Narrow Photon Beams Research Articles

Prospect for measurements of (γ, n) reaction cross-sections of p-nuclei at ELI-NP

The gamma beam system under construction at the ELI-NP facility in Romania is projected to give the nuclear physics community access to an experimental system providing a high-intensity, narrow bandwidth photon beam at variable energy. With high-efficiency detector systems in place, the experimental programme will have a strong potential for in-depth studies of rare stable isotopes originating from the astrophysical p-process. In particular, the neutron detection systems are already implemented through a dedicated 3He long neutron counter array, called ELIGANT-TN, that is completed and in use. In this mini-review, we will give a summary of the current status of existing (γ, n) cross-section data, as well as the methods to obtain them, and highlight the future potential to expand and improve such data using the ELI-NP instrumentation and beam-lines.

Determination of volume averaging correction factors using an elliptical absorbed dose model for Gamma Knife Perfexion.

The purpose of this study is to calculate volume averaging correction factors for detectors used in the dosimetry of Gamma Knife's narrow photon beams, and to determine the impact of volume averaging on the field output correction factor. Simulations of different Gamma Knife fields were done using elliptical dose model formalism with newly introduced fit functions. To determine volume averaging correction factors a calculation of the absorbed dose over the volume of the detector was performed. The elliptical dose model was tested with respect to absorbed dose distribution for different volumes and compared with the calculations of Leksell GammaPlan v.11.3.1. The largest differences in absorbed dose calculated by the elliptical model and Leksell GammaPlan are 2.25%, 1.5%, and 0.6% for 16, 8, and 4mm field sizes, respectively. Volume averaging correction factors were determined for six ionization chambers, five semiconductor detectors, a diamond, and two plastic scintillator detectors. In general, for all examined detectors the impact of volume averaging is more pronounced for smaller field sizes. All studied ionization chambers had a larger volume than other detectors, therefore the volume averaging correction factors for ionization chambers are larger for all investigated field sizes. Besides the fact that plastic scintillator detectors can be considered tissue-equivalent, volume averaging correction factor should be applied. Volume averaging correction factors for different detectors are determined and suitable detectors for dosimetry of Gamma Knife's narrow photon beams are recommended. It is shown that volume averaging has a dominant contribution to a field output correction factor.

96. Evaluation of the equivalent dose to the crystalline lens by dose equivalent Hp(3)

Purpose Individual dosimetry provides the tools for measuring doses from ionizing radiation of exposed workers. Recent scientific and epidemiological evidence highlights the need for adequate measures to protect the eye with particular regard to the crystalline lens [1] . The ICRP 103 proposes a depth of d = 3 mm for monitoring the crystalline dose (Hp(3)), stating that also the Hp(0.07) with calibration on slab can be used [2] . In our Dosimetry Service the operating quantity Hp (3) has been introduced and compared with Hp(0.07). Methods A SLAB phantom calibration was performed at a LAT center in terms of Hp (3). The type of dosimeter is ext-rad TLD-100 of Lithium Fluoride LiF:Mg,Ti. Dosimeters were sent to be irradiated in Hp(3) with narrow photon beam at various energies. The irradiation parameters are in the Table. Hp(0.07) and Hp(3) were measured for 26 workers. The monthly measures collected relate to the semester January-June 2017. Results The Figure shows for each operator the sum of the Hp(0.07) (red) and the Hp(3) (blue). The sum of the Hp(3) is greater than the sum of the Hp(0.07) as well as every single monthly value. Percentage differences were calculated between all the values of the Hp(0.07) and the Hp(3) and the average value is 10% ± 3%. Conclusions In the same conditions of irradiation Hp(3) is greater than Hp(0.07). Expected result as to a depth of d = 0.07 mm the absorbed dose is lower than that at a depth of 3 = mm at the energies considered. Download : Download high-res image (65KB) Download : Download full-size image Download : Download high-res image (93KB) Download : Download full-size image

An Analytical Model for Dosimetry of Nonstandard Photon Beams with Small, Round Cross Sections

An analytical model of the dose kernel of a narrow photon beam (pencil beam) with a bremsstrahlung spectrum with maximal energy at 6 MeV was created, allowing determination of the primary and scattered components of the absorbed dose to be determined in a water phantom with error levels acceptable in practice. A simple method for the dosimetry of photon beams with small round cross sections with 6-MV bremsstrahlung spectra using this model is proposed, combining absolute measurement of the dose absorbed in the water at a reference point in the machine-specific reference geometry and calculation of the deep dose distribution using simple analytical equations for round beams with cross sections of any radius.

Magnetic field influences on the lateral dose response functions of photon-beam detectors: MC study of wall-less water-filled detectors with various densities

The distortion of detector reading profiles across photon beams in the presence of magnetic fields is a developing subject of clinical photon-beam dosimetry. The underlying modification by the Lorentz force of a detector’s lateral dose response function—the convolution kernel transforming the true cross-beam dose profile in water into the detector reading profile—is here studied for the first time. The three basic convolution kernels, the photon fluence response function, the dose deposition kernel, and the lateral dose response function, of wall-less cylindrical detectors filled with water of low, normal and enhanced density are shown by Monte Carlo simulation to be distorted in the prevailing direction of the Lorentz force. The asymmetric shape changes of these convolution kernels in a water medium and in magnetic fields of up to 1.5 T are confined to the lower millimetre range, and they depend on the photon beam quality, the magnetic flux density and the detector’s density. The impact of this distortion on detector reading profiles is demonstrated using a narrow photon beam profile. For clinical applications it appears as favourable that the magnetic flux density dependent distortion of the lateral dose response function, as far as secondary electron transport is concerned, vanishes in the case of water-equivalent detectors of normal water density. By means of secondary electron history backtracing, the spatial distribution of the photon interactions giving rise either directly to secondary electrons or to scattered photons further downstream producing secondary electrons which contribute to the detector’s signal, and their lateral shift due to the Lorentz force is elucidated. Electron history backtracing also serves to illustrate the correct treatment of the influences of the Lorentz force in the EGSnrc Monte Carlo code applied in this study.

Spectral distribution of particle fluence in small field detectors and its implication on small field dosimetry.

Correction factors for the relative dosimetry of narrow megavoltage photon beams have recently been determined in several publications. These corrections are required because of the several small-field effects generally thought to be caused by the lack of lateral charged particle equilibrium (LCPE) in narrow beams. Correction factors for relative dosimetry are ultimately necessary to account for the fluence perturbation caused by the detector. For most small field detectors the perturbation depends on field size, resulting in large correction factors when the field size is decreased. In this work, electron and photon fluence differential in energy will be calculated within the radiation sensitive volume of a number of small field detectors for 6 MV linear accelerator beams. The calculated electron spectra will be used to determine electron fluence perturbation as a function of field size and its implication on small field dosimetry analyzed. Fluence spectra were calculated with the user code PenEasy, based on the PENELOPE Monte Carlo system. The detectors simulated were one liquid ionization chamber, two air ionization chambers, one diamond detector, and six silicon diodes, all manufactured either by PTW or IBA. The spectra were calculated for broad (10 cm × 10 cm) and narrow (0.5 cm × 0.5 cm) photon beams in order to investigate the field size influence on the fluence spectra and its resulting perturbation. The photon fluence spectra were used to analyze the impact of absorption and generation of photons. These will have a direct influence on the electrons generated in the detector radiation sensitive volume. The electron fluence spectra were used to quantify the perturbation effects and their relation to output correction factors. The photon fluence spectra obtained for all detectors were similar to the spectrum in water except for the shielded silicon diodes. The photon fluence in the latter group was strongly influenced, mostly in the low-energy region, by photoabsorption in the high-Z shielding material. For the ionization chambers and the diamond detector, the electron fluence spectra were found to be similar to that in water, for both field sizes. In contrast, electron spectra in the silicon diodes were much higher than that in water for both field sizes. The estimated perturbations of the fluence spectra for the silicon diodes were 11-21% for the large fields and 14-27% for the small fields. These perturbations are related to the atomic number, density and mean excitation energy (I-value) of silicon, as well as to the influence of the "extracameral"' components surrounding the detector sensitive volume. For most detectors the fluence perturbation was also found to increase when the field size was decreased, in consistency with the increased small-field effects observed for the smallest field sizes. The present work improves the understanding of small-field effects by relating output correction factors to spectral fluence perturbations in small field detectors. It is shown that the main reasons for the well-known small-field effects in silicon diodes are the high-Z and density of the "extracameral" detector components and the high I-value of silicon relative to that of water and diamond. Compared to these parameters, the density and atomic number of the radiation sensitive volume material play a less significant role.

Proton microbeam radiotherapy with scanned pencil-beams – Monte Carlo simulations

Irradiation, delivered by a synchrotron facility, using a set of highly collimated, narrow and parallel photon beams spaced by 1 mm or less, has been termed Microbeam Radiation Therapy (MRT). The tolerance of healthy tissue after MRT was found to be better than after standard broad X-ray beams, together with a more pronounced response of malignant tissue. The microbeam spacing and transverse peak-to-valley dose ratio (PVDR) are considered to be relevant biological MRT parameters. We investigated the MRT concept for proton microbeams, where we expected different depth-dose profiles and PVDR dependences, resulting in skin sparing and homogeneous dose distributions at larger beam depths, due to differences between interactions of proton and photon beams in tissue. Using the FLUKA Monte Carlo code we simulated PVDR distributions for differently spaced 0.1 mm (sigma) pencil-beams of entrance energies 60, 80, 100 and 120 MeV irradiating a cylindrical water phantom with and without a bone layer, representing human head. We calculated PVDR distributions and evaluated uniformity of target irradiation at distal beam ranges of 60–120 MeV microbeams. We also calculated PVDR distributions for a 60 MeV spread-out Bragg peak microbeam configuration. Application of optimised proton MRT in terms of spot size, pencil-beam distribution, entrance beam energy, multiport irradiation, combined with relevant radiobiological investigations, could pave the way for hypofractionation scenarios where tissue sparing at the entrance, better malignant tissue response and better dose conformity of target volume irradiation could be achieved, compared with present proton beam radiotherapy configurations.

Transportation of Gaussian light beam in two-layer clouds by Monte Carlo simulation

Based on the radiative transfer theory, the backscattering characteristics of water clouds and ice-water two layers clouds irradiated by infinite narrow collimated light beam are studied by using the Monte Carlo method. The incident wavelength is 0.532 μupm, and the cloud particle shape is assumed to be of sphere or plate. The single scattering characteristics of the clouds are computed based on the Mie theory, and the scattering angle sampling is based on the Mie phase function. The photon step adjustment is considered when the step is large enough to cross the cloud layer. The variations of reflection functions of the water clouds and ice-water two layers clouds with the radial length r and zenith angle are given, and the interior light intensity distribution of clouds are given in two dimensions. From the computed results, we find that the reflection characteristics of the two layer clouds are greatly different from those of the pure water clouds. The reflection intensity of ice clouds covered with water clouds is bigger than that of ice clouds covered with water clouds. This reason is that the sizes of ice clouds are larger than those of the water clouds, so more photons will be scattered into the interior of the clouds.#br#The cloud layer is assumed to be linear and invariant, so the response to an infinitely narrow photon beam will be described by a Green's function of the clouds, and the response to the Gaussian beam can be computed from the convolution of the Green's function according to the profile of the Gaussian photon beam. The multiple scattering characteristics of the Gaussian photon beam are computed from the convolution of the impulse response, i.e., the response to an infinitely narrow photon beam, according to the profile of the Gaussian light photon beam. From the computed results, we find that the reflection function of clouds for Gaussian incidence has a great difference from that for the infinite narrow beam incidence. The reflected light intensity is inversely proportional to the size of the Gaussian beam at the location near r=0. So the laser spot must be considered when detecting the clouds by using of the lidar, and the method presented in this paper can give theoretical support.

Development and application of a dose verification tool using a small field model for TomoTherapy

Helical TomoTherapy® is a radiation delivery technique that uses the superposition of many small fields to precisely deliver the prescribed dose to the patient. This work presents a dose verification tool that can be used as part of a quality assurance program for a tomotherapy system. This tool is based on a small field model that takes into account the two main effects that influence the dose distribution in small fields: the extended shape of the radiation source and the loss of lateral charged particle equilibrium (CPE) within the field. The dose verification tool was implemented for simple beam configurations and used to study the influence of temporal beam parameter variations on the delivered dose. After comparing measured and calculated output factors (OFs) and dose profiles for different field configurations, it was found that they agree well to within the globally-defined gamma acceptance criteria of 2%/2mm. The study demonstrated that none of the studied systematic and random variations applied resulted in failed gamma scores using gamma acceptance criteria of 3%/3mm. The developed model implemented in the verification tool allows to evaluate the performance of devices applying narrow photon beams in the treatment delivery and, in particular, to evaluate the delivery performance of a tomotherapy unit.

SU‐E‐T‐328: The Volume Effect Correction of Probe‐Type Dosimetric Detectors Derived From the Convolution Model

Purpose:To derive and introduce a new correction factor kV, the “volume effect correction factor”, that accounts for not only the dose averaging over the detector's sensitive volume but also the secondary electron generation and transport inclusive of the disturbance of the field of secondary electrons within the detector.Materials and Methods:Mathematical convolutions and Fourier's convolution theorem have been used. Monte Carlo simulations of photon pencil beams were performed using EGSnrc. Detector constructions were adapted from manufacturers' information.Results:For the calculation of kV, the three basic convolution kernels have to be taken into account: the dose deposition kernel KD(x) (fluence to dose), the photon fluence response kernel KM(x) (photon fluence to detector signal) and the “dose response kernel” K(x) (dose to detector signal). K(x) is calculated from FT[K(x)] = [1/sqrt(2”)]FT[KM(x)]/FT[KD(x)], where the magnitude of kV(x) can be thereby calculated for arbitrary photon beam profiles and the areanormalized K(x).Conclusions:n order to take into account for the dimensions of dosimetric detectors in narrow photon beams, the “volume effect correction factor” kV has been introduced into the fundamental equation of probe‐type dosimetry, and the convolution method has proven to be a method for the derivation of its numerical values. For narrow photon beams, whose width is comparable to the secondary electron ranges, kV can reach very high values, but it can be shown that the signals of small diamond detectors are well representing the absorbed dose to water averaged over the detector volume.

Dosimetric Evaluation of Heterogeneities in Small Circular Fields of 6 MV Photon Beams with EBT2 and EDR2 Films: Comparison with Monte Carlo Calculation

The influence of dose variation due to heterogeneities in narrow photon beams used in stereotactic radiosurgery has been investigated. Since the lateral electronic disequilibrium and existence of steep dose gradients in small fields and the presence of heterogeneities can intensify these problems, in this study the effects of heterogeneities on 6 MV small photon beams produced by circular cone collimators with 5, 10, 15, 20 and 30 mm diameters are investigated. The heterogeneities include 3 cm Cork with density of 0.2 g/cm3 instead of lung and 3 cm Polytetrafluoroethylene (P.T.F.E) with density of 2.2 g/cm3 as bone. The measurements were carried out with EBT2 gafchromic and EDR2 radiographic films. Simulation was done by MCNP Monte Carlo Code (MCNP5). The depth dose curves in heterogeneous phantom were compared with homogeneous phantom. A good agreement was obtained within film and Monte Carlo calculations in presence of low density heterogeneity and also in the presence of high density heterogeneity. Monte Carlo results showed good agreement after stopping power correction.

Comparison of trigeminal neuralgia radiosurgery plans using two film detectors for the commissioning of small photon beams

Trigeminal neuralgia (TN) is a chronic, episodic facial pain syndrome that can be extremely intense, and it occurs within the regions of the face that are innervated by the three branches of the trigeminal nerve. Stereotactic radiosurgery (SRS) is the least invasive procedure to treat TN. SRS uses narrow photon beams that require high spatial resolution techniques for their measurement. The use of radiographic or radiochromic films for small‐field dosimetry is advantageous because high spatial resolution and two‐dimensional dose measurements can be performed. Because these films have different properties, it is expected that the calculated dose distributions for TN patients will behave differently, depending on the detector used for the commissioning of the small photon beams. This work is based on two sets of commissioned data: one commissioned with X‐OMAT V2 film and one commissioned with EBT2 film. The calculated dose distributions for 23 TN patients were compared between the commissioning datasets. The variables observed were the differences in the half widths of the 35 and 40 Gy isodose lines (related to the entrance distance to the brainstem) and the volume of the brainstem that received a dose of 12 Gy or more (V12). The results of this comparison showed that there were statistically significant differences between the two calculated dose distributions. The magnitudes of these differences were up to 0.33 mm and 0.38 mm for the 35 and 40 Gy isodose lines. The corresponding difference for the V12 was up to 2.1 cc. It is clear that these differences may impact the treatment of TN patients, and then it must be important to perform this type of analysis when observing complication rates. Clinical reports on irradiation techniques for trigeminal neuralgia should consider that different detectors used for commissioning treatment planning systems might result in small but significant differences in dose distributions.PACS number: 87.55.km

SU-E-T-113: Volume Effect Correction Factor KV for Small-Field Photon Dosimetry with Ionization Chambers.

The volume effect of ionization chambers gives rise to a spatial averaging effect that can be expressed mathematically as the convolution of the true dose profile with the detector's response function. The latter has been shown to be best described by Gaussian distribution. Based on this knowledge, the volume effect correction factor kV is derived. To derive kV, a sixth degree polynomial is fitted to the true dose profile: D(x) = a0 + a2×2 + a4×4 + a6×6. The measured dose profile M(x) is calculated as the convolution product of D(x) with a one-dimensional normalized Gauss function with standard deviation s. Therefore kV at the dose maximum has the value D(0)/M(0), which is a function of the coefficients a0,2,4,6 and the detector specific s. In the case where D(x) is unknown, kV can be derived analogously from M(x) so that M(x) = b0 + b2×2 + b4×4 + b6×6, where kV can now be expressed as a function of the coefficients b0,2,4,6 and s. The magnitudes of kV,lat and kV,long were calculated for 1 to 5 cm dose profiles using measured s values, both in the lateral and the longitudinal directions, for a set of common ionization chambers. At field widths above 2 cm, the values of kV,lat fall below 1.01 for all the chambers evaluated, whereas it needs field widths above 4 cm to get all values of kV,long below 1.01. Since the detector's signal is integrated over the sensitive volume, the total kV can be calculated as kV,total = kV,lat . kV,long. In this work, a correction is developed to eliminate the volume effect of ionization chambers when they are positioned in the maxima of dose profiles, particularly for the performance of output factor measurements for the calibration of narrow photon beams.

Model‐based calculations of off‐axis ratio of conic beams for a dedicated 6 MV radiosurgery unit

Because the small-radius photon beams shaped by cones in stereotactic radiosurgery (SRS) lack lateral electronic equilibrium and a detector's finite cross section, direct experimental measurement of dosimetric data for these beams can be subject to large uncertainties. As the dose calculation accuracy of a treatment planning system largely depends on how well the dosimetric data are measured during the machine's commissioning, there is a critical need for an independent method to validate measured results. Therefore, the authors studied the model-based calculation as an approach to validate measured off-axis ratios (OARs). The authors previously used a two-component analytical model to calculate central axis dose and associated dosimetric data (e.g., scatter factors and tissue-maximum ratio) in a water phantom and found excellent agreement between the calculated and the measured central axis doses for small 6 MV SRS conic beams. The model was based on that of Nizin and Mooij ["An approximation of central-axis absorbed dose in narrow photon beams," Med. Phys. 24, 1775-1780 (1997)] but was extended to account for apparent attenuation, spectral differences between broad and narrow beams, and the need for stricter scatter dose calculations for clinical beams. In this study, the authors applied Clarkson integration to this model to calculate OARs for conic beams. OARs were calculated for selected cones with radii from 0.2 to 1.0 cm. To allow comparisons, the authors also directly measured OARs using stereotactic diode (SFD), microchamber, and film dosimetry techniques. The calculated results were machine-specific and independent of direct measurement data for these beams. For these conic beams, the calculated OARs were in excellent agreement with the data measured using an SFD. The discrepancies in radii and in 80%-20% penumbra were within 0.01 cm, respectively. Using SFD-measured OARs as the reference data, the authors found that the calculated OARs were more accurate than those measured with a microchamber or film dosimetry. The model produces sufficiently accurate conic beam dosimetric data that can be used to validate direct measurement results for such beams.

Total reflection coefficients of low-energy photons presented as universal functions

The possibility of expressing the total particle and energy reflection coefficients of low-energy photons in the form of universal functions valid for different shielding materials is investigated in this paper. The analysis is based on the results of Monte Carlo simulations of photon reflection by using MCNP, FOTELP, and PENELOPE codes. The normal incidence of the narrow monoenergetic photon beam of the unit intensity and of initial energies from 20 keV up to 100 keV is considered, and particle and energy reflection coefficients from the plane homogenous targets of water, aluminum, and iron are determined and compared. The representations of albedo coefficients on the initial photon energy, on the probability of large-angle photon scattering, and on the mean number of photon scatterings are examined. It is found out that only the rescaled albedo coefficients dependent on the mean number of photon scatterings have the form of universal functions and these functions are determined by applying the least square method.

Development of an efficient scanning and purging magnet system for IMRT with narrow high energy photon beams

Due to the clinical advantages of Intensity Modulated Radiation Therapy (IMRT) high flexibility and accuracy in intensity modulated dose delivery is desirable to really maximize treatment outcome. Although it is possible to deliver IMRT by using broad beams in combination with dynamic multileaf collimation the process is rather time consuming and inefficient. By using narrow scanned high energy photon beams the treatment outcome can be improved, the treatment time reduced and accurate 3D in vivo dose delivery monitoring is possible by PET-CT based dose delivery imaging of photo nuclear reactions in human tissues. Narrow photon beams can be produced by directing a low emittance high energy electron beam on a thin target, and then cleaning the therapeutic photon beam from transmitted high energy electrons, and photon generated charged leptons, with a dedicated purging magnet placed directly downstream of the target. To have an effective scanning and purging magnet system the purging magnet should be placed immediately after the bremsstrahlung target to deflect the transmitted electrons to an efficient electron stopper. In the static electron stopper the electrons should be safely collected independent of the desired direction of the therapeutic scanned photon beam. The SID (Source to Isocenter Distance) should preferably be short while retaining the ability to scan over a large area on the patient and consequently there are severe requirements both on the strength and the geometry of the scanning and purging magnets. In the present study an efficient magnet configuration with a purging and scanning magnet assembly is developed for electron energies in the 50–75 MeV range and a SID of 75 cm. For a bremsstrahlung target of 3 mm Be these electron energies produce a photon beam of 25–17 mm FWHM (Full Width Half Maximum) at a SID of 75 cm. The magnet system was examined both in terms of the efficiency in scanning the narrow bremsstrahlung beam and the deflection of transmitted and photon generated electrons. The simulations show that its is possible to have a scan area on the patient of up to 43 × 40 cm 2 for an incident electron energy of 50 MeV and 28 × 40 cm 2 at 75 MeV, while at the same time adequately deflecting the transmitted electron beam.

Development and validation of a beam model applicable to small fields

A beam model for dose verification of narrow photon beams in water is presented. This model includes the two main effects affecting dose distributions for small fields: the spatial extension of the radiation source and the lateral non-equilibrium conditions of the energy transfer in the absorber. The spatial extension of the radiation source is determined experimentally using two methods: a ‘slit-method’ for the inner part and the measurement of relative output factors free in air for the outer part. The lateral non-equilibrium is taken into account using dose deposition kernels obtained with Monte Carlo calculations and subsequent convolution techniques. The model was validated in water for a wide range of field sizes in a 6 MV photon beam. Good agreement between measured and calculated dose profiles and output factors was found for all the cases studied. The model is considered to be especially useful for narrow-beam IMRT such as typically used in TomoTherapy units. Thus, it can be used as a supplemental dosimetry check for dose delivery performance and as an independent treatment verification tool for cases involving small radiation fields.

Fourier deconvolution reveals the role of the Lorentz function as the convolution kernel of narrow photon beams

The two-dimensional lateral dose profiles D(x, y) of narrow photon beams, typically used for beamlet-based IMRT, stereotactic radiosurgery and tomotherapy, can be regarded as resulting from the convolution of a two-dimensional rectangular function R(x, y), which represents the photon fluence profile within the field borders, with a rotation-symmetric convolution kernel K(r). This kernel accounts not only for the lateral transport of secondary electrons and small-angle scattered photons in the absorber, but also for the ‘geometrical spread’ of each pencil beam due to the phase-space distribution of the photon source. The present investigation of the convolution kernel was based on an experimental study of the associated line-spread function K(x). Systematic cross-plane scans of rectangular and quadratic fields of variable side lengths were made by utilizing the linear current versus dose rate relationship and small energy dependence of the unshielded Si diode PTW 60012 as well as its narrow spatial resolution function. By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential function exp(−2πλνx) of the spatial frequency νx. Thereby, the line-spread function K(x) was identified as the Lorentz function K(x) = (λ/π)[1/(x2 + λ2)], a single-parameter, bell-shaped but non-Gaussian function with a narrow core, wide curve tail, full half-width 2λ and convenient convolution properties. The variation of the ‘kernel width parameter’ λ with the photon energy, field size and thickness of a water-equivalent absorber was systematically studied. The convolution of a rectangular fluence profile with K(x) in the local space results in a simple equation accurately reproducing the measured lateral dose profiles. The underlying 2D convolution kernel (point-spread function) was identified as K(r) = (λ/2π)[1/(r2 + λ2)]3/2, fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.

Analytical calculation of central‐axis dosimetric data for a dedicated radiosurgery linear accelerator

Narrow beams are extensively used in stereotactic radiosurgery. The accuracy of treatment planning dose calculation depends largely on how well the dosimetric data are measured during the machine commissioning. Narrow beams are characterized by the lack of lateral electronic equilibrium. The lateral electronic disequilibrium in the radiation field and detector's finite size are likely to compromise the accuracy in dose measurements in these beams. This may have a profound impact on outcome in patients who undergo stereotactic radiosurgery. To confirm the measured commissioning data for a dedicated 6-MV linear accelerator-based radiosurgery system, we developed an analytical model to calculate the narrow photon beam central-axis dose. This model is an extension of a previously reported method of Nizin and Mooij for the calculation of the absorbed dose under lateral electronic disequilibrium conditions at depth of dmax or greater. The scatter factor and tissue-maximum ratio were calculated for narrow beams using the parametrized model and compared to carefully measured results for the same beams. For narrow beam radii ranging from 0.2 to 1.5 cm, the differences between the analytical and measured scatter factors were no greater than 1.4%. In addition, the differences between the analytical and measured tissue-maximum ratios were within 3.3% for regions greater than the maximum dose depth. The estimated error of this analytical calculation was less than 2%, which is sufficient to validate measurement results.

Dosimetric characteristics of an unshielded p-type Si diode: linearity, photon energy dependence and spatial resolution

The unshielded Si diode PTW 60012, used for accurate measurements of the transversal dose profiles of narrow photon beams, has been investigated with regard to its linearity, photon energy dependence and spatial resolution. The diode shows a slight supralinearity, i.e. increase of the response with pulse dose, by 3% over the pulse dose range 0.1 to 0.8mGy. In p-type silicon, supralinearity results from the increased chance for radiation-induced electrons to escape recombination when the pulse dose increases. Over the energy range from 6 to 15 MV, the response decreases by about 4%. This small variation of the response results from partial compensation between the influences of the secondary electron energy on the mass stopping power ratio silicon/water and on electron backscattering from the silicon chip. The lateral response function of the examined diode has a full half width of 1.3mm. Dose profiles of 5mm half-width can still be recorded with negligible error.