Novel breathing motion model for radiotherapy

Purpose: An accurate model of breathing motion under quiet respiration is desirable to obtain the most accurate and conformal dose distributions for mobile lung cancer lesions. On the basis of recent lung motion measurements and the physiologic functioning of the lungs, we have determined that the motion of lung and lung tumor tissues can be modeled as a function of five degrees of freedom, the position of the tissues at a user-specified reference breathing phase, tidal volume and its temporal derivative airflow (tidal volume phase space). Time is an implicit variable in this model. Methods and Materials: To test this hypothesis, a mathematical model of motion was developed that described the motion of objects p in the lungs as linear functions of tidal volume and airflow. The position of an object was described relative to its position P → 0 at the reference tidal volume and zero airflow, and the motion of the object was referenced to this position. Hysteresis behavior was hypothesized to be caused by pressure imbalances in the lung during breathing and was, in this model, a function of airflow. The motion was modeled as independent tidal volume and airflow displacement vectors, with the position of the object at time t equal to the vector sum r → P \( t \) = r → v \( t \) + r → f \( t \) where r → v \( t \) and r → f \( t \) were displacement vectors with magnitudes approximated by linear functions of the tidal volume and airflow. To test this model, we analyzed five-dimensional CT scans (CT scans acquired with simultaneous real-time monitoring of the tidal volume) of 4 patients. The scans were acquired throughout the lungs, but the trajectories were analyzed in the couch positions near the diaphragm. A template-matching algorithm was implemented to identify the positions of the points throughout the 15 scans. In total, 76 points throughout the 4 patients were tracked. The lateral motion of these points was minimal; thus, the model was described in two spatial dimensions, with a total of six parameters necessary to describe the 30 degrees of freedom inherent in the 15 positions. Results: For the 76 evaluated points, the average discrepancy (the distance between the measured and prediction positions) of the 15 locations for each tracked point was 0.75 ± 0.25 mm, with an average maximal discrepancy of 1.55 ± 0.54 mm. The average discrepancy was also tabulated as a fraction of the breathing motion. Discrepancies of Conclusion: The motion tracking algorithms are being improved and automated to provide more motion data to test the models. This may allow a measurement of the motion-fitting parameters throughout the lungs. If the parameters vary smoothly, interpolation may be possible, yielding a continuous mathematical model of the breathing motion throughout the lungs. The utility of the model will depend on its stability as a function of time. If the model is only robust during the measurement session, it may be useful for determining lung function. If it is robust for weeks, it may be useful for treatment planning and gating of lung treatments. The use of tidal volume phase space for characterizing breathing motion appears to have provided, for the first time, the potential for a patient-specific mathematical model of breathing motion.