Using Monte-Carlo-Simulated Radiation Transport to ...

Technical Report Received: July 31, 2009 Accepted after revision: March 4, 2010 Published online: May 12, 2010

Stereotact Funct Neurosurg 2010;88:208–215 DOI: 10.1159/000314355

Using Monte-Carlo-Simulated Radiation Transport to Calculate Dose Distribution in Rats before Irradiation with Leksell Gamma Knife쏐 4C: Technical Note Béatrice Marcelin a Per Kjäll c Jonas Johansson c Anders Lundin c Håkan Nordström c Markus Eriksson c Christophe Bernard a Jean Régis a, b

a

INSERM U751, Université de la Méditerranée, and b Service de Neurochirurgie Fonctionnelle et Stéréotaxique, Hôpital La Timone, Marseille, France; c Elekta Instrument AB, Stockholm, Sweden

Key Words Leksell Gamma Knife쏐 ⴢ Monte Carlo simulation ⴢ Epilepsy ⴢ Leksell GammaPlan쏐

Abstract Background: Gamma knife surgery (GKS) is used at subnecrotic doses for temporal lobe epilepsy (TLE) treatment. Rat models of TLE have been used to probe the mechanisms underlying GKS. Previous GKS studies on rats have used the Leksell GammaPlan쏐 (LGP) treatment planning system to determine the irradiation time to achieve the dose to deliver. Since LGP is not designed for such small structures, it is important to calibrate the system for the rat brain. Methods: We have used a Monte Carlo simulation (MCS) radiation transport scheme, with CT data as anatomical and tissuespecific information, to simulate the dose distribution in a rat brain when using a Leksell Gamma Knife쏐. Results: We show how dose distributions obtained by MCS quantitatively compare to those predicted by LGP, and discuss whether LGP should be used for studies involving rats. The energy deposited when using the 4-mm collimators was calculated for targets on both sides of the rat brain in the dorsal hippo-

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campus, which allowed us to determine the exact time to irradiate rats with a given dose. Conclusion: The MCS method used in this study can easily be used for future GKS studies on small animals when accurate dose distributions are required. Copyright © 2010 S. Karger AG, Basel

Introduction

Gamma knife surgery (GKS) is, besides for the treatment of tumors and arteriovenous malformations, also used for the treatment of many neurological disorders such as trigeminal neuralgia, pain control and focal epilepsy, e.g. temporal lobe epilepsy (TLE) [1]. TLE is the most common type of epilepsy in adults, and 30% of the patients are resistant to drug treatment [2, 3]. One alternative treatment is resective surgery; however, resections are not always possible because they can cause severe neurological and neuropsychological damage, depending on the structures that need removal [4]. Another alternative is radiosurgery, e.g. GKS. GKS was initially developed by Lars Leksell at the Karolinska Hospital in Stockholm to Jean Régis Service de Neurochirurgie Fonctionnelle et Stéréotaxique Hôpital d’Adulte La Timone, 264 Boulevard Saint-Pierre FR–13005 Marseille (France) Tel. +33 4 91 38 70 58, Fax +33 4 91 38 70 56, E-Mail jregis @ ap-hm.fr

destroy a precise tissue volume in the brain (gamma knife, as an alternative to a scalpel blade). Subsequently, GKS also became a means to biologically modify a predefined target without necessarily provoking a necrosis of the cells in the targeted volume, and to achieve the therapeutic effect with a single irradiation dose [5]. In TLE, subnecrotic doses by GKS can lead to the abolition of seizures or at least a decrease in their frequency [6]. Classically, patients with TLE are treated with a subnecrotic dose of around 25 Gy, corresponding to the 50% isodose surface [6]. There is clinical and experimental evidence that GKS is able to induce biological modifications in the underlying circuitry [5, 7]. But the detailed mechanisms of these modulations and dosimetric parameters enabling the induction of such plasticity without necrosis are still unknown [5]. A first step toward understanding these mechanisms is to observe the morphological and functional changes induced by subnecrotic doses via GKS on animal models. Several studies have been performed to analyze the consequences of GKS in different rat models of TLE, where several doses have been tested (up to 60 Gy, maximal dose at the isocenter) without necrosis [8–10]. The quality of the correlation between the radiation dose and its biological consequences clearly depends upon the knowledge of the radiation dose actually given. In previous studies, the exposure time was calculated using the Leksell GammaPlan쏐 (LGP). However, two aspects of the experimental situation call the validity of using LGP into question: (1) LGP is designed for humans, whose brain volume is about 2.25 ! 103 times larger than the rat brain volume (human brain volume: approx. 1,350 cm3; rat brain volume: approx. 600 mm3), and (2) the rat skull and cranial bones are much closer to the irradiated tissue, on the order of a few millimeters only. It is well known that both qualitative and quantitative characteristics of dose distributions are strongly dependent on the presence of tissue inhomogeneities, e.g. an interface between bone and brain tissue, in the volume being irradiated. Therefore, in order to obtain detailed information about the dose distribution in such small structures, it is important to use a radiation transport model that takes into account the specific features of the animal’s head; a functionality that, at a first glance, LGP does not offer. The ideal solution would be to physically measure the radiation dose directly, but for such small fields and inside a living animal, physical measurements pose very difficult problems. A formalized experimental study was performed by Novotný et al. [11], who evaluated the dose distribution predicted by LGP both in a rat cadaver and in a polymer gel phantom by using 3 types of dosimeters:

a thermoluminescent dosimeter (TLD), a semiconductor detector and a polymer gel dosimeter. A fair agreement was found between the measurements and predictions, but since these measurements were not performed on living animals, and since the rat skull geometry used to calculate the irradiation time was only approximate due to limitations of LGP, it may be difficult to transfer their results to any given target in any given rat. An alternative is to calculate the dose with a reliable dose calculation method that is capable of taking tissue inhomogeneities into account. Here, we have used the so-called Monte Carlo simulation (MCS) method. By this method, one simulates the transport of the radiation all the way from the source through the tissue being exposed, in such a way that all relevant interactions between the radiation and the materials and tissues being irradiated are mimicked as accurately as possible. In these interactions, the amount of energy being deposited in the tissue as well as the final energy and direction of the particles are calculated. The energy, and hence the dose, is acquired by summing all energy depositions in small volumes of the tissue for which the knowledge of the dose is desired. Since this is a method based on stochastic principles, the larger the number of initial particles followed (i.e. simulated), the lower the uncertainty of the relevant quantities (in our case, the resulting dose distribution). The radiation interacts with the tissue, and therefore, a detailed knowledge of the chemical composition and physical state of the tissue is needed. We used CT data to acquire the necessary anatomical information. The various tissue types in and around the target volume were segmented in the CT data set and the corresponding tissue characteristics were assigned on the basis of the material libraries included in the MCS transport scheme used. The objective was to accurately determine the dose by the MCS transport scheme and compare it to the dose calculated by LGP, focusing particularly on the superficial dose.

MCS Dose Distribution in Rats for GKS

Stereotact Funct Neurosurg 2010;88:208–215

Materials and Methods CT Imaging Six Wistar-Han rats were used for this study. Rats 1–3, weighing around 400 g (396, 389 and 397 g), and rats 4–6, weighing around 300 g (303, 304 and 298 g), were anesthetized intraperitoneally with a mixture of ketamine (100 mg/kg) and xylazine (10 mg/kg). The rats were scanned in a Scanner X (GE, HiSpeed NX/i Pro) by the company Voxcan (Marcy l’Etoile, France). The parameters of the acquisition were: voltage = 80 kV; current = 130 mA; rot = 1 turn/0.7 s, 0.8 mm/rot (helical), pitch = 0.8:1; slice thickness = 0.5 mm, and dual field of view = 100 mm.

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Table 1. Simulation parameters

Value 1!1010 251,012,348 400!106 16 1.17/1.32 10/10/1 0.1/0.1 153.44 15.1 0.1

Number of particles simulated in the phase space Number of particles in the phase space Number of particles simulated Size of spherical phase space (radius of sphere), cm Initial energies, MeV Cutoff energy (electron/positron/photon), keV Multiple scattering model parameters (C1/C2) Activity of sources at time of irradiation (November 1, 2008), TBq Dimensionality of dose matrix, mm Resolution of dose matrix, mm

The animals were scanned in dorsal decubitus position. It was not possible to scan them with the Régis-Valliccioni stereotactic frame attached because of the frame’s material composition. The incisor bar is made of titanium and aluminum, which would have caused artifacts in the signal. Since the MCS system extracts all anatomical information from the CT images, the images need to be as artifact-free as possible. For each acquisition, 2 reconstructions were performed using 2 different filters: (1) a bone filter which provides sharp gradients in the images between the different tissues (bone and soft tissues), but which lets through some beam-hardening artifacts, and (2) a standard filter which reduces noise and artifacts but provides a smoother gradient between each tissue. Target Positioning The stereotactic coordinates of the targets were: 3.6 mm posterior to the bregma, 2 mm lateral to the midline (both hemispheres) and 3.5 mm below the surface of the brain [12]. The Régis-Valliccioni stereotactic frame is designed to allow the use of the Paxinos and Watson rat brain atlas [12] with no need of any prior MRI [13]. The CT scan images were in standard DICOM (Digital Imaging and Communications in Medicine) format. We used the software BrainSuite 2.0 (http://brainsuite.usc.edu) to create a volume with all of the DICOM images for each rat. The images from the bone filter reconstruction were used because this reconstruction allowed us to see the sutures on the surface of the brain, and we needed the position of the bregma to determine the coordinates of the target in BrainSuite, based on the stereotactic coordinates mentioned above. Given the target positions, the coordinate axes and orientations were extracted from BrainSuite and aligned with the coordinate system used by the MCS system. Irradiation The rats were anesthetized intramuscularly with a mixture of ketamine (50 mg/kg) and xylazine (6 mg/kg). They were placed in a prone position in the Régis-Valliccioni stereotactic frame (Neuropace, Neuilly, France) and irradiated by a Leksell Gamma Knife쏐 4C (LGK). During irradiation, the 4-mm collimator helmet was used and the irradiation time calculated based on the results of the simulation of the energy deposition (see below) to achieve a maximum dose in each target of around 40 Gy. An output factor of 0.87 was used for the 4-mm collimator, as suggested by the manufacturer.

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The MCS Code In this study, an internally developed MCS code system based on the well-known code Penelope, developed in Barcelona, Spain [14–17], was used. Our code is an extension of Penelope in the sense that it is adapted to run on multiple processors so that the geometries and materials through which the radiation is transported can be obtained in 3 different ways: they can be entered in the form of models generated by a computer-aided design system, as structures segmented from CT data, or as geometrical bodies assembled manually from simple mathematical surfaces. The rats in our study were modeled with the aid of segmented CT data, and the geometry of the treatment unit was represented by a computer-aided design model. Our MCS system is built around and interacts with the unchanged code of Penelope, so Penelope still constitutes the ‘physics engine’ of our system. Further, our system is designed so that all aspects of the simulation are administered and entered via a graphical user interface. A detailed description of the MCS system used is provided by Lundin et al. [18]. Since irradiations were performed on several different rats, we presimulated a large number of particles and stored the resulting radiation field on a so-called phase-space surface. A phase-space surface contains the information of all the particles reaching the surface, such as their particle type, energy and direction of motion; thus, in a sense, it represents a radiation field frozen in time just before it interacts with, in our case, the tissue of a rat. The main benefit of using a phase-space surface is that it reduces the simulation time from the radiation sources to the surface, collecting the particles for every subsequent simulation including a rat; in the case of a multi-narrow-beam treatment device such as the LGK, the time saved is substantial. The phase space for the 4-mm collimator we used took approximately 63 h to generate, and the dose distribution in each rat took about 3–4 h to generate; thus, in effect, by using a phase space, we reduced the total simulation time by a factor of about 18. Nevertheless, running an MCS is time-consuming and, therefore, fast computers with significant amounts of memory are needed. The simulations described in this report were run on an IBM LS20 blade server with 14 blades. Each blade has 2 dual-core AMD Opteron 280 processors at 2.4 GHz with 4 GB of memory, i.e. 56 CPU cores with 56 GB of memory in total. The master node is an IBM e346 server with 2 dualcore Intel Xeon 3.4-GHz processors with 4 GB of memory, and a 6 ! 300 GB RAID. All parameters used in the simulations are described in table 1.

Marcelin /Kjäll /Johansson /Lundin / Nordström /Eriksson /Bernard /Régis

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Fig. 1. Outer circles: 50% isodose lines of single shots (i.e. single isocenters) and also approximately the total 50% isodose line. Middle circles: 90% isodose lines of single shots. Inner ellipsoid: total 90% isodose line. The total dose profile along line A–B is shown in figure 2. Source of atlas image: Paxinos and Watson [12].

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Results

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Accuracy The geometrical accuracy is very important in order to link the in vitro electrophysiological and the morphological observations with the dose received at each point of the irradiated volume. Indeed, for the morphological observations, coronal slices are performed. Using the Paxinos and Watson rat brain atlas [12], we can determine the exact position of the slice we observe, and thus it is crucial to know what dose has been delivered to each point of the slice.

Using the simulation parameters given in table 1, we obtained the results listed in table 2. Note that, since 2 targets were treated, 1 on each side of the brain, with a distance between the targets of approximately 4 mm, there was an overlap that had to be taken into account in order to obtain the true dose rate at the 2 isocenters. The same irradiation time was used for both targets. Figure 1 shows a cross-section with the 2 targets identified, and figure 2 shows the dose distribution along the line indicated. Close to the surface, there is a so-called buildup region in which the amount of deposited energy per unit of mass of tissue (i.e. the dose) rises sharply to a maximum value, after which it declines (for a narrow beam) approximately exponentially (fig. 3). LGP uses the exponential approximation of energy deposition as a function of depth (for each single beam), as indicated in figure 3, and therefore does not model the dose deficiency in the region close to the surface, which leads to an exaggeration of the dose close to the surface when using LGP. It was mainly the desire to accurately model the dose distribution close to the surface that led to our decision to use dose distributions obtained by MCS and not by LGP in this study. What doses would LGP have predicted for these geometries further away from the surface considering that, in its present form, it is not designed to work with such a



Rat No.

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1 The number of particles used in the simulation was so large that the uncertainty (at 1 ␴) was much lower than 1%, both at the center of the dose distribution as well as where the overlap was calculated. The major source of uncertainty was in the segmentation of the CT data set, and the total uncertainty in the dose rate including the overlap was estimated to be in the region of 1–5%. 2 The unit of the overlap is ‘fraction of maximum dose at isocenter’. The irradiation time used for all rats was 9.22 min.

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beam. Normalized to a depth of 80 mm. The curve with the buildup region depicts the true behavior close to a surface, whereas the pure exponential model (dashed curve) – as used by LGP – clearly exaggerates the dose close to the surface. Notice that both curves have the same depth dependence for depths greater than approximately 4–5 mm.

to. A: Histogram depicting the number of beams with a certain attenuation depth. B: First 18 mm of the depth-dose curve of figure 3, normalized to 100% at a depth of 5 mm. C: ‘Depth-dose’ curve assumed by LGP; the irradiation geometry here is a water sphere with a radius of 10 mm and with the isocenter placed 8 mm from the center of the sphere in the direction of the y-axis.

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1.10 1.05 Dose relative to dose at center

small object as a rat skull in an exact way? Approximate geometries such as spheres or ellipsoids must be used. However, LGP allows entering spherical structures with radii greater than 20 mm. In order to circumvent the limitation on size and to be able to study the behavior of the dose calculation algorithm in isolation, a simple but exact implementation of the dose calculation algorithm was created outside LGP. Both ellipsoidal and spherical approximations of the rat skull were investigated and compared, but the differences in doses calculated for spheres and ellipsoids of similar sizes with such small dimensions as 10–20 mm were negligible. Thus, only results obtained via the spherical approximation are presented below. Figure 4 shows the ratio between doses calculated by the LGP algorithm and doses calculated by MCS at the center of spheres with different radii. The difference between the 2 dose calculation algorithms increases for small radii, as expected from figure 3. In figure 4, for a particular sphere, all beams traveled the same distance inside the sphere since the isocenter was located at the center of the sphere, which was clearly not the case for an isocenter located off the center point in the sphere. Table 3 gives the dose rates when the focus point moves along the y-axis (the vertical axis). It is seen that there is a fair agreement between MCS and LGP even as close as 2 mm from the surface, which – considering figure 3 – is a somewhat ‘unexpected’ result. The reason for this ‘unexpected’ agreement can be seen in figure 5. In this figure, a modified LGP model that takes into account the buildup behavior as seen in figure 3 was compared to the original LGP model. For this irradiation geometry, approximately half of the beams (106 beams) had an attenuation depth greater than 5 mm, while the other ‘half’ (95 beams) had an attenuation depth in the interval between 2 and 5 mm. Beams with an attenuation depth greater than 5 mm were accurately modeled by the algorithm in LGP, as seen in figures 3 and 5, while the dose contribution of beams with a shorter attenuation depth was overestimated by LGP. However, the beams with an attenuation depth of less than 5 mm were still sufficiently ‘high up’ on the depth-dose curve to provide a dose contribution not too dissimilar from the one (erroneously) predicted by LGP. Thus, even though the target point was only 2 mm from the surface, the majority of beams provided a dose – as predicted by LGP – that was similar or equal to the dose predicted when taking buildup into account. An empirical argument for the same reasoning can be found in the study by Kamiryo et al. [19]. Figure 6 compares doses measured with a TLD in a spherical plastic

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MCS-calculated doses shown in table 3, with error bars corresponding to 3 ␴. Diamonds: taken from figure 4 in Kamiryo et al. [19] (by measuring in the figure), with error bars assigned to the measured values representing 1 ␴. There is no information in Kamiryo et al. [19] about which axis in the phantom the measurements were performed along, but the dose drops faster for small distances from the surface along the z-axis than along the y-axis, thus it is reasonable to assume that the measurements were performed along the y-axis.

phantom with a radius of 10 mm with the MCS-calculated doses listed in table 3. Within the experimental uncertainties, the agreement was rather good. Novotný et al. [11] provide additional arguments for the applicability of LGP with the aid of detailed empirical results from TLD, diode and polymer gel measurements. To summarize, table 3 and figures 5 and 6 indicate that LGP predicts dose distributions in fair agreement with MCS even for very small targets and close to the surface of targets in spherical water geometries.

Discussion

Despite the agreement between LGP and MCS we have discussed here, it is important to report how irradiation times are determined in rats, since the intended dose may not correspond to the real one. A literature survey shows that this information is rarely provided, precluding a Stereotact Funct Neurosurg 2010;88:208–215

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Table 3. Dose rates calculated for the focus point when it is moved to different positions along the y-axis in a spherical phantom with a radius of 10 mm (in LGK systems, the y-axis is the vertical axis)

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3.04 3.58 3.72 3.76 3.72 3.75 3.74 3.71

3.79 3.77 3.75 3.74 3.73 3.72 3.72 3.71

1.25 1.05 1.01 0.99 1.00 0.99 0.99 1.00

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Dose rates simulated for a LGK 4C unit with a total activity of 153.44 TBq, and with 13 Co60 pellets in each source capsule. An output factor of 0.87 was used for the LGP-calculated doses for the 4-mm collimator, as suggested by the manufacturer.

straightforward comparison between the different studies. It must be emphasized that we have been concerned only with the dose rate at the isocenter (i.e. at a single point) and not with the geometrical form of the dose distribution, and since LGP does not take into account differences in the radiophysical characteristics of different materials, there is no inclusion of effects of bone-tissueair interfaces when using LGP. Complex geometries and material compositions can only be handled accurately with more sophisticated dose calculation models such as the MCS. In their study, Novotný et al. [11] also rightly pointed out the importance of an accurate modeling of the surface of the anatomy in order to obtain accurate predictions of the absolute dose. From the discussion above, it is clear that a lack of information about where the surface is located and about the shape of the surface may result in significant dose inaccuracies for superficial targets. The accuracy of the geometrical anatomy used in the MCS approach presented here is a direct function of the accuracy of the diagnostic modality used and of the computer algorithms used to extract the anatomy from the diagnostic information. Being aware that not all researchers in this field have access to detailed MCS-generated dose distributions for their specific studies, a possible approach would be to calculate a set of universally applicable adjustment factors with the aim of ‘correcting’ for the lack of geometrical and material fidelity in LGP-calculated dose distributions when irradiating small animals such as rats. However, geometries, sizes and irradia214


tion locations may differ significantly between studies and, therefore, attempting to find universally applicable correction factors based on a relatively small number of dosimetric situations does not seem to be an approach assisting the progress in this field, especially not when it is suspected that important information about the clinical outcome may be obtained from the details of the dose distribution generated. It was not possible to scan the rats with the stereotactic frame in place because of the artifacts the frame would have caused (see Materials and Methods). The rats were in the decubitus position and we determined the coordinates in BrainSuite 2.0 looking at the bregma. Comparing the position of the rat on the images with the position of the rat in the frame, we found a maximum uncertainty of 3–5% in the determination of the coordinates of the targets. But, for a range of weights, although the uncertainty ranges from 0 to 5%, the irradiation time determined by MCS was basically the same (table 2); thus, we can consider this error as negligible. We have performed an analysis for the irradiation of the dorsal hippocampus to set the ground for a future study designed to analyze the consequences of GKS on theta activity, a rhythm central to numerous cognitive processes which is predominant in the dorsal hippocampus [20] as well as on spatial memory performance, which also depends upon the dorsal hippocampus [20]. Our results can be generalized to any target in the rat brain. In rat models of TLE, it is possible to achieve seizure control with subnecrotic doses [8–10]. The efficacy in controlling seizure increases with the dose, and the therapeutic window ranges from 20 to 60 Gy (maximal dose at the isocenter) without neuronal damage. In humans, several doses have been tested to find the therapeutic window and to optimize the irradiation parameters. A dose of 24 Gy (50% isodose) is reported to be more efficient than 18 or 20 Gy on TLE [21–23], and is therefore the standard dose used. Thus, the window of 20–60 Gy in rats seems to be very large, compared to the results obtained in humans. A possible explanation is that, since LGP, in principle, always exaggerates the dose close to tissue interfaces, as is seen in figure 3 and as described in the discussion above, the actual doses given when reporting LGP doses in the upper part of the interval between 20 and 60 Gy were in fact significantly lower. The use of MCS as described in this study has the potential to narrow the therapeutic window in rats, therefore to allow the observation of the biological effects more accurately and, as a consequence, to enable the transfer of the results to the treatment of humans. Marcelin /Kjäll /Johansson /Lundin / Nordström /Eriksson /Bernard /Régis

Acknowledgments

Conclusion

The MCS system described in this report is a useful tool for accurate radiation transport simulations in animal models. By combining high-resolution CT data with a flexible, yet simple, way to handle complex irradiation geometries and a high-performance computation system, one can in a short time obtain dose distribution data of high accuracy. This can be used to study epilepsy in rat models, but can as well be extended to any other indications for which GKS is deemed applicable.

This study was supported by INSERM, Fondation de l’Avenir and Elekta (Sweden). B.M. received a CIFRE (Conventions Industrielles de Formation par la Recherche) fellowship from Elekta SA (France) and the ANRT (Association Nationale de la Recherche et de la Technologie). We thank Neuropace for lending us the stereotactic frame.

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