Determination of 3D dose distribution from intracavitary brachytherapy of cervical cancer by MRI of irradiated ferrous sulphate gel

Radiotherapyand Oncology 43 (1997) 219-227

Determination of 3D dose distribution from intracavitary brachytherapy of cervical cancer by MRI of irradiated ferrous sulphate gel Bj@n H. Knutsen”, Arne Wetting a,b, Taran P. Hellebusta, Dag R. O1sena,c,* ‘Department of Medical Physics, The Norwegian Radium Hospital, Montebello, 0310 Oslo, Norway ‘Department of Physics, Norwegian University of Science and Technology, 7034 Trondheim, Norway ‘Department of Health Sciences, The College of Oslo, Oslo, Norway

Received 17 June 1996; revised version received 20 December 1996: accepted 21 January 1997

Abstract Background and purpose: MRI ferrous sulphategel dosimetry has proven to be a valuable methodfor assessment of dosedelivered in teletherapy. The intention of this study was to investigate ferrous sulphate gel as a possible dosimeter for intracavitary brachytherapy applications. Materials and methods: A plastic duplicate of a cervix ring applicator set was submergedin Fe”-infused gelatin gel. The gel was subsequentlyirradiated by a stepwise moving ‘921rsource,using automatic afterloading equipment (Microselectron, Nucletron-Oldelft International BV, Veenendaal,The Netherlands).A 3D dosedistribution was reconstructedfrom MR imagesof the gel. Results: The gel dose measurementswere found to be of the sameaccuracy as TLD measurements.Isodose curves based on gel dosimetry and isodosecurves computedby a doseplanning systemwere generally lessthan 2 mm apart.MR imagesshowing the position of the applicator set in a patient during treatmentwere usedto obtain imagesdescribingpatient anatomy in the sagittal and ring planesof the applicator set.Isodosecurves computedfrom the gel measurements were then superimposed on these images, illustrating one possible way of linking dosimetrical and anatomicaldata. Conclusions: Our study showsthat MRl ferrous sulphategel dosimetryis a useful tool for studiesof dosedistributions in brachytherapy

and their relation to critical organs. Possible improvements of the gel dosimeter lie in reducing the diffusion of ferric ions and increasing the

radiation sensitivity of the gel. 0 1997Elsevier ScienceIreland Ltd. Keywords:

MRI; Gel dosimetry; Brachytherapy;Cacervix; Afterloading

1. Introduction

Intracavitary brachytherapy, given alone or in succession of external radiotherapy, has proven successful with respect to curation of carcinoma of the cervix. However, complications may arise as the treatment volume is close to the radiation sensitive organs, the rectum and the bladder. High doses delivered to these organs may induce late occurring lesions [9,22], while too low doses delivered to the target volume will lower the probability of local tumor control. A dosimetrical method which accurately measures the dose distribution resulting from intracavitary brachytherapy, and its relation to critical organs, is therefore of great importance. * Correspondingauthor.

In the early days of brachytherapy, doses to the rectum and the bladder were measured directly by insertion of an ionization chamber [9]. As computers became more common and powerful, doses were determined in anatomical reference points by treatment planning computers [.5]. At first the reference points were localized using two orthogonal contrast radiographs. Introduction of the CT led to improved accuracy in the determination of reference points [4]. CT-assisted dose calculations have since shown that the maximum doses to the rectum and the’bladder are generally higher than those predicted from orthogonal radiographs [13,23]. Afterloading systems using a stepwise moving 1921r source are common tools for brachytherapy today. Treatments are designed from theoretically calculated dose distributions. Due to the complexity of the radiation fields,

0167-8140/97/$17.00 0 1997 Elsevier Science Ireland Ltd. All rights reserved PIZ SO167-8140(97)01925-7

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experimental verification of the dose distributions is required. Measurements by conventional dosimeters (thermoluminescent dosimeters (TLDs), ionization chambers, diodes) are time consuming, as only a limited number of points can be measured at one time. Introduction of the moving 19’Ir source also leads to errors in the conventional dosimetry, since the sensitivities of ionization chambers and diodes are dependent on the irradiation angle. Measurements by LiF TLDs are not ideal either, because of the energy dependent sensitivity of the TLDs. In water equivalent media, the 19*Irradiation energy spectrum is displaced towards lower energies as the distance between the radiation source and the TLD increases [15]. Gel dosimetry by MRI is a unique method of providing a 3D dose distribution with high spatial resolution in a minimum of time [8,16]. The measuring points are separated by a distance equal to the pixel size of the MR images, typically less than 1 mm. A gel infused with Fe*+constitutes an integrating dosimeter. Thus, the radiation field is not perturbed by any detector. Furthermore, the sensitivity is independent of radiation energy, dose rate and irradiation angle [ 161. Dose distributions obtained by gel dosimetry may be used to verify dose distributions computed by treatment planning systems. Previously, gel dosimetry has been applied in measurements of external radiotherapy, e.g. conformal therapy [3] and dynamic wedge [2]. However, due to the large dose gradients involved in brachytherapy, the properties of gel dosimetry become particularly advantageous. The main drawbacks of gel dosimetry are the relatively low sensitivity (minimal detectable dose -1 Gy) and the post irradiation diffusion of ferric ions (blurring of the correct dose distribution with time) [6,16]. In this study, a Fe” doped gelatin gel was irradiated by a 19’Ir source using afterloading equipment. A 3D dose distribution was calculated from MR images of the gel. Isodose curves derived from the measurements were compared to those calculated by a treatment planning system. The isodose curves were superimposed on images of patient anatomy to illustrate one possible clinical application of the data obtained by gel dosimetry.

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AG, Buchs, Switzerland) and 50 mM HzS04 (E. Merck AG, Darmstadt, Germany), all mixed in triply distilled water. This recipe is based on the work of Olsson [16]. However, NaCl has been replaced by benzoic acid, because the latter has proven to act as a radiation sensitizer in Fe2+-infused gelatin gel [19]. The gelatin was mixed with 314 of the water volume and allowed to soak for 30 min. This mixture was then heated and kept between 40 and 45’C until all the gelatin was dissolved. The resulting homogeneous liquid was put in a refrigerator for cooling. Meanwhile, the rest of the ingredients were mixed with the remaining water and heated to between 50 and 60°C while being stirred in a magnetic stirrer. Heating and stirring continued until all the benzoic acid had been dissolved. The solution was allowed to cool at room temperature. When both the gelatin solution and the Fe*‘-solution had reached 45”C, the two solutions were mixed.The resulting solution was stirred for a couple of minutes to assure homogeneity. Most of the Fe’+-doped solution was poured into a plastic container of width 11 cm, length 21 cm and filled to a height of 11 cm. A plastic lid had previously been made for the container. The lid had been interlocked with the cervix applicator set to form a rigid unit. By fastening the lid to the container, the applicator set was held firmly in place, the ring and the intrauterine tube completely submerged in the gelatin solution (Fig. 1). The gel was then put in the refrigerator overnight for the gelatin to solidify. From the remaining Fe*+-infused gelatin solution, small samples for calibration were made using a 4.9 mm thick slab of plastic material (Perspex), in which 6 x 4 holes had been drilled, each of diameter 37 mm and depth 45 mm. Eight holes were filled with the solution, and the slab was then stored in a refrigerator overnight. Both the calibration samples and the large gel were allowed to equilibrate to room temperature before irradiation.

2. Materials and methods 2.1. Gel preparation Fe*+-infused gelatin solution was prepared to give one large bulk (2.8 1) of homogeneous liquid. The solution was subsequently divided into eight small samples (-0.04 1) to be used for calibrating the dose response of the gel, and one large gel volume (-2.4 1) to be irradiated according to a brachytherapy treatment scheme. The ingredients of the gel were 5% gelatin by weight (Type A, 300 bloom, Sigma, St. Louis, MO, USA), 1.5 mM FeS04 (Riedel-deHa& AG, Hannover, Germany), 1.5 mM benzoic acid (Fluka Chemie

Fig. 1. The plastic container filled with gel and with the applicator set positioned as in the irradiation setup.

B.H. Knutsen et al /Radiotherapy 2.2. Irradiation

and NMR imaging

The gel samples to be used for calibration purposes were irradiated by 4 MeV photons from a linear accelerator (Clinac 600 C, Varian, Palo Alto, CA, USA). One sample was left unirradiated while the other seven were given doses from 10 to 70 Gy, in 10 Gy intervals. The large gel enclosing the cervix applicator set was irradiated by a stepwise moving 1921rsource using an afterloading system (Microselectron, Nucletron-Oldelft International BV, Veenendaal, The Netherlands). The applicator set consisted of a uterine applicator (45” angle, 40 mm intrauterine tube) and a ring applicator (diameter 30 mm), rigidly interlocked. Both applicators were made of plastic, since the gel later was to be imaged using MRI. At the time of irradiation, the source activity was 145 GBq. Total irradiation time was 3200 s, equally distributed between 16 source positions, estimated to deliver a dose of 21.5 Gy to point A [12]. This dosage was chosen in order to optimally exploit the dynamic dose range of the gel. For comparison, dose measurements were also made with LiF TLDs (TLD 100, rods, 1 x 6 mm). Ninety-two TLDs were placed in the sag&al plane of the applicator set (Fig. 2), using a Perspex phantom. Measurements were repeated three times and the average dose to each measurement point was used in the comparison of TLD and gel dosimetry. Since TLDs have a much smaller dynamic dose range than the gel, the dose to point A was 1.7 Gy. The TLDs were given a calibration dose of 2 Gy from a 6oComachine. MR images were acquired using a 1.5 T magnetic tomograph with a head coil (General Electric Medical Systems, Waukesha, WI, USA). A set of slices through the gel were

Fig. 2. Radiograph showing the ca.cervix applicator set in the Perspex phantom. The 92 TLD measurement points are marked with crosses. The TLDs are placed in the sagittal plane of the applicator set.

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imaged both before and after irradiation. To ensure that the slice positions in the two imaging sessions were reproduced, the gel container was fixed in a framework which could be accurately positioned relative to the head coil. In both imaging sessions, two images were obtained for each slice position. Using spin-echo pulse sequences of equal echo time, 20 ms, the two images differed only in their repetition times, which were 2000 and 600 ms, respectively. Signal values were taken as the average of two acquisitions. Within one imaging session, the receiver gain was held constant. Altogether four images were obtained for each slice position. The time span from the beginning of the irradiation to the completion of the NMR imaging was always kept at less than 2 h to minimize deterioration of the data set caused by diffusion of iron ions. Thirty slice positions were used in image acquisition of the large gel irradiated by 1921r.The image planes were parallel to the ring plane of the applicator set, and evenly spread from a position behind the ring to a position in front of the intra-uterine tube. Slice thickness as well as spacing between slices was 3 mm, and the field of view (FOV) was 16 x 16 cm’. The image matrix contained 256 x 256 elements, giving a pixel size of 0.625 mm. Odd and even numbered slices were acquired separately (interleave mode on the GE Signa). The calibration gel samples were imaged in a plane parallel to the bottom of the Perspex slab. Images were obtained for one image position, 1 cm from the bottom of the holes. Slice thickness was 1 cm, thereby covering the depth dose maximum of 4 MV photons in water equivalent material. 2.3. Image processing

and dose calculation

The NMR images were transferred to a UNIX workstation for processing, using Interactive Data Language (IDL version 4.0, Research Systems, Boulder, CO, USA). The proton spin-lattice relaxation rate (RI) was calculated for all pixels and slice locations. The relaxation rate images were computed from the ratio between two corresponding images acquired with repetition times of 600 and 2000 ms, respectively, and an echo time of 20 ms. Given the spinecho pulse sequence applied in the present study, RI could be found directly from this ratio using a look-up table (Appendix A). The MR images of the unirradiated gel were subjected to a 7 x 7 median filter prior to the ratio calculations, whereas the post-irradiation images were median filtered over a 3 x 3 kernel. Different kernel sizes were used with the two image sets because the post-irradiation images displayed large gradients in signal intensity, whereas the pre-irradiation ones showed a generally homogeneous signal intensity throughout the gel. A relatively strong filtering of the latter images could therefore be permitted without perturbing inherent gradients. All the ratio images were subsequently run through a 3 x 3 median filter. Using the resulting ratio values as entries to the look-up table, pre- and post-irradiation RI-images were computed.

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The dose response of the gel was calibrated from the relaxation rate image of the irradiated cylindrical gel samples. In this image, circular regions of interest (ROIs) (radius 20 pixels) were defined within each sample. Averaging the RI values within each ROI, a 2nd order polynomial describing R, as a function of absorbed dose was found through regression analysis. Returning to the relaxation rate images of the gel and applicator set, the pre-irradiation images were subtracted from the post-irradiation images. Subtraction of background RI-values was performed because inhomogeneities had been observed during preliminary experiments. After median filtering the subtraction images, dose images were calculated using the linear and quadratic coefficients of the fitted calibration curve. In effect, information from four MR images acquired for each slice position had boiled down to one dose image describing the slice. Dose images of three particularly interesting planes, namely the sagittal, coronal and ring planes of the applicator set, were reconstructed by linear interpolation between the 30 parallel images. The interpolated images were subjected to a 3 x 3 median filter. A three dimensional grid of dose data points (75 x 75 x 75) was digitally transferred from a dose planning system (Plato, Nucletron-Oldelft) to the UNIX workstation via a data cartridge. Spatial resolution of the grid was 4 mm. By bilinear interpolation in the 3D grid, the planned dose distributions of the three reference planes were reconstructed. For the sagittal plane, a dose distribution was also computed from TLD measurements. This distribution was computed by triangulation and linear interpolation between the 92 measurement points r241. The dose distributions computed from dose planning data and TLD measurements were compared to the distribution derived from the gel measurements, in order to evaluate the quality of the latter measurements. Alignment of the 3D dose data sets of different origins was achieved using well defined points on the applicator set to define a common coordinate system.

3. Results The calibration curve is shown in Fig. 3. The relaxation rate initially increases linearly with the dose, but for high doses the deviation from a linear response becomes evident. Isodose plots computed from MRI-derived dose images are shown in Fig. 4. They demonstrate that the dose distribution is not cylindrically symmetric around the intrauterine tube. A given isodose curve encloses a larger area in the coronal plane of the applicator set than it does in the sag&al plane. This asymmetry is a desired feature of radiation fields for intracavitary brachytherapy of ca.cervix, and aims at minimizing the dose absorbed in the critical organs, such as the rectum and the bladder. Fig. 4 also shows another prominent characteristic of brachytherapy radiation fields,

and Oncology 43 (1997) 219-227

3.5 3.0 -~ 2.5 --

0.5 1

0.0 0

10

20

30

40

50

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Dose KM Fig. 3. Dose-response curve for the gel. The data points have been fitted to a 2’ polynomial, RI = a + bD + CD*. Polynomial coefficients are: a = 1.244 SC’, b = 0.03603 s-‘Gy-‘, c = - 1.243 x W4 s-‘Gy-‘.

namely the extremely steep dose gradients in the immediate vicinity of the applicators. Isodose curves computed by linear interpolation between TLD measurement points were plotted together with the corresponding isodose curves derived from the gel measurements. The plot in Fig. 5 shows good agreement between dose measurements made by gel and TLDs. In Fig. 6, isodose curves derived from the gel measurements are superimposed on isodose curves computed by a dose planning system. The isodoses derived from the gel images are somewhat flawed from edge effects near the applicator set and by noise at the lowest dose level. Still, the plots show a generally good agreement between theoretically calculated and measured isodose curves: The spatial distance between corresponding isodose curves is predominantly less than 2 mm.

4. Discussion The two gelling substances most widely used for gel dosimetry are agarose and gelatin. Gelatin was chosen for this study, although agarose has been known to give dosimeters of approximately twice as high radiation sensitivity [ 10,16,21]. However, in order to achieve this high sensitivity, the agarose solution has to be oxygenated before it is allowed to solidify. To dissolve the agarose powder, the solution must be heated to between 90 and 95”C, thereby releasing oxygen. Unless reoxygenated, the sensitivity of the agarose gel drops by some 25%, and its range of linear dose response decreases [21]. The gelatin solution only needs to be heated to between 40 and 45’C to dissolve the gelatin. No reoxygenation is required, simplifying the gel preparation. The sensitivity of the gelatin gel is still sufficient for dose measurements by MRI [lo]. Moreover, sensitivity may be improved by adding benzoic acid to the gel [ 1,7]. A resulting sensitivity increase by a factor 2.5 has been reported [ 191. The sensitivity of agarose gel depends on the gel’s cooling rate. In the middle of a large bulk of agarose gel, where

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Fig. 4. Isodose plots of the 19*Irirradiated gel. The 25, 50, 100, 200 and 300% isodoses are shown; the 100% isodose equals 40 Gy in this experiment. The images represent the sagittal plane (a), the coronal plane (h) and the ring plane (c) of the applicator set. Note that the lowest isodoses in (a) and (b) seem to be restricted by straight vertical lines on either side of the plot. This is artificial and marks the boundaries of the volume in which MR images were obtained.

the cooling rate is low, the sensitivity is higher than in the periphery. Addition of another polysaccharide to the agarose has been found to eliminate the cooling rate dependence. However, the gram price of this additive is too high for routine use. Gelatin gives homogeneous sensitivity regardless of the size of the gel [ 171.This makes it possible to calibrate the dose response of the large gel by irradiating small gel samples to predetermined doses. Gelatin also allows less diffusion of ferric ions than agarose gels, the diffusion constant of gelatin gel being approximately half that of agarose gel [18,20,21]. Given the relatively low minimal detectable dose of gel dosimetry (-1 Gy) and the dose rates involved in gynecological brachytherapy with Microselectron (-0.3-0.8 Gy/min to point A), long irradiation times are necessary in order to achieve adequate dose to the gel. Minimizing the rate of ferric ion diffusion is therefore essential. Addition of xylenol orange to gelatin gel has been reported to reduce the diffusion coefficient by 50% [20], at the cost of an accompanying 25% reduction in sensitivity. Thus, xylenol orange is an additive which may prove helpful when studying dose distributions with strong gradients, as is the case in this study. In the present study, irradiation was planned as a compromise between two conflicting interests. On one hand, the desire to have the largest possible volume with good signal to noise ratio (SNR) called for as long an irradiation time as possible. On the other hand, in order to avoid severe deterioration of the data from ferric ion diffusion, the irradiation time needed to have an upper limit. Since emphasis was put on a good SNR, a small volume of gel near the applicator set received doses higher than the maximum calibration dose. The dose response for both agarose [21] and gelatin gel [lo] has been shown to approach a saturation level for high doses. The 2” polynomial mimics such a behavior up to its maximum at 145 Gy, thereby offering a rationale for extrapolating the calibration curve beyond the maximum calibration dose at 70 Gy. However, as the dose estimates

increase beyond 70 Gy, they have to be viewed with increasing scepticism. The problem of exceeding the maximum calibration dose when measuring a brachytherapy treatment scheme can be avoided. One tentative solution would be to calibrate the gel’s dose response all the way up to, say 150 Gy. Unfortunately, saturation of the dose response may give poor differentiation between relaxation rates at high doses, and noise may consequently inflict large uncertainties in the dose estimates. Another method might be to examine the gel volume near the applicator set (high dose rate) and the volume further from the applicators (low dose rate), after separate irradiation sessions. To implement this idea, the former could be irradiated to doses below maximum calibration dose and imaged by MRI. Subsequent to the image acquisition, the gel could be irradiated further, and image acquisition repeated, thereby improving the SNR in the low dose rate volume. Since this part of the gel has lower dose gradients than the high dose rate volume, diffusion of ferric ions would not be so prominent, and the irradiation could be prolonged. The best results for measurements in the low dose rate volume would be achieved with a recently purchased 19’1rsource. The stochastic noise in the dose images was evaluated using the relaxation rate image of the irradiated calibration samples. For calibration purposes, a region of interest within each sample had previously been defined. The standard deviation of the pixels within each ROI was taken to represent stochastic noise in RI measurements at the respective calibration dose levels. It was assumed that noise is inversely proportional to the square root of the slice thickness. Therefore, noise in the RI images of the irradiated applicator gel (slice thickness, 3 mm) was estimated from the noise in the calibration image (slice thickness, 10 mm) by multiplying the latter by J10/3). The resulting noise in the unirradiated calibration sample was taken to represent noise in the RI images of the unirradiated applicator gel. Denoting noise

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Fig. 5. Isodose curves computed from TLD measurements (red) superimposed on curves based on gel measurements (green). The TLD dose values have been multiplied by a factor compensating for the difference in irradiation time and source strength compared to the gel dose values. The 100% isodose curve represents 40 Gy delivered to the gel. The thick, green line encloses the area in which the TLDs were placed. Fig. 6. Isodose curves from gel measurements (red) superimposed upon isodose curves from dose planning system (Plato, Nucletron-Oldelft) (light blue) in the sagittal (a), coronal (b) and ring planes (c) of the applicator set. The isodose levels are 25.50, 100 and 200%. The 100% isodose corresponds to 40 Gy in the dose images of the gel. The dark blue bands cover an area reaching 2 mm to either side of the isodoses obtained from the dose planning system, thus representing the tolerance limits for deviation between measured and planned isodoses.

at the different calibration doses No, Nto, &a, etc., noise in the subtraction images was calculated as liri = ~~

(i = 0, 10, 20...).

Dose versus estimated noise in relaxation rate images (dotted line) and subtraction images (solid line) are shown in Fig. 7a. Combining subtraction image noise and the cali-

bration curve from Fig. 3, relative dose uncertainty was computed as a function of dose (Fig. 7b). At the 10 Gy level, 20% uncertainty may be expected, falling rapidly to values between 8 and 9% for doses between 30 and 70 GY. The above mentioned dose uncertainties were computed from unfiltered images. In order to reduce the intrinsic image noise, median filtering was consequently chosen.

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z" 0.04 --

< 4 z

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I

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6-4 2 -0 0

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Fig. 7. (a) Estimated stochastic noise as a function of calibration dose. The squares connected by dotted lines represent noise in relaxation rate images of the irradiated applicator gel. The triangles connected by solid lines represent noise in subtraction images; i.e. RI images of unirradiated gel subtracted from corresponding images of irradiated gel. (b) Relative dose uncertainty (%) as a function of dose.

The rationale for this choice was that median filtering preserves intensity edges in an image, a desirable feature considering the sharp junctions between applicator and gel in the present images. In the images of irradiated applicator gel, filtering was performed over small regions (3 x 3 pixels) to minimize the perturbation of the sharp dose gradients. In the images of mm-radiated gel lacking such gradients, a kernel size of 7 x 7 pixels was used. The linear interpolations applied in computing dose images of the three reference planes were bound to smooth the dose gradients to some extent. However, the results show that with the small spacing between the images (3 mm), this effect did not significantly alter the dose distribution (Fig. 8). Fig. 5 shows good agreement between TLD and gel measurements. Systematic discrepancies due to increased sensitivity of TLDs with source distance [ 151, cannot be verified from this figure. According to Fig. 7b, the dose uncertainty at the 25% isodose level (corresponding to 10 Gy) is estimated to be 20%. This is several magnitudes larger than the deviation which may be expected from increased TLD sensitivity, considering the distances between the TLDs and the lg21rsource positions in the present study. A tolerance of 2% dose deviation, subsidiary 2 mm distance between isodose curves, has been recommended as criteria for agreement between dose measurements and calculated dose plans [14]. The first requirement was not fulfilled by the measurements in this study; the deviations being in the range of flO%. However, in regions of high dose gradients, the distance between isodose curves is considered a more appropriate criterion. Fig. 6 shows that the distance requirement is fulfilled with a few exceptions; parts of the isodose curves trace the surface of the applicator set, and not physical isodoses. This is due to edge effects in the original MR images; an unavoidable attribute of the MRI

equipment. Other exceptions are some regions where the lowest isodose curves slip outside the 2 mm limits. This is a matter of insufficient SNR. An experimental approach using two consecutive sessions of irradiation and imaging, as outlined previously, would improve results in this respect. Fig. 7 shows one way to exploit the information obtained from gel dosimetry. MR images of patients with similar applicators to the ones used in this study had previously been obtained. From these axial images, images corresponding to planes through the sagittal, coronal and ring planes of the applicator set were reconstructed. Using the cervix applicator set to define an orthogonal coordinate system, the spatial informations from the patient images and the dose images were aligned. Isodoses from the gel dosimetry were superimposed on the patient images. Images such as the ones shown in Fig. 7 can be used for preliminary, qualitative analyses of planned or delivered brachytherapy. A natural extension, not implemented in this study, would be to extract dose-volume histograms for selected organs. The applicator set in those patient images that were available for this study had an intra-uterine tube of 60 mm length, and the diameter of the ring applicator was 34 mm. Thus, the anatomy is somewhat displaced compared to what would have been the case with a 40/30 applicator set inserted. However, these images are included to illustrate the principle of linking dosimetrical and anatomical data. The images show how both the bladder and the rectum are displaced by the ring applicator. This study shows that MRI ferrous sulphate gel dosimetry is a method well suited for obtaining a 3D dose distribution of high spatial resolution. Its accuracy is of the same order as for TLD measurements, and dose distributions obtained with gel dosimetry are in good agreement with

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Fig. 8. Sagittal plane (a) and ring plane (b) of the gel dose distribution superimposed on patient images. (a) The patient is oriented front up, head to the left. The bladder is seen as a dark gray region above the intrauterine tube. The black areas represent intestine. (b) The patient is viewed from the feet, front up. The isodose cm-ves shown in both figures are 25, 50, 100 and 200%; the 100% isodose represents 40 Gy.

those computed with the dose planning system. The new approach of linking dosimetrical data with patient data by image processing provides a simple tool for treatment analysis in brachytherapy. Optimization of the gel with respect to radiation sensitivity and ferric ion diffusion, along with more careful filtering of the digital images, are ways of making gel dosimetry an even better tool. Future studies will be undertaken in order improve these aspects of gel dosimetry.

tion times, TRI and TR2, the signal ratio in pixel i is given by 1 -2exp(-(TR1 - TE/2)/TI,)+exp(-TRl/Tli) ri= l-2exp(-(TR2-TE/2)/T1,)+exp(-TR2/Tli)

(2)

Introducing si = exp(-TRJT,J, u = TRlITR, and v = -(TE/2)ITR1, Eq. (2) may be rewritten ri=[1-si(2sy-1)]/[1-s;(2s;-1)]

(3)

S, can then be found iteratively from Acknowledgements

Sj(n+ l)= 1 -Vi[l -si(n)“(2si(n)“-

We thank Nucletron-Oldelft for supplying the plastic ring applicator set used in the experiments and Dr Viggo Blomli for kindly making patient MR-images available to us.

Using S;(O)= 1 - vi, Rli = l/Tli is eventually found from

Appendix A Relaxation rates in this study were calculated using a modified version of the ratio method, as presented by Bengtsson [2]. The relaxation rates are computed from the ratio between signal intensities in two MR images acquired with equal echo time but different repetition times. The formula used for signal intensity following a spin-echo pulse sequence with echo time TE and repetition time TR, is eluded from the Bloch equations [ 111: Z=ZO[l -2exp( -(TR-TE/2)/T1) +exp(- TR/Tl)]exp( -TE/T2)

(1)

Assuming two images, 11and Zz,with corresponding repeti-

Rli= -ln(si)/TRl

1)]/2si(n)“-

1

(4)

(5)

In order to test the algorithm, 10 000 numbers ranging from 80 to 3000, evenly spaced, were defined to represent T1 values. Previous experiments had shown that repetition times TR1 = 600 ms and TRI = 2000 ms would give good results. Echo time, TE, was set to 20 ms. Using Eq. (2), 10000 ratio values were computed and used as inputs to the iteration process. The iterations continued until the difference between si(n + 1) and si(n) was less than 0.01% for all i. Twenty-four iterations were required. Eq. (5) was applied to find the iteratively estimated R, values. Comparing these to the corresponding, predefined RI values, the maximum difference was found to be O.lS%.When calculating RI-images from ratio images, a look-up table was applied. The table contained 40000 T1-values, computed by 50 iterations of Eq. (4). The entry to the look-up table was found by multiplying the ratio by 40 000. Ratio images are converted to relaxation rate images within a fraction of a second.

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