Application of a spring-dashpot system to clinical lung tumor motion data

The treatment efficacy of radiation therapy for lung tumors can be increased by compensating for breath-induced tumor motion. In this study, we quantitatively examine a mathematical model of pseudomechanical linkages between an external surrogate signal and lung tumor motion.

A spring-dashpot system based on the Voigt model was developed to model the correlation between abdominal respiratory motion and tumor motion during lung radiotherapy. The model was applied to clinical data obtained from 52 treatments ("beams") from 10 patients, treated on the Mitsubishi Real-Time Radiation Therapy system, Sapporo, Japan. In Stage 1, model parameters were optimized for individual patients and beams to determine reference values and to investigate how well the model can describe the data. In Stage 2, for each patient the optimal parameters determined for a single beam were applied to data from other beams to investigate whether a beam-specific set of model parameters is sufficient to model tumor motion over a course of treatment.

In Stage 1, the baseline root mean square (RMS) residual error for all individually optimized beam data was 0.90 ± 0.40 mm (mean ± 1 standard deviation). In Stage 2, patient-specific model parameters based on a single beam were found to model the tumor position closely, even for irregular beam data, with a mean increase with respect to Stage 1 values in RMS error of 0.37 mm. On average, the obtained model output for the tumor position was 95% of the time within an absolute bound of 2.0 and 2.6 mm in Stages 1 and 2, respectively. The model was capable of dealing with baseline, amplitude and frequency variations of the input data, as well as phase shifts between the input abdominal and output tumor signals.

These results indicate that it may be feasible to collect patient-specific model parameters during or prior to the first treatment, and then retain these for the rest of the treatment period. The model has potential for clinical application during radiotherapy treatment of lung tumors.