A comparison of two clinical correlation models used for real-time tumor tracking of semi-periodic motion: A focus on geometrical accuracy in lung and liver cancer patients

Purpose A head-to-head comparison of two clinical correlation models with a focus on geometrical accuracy for internal tumor motion estimation during real-time tumor tracking (RTTT). Methods and materials Both the CyberKnife (CK) and the Vero systems perform RTTT with a correlation model that is able to describe hysteresis in the breathing motion. The CK dual-quadratic (DQ) model consists of two polynomial functions describing the trajectory of the tumor for inhale and exhale breathing motion, respectively. The Vero model is based on a two-dimensional (2D) function depending on position and speed of the external breathing signal to describe a closed-loop tumor trajectory. In this study, 20 s of internal motion data, using an 11 Hz (on average) full fluoroscopy (FF) sequence, was used for training of the CK and Vero models. Further, a subsampled set of 15 internal tumor positions (15p) equally spread over the different phases of the breathing motion was used for separate training of the CK DQ model. Also a linear model was trained using 15p and FF tumor motion data. Fifteen liver and lung cancer patients, treated on the Vero system with RTTT, were retrospectively evaluated comparing the CK FF, CK 15p and Vero FF models using an in-house developed simulator. The distance between estimated target position and the tumor position localized by X-ray imaging was measured in the beams-eye view (BEV) to calculate the 95th percentile BEV modeling errors (ME_95,BEV). Additionally, the percentage of ME_95,BEV smaller than 5 mm (P_5mm) was determined for all correlation models. Results In general, no significant difference (p > 0.05, paired t-test) was found between the CK FF and Vero models. Based on patient-specific evaluation of the geometrical accuracy of the linear, CK DQ and Vero correlation models, no statistical necessity (p > 0.05, two-way ANOVA) of including hysteresis in correlation models was proven, although during inhale breathing motion, the linear model resulted in a decreased P_5mm with 5-6% compared to both the DQ CK and Vero models. Conclusion Dual-quadratic CyberKnife and 2D Vero correlation models were interchangeable in terms of geometrical accuracy with the CK linear ME_95,BEV = 4.1 mm, CK dual-quadratic ME_95,BEV = 3.9 mm and Vero ME_95,BEV = 3.7 mm, when modeled with FF sequence. CK DQ modeling based on 15p acquired in 20 s may lead to problems for internal motion estimation.