Are the Dose Response Functions of Ionization Chambers Gaussian Or Non-Gaussian?
H K Looe1*, D Harder2, B Poppe1, (1) WG Medical Radiation Physics, Pius-Hospital and Carl von Ossietzky University, Oldenburg, Germany (2) University of Goettingen, GermanySU-E-T-70 Sunday 3:00PM - 6:00PM Room: Exhibit Hall
Purpose: Experimental results from independent investigations have shown that the dose response functions K(x) of a large variety of ionization chambers can be characterized by Gaussian functions. Theoretical considerations and Monte-Carlo simulations, however, have revealed that the K(x) are non-Gaussian. In this work, experimental and Monte-Carlo studies were compared to understand the origin of the general occurrence of Gaussian kernels for ionization chambers with different geometries, using Fourier analysis.
Methods: The measured dose profile M(x) is related to the true dose profile D(x) via the convolution M(x) = D(x) * K(x). The best σ-values of K(x) for three ionization chambers with different geometries: (i) cylindrical; (ii) square; and (iii) parallel-plate were determined experimentally by comparing M(x) with D(x) * K(x). Monte Carlo simulations of the fluence response kernels KM(x) were performed by stepwise shifting a slit beam across each chamber. The function K(x) of each chamber is obtained by deconvolving KM(x) with the dose deposition kernel KD(x).
Results: Our experiments show that the K(x) of the investigated ionization chambers can be all characterized by Gaussian functions, regardless of their geometries. However, the true K(x) obtained with Monte-Carlo simulations are non-Gaussian, exhibiting increased response at the positions of the inner electrode and the chamber wall. Fourier analysis of the true K(x) and its Gaussian approximation G(x) has revealed that FT[G(x)] closely resembles FT[K(x)] at spatial frequencies below about 0.15 mm⁻¹. Furthermore, Fourier transforms of a 2 cm wide dose profile convolved with G(x) or K(x) are not showing noticeable differences.
Conclusion: The Gaussian kernel G(x) experimentally observed are approximations adequately characterizing the spatial resolution of ionization since clinical dose profiles have only negligible components at frequencies higher than 0.1 mm⁻¹ due to physical and geometrical reasons.
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