A Pattern Fusion Algorithm to Determine the Effectiveness of Predictions of Respiratory Surrogate Motion Multiple-Steps Ahead of Real Time

Purpose: Ensuring that tumor motion is within the radiation field for high-dose and high-precision radiosurgery in areas greatly influenced by respiratory motion. Therefore tracking the target or gating the radiation beam by using real-time imaging and surrogate motion monitoring methods are employed. However, these methods cannot be used to depict the effect of respiratory motion on tumor deviation. Therefore, an investigation of parameters for method predicting the tumor motion induced by respiratory motion multiple steps ahead of real time is performed. Currently, algorithms exist to make predictions about future real-time events, however these methods are tedious or unable to predict far enough in advance.

Methods and Materials: The algorithm takes data collected from the Varian RPM$ System, which is a one-dimensional (1D) surrogate signal of amplitude versus time. After the 1D surrogate signal is obtained, the algorithm determines on average what an approximate respiratory cycle is over the entire signal using a rising edge function. The signal is further dividing it into three components: (a) training component is the core portion of the data set which is further divided into subcomponents of length equal to the input component; (b) input component serves as the parameter searched for throughout the training component, (c) analysis component used as a validation against the prediction. The prediction algorithm consists of three major steps: (1) extracting top-ranked subcomponents from training component which best-match the input component; (2) calculating weighting factors from these best-matched subcomponents; (3) collecting the proceeding optimal subcomponent and fusing them with assigned weighting factors to form prediction. The prediction algorithm was examined for several patients, and its performance is assessed based on the correlation and root mean square error (RMSE) between prediction and known output.

Results: Respiratory motion data was simulated for 30 cases and 555 patients and phantoms using the RPM system. Simulations were used to optimize prediction algorithm parameters. The simulation cases were used to determine optimal filters for smoothing and number of top-ranked subcomponents to determine optimal subcomponents for prediction. Summed difference results in a value of 0.4770 for the 15 Point Savitzky-Golay filter.

After determining the proper filter for data preprocessing the number of required top-ranked subcomponents for each method was determine. Equal Weighting has a maximum average correlation, c=0.997 when using 1 Subcomponent, Relative Weighting has a maximum average correlation, c=0.997 when using 2 Subcomponents, Pattern Weighting has a maximum average correlation c=0.915 when using 1 subcomponent, Derivative Equal Weighting has a maximum average correlation c=0.976 when using 2 Subcomponents, and Derivative Relative Weighting has a maximum average correlation of c=0.976 when using 5 Subcomponents.

The correlation coefficient and RMSE of prediction versus analysis component distributions demonstrate an improvement during optimization for simulations. This is true for both the full and half cycle prediction. However, when moving to the clinical data the distribution of prediction data, both correlation coefficient and RMSE, there is not an improvement as the optimization occurs. Therefore, a comparison of the clinical data using the 5 Pt moving filter and arbitrarily chosen number of subcomponents was performed. In the clinical data, average correlation coefficient between prediction and analysis component 0.721+/-0.390, 0.727+/-0.383, 0.535+/-0.454, 0.725+/-0.397, and 0.725+/-0.398 for full respiratory cycle prediction and 0.789+/-0.398, 0.800+/-0.385, 0.426+/-0.562, 0.784+/-0.389, and 0.784+/-0.389 for half respiratory cycle prediction for equal weighting, relative weighting, pattern, derivative equal and derivative relative weighting methods, respectively. Additionally, the clinical data average RMSE between prediction and analysis component 0.196+/-0.174, 0.189+/-0.161, 0.302+/-0.162, 0.200+/-0.169, and 0.202+/-0.181 for full respiratory cycle prediction and 0.155+/-0.171, 0.149+/-0.138, 0.528+/-0.179, 0.174+/-0.150, and 0.173+/-0.149 for half respiratory cycle prediction for equal weighting, relative weighting, pattern, derivative equal and derivative relative weighting methods, respectively. The half cycle prediction displays higher accuracy over the full cycle prediction. Wilcoxon signed-rank test reveals statistically highly significant values (p<0.1%) for 4 out of 5 algorithms favoring the half cycle prediction (Equal, Relative, Derivative Equal, and Derivative Relative Weighting Methods). In this method, the relative weighting method has the most correlations coefficients with values greater than 0.9 and also yields the largest number of highest correlations over other prediction methods.

Conclusions: In conclusion, the number of subcomponents used for prediction may be better determined based on individual breathing pattern. The prediction accuracy using patient data is better using half cycle prediction over full cycle prediction for all algorithms for the majority of methods tested. Finally, relative weighting method performed better than other methods.