The development and experimental evaluation of a simple analytical model for the TPR in the build-up region of megavoltage photon beams

PURPOSE: The purpose of this work was to develop a simple analytical model for the tissue phantom ratio (TPR) in the build-up region of megavoltage photon beams and to experimentally evaluate the model under a variety of clinically relevant field configurations. METHODS: Considering electron contamination and primary photons as the main components of the absorbed dose in the build-up region, an analytic expression for the TPR was derived. The electron contamination component was addressed with a biexponential function; the primary photon component was treated as nonlocal energy transport, i.e., assuming the energy deposited by secondary electrons can be described by a biexponential mode similar to that of contaminating electrons. The model contains five independent constants, which were fitted experimentally. The accuracy of the model was evaluated by comparing its results with in-phantom measurements taken on square, rectangular, irregular, and wedged fields, for 6 and 15 MV photon beams on a GE-Saturne 41 accelerator. More specifically, the accuracy of the model was quantified using the gamma index with 2% dose and 2 mm spatial tolerances as described by Low et al. [Med. Phys. 25, 656-661 (1998)]. RESULTS: For square cerrobende blocked fields, the maximum recorded gamma indices were 0.42 and 0.54 for 6 and 15 MV beams, respectively. For "I" shaped fields, the corresponding maxima were 0.64 and 0.52, respectively, while for "cross" shaped fields they were 0.42 and 0.76. For rectangular 10 × 30 cm fields, the corresponding maxima were 0.32 and 0.42, and for 7 × 20 cm fields, they were 0.70 and 0.35, respectively. For square 10 × 10 cm and 15 × 15 cm fields with an acrylic tray, the maxima were 0.57 and 0.45 for 6 MV and 0.32 and 0.77 for 15 MV beams, respectively. For a 10 × 10 cm 60° wedged field, the maxima were 0.53 and 0.33 for 6 and 15 MV beams, respectively. In all examined cases of irregular, rectangular, square (with and without tray), and wedged fields, the gamma index was less than unity. Thus, the model correctly predicted TPR in all cases, using the defined criteria. CONCLUSIONS: A simple analytical model for the TPR in the build-up region was developed and evaluated experimentally. The model's predicted TPR values were compared with physical measurements for irregular, square (with and without tray), rectangular, and wedged fields, for 6 and 15 MV photon beams. In every case examined, the results of the model agreed with the experimental measurements based on specific quantitative agreement criteria. The model appears useful for predicting the TPR in the build-up region of megavoltage beams for different types of fields, in different configurations.

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