K Willborn

Two‐dimensional ionization chamber arrays for IMRT plan verification

In this paper we describe a concept for dosimetric treatment plan verification using two-dimensional ionization chamber arrays. Two different versions of the 2D-ARRAY (PTW-Freiburg, Germany) will be presented, a matrix of 16 x 16 chambers (chamber cross section 8 mm x 8 mm; the distance between chamber centers, 16 mm) and a matrix of 27 x 27 chambers (chamber cross section 5 mm x 5 mm; the distance between chamber centers is 10 mm). The two-dimensional response function of a single chamber is experimentally determined by scanning it with a slit beam. For dosimetric plan verification, the expected two-dimensional distribution of the array signals is calculated via convolution of the planned dose distribution, obtained from the treatment planning system, with the two-dimensional response function of a single chamber. By comparing the measured two-dimensional distribution of the array signals with the expected one, a distribution of deviations is obtained that can be subjected to verification criteria, such as the gamma index criterion. As an example, this verification method is discussed for one sequence of an IMRT plan. The error detection capability is demonstrated in a case study. Both versions of two-dimensional ionization chamber arrays, together with the developed treatment plan verification strategy, have been found to provide a suitable and easy-to-handle quality assurance instrument for IMRT.

Spatial resolution of 2D ionization chamber arrays for IMRT dose verification: single-detector size and sampling step width.

The spatial resolution of 2D detector arrays equipped with ionization chambers or diodes, used for the dose verification of IMRT treatment plans, is limited by the size of the single detector and the centre-to-centre distance between the detectors. Optimization criteria with regard to these parameters have been developed by combining concepts of dosimetry and pattern analysis. The 2D-ARRAY Type 10024 (PTW-Freiburg, Germany), single-chamber cross section 5 x 5 mm(2), centre-to-centre distance between chambers in each row and column 10 mm, served as an example. Additional frames of given dose distributions can be taken by shifting the whole array parallel or perpendicular to the MLC leaves by, e.g., 5 mm. The size of the single detector is characterized by its lateral response function, a trapezoid with 5 mm top width and 9 mm base width. Therefore, values measured with the 2D array are regarded as sample values from the convolution product of the accelerator generated dose distribution and this lateral response function. Consequently, the dose verification, e.g., by means of the gamma index, is performed by comparing the measured values of the 2D array with the values of the convolution product of the treatment planning system (TPS) calculated dose distribution and the single-detector lateral response function. Sufficiently small misalignments of the measured dose distributions in comparison with the calculated ones can be detected since the lateral response function is symmetric with respect to the centre of the chamber, and the change of dose gradients due to the convolution is sufficiently small. The sampling step width of the 2D array should provide a set of sample values representative of the sampled distribution, which is achieved if the highest spatial frequency contained in this function does not exceed the Nyquist frequency, one half of the sampling frequency. Since the convolution products of IMRT-typical dose distributions and the single-detector lateral response function have no or very small frequency contributions beyond 0.1 mm(-1), the mathematical approach introduced by Nyquist and Shannon shows that the sampling frequency of 0.2 mm(-1) is appropriate. Overall it is shown that the spatial resolution of the 2D-ARRAY Type 10024 is appropriate for the dose verification of IMRT plans. The insights obtained are also applied in the discussion of other available two-dimensional detector arrays.

DAVID - a translucent multi-wire transmission ionization chamber for in-vivo verification of IMRT and conformal irradiation techniques

Permanent in vivo verification of IMRT photon beam profiles by a radiation detector with spatial resolution, positioned on the radiation entrance side of the patient, has not been clinically available so far. In this work we present the DAVID system, which is able to perform this quality assurance measurement while the patient is treated. The DAVID system is a flat, multi-wire transmission-type ionization chamber, placed in the accessory holder of the linear accelerator and constructed from translucent materials in order not to interfere with the light field. Each detection wire of the chamber is positioned exactly in the projection line of a MLC leaf pair, and the signal of each wire is proportional to the line integral of the ionization density along this wire. Thereby, each measurement channel essentially presents the line integral of the ionization density over the opening width of the associated leaf pair. The sum of all wire signals is a measure of the dose-area product of the transmitted photon beam and of the total radiant energy administered to the patient. After the dosimetric verification of an IMRT plan, the values measured by the DAVID system are stored as reference values. During daily treatment the signals are re-measured and compared to the reference values. A warning is output if there is a deviation beyond a threshold. The error detection capability is a leaf position error of less than 1 mm for an isocentric 1 cm x 1 cm field, and of 1 mm for an isocentric 20 cm x 20 cm field.

The effect of a carbon-fiber couch on the depth-dose curves and transmission properties for megavoltage photon beams.

Purpose:To investigate the attenuation of a carbon-fiber tabletop and a combiboard, alongside with the depth-dose profile in a solid-water phantom.Material and Methods:Depth-dose measurements were performed with a Roos chamber for 6- and 10-MV beams for a typical field size (15 cm × 15 cm, SSD [source-surface distance] 100 cm). A rigid-stem ionization chamber was used to measure transmission factors.Results:Transmission factors varied between 93.6% and 97.3% for the 6-MV beam, and 95.1% and 97.7% for the 10-MV photon beam. The lowest transmission factors were observed for the oblique gantry angle of 150° with the table-combiboard combination. The surface dose normalized to a depth of 5 cm increased from 59.4% (without table, 0° gantry), to 108.6% (tabletop present, 180° gantry), and further to 120% (table-combiboard combination) for 6-MV photon beam. For 10 MV, the increase was from 39.6% (without table), to 88.9% (with table), and to 105.6% (table-combiboard combination). For the 150° angle (tablecombiboard combination), the dose increased from 59.4% to 120% (6 MV) and from 39% to 108.1% (10 MV).Conclusion:Transmission factors for tabletops and accessories directly interfering with the treatment beam should be measured and implemented into the treatment-planning process. The increased surface dose to the skin should be considered.Ziel:In dieser Arbeit werden die Absorptionseigenschaften sowie der Dosisaufbaueffekt eines neuen Bestrahlungstisches aus Carbon in Kombination mit einer Lagerungshilfe aus demselben Material (Combiboard) analysiert.Material und Methodik:Mit einer Roos-Kammer wurden Tiefendosiskurven für ein Bestrahlungsfeld typischer Größe (15 cm × 15 cm, SSD [Oberflächen-Haut-Abstand] 100 cm) für 6 MV und 10 MV untersucht. Die Transmission wurde mit Hilfe einer Stielionisationskammer gemessen.Ergebnisse:Die ermittelten Transmissionswerte variierten zwischen 93,6% und 97,3% für 6 MV und zwischen 95,1% und 97,7% für 10 MV. Die niedrigsten Transmissionswerte wurden für die schräge Einstrahlung von 150° durch Tisch und Combiboard gefunden. Die Oberflächendosis, bezogen auf eine Tiefe von 5 cm, erhöhte sich für 6 MV von 59,4% (ohne Tisch, 0°-Gantry) auf 108,6% (Tisch, 180°-Gantry) und weiter auf 120% (Tisch-Combiboard-Kombination, 180°-Gantry). Für 10 MV wurden Oberflächendosen von 39,6% (ohne Tisch), 88,9% (mit Tisch) und 105,6% (Tisch-Combiboard-Kombination) ermittelt. Für den schrägen Einstrahlwinkel erhöhte sich die Dosis auf 120% (Tisch-Combiboard-Kombination) für 6 MV bzw. auf 108,1% für 10 MV.Schlussfolgerung:Tische und Hilfsmittel aus Carbon können die dosimetrischen Eigenschaften des Strahlenbündels merklich beeinflussen und sollten für jeden Tisch individuell untersucht werden. Eine mögliche Erhöhung der Hautoberflächendosis sollte berücksichtigt werden.

Clinical performance of a transmission detector array for the permanent supervision of IMRT deliveries.

BACKGROUND AND PURPOSEnClinical evaluation of a novel dosimetric accessory serving the permanent supervision of MLC function.nnnMATERIALS AND METHODSnThe DAVID system (PTW-Freiburg, Germany) is a transparent, multi-wire transmission ionization chamber, placed in the accessory holder of the treatment head. Since each of the 37 individual wires is positioned exactly below the associated leaf pair of the MLC, its signal records the opening of this leaf pair during patient treatment.nnnRESULTSnThe DAVID system closes a gap in the quality assurance program, permitting the permanent in-vivo verification of IMRT plans. During dosimetric plan verification with the 2D-ARRAY (PTW-Freiburg, Germany), reference values of the 37 DAVID signals are collected, with which the DAVID readings recorded during daily patient treatment are compared. This comparison is visually displayed in the control room, and warning and alarm levels of any discrepancies can be defined. The properties of the DAVID system as a transmission device, its sensitivity to beam delivery and leaflet errors as well as its stability have been analyzed for clinically relevant examples. In a recent version, the DAVID system has been equipped with 80 wires.nnnCONCLUSIONSnThe DAVID system permits the on-line detection of clinically relevant MLC discrepancies in IMRT deliveries.

Internal scatter, the unavoidable major component of the peripheral dose in photon-beam radiotherapy

In clinical photon beams, the dose outside the geometrical field limits is produced by photons originating from (i) head leakage, (ii) scattering at the beam collimators and the flattening filter (head scatter) and (iii) scattering from the directly irradiated region of the patient or phantom (internal scatter). While the first two components can be modified, e.g. by reinforcement of shielding components or by re-modeling the filter system, internal scatter remains an unavoidable contributor to the peripheral dose. Its relative magnitude compared to the other components, its numerical variation with beam energy, field size and off-axis distance as well as its spectral distribution are evaluated in this study. We applied a detailed Monte Carlo (MC) model of our 6/15 MV Siemens Primus linear accelerator beam head, provided with ideal head leakage shielding conditions (multi-leaf collimator without gaps) to assess the head scatter contribution. Experimental values obtained under real shielding conditions were used to evaluate the head leakage contribution. It was found that the MC-computed internal scatter doses agree with the results of our previous measurements, that internal scatter is the major contributor to the peripheral dose in the near periphery while head leakage prevails in the far periphery, and that the lateral decline of the internal scatter dose can be represented by the sum of two exponentials, with an asymptotic tenth value of 18 to 19 cm. Internal scatter peripheral doses from various elementary beams are additive, so that their sum increases approximately in proportion with field size. The ratio between normalized internal scatter doses at 6 and 15 MV is approximately 2:1. The energy fluence spectra of the internal scatter component at all points of interest outside the field have peaks near 500 keV. The fact that the energy-shifted internal scatter constitutes the major contributor to the dose in the near periphery has a general bearing for dosimetry, i.e. for energy-dependent detector responses and dose conversion factors, for the relative biological effectiveness and for second primary malignancy risk estimates in the peripheral region.

The dose response functions of ionization chambers in photon dosimetry – Gaussian or non-Gaussian?

This study is concerned with the spatial resolution of air-filled ionization chambers in photon-beam dosimetry, i.e. with their dose response functions. These act as convolution kernels K(x,y), transforming true dose profiles D(x,y) into the measured signal profiles M(x,y). One-dimensional dose response functions have been experimentally determined for nine types of cylindrical ionization chambers both in their lateral and longitudinal directions, as well as across two plane-parallel chambers and for the single chambers of two 2D arrays. All these 1D dose response functions are closely described by Gaussian functions. The associated energy-dependent values of the standard deviations σ have been measured for 6 and 15 MV photons with an uncertainty of 0.02mm. At depths beyond secondary electron fluence build-up, there was no detectable depth dependence of the σ values. The general occurrence of Gaussian dose response functions, their extension beyond the geometrical boundaries of the chambers, and the energy dependence of their standard deviations can be understood by considering the underlying system of convolutions, which is the origin of the influences of secondary electron transport. Monte-Carlo simulations of the convolution kernels for a cylindrical, a square, and a flat ionization chamber and their Fourier analysis have been employed to show that the Gaussian convolution kernels are approximations to the true dose response functions, valid in the clinically relevant domain of the spatial frequency. This paper is conceived as the starting point for the deconvolution methods to be described in a further publication.

Performance parameters of a liquid filled ionization chamber array

PURPOSEnIn this work, the properties of the two-dimensional liquid filled ionization chamber array Octavius 1000SRS (PTW-Freiburg, Germany) for use in clinical photon-beam dosimetry are investigated.nnnMETHODSnMeasurements were carried out at an Elekta Synergy and Siemens Primus accelerator. For measurements of stability, linearity, and saturation effects of the 1000SRS array a Semiflex 31013 ionization chamber (PTW-Freiburg, Germany) was used as a reference. The effective point of measurement was determined by TPR measurements of the array in comparison with a Roos chamber (type 31004, PTW-Freiburg, Germany). The response of the array with varying field size and depth of measurement was evaluated using a Semiflex 31010 ionization chamber as a reference. Output factor measurements were carried out with a Semiflex 31010 ionization chamber, a diode (type 60012, PTW-Freiburg, Germany), and the detector array under investigation. The dose response function for a single detector of the array was determined by measuring 1 cm wide slit-beam dose profiles and comparing them against diode-measured profiles. Theoretical aspects of the low pass properties and of the sampling frequency of the detector array were evaluated. Dose profiles measured with the array and the diode detector were compared, and an intensity modulated radiation therapy (IMRT) field was verified using the Gamma-Index method and the visualization of line dose profiles.nnnRESULTSnThe array showed a short and long term stability better than 0.1% and 0.2%, respectively. Fluctuations in linearity were found to be within ±0.2% for the vendor specified dose range. Saturation effects were found to be similar to those reported in other studies for liquid-filled ionization chambers. The detectors relative response varied with field size and depth of measurement, showing a small energy dependence accounting for maximum signal deviations of ±2.6% from the reference condition for the setup used. The σ-values of the Gaussian dose response function for a single detector of the array were found to be (0.72±0.25) mm at 6 MV and (0.74±0.25) mm at 15 MV and the corresponding low pass cutoff frequencies are 0.22 and 0.21 mm(-1), respectively. For the inner 5×5 cm2 region and the outer 11×11 cm2 region of the array the Nyquist theorem is fulfilled for maximum sampling frequencies of 0.2 and 0.1 mm(-1), respectively. An IMRT field verification with a Gamma-Index analysis yielded a passing rate of 95.2% for a 3 mm∕3% criterion with a TPS calculation as reference.nnnCONCLUSIONSnThis study shows the applicability of the Octavius 1000SRS in modern dosimetry. Output factor and dose profile measurements illustrated the applicability of the array in small field and stereotactic dosimetry. The high spatial resolution ensures adequate measurements of dose profiles in regular and intensity modulated photon-beam fields.

The dose-area product, a new parameter for the dosimetry of narrow photon beams

In the dosimetry of narrow photon fields with side lengths of the order of 1 cm, the traditional parametrisation via the absolute dose on the beam axis and the relative lateral dose distribution has to deal with the difficulty to find sufficiently small detectors and to adjust them accurately on the narrow-beam axis. This can be avoided by reconsidering the parametrisation, using as normalization factor the surface integral of the dose in the plane perpendicular to the beam axis, abbreviated as the dose-area product (DAP). We investigated and confirmed the ability of a large-area parallel-plate ionisation chamber, with a sensitive volume shaped as a flat cylinder of 81.6 mm diameter and 2 mm thickness, to perform the integration over the full lateral dose profile of narrow photon beams with side lengths up to 5 cm. The lateral adjustment of this large-area detector relative to a narrow photon beam is not critical. The large-area ionisation chamber was calibrated in terms of the DAP by reference to a 0.3 cm3 ionisation chamber. A field-size dependent modified output factor was defined as the ratio of the DAP measured at 5 cm phantom depth for 100 cm SSD, and the monitor reading. A prominent phenomenon of narrow photon fields is the field-size and source-distance independence of the relative axial profile of the DAP as function of the thickness of a pre-absorber or of the depth in a phantom. For narrow-beam treatment planning in IMRT, the DAP is combined with the energy- and field size-dependent relative lateral dose distribution which is represented, for example, by a Gaussian convolution kernel. Another useful feature of the DAP is the possibility of its direct control during patient irradiation by means of an on-line monitor with spatial resolution, arranged in the accessory holder.

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(-2pilambdanu(x)) of the spatial frequency nu(x). Thereby, the line-spread function K(x) was identified as the Lorentz function K(x) = (lambda/pi)[1/(x(2) + lambda(2))], a single-parameter, bell-shaped but non-Gaussian function with a narrow core, wide curve tail, full half-width 2lambda and convenient convolution properties. The variation of the kernel width parameter lambda 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) = (lambda/2pi)[1/(r(2) + lambda(2))](3/2), fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.