Description of tissue phantom ratio in a quadratic exponential function of depth / 中华放射肿瘤学杂志

ABSTRACT

Objective To develop a mathematical model for clinical calculation of and to verify its practical accuracy in tissue phantom ratios (TPRS). Methods An exponential attenuation algorithm was designed to express the TPRS through a function of any depth and field size of the primary beam with a beam hardening correction coefficient. In our model,the variation of attenuation coefficient with the field size was described by an attenuation factor and the hardening coefficient was replaced by a correction factor. Results From fitting in with the published TPR data of 6, 18 and 24?MV X-rays at the normalization depth sufficient for electron equilibrium, it was found that the attenuation factor can be described by a second-order function of field sizes. And the correction factor exhibited a linear relation to the attenuation factor. In order to determine the five parameters needed to calculate the above attenuation factor and correction factor, only eight TPR values at four extreme and mode rate field sizes were measured. A linear fit to the quality index(QI) showed that these parameters were strongly energy-dependent with R2 ranging from 0.844 to 1.000. The attenuation coefficient and hardening coefficient of the primary beam were calculated directly from two parameters. The derived initial attenuation coefficients from QI fitted well to published experimental data and the hardening coefficients were also consistent with measured data. Compared with practical measured results,the error rate of derived functional TPRS,presented within 1.5% at 6?MV, 1.2% at 18?MV and 1.1% at 24?MV X-ray.The principal attenuation and havdening coefficients were also obtained from our developed model.Conclusions The derived model is able to accurately describe the central axis dose distribution of the primary photon beam and be used to calculate the clinical TPR table from limited TPR values.