Radiobiological evaluation considering setup error on single‐isocenter irradiation in stereotactic radiosurgery

Abstract

Purpose: We calculated the dosimetric indices and estimated the tumor control probability (TCP) considering six degree-of-freedom (6DoF) patient setup errors in stereotactic radiosurgery (SRS) using a single-isocenter technique.Methods: We used simulated spherical gross tumor volumes (GTVs) with diameters of 1.0 cm (GTV 1), 2.0 cm (GTV 2), and 3.0 cm (GTV 3), and the distance (d) between the target center and isocenter was set to 0, 5, and 10 cm. We created the dose distribution by convolving the blur component to uniform dose distribution. The prescription dose was 20 Gy and the dose distribution was adjusted so that D95 (%) of each GTV was covered by 100% of the prescribed dose. The GTV was simultaneously rotated within 0°-1.0°(δR) around the x-, y-, and z-axes and then translated within 0-1.0 mm (δT) in the x-, y-, and z-axis directions. D95, conformity index (CI), and conformation number (CN) were evaluated by varying the distance from the isocenter. The TCP was estimated by translating the calculated dose distribution into a biological response. In addition, we derived the x-y-z coordinates with the smallest TCP reduction rate that minimize the sum of squares of the residuals as the optimal isocenter coordinates using the relationship between 6DoF setup error, distance from isocenter, and GTV size.Results: D95, CI, and CN were decreased with increasing isocenter distance, decreasing GTV size, and increasing setup error. TCP of GTVs without 6DoF setup error was estimated to be 77.0%. TCP were 25.8% (GTV 1), 35.0% (GTV 2), and 53.0% (GTV 3) with (d, δT , δR) = (10 cm, 1.0 mm, 1.0°). The TCP was 52.3% (GTV 1), 54.9% (GTV 2), and 66.1% (GTV 3) with (d, δT , δR) = (10 cm, 1.0 mm, 1.0°) at the optimal isocenter position. Conclusion:The TCP in SRS for multiple brain metastases with a single-isocenter technique may decrease with increasing isocenter distance and decreasing GTV size when the 6DoF setup errors are exceeded (1.0 mm, 1.0°). Additionally, it might be possible to better maintain TCP for GTVs with 6DoF setup errors by using the optimal isocenter position.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

“…3, 4). As was also shown by the results of previous studies, we observed that the physical dose reduction rate of the GTV increased due to a smaller GTV size, an increased distance from the isocenter, and an increased error in the 6DoF setup [11,12,14]. Some studies reported an increase in the PTV margin because the physical dose of the GTV decreases with increasing distance from the isocenter [13,40].…”

“…2021b software (MathWorks, Natick, MA, USA) was used. The coordinates (unit: cm) of the GTVs were set so that the distance (d) from the center of the GTV to the set at the origin of the coordinate axes was 0-10 cm [14,27]. First, a uniform dose distribution was created by adding a margin to each GTV (Fig.…”

“…1). Next, to create a uniform dose distribution with a probability density that follows a three-dimensional normal distribution, convolution integration was performed on the blurred component of the dose, and the blurred dose distribution for each GTV in Equations ( 1) and (2) was calculated [14]. Finally, the prescription dose was set to 27 Gy in three fractions for each GTV in Eq.…”

“…In many single-isocenter irradiation cases, the isocenter is not located at the center of the target, and single-isocenter irradiation has a disadvantage in that the effect of patient setup errors, including translational and rotational errors, may be greater than in conventional irradiation methods where the isocenter is set at the center of the target. Several research groups have examined the uncertainty in the target dose due to the setup error of single-isocenter irradiation [11][12][13][14]. We reported the optimal distances from the isocenter where targets from 1.0 cm to 3.0 cm satisfy several tolerances for a set of patient setup errors [11,12].…”

“…Rojas et al derived the optimal planning target volume (PTV) margin required to meet the tolerances [13]. Although there have been evaluations of the target's tumor control probability (TCP) and normal tissue complication probability (NTCP) in the presence of some setup errors, most of those studies performed only physical evaluations [14,15]. Mathematical models have long been used to elucidate physiological and pathological processes in humans, and the models have been extended to many areas of medicine [16,17].…”