During radiotherapy, maintaining the patient in a relaxed and comfortable state helps ensure respiratory regularity and reproducibility, thereby supports accurate respiratory tracking/gating treatment. Criteria to evaluate respiratory naturalness, regularity, and phase robustness are therefore needed to aid for the treatment system numerically and medical observers visually. This study introduces a new concept of respiratory tumor kinematics that describes the trajectory of tumor motion with respiration, leading to the minimum jerk theory. Using this theory, this study proposes novel respiratory criteria for respiratory naturalness, regularity, and phase robustness.
According to respiratory tumor kinematics, tumor motion follows the minimum curvature/jerk trajectory in 4D spacetime. Using this theory, the following three respiratory criteria are proposed: (1) respiratory naturalness , the residual sum of the squared difference between the normalized average free respiratory wave (single inhalation/exhalation averaged over each 10 phases) and the normalized minimum jerk theoretical respiratory wave; (2) respiratory regularity , the cumulative jerk squared cost function sampling every 0.2 s with a peak adjustment coefficient, 16; and (3) respiratory phase robustness (LΔ), a second-order partial differential in the respiratory position for regarded Cj16 as the respiratory position function. To verify these respiratory criteria, values obtained from CyberKnife tracking marker log data for 15 patients were compared with regard to the correlation error between the correlation model and the imaged tumor position, as well as with the number of remodels. The Cj16 growth curve was also compared between 15 patients and 15 healthy volunteers.
In the 15 patients, data with Us < 1 and Cj16(60 s) < 10 000 satisfied average/maximum correlation errors of less than 1/3 mm. Data with higher Us values (less respiratory naturalness) and higher Cj16(60 s) values (less respiratory regularity) demonstrated more than 3 mm average/5 mm maximum correlation errors and an increased number of remodels. The data for the 15 patients and 15 volunteers demonstrated that the Cj16 growth curve over 120 s from the start of sampling indicated patient-specific respiratory trends and that the distribution of LΔ clearly showed the respiratory phase shift. In 22 of 30 subjects, the degree of change in the Cj growth curve trends from 60 to 120 s was 22% ± 13% (average ± SD). In contrast, the residual data observed when Cj16 > 1000 showed minimum and mean changes of 91% and 180%, respectively.
The authors developed and verified novel respiratory criteria for respiratory naturalness, regularity, and phase robustness obtained using respiratory tumor kinematics and minimum jerk analysis. These criteria should be useful in monitoring respiratory trends on a real-time basis during treatment, as well as in selecting optimal breathing for tracking/gating radiation treatment and defining numerical goals for respiratory training/gating.