Abstract
Purpose We developed a mathematic empirical model for describing the small field penumbra in order to analyze the potential dose perturbation caused by overlapping field to avoid the dose calculation errors in linear accelerator-based radiosurgery. Materials and methods A ball phantom was fabricated for measuring penumbra at 4 different gantry angles in the coplanar plane. A least square root estimation (LSRE) Model was created to fit the measured penumbra dose profile and to predict the penumbra dose profile at any gantry angles. The Sum of Squared Errors (SSE) was used for finding the parameters n and t for the best fitting of the LSRE model. Geometric and mathematical methods were used to derive the model parameters. Results The results showed that the larger the gantry angle of the field, the more the expansion of the penumbra dose profile. The least square root estimation model for describing small field penumbra is as follows: where PenumbraD(š) denotes the dose profile D(š) at the penumbra region, T is the penumbra height (usually in scalar 100), n is the parameter for curvature, š = x − W d/2 (x and š are the values in cm on x-axis), and t is the radiation transmission of the collimator. Geometric analysis establishes the correlation between the penetration depth of the exposure and its effect on the penumbra region in ball phantom. The penumbra caused by an exposure at any arbitrary angles can be geometrically derived by using a one-variable quadratic equation. Conclusion The dose distribution in penumbra region of small field can be created by the LSRE model and the potential overdosage or underdosage owing to overlapping field perturbation can be estimated.
Highlights
With the adoption of advanced technologies in modern radiotherapy such as stereotactic radiosurgery, stereotactic body radiation therapy, and intensity-modulated radiation therapy, there is an increased interest in the small-field dosimetry of photon beams
Scattered radiation from the former two components is added to form the total penumbra, namely, the physical penumbra. e physical penumbra width is defined as the lateral distance from the central axis between 20% and 80% of the central axis dose at a reference depth. e height of a penumbra is defined as the intersection point of the central
When the film was scanned with a red color filter, the calibration curve was steeper and with a higher optical density (OD)-dose resolution
Summary
With the adoption of advanced technologies in modern radiotherapy such as stereotactic radiosurgery, stereotactic body radiation therapy, and intensity-modulated radiation therapy, there is an increased interest in the small-field dosimetry of photon beams. A beamlet used in linear accelerator-based radiosurgery is the smallest field formed by one single leaf of the MLC facing the opposite one and is only a portion of the target of dose delivery [1]. E analysis of small field penumbra is important in linear accelerator-based radiosurgery It includes geometric, transmission, and photon scattered components. Transmission penumbra occurs when the beam passes through the edge of the jaw or MLC before it reaches the full attenuation point of the jaw and the MLC. Scattered radiation from the former two components is added to form the total penumbra, namely, the physical penumbra. Scattered radiation from the former two components is added to form the total penumbra, namely, the physical penumbra. e physical penumbra width is defined as the lateral distance from the central axis between 20% and 80% of the central axis dose at a reference depth. e height of a penumbra is defined as the intersection point of the central
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