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Determination of the spatial response of ionization chambers in electron and photon radiation fields

21.08.2013

Motivation

In radiation therapy, tumours are treated using high-energy photon and electron radiation fields which are generated by clinical linacs. The aim is to focus the applied dose on the area where the tumour is located, hereby keeping the radiation stress on the surrounding healthy tissue low. The development of imaging procedures over the past 15 years has allowed the location of tumours to be determined with increasing accuracy; thus, it is possible to adapt the irradiation exactly to the tumour profile using appropriate collimators as is the case, for instance, in intensity-modulated radiotherapy (IMRT) by means of so-called "multileaf collimators" (MLCs). Both for IMRT and for other therapeutic forms in which the radiation field is adapted to the tumour profile, it is decisive to know the exact spatial distribution of the radiation field in order to be able to control the irradiation of the tumour. Over the past few years, various procedures have been elaborated or developed to allow dose distributions to be measured with high spatial resolution. Among other techniques, small-volume ionization chambers, semiconductor detectors, diamond detectors, polymer colloids as well as storage foils have been used for this purpose. What is important – besides high resolution – for practical applications is that the detectors are easy to handle, that they are not too cost-intensive, and that they also allow measurements to be performed fast and easily and to be repeatable under the same conditions. These parameters make ionization chambers particularly well suited for clinical application.

Reducing the volume of ionization chambers can improve the resolution. Their volume cannot, however, be reduced arbitrarily, since this also reduces the signal-to-noise ratio. The measured dose is averaged over the total chamber volume, hence the measured field is no longer in agreement with the true field (see schematic representation in Fig. 1). The transition from the true field distribution D(x) to the measured field distribution Dm(x) can be described mathematically by a convolution of the true field distribution with the spatial response function of the detector K(x):

Thus, it is only when the response function K(x) is exactly known that the actual field distribution can be determined from the measured field distribution.

Figure 1 : Schematic representation of the difference between the true and the measured dose profile due to the finite volume of the measuring chamber. A rectangular dose profile is laterally flattened when the measurement is carried out with an ionization chamber.

Procedure

Within the scope of the European research project "Metrology for radiotherapy using complex radiation fields" (EMRP-HLT09), the spatial response function of four ionization chambers of the types PTW31010, PTW31016, FC65G, and NE2561 and that of a silicon diode of the type PTW60012 have been experimentally determined. For this purpose, two methods have been applied and compared with each other (see also Fig. 2):

The chamber is moved behind a gap between two lead bricks, and the chamber's signal is measured at regular intervals. Performing the measurement behind a gap allows the spatial response to be measured directly.

The chamber is moved out of the shadow of a lead brick's edge and measured at regular intervals. Performing the measurement behind a lead brick's edge simulates a step function. The response function K(x) is determined from the numerical derivation of the measured field distribution Dm(x) [1]:

The measurements were carried out at PTB in the photon and electron radiation fields of a clinical linac of the type "Elekta Precise". To determine the response, photon radiation with nominal acceleration voltages of 4 MV, 8 MV and 25 MV as well as electron radiation with nominal energies of 6 MeV, 15 MeV and 20 MeV were used. Measurements were performed in air and in water.

Figure 2 : Schematic representation of the measurements (a) at the lead brick's gap and (b) at the lead brick's edge. The chamber is displaced from right to left behind the lead brick and measured at regular intervals. In the case of the edge measurement (b), the response function is determined from the derivation of the measured field distribution.

Result

The spatial response functions of the investigated chambers could be measured for photon and electron radiation fields with a - so far - unprecedented resolution.

The different response functions for photons and electrons are illustrated in Fig. 3 with the example of the chamber of the type FC65G; both are measurements in air at a nominal acceleration voltage of 8 MV and a nominal electron energy of 15 MeV, respectively. For photons, a typical structure with three peaks can be seen. The peaks are located at the positions of the electrodes of the ionization chamber, which suggests that the photons interact especially with the solid components of the chamber and generate secondary particles in these locations. These secondary particles, in turn, generate ion pairs which can be measured in the air volume between the electrodes. In the case of electrons, in contrast, the response function exhibits only one peak which corresponds to the width of the chamber, with a local minimum at the position of the inside electrode. Thus, electrons interact directly in the air volume between the electrodes and generate the ion pairs which cause the signal. The local minimum can be interpreted as a shadow of the inside electrode.

Figure 3 : Response function of the chamber of the type FC65G measured in air in a hoton radiation field (blue) and in an electron radiation field (red).

To describe the curves, a geometrical ansatz similar to the approach of van't Veld et al. [2] was chosen. For this ansatz, we assumed that the number of ion pairs - and thus the response - is proportional to the path which the ionizing radiation covers inside the detector, weighted with coefficients for various materials which are adapted to the measurement curve. Since the set-up of the curve is concentric, this results in a sum from elliptical functions:

Here, Ca, Cl, Ci stand for the weighting factors of the outside wall, of the air volume and of the inside electrode; the symbols R1, R2, R3 and R4 stand for the outside and the inside radius of the chamber wall and of the central electrode. After the extension of the function for the concentric peak and the convolution with a Gaussian core, one obtains the theoretical curve shown in Fig. 4, which is shown together with the experimentally determined curve of the chamber of the type NE2561 for an acceleration voltage of 4 MV.

Figure 4 : Response of the chamber of the type NE2561. The measured values for photons at 4 MVX in air are represented in red. At the position of the outside and of the inside electrode (which is hollow inside), peaks can be seen. The black curve shows a fit with the geometric model described above.

References

  1. Garcia-Vicente, F.; Delgado, J. M. und Peraza, C.:
    Experimental determination of the convolution kernel for the study of the spatial response of a detector,
    Med. Phys. 25, p. 202-207 (1998)
  2. van't Veld, A. A.; van Luijk, P.; Praamstra, F. und van der Hulst, P. C.:
    Detector line spread functions determined analytically by transport of Compton recoil electrons,
    Med. Phys. 28, p. 738-751 (2001)