Optimizing principal component models for representing interfraction variation in lung cancer radiotherapy

Abstract

Purpose: To optimize modeling of interfractional anatomical variation during active breath-hold radiotherapy in lung cancer using principal component analysis ͑PCA͒. Methods: In 12 patients analyzed, weekly CT sessions consisting of three repeat intrafraction scans were acquired with active breathing control at the end of normal inspiration. The gross tumor volume ͑GTV͒ and lungs were delineated and reviewed on the first week image by physicians and propagated to all other images using deformable image registration. PCA was used to model the target and lung variability during treatment. Four PCA models were generated for each specific patient: ͑1͒ Individual models for the GTV and each lung from one image per week ͑week to week, W2W͒; ͑2͒ a W2W composite model of all structures; ͑3͒ individual models using all images ͑weekly plus repeat intrafraction images, allscans͒; and ͑4͒ composite model with all images. Models were reconstructed retrospectively ͑using all available images acquired͒ and prospectively ͑using only data acquired up to a time point during treatment͒. Dominant modes representing at least 95% of the total variability were used to reconstruct the observed anatomy. Residual reconstruction error between the model-reconstructed and observed anatomy was calculated to compare the accuracy of the models. Results: An average of 3.4 and 4.9 modes was required for the allscans models, for the GTV and composite models, respectively. The W2W model required one less mode in 40% of the patients. For the retrospective composite W2W model, the average reconstruction error was 0.7Ϯ 0.2 mm, which increased to 1.1Ϯ 0.5 mm when the allscans model was used. Individual and composite models did not have significantly different errors ͑p = 0.15, paired t-test͒. The average reconstruction error for the prospective models of the GTV stabilized after four measurements at 1.2Ϯ 0.5 mm and for the composite model after five measurements at 0.8Ϯ 0.4 mm. Conclusions: Retrospective PCA models were capable of reconstructing original GTV and lung shapes and positions within several millimeters with three to four dominant modes, on average. Prospective models achieved similar accuracy after four to five measurements.

Classifying geometric variability by dominant eigenmodes of deformation in regressing tumours during active breath-hold lung cancer radiotherapy

“…Here, we briefly describe the PCA modelling process. For a more detailed description, the reader is referred to the original paper (Badawi et al , 2010). …”

“…Eigenvalues are equal to the variance of each eigenmode. Generally, eigenmodes associated with small eigenvalue do not contribute substantially to modelling of geometric variability as seen in the input geometries and can be ignored (Badawi et al , 2010; Sohn et al , 2005). Thus, a reduced interfraction model p’ (t) can be formed as: $$\mathbf{p}\mathbf{\prime }(t)=\overline{\mathrm{boldp}}+{\displaystyle \sum _{l=1}^L{c}_l(t){\mathrm{boldq}}_l}$$ where p̄ is the mean structure shape over the entire treatment course, { q 1 , q 2 ,…, q L } is the set of eigenvectors, L is the number of principal components, or dominant eigenmodes, to keep in the reduced model, and { c 1 (t), c 2 (t),…., c L (t)} is the set of principal component coefficients which reconstruct each specific time instance of p ( t ) at particular treatment time, t .…”

“…In our previous work (Badawi et al , 2010), only the first L dominant eigenmodes were used to reconstruct a reduced, low noise model p’ (t) of the original GTV shapes. Similarly, one can select any subset of basis vectors and, using Eq.…”

“…We term these trending only or non-trending only reduced model reconstructions the ‘separate models’. Finally, we performed a reconstruction with all dominant eigenmodes, as in our previous work (Badawi et al , 2010). This process resulted in three sets of GTVs for each patient, where each set contained a GTV at each imaged fraction during treatment.…”

“…Principal component analysis (PCA) has been used to develop and optimize models for representing geometric variation during radiotherapy (Badawi et al , 2010; Birkner et al , 2007; Budiarto et al , 2011; Li et al , 2010; Price and Moore, 2007; Sohn et al , 2005). Complex geometries of GTV and other structures were compressed into a set of few principal components (PCs) that change with time.…”