanded within polymer gel dosimeter. Compared to UD gel, the dynamic range of measured dose by LD gel was reduced and linearity was reported between 2 and approximately 8 Gy.[1] De Deene et al. suggested polymer hydrogel foam for radiation treatment verification in LD tissues. They observed that spin–spin relaxation rate (R2) values in LD gel depend on echo time (TE) interval in a multi-echo sequence, which was attributed to R2 dispersion.[3] In 2013, De Deene et al. designed heterogeneous phantom, which consists of UD and LD polymer gel dosimeters. A significant deviation with an overestimation of measured dose compared to treatment planning system (TPS)-calculated dose distribution was observed.[2]

Diffusive R2 dispersion caused by susceptibility-induced internal gradient leads to a significant deviation in measured R2 in LD gel dosimeters from the real value.[2] The internal gradient is caused by magnetic susceptibility differences between the styrofoam beads and gel fraction. There have been few publications discussing the effect of internal magnetic gradient on dose response of LD gel dosimeters;[2],[3] however, none of them studied variations of R2 measured value in LD gel dosimeter, caused by internal magnetic field.

Here, we studied the effect of internal gradient on response of LD gel dosimeter numerically.


Based on specific physical changes that take place in an irradiated gel dosimeter, the dose information can be read out using different imaging modalities. To date, the most-extensively used imaging technique for polymer gel dosimetry is magnetic resonance imaging (MRI).

Polymer gels consist of monomer aqueous solution and a gelling agent. The conversion of co-monomers to polymer aggregates upon irradiation results in change of the spin–lattice relaxation rate (R1) and R2.[4] Since, in polymer gel dosimeters, the dose-response of R2 is more pronounced than that of R1, usually R2 is used for dose mapping.[5]

A multiple spin–echo pulse sequence produces a series of base images, each at a different TE. R2 value is obtained by fitting an exponential spin–spin relaxation time (T2) decay curve, to signal intensities of corresponding pixels in the base images versus TE:[6]

S = S0exp (−R2TE) (1)

The recorded R2 is weighted average of relaxation rates for different proton pools in the entire sample:[7]

R 2 = fmobR 2, mob + fpolyR 2, poly + fgelaR 2, gela (2)

fmob, fpoly, and fgela are the corresponding fractions of protons in the mobile, polymer, and gelatin pools, respectively. The mobile proton pool initially contains protons from water and dissolved co-monomers. As irradiation proceeds, the co-monomers convert to polymer. In other words, fpoly increases while fmob decreases, as a result of irradiation. The third pool contains protons from the gelling agent. Each one has distinguished R2 values depending on the intrinsic characteristics of the pool. In an un-irradiated polymer gel dosimeter, fpoly is zero and fgel and fmob are determined from their initial concentrations:

R20 = fmobR2mob + fgela R2gela(3)

Substituting equation (3) into equation (1) yields:

LD gel dosimeter is a UD gel whose density is reduced by either beating the gel into a foam-like consistency or embedding expanded polystyrene spheres in the gel solution. Although components of UD and LD gel dosimeters have same initial concentration, significant differences were observed between their R20.[3]

LD gel dosimeter has a porous structure, which is created by foam beads. When it is placed in a homogeneous magnetic field, susceptibility differences (Δχ) between foam beads (pore space) and the surrounding gel cause substantial magnetic field gradients.[8] These susceptibility induced gradients are called “internal gradients” (Gint) which depend on both susceptibility difference and pore geometry. Diffusion of spins in Gint leads to extra transverse relaxation.[8] The total signal amplitude due to both spin–spin relaxation and diffusion weighting is given by the following well-known equation:[9]

As a result, the measured R20 of an un-irradiated LD gel dosimeter is presented as follows:

Here, R20bulk represents the R2 value measured in the absence of the internal gradients. In other words, R20bulk value is measured from an un-irradiated UD gel dosimeter. D is self-diffusion coefficient and b is the diffusion weighting or b-factor. TE is the echo time used by the multiple spin–echo pulse sequence (TE = n TE, where TE is the inter-echo time spacing).

For a spin–echo sequence in the presence of a constant gradient, the b-factor is:[7]

Here, the b-factor is a function of gyromagnetic ratio g, TE, and internal gradient G. Since LD and UD gel dosimeters are imaged simultaneously, the gradient strength of frequency encoding and phase encoding and slice-selective gradients are considered constant for both of them and their contribution in diffusion is negligible.

Substituting equation (7) into equation (6) yields:

 > Materials and Methods Top

Gel preparation

MAGAT gel dosimeter was chosen for this study. The gel was prepared in a laboratory condition, using protocol proposed by Hurley et al.[10]

Gel dosimeter consisted of 86% deionized water, 8% gelatin (300 Bloom, Sigma Aldrich), 6% methacrylic acid (purity grade approximately 99%, Sigma-Aldrich), and 50 mM of tetrakis (hydroxymethyl) phosphonium chloride (THPC) (technical grade 80% in water, Sigma-Aldrich) in weight percentage.

Gelatin was soaked in 80% of de-ionized water for 10 min at room temperature to become swollen and uniform. Then, the mixture was heated under magnetic stirring until the temperature reached 50°C and a clear solution was gained. The mixture was cooled down to 35°C, and then methacrylic acid was added. Ten minutes later, a solution of antioxidant was prepared with THPC and the remaining 20% of de-ionized water and added to the solution.

Two sets of gel dosimeters were prepared (LD gel and one UD). In UD polymer gel dosimeters, the prepared solution was split into three testing vials with a capacity of 10 cc. To prepare LD gels, the solution was transfused into the vials containing polystyrene spheres with diameter approximately between 0.8 and 1.3 mm (StyrofoamTM spheres, Isopan, Regensburg, Germany). To prevent possible photo-polymerization, the gel samples were stored in card box.[11] They were left in a conventional refrigerator at 4°C for about 1 h to solidify and then transferred into a cupboard.

Magnetic resonance imaging evaluation

Since the gel temperature at the time of MR imaging has a great influence on R2 values,[5],[12] samples were taken to MRI room 24 h before the start of the procedure. This prevents samples from any temperature fluctuation.

MR images of the gel were captured using Siemens Magnetom Avanto 1.5 T scanner (Siemens Medical Solutions, Erlangen, Germany). The vials were placed in the head-coil and T2 was determined using a multi spin–echo sequence. For all the measurements, the following imaging parameters were applied: 32 time echo (TE) ranging from 20 to 640 ms with increment rate of 20, time to repeat (TR) =4000 ms, slice thickness = 0.5 mm, pixel size 1 mm × 1 mm, two acquisitions (number of excitations = 2), and field of view = 200 × 150 mm.

All images were analyzed using self-written Matlab code. R2 values were calculated by fitting an exponential T2 decay curve to the signal intensities of corresponding pixels in the base images versus TE.

Self-diffusion coefficient measurement

The self-diffusion coefficient of water molecules in the NMR tubes of MAGAT gel was measured using a standard pulsed gradient spin–echo sequence (δ =3 ms, Δ = 12 ms, TR = 10 s).[13] Here, δ is the duration of rectangular pulse pairs with gradient of G in both imaging directions, which are separated by the time interval of Δ.

 > Results Top

Echo signal analysis in low- and unit-density gel dosimeters

[Figure 1]b shows mean echo signal intensities averaged over a circular region of interest (ROI) in LD and UD gel vials [Figure 1]a for all 32 echo images. Mono-exponential decay is observed for both types of dosimeter gels. It is seen that in UD gel, the first echo signal is smaller than the second one. The first echo signal was excluded from R 2 estimation of UD gel processes presented in this article. In LD gel dosimeter, the first echo signal is greater than the second one. At the same time, the signal intensity of LD gel dosimeter is less than that of UD and it decays faster. As it is shown in [Figure 1]b, R2mean values of LD and UD gel dosimeter in selected ROI are 5.62 and 2.19 (1/s), respectively. R2mean of the LD gel is more than twice than that of the UD gel dosimeter.
Figure 1: (a) Selected region of interest for signal averaging in low- and unit-density gel vials. (b) Echo signal intensity as a function of echo time for low- and unit-density gel dosimeters

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Pixel-by-pixel R2 measurement in low- and unit-density gel dosimeters

[Figure 2]a shows a rectangular ROI in LD gel dosimeter. The same ROI was chosen in UD gel dosimeter. Distinct fluctuation is seen in R2 values of LD gel (standard deviation [SD] = 53%), while in UD gel dosimeters, just a small deviation (SD ≤4%) is noticed.
Figure 2: (a) Rectangular region of interest for R2 calculation across the low-density gel vial. (b) Measured R2 value inside the rectangular region of interest in low- and unit-density gel dosimeters (R2 values are averaged over the columns of region of interest)

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As shown in [Figure 2]b, the lowest R2 values in LD dosimeter gels are very close to the R2 values of UD gel dosimeter.

R2 and echo signal analysis in different pixel sites in low- and unit-density gel

For analysis of R2 fluctuation in LD gel, three different sites are selected due to the observed signal intensity in LD gel image. The first one is a site with high signal intensity (site 1: gel middle), the second is a site with lowest signal intensity (site 2: foam bead middle), and the third one is adjacent to site 2 (site 3: adjacent to foam bead). [Figure 3]a shows labeled pixels in three different sites (in the image, labeled pixels are shown larger from the real one to be distinguishable). [Figure 3]b shows the corresponding mono-exponential signal decay behavior of labeled pixels and circular ROI. There are distinct decay behaviors depending on the position of pixels. Site 1 (foam middle) has the smallest R2 value, while site 3 has the largest R2 value. The signal decay curve and R2 value of LD gel in the circular ROI are between site 2 (gel middle) and site 3 (close to foam).
Figure 3: (a) Different positions of chosen pixels for signal intensity measurements in low-density gel dosimeter (site 1: middle of the foam, site 2: middle of the gel, site 3: adjacent to the foam). (b) Signal decay of the low-density gel dosimeter at the individual sites denoted in (a). (d) Signal decay of the unit-density gel dosimeter at three random sites shown in (c)

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Since signal intensity is uniform in MR image of UD gel, three pixels are selected randomly. Positions of selected pixels and their signal decay corresponding curves in UD gel dosimeter are shown in [Figure 3]c and [Figure 3]d, respectively. As it can be seen, three signal decay curve are of the same order with SD = 2%.

Self-diffusion coefficient

The UD sample was found to have an average self-diffusion coefficient, D, of 2.67 × 10−9 m 2 s −1.

Internal gradient

[Figure 4] shows the strength of internal gradients from the numerical calculation (Equation 9) for LD gel. [Table 1] shows the mean values for R2 (R2mean) of UD and LD gel dosimeters, mean Gint (gmean) and maximum Gint (Gmax) in LD gel. As shown in [Figure 4] and [Table 1], calculated internal gradient varies across the pixels between 0.0123 and 0.0402 mT/m.
Figure 4: Calculated Gint in low-density gel dosimeter

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Table 1: R2mean of unit- and low-density gel dosimeters, mean internal gradient (Gmean), maximum internal gradient (Gmax), and minimum internal gradient (Gmin) in low-density gel dosimeter

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 > Discussion Top

This work presented quantification of the internal gradient in MRI-LD gel dosimetry system along with investigating its effect on R2 value.

Although UD and LD dosimeter gels had the same initial composition, distinct differences were seen between their signal decay and R2 measured value. These results comply well with the results reported by De Deene et al. in 2006.[3] The difference between signal decays can be attributed to the diffusion of water molecules in the presence of internal gradient in LD gels. Internal magnetic field originates from magnetic susceptibility differences between the foam beads and the gel phase. The diffusion of water molecules due to the internal gradient results in an irreversible phase dispersion that will eventually be reflected in R2 increase.

[Figure 2]b shows significant fluctuation of pixel-by-pixel R2 measurement in LD gel, which represents the disordered distribution of internal gradient. According to Equation 8, R2 value in a LD gel depends on the power of internal gradient, where any changes in this gradient result in large fluctuation in R2 values.[8]

[Figure 3] shows how internal gradient causes variations of R2 in different sites inside LD dosimeter gel. Depending on pixel positions, distinct decay behaviors were observed. The smallest R2 value belonged to the point inside of a foam bead, where the gel penetrated. In small pores of foam beads, internal gradient is much smaller than the local gradient of the magnetic fields, and the diffusion contribution to signal decay is negligible.[14] R2 values of LD in these selected points become equal or very close to that of UD gel dosimeter. A bit larger R2 for point inside of the foam beads comparing UD gel can be associated to the nearby internal gradients.[8]

The higher R2 value in site 3 indicates larger gradients adjacent to the foam beads. On the other hand, the maximum value of internal gradient tends to occur at the interface of the gel and foam beads. Compared to site 3, signal decay was slower at the centers of a position of the gel without foam beads (site 2), where local minima in the internal fields occur (ignoring internal gradients inside foam beads). These results are in good agreement with the results reported by Cho et al. in 2009.[8] They selected an experiment to visualize internal magnetic field arising from susceptibility contrast with array of cylindrical glass tubes (solid matrix) and surrounding water (pore fluids) in a uniform magnetic field. They showed that the spatially resolved decay rate due to diffusion in the internal magnetic field is proportional to the strength of local gradient.

In a gel dosimetry process, a dose image is obtained through calibration with an experimentally derived R2 versus dose plot. The R2 value in each calibration vial is defined as the R 2mean in a selected ROI.[6] As shown in [Figure 3]b, there are significant differences between R2mean and R2 for different pixel sites inside LD gel, while just 2% SD is reported for UD gel. It means, despite UD gel, correlating R2 value of a selected ROI to the pixel value in an irradiated LD gel leads to over- or under-estimation of measured absorbed dose.

In UD dosimeter gel, the spurious signal intensity of the first echo was observed which is in agreement with Watanabe and Kubo's results.[15] In UD dosimeter gels, the first echo had lower signal intensity compared to the second echo, which originates from imperfect 180° radiofrequency (RF) pulses.[16] In LD gel dosimeter, the first echo signal was greater than the second one. Watanabe and Kubo claimed that as the dose increases, the first echo signal becomes greater than the second one. The similarity between LD gels and highly absorbed dose gel dosimeters is their low signal-to-noise ratio (SNR). LD gel dosimeters have low SNR, while in UD gel dosimeter, SNR decrease as absorbed dose increases.[2] A correlation between SNR and imperfection of 180° RF pulses can be considered, but further investigation is needed.

The accuracy of the estimated R2 values is crucial if the calibration data taken with the uniform polymer gel are directly applied to the LD region. Alternatively, we can use a different calibration for the LD material. As far as we know how the LD spheres are distributed in the LD region, the distribution is the same as that of the calibration phantom. However, this method is of limited use as this study showed.

 > Conclusion Top

In this study, susceptibility-induced internal gradient is visualized and quantified numerically, as an important cause of inaccuracy in LD gel dosimeters. It is shown that in a LD gel, diffusive R2 dispersion in internal gradient leads to overestimation of R2 values. Pixel-by-pixel R2 measurement, inside a LD gel, showed significant deviation from R2 map of UD gel dosimeter. It is shown that the variation of R2 value is pixel position dependent which defines the magnitude of internal gradient. The R2mean value in a selected ROI, therefore, differs from pixel by pixel of R2 measurement, significantly. Noticeable difference between R2mean in a selected ROI and pixel-by-pixel R2 is considered as a main source of inaccuracy in dose mapping in LD gels.


The assistance of Mr. Shojaee moghadam from Payambaran Hospital for MR imaging of polymer gel dosimeters is acknowledged.

Financial support and sponsorship

This study was supported by Grant No. 25920 from Tehran University of Medical Sciences.

Conflicts of interest

There are no conflicts of interest.

 > References Top

Haraldsson P, Karlsson A, Wieslander E, Gustavsson H, Bäck SA. Dose response evaluation of a low-density normoxic polymer gel dosimeter using MRI. Phys Med Biol 2006;51:919-28.  Back to cited text no. 1
De Deene Y, Vandecasteele J, Vercauteren T. Low-density polymer gel dosimeters for 3D radiation dosimetry in the thoracic region: A preliminary study. J Phys Conf Ser 2013;444:012026.  Back to cited text no. 2
De Deene Y, Vergote K, Claeys C, De Wagter C. Three dimensional radiation dosimetry in lung-equivalent regions by use of a radiation sensitive gel foam: Proof of principle. Med Phys 2006;33:2586-97.  Back to cited text no. 3
Maryanski MJ, Gore JC, Kennan RP, Schulz RJ. NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiation: A new approach to 3D dosimetry by MRI. Magn Reson Imaging 1993;11:253-8.  Back to cited text no. 4
Baldock C, De Deene Y, Doran S, Ibbott G, Jirasek A, Lepage M, et al. Polymer gel dosimetry. Phys Med Biol 2010;55:R1-63.  Back to cited text no. 5
Deene YD, Walle R, Achten E, Wagter CD. Mathematical analysis and experimental investigation of noise in quantitative magnetic resonance imaging applied in polymer gel dosimetry. Signal Proc 1998;70:85-101.  Back to cited text no. 6
Zimmerman JR, Brittin WE. Nuclear magnetic resonance studies in multiple phase systems: Lifetime of a water molecule in an adsorbing phase on silica gel. J Phys Chem 1957;61:1328-33.  Back to cited text no. 7
Cho H, Ryu S, Ackerman JL, Song YQ. Visualization of inhomogeneous local magnetic field gradient due to susceptibility contrast. J Magn Reson 2009;198:88-93.  Back to cited text no. 8
Duthoy W, De Gersem W, Vergote K, Coghe M, Boterberg T, De Deene Y, et al. Whole abdominopelvic radiotherapy (WAPRT) using intensity-modulated arc therapy (IMAT):First clinical experience. Int J Radiat Oncol Biol Phys 2003;57:1019-32.  Back to cited text no. 9
Hurley C, Venning A, Baldock C. A study of a normoxic polymer gel dosimeter comprising methacrylic acid, gelatin and tetrakis (hydroxymethyl) phosphonium chloride (MAGAT). Appl Radiat Isot 2005;63:443-56.  Back to cited text no. 10
Pak F, Farajollahi A, Movafaghi A, Naseri A. Influencing factors on reproducibility and stability of MRI NIPAM polymer gel dosimeter. Bioimpacts 2013;3:163-8.  Back to cited text no. 11
Spevacek V, Novotny J Jr., Dvorak P, Novotny J, Vymazal J, Cechak T, et al. Temperature dependence of polymer-gel dosimeter nuclear magnetic resonance response. Med Phys 2001;28:2370-8.  Back to cited text no. 12
De Deene Y, De Wagter C, Van Duyse B, Derycke S, Mersseman B, De Gersem W, et al. Validation of MR-based polymer gel dosimetry as a preclinical three-dimensional verification tool in conformal radiotherapy. Magn Reson Med 2000;43:116-25.  Back to cited text no. 13
Pappas E, Seimenis I, Angelopoulos A, Georgolopoulou P, Kamariotaki-Paparigopoulou M, Maris T, et al. Narrow stereotactic beam profile measurements using N-vinylpyrrolidone based polymer gels and magnetic resonance imaging. Phys Med Biol 2001;46:783-97.  Back to cited text no. 14
Watanabe Y, Kubo H. A variable echo-number method for estimating R2 in MRI-based polymer gel dosimetry. Med Phys 2011;38:975-82.  Back to cited text no. 15
Hürlimann MD. Effective gradients in porous media due to susceptibility differences J Magn Reson 1998;131:232-40.  Back to cited text no. 16


  [Figure 1], [Figure 2], [Figure 3], [Figure 4]

  [Table 1]


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