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Degrees of Freedom in Respiratory Deformation Vector Field Models with Multi-linear Analysis

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A Iliopoulos

AS Iliopoulos1*, N Pitsianis2,1, X Sun1, FF Yin4, L Ren4, (1) Duke University, Durham, North Carolina, (2) Aristotle University of Thessaloniki, Greece, (3) Duke University Medical Center, Durham, NC


SU-F-J-138 (Sunday, July 31, 2016) 3:00 PM - 6:00 PM Room: Exhibit Hall

Purpose: To investigate non-parametric modeling and model-based estimation of respiratory deformation vector fields (DVF); and to lift the limitation on degrees of freedom (DoF) of globally bilinear models, such as those computed via conventional principal components analysis (PCA).

Methods: The investigation into the DoF of deformation models consists of three major components: (a) Models based on multi-linear analysis (MLA) of DVF data, related to conventional bilinear PCA-based models but allowing for higher model DoF. We compare the different models and show limitations of low-DoF models in capturing inhomogeneous motions and in adapting to motion pattern changes. (b) An analytical deformation phantom, designed with multiple control-point trajectories over 10 phases, exhibiting respiratory-motion properties such as hysteresis, spatially and temporally variant phase-shifts, etc. Changes in motion structure were simulated by modifying trajectory parameters. (c) Exploratory study of 14-phase respiratory DVF data from five healthy volunteers. Deformation models were tested in estimating end-of-expiration to end-of-inspiration motion, where the latter phase was not used for model generation.

Results: Deformation estimation with the higher-DoF MLA model yielded consistently lower errors than with the conventional bilinear PCA (of lowest DoF). In the analytical-DVF experiments, the MLA model showed highrt adaptability, with phase-wise average displacement error below 0.1mm, whereas for PCA it could exceed 2mm (voxel-wise errors up to 0.3mm and 6.4mm, respectively). In the volunteer experiments, PCA-model resulted in average error of over 0.6mm for two volunteers, and voxel-wise errors exceeded 1mm for three. Corresponding average and voxel-wise errors were reduced by 0.25mm and by up to 1.25mm, respectively, with the high-DoF MLA model.

Conclusion: DVF models with insufficient DoF are limited in encoding respiratory motion structure and in adaptivity to motion variations. Multi-linear analysis is used to uncover and mitigate these limitations, and, more importantly, indicates greater potential with nonlinear methods and models.

Funding Support, Disclosures, and Conflict of Interest: NIH Grant No. R01-184173

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