Conversion of measured percentage depth dose to tissue maximum ratio values in stereotactic radiotherapy

For many treatment planning systems tissue maximum ratios (TMR) are required as input. These tissue maximum ratios can be measured with a 3D computer-controlled water phantom; however, a TMR measurement option is not always available on such a system. Alternatively TMR values can be measured 'manually' by lowering the detector and raising the water phantom with the same distance, but this makes TMR measurements time consuming. Therefore we have derived TMR values from percentage depth dose (PDD) curves. Existing conversion methods express TMR values in terms of PDD, phantom scatter factor (Sp), and inverse square law. For stereotactic treatments circular fields ranging from 5-50 mm (19 cones) are used with the treatment planning system XKnife (Radionics). The calculation of TMR curves for this range is not possible with existing methods. This is because PDD curves of field sizes smaller than 5 mm (smallest cone size) are needed, but these cones are not provided. Besides, for field sizes smaller than 40 mm, the phantom scatter factor is difficult to determine and will introduce significant errors. To overcome these uncertainties, an alternative method has been developed to obtain TMR values from PDD data, where absolute doses are expressed in terms of PDD, total scatter factor and inverse square law. For each depth, the dose as a function of field size is fitted to a double exponential function. Then the TMR is calculated by taking the ratio of this function at the depth of interest and the reference depth, for the correct field size. For all 19 cones the total scatter factor and PDDs have been measured with a shielded diode in water for a 6 MV photon beam. Calculated TMR curves are compared with TMR values measured with a diode. The agreement is within 2%. Therefore this relatively simple conversion method meets the required accuracy for daily dose calculation in stereotactic radiotherapy. In principle this method could also be applied for other small field sizes such as those formed with a mini multileaf collimator.