Distribution of lung tissue hysteresis during free breathing

Purpose: To characterize and quantify free breathing lung tissue motion distributions.Methods: Forty seven patient data sets were acquired using a 4DCT protocol consisting of 25 ciné scans at abutting couch positions on a 16‐slice scanner. The tidal volume of each scan was measured by simultaneously acquiring spirometry and an abdominal pneumatic bellows. The concept of a characteristic breath was developed to manage otherwise natural breathing pattern variations. The characteristic breath was found by first dividing the breathing traces into individual breaths, from maximum exhalation to maximum exhalation. A linear breathing drift model was assumed and the drift removed for each breath. Breaths that exceeded one standard deviation in period or amplitude were removed from further analysis. A characteristic breath was defined by normalizing each breath to a common amplitude, aligning the peak inhalation times for all of the breaths, and determining the average time at each tidal volume, keeping inhalation and exhalation separate. Breathing motion trajectories were computed using a previously published five‐dimensional lung tissue trajectory model which expresses the position of internal lung tissue, X ⇀ , as:X ⇀ ( v , f : X ⇀ 0 ) = X ⇀ 0 + α ⇀ ( X ⇀ 0 ) v + β ⇀ ( X ⇀ 0 ) f , whereX ⇀ 0 is the internal lung tissue position at zero tidal volume and zero airflow, the scalar values v and f are the measured tidal volume and airflow, respectively, and the vectors α ⇀ and β ⇀ are fitted free parameters. In order to characterize the motion patterns, the trajectory elongations were examined throughout the subject's lungs. Elongation was defined here by generating a rectangular bounding box with one side parallel to the α ⇀ vector and the box oriented in the plane defined by the α ⇀ and β ⇀ motion vectors. Hysteresis motion was defined as the ratio of the box dimensions aligned orthogonal to and parallel to the α ⇀ vector. The 15th and 85th percentile of the elongation were used to characterize tissue trajectory hysteresis.Results: The 15th and 85th percentile bounding box elongations were 0.090 ± 0.005 and 0.083 ± 0.013 in the upper left lung and 0.187 ± 0.037 and 0.203 ± 0.053, in the lower left lung. The 15th and 85th percentiles for the upper right lung were 0.092 ± 0.006 and 0.085 ± 0.013, and 0.184 ± 0.038, and 0.196 ± 0.043 in the lower right lung. Both percentiles were calculated for tidal volume displacements between 5 and 15 mm. In the left lung, the average elongations in the upper and lower lung wereζ ¯ = 0.120 ± 0.064 andζ ¯ = 0.090 ± 0.055 , respectively. The average elongations in the upper and lower right lung wereζ ¯ = 0.107 ± 0.060 andζ ¯ = 0.082 ± 0.048 , respectively. The elongation varied smoothly throughout the lungs.Conclusions: The hysteresis motion was relatively small compared to the volume‐filling motion, contributing between 8% and 20% of the overall motion. Statistically significant differences were observed in the range of hysteresis contribution for upper and lower lung regions. The characteristic breath process provided an excellent method for defining an average breath. The characteristic breath had continuous tidal volume and airflow characteristics when the breath was continuously repeated, useful for generating patterns representative of realistic motion for breathing motion studies.