  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 comprising 52 treatment
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 plus or minus 0.40 mm. 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 mm and 2.6 mm in Stage 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 tumor
and output abdominal 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.
