Purpose: Little is known about the effect of force on organ deformation and consequently its impact on precision dose delivery. The purpose of this study was to evaluate the fundamental relationship between anatomic deformation and its causative physical force to ascertain if a threshold limit exists for deformable image registration (DIR) accuracy in uniform low contrast anatomy, beyond which its applicability may be clinically inappropriate. Methods: To simulate a simplified model, a tissue equivalent deformable bladder phantom with 21 implanted fiducial markers was developed using a viscoelastic polymer. The bladder phantom was deformed by applying a force in increments from 10 to 70 N. DIR accuracy was studied using intensity based MIM and Velocity B-spline algorithms by comparing the 3D vector of the 21 marker locations at the original target image with the synthetically derived marker positions from each target image obtained from DIR. Results: The relationship between applied force in 1D deformation along the axis of applied force and 3D deformation of the phantom showed a linear response. The maximum and average displacements of markers exhibited a nonlinear response to the applied force. In the absence of implanted markers, DIR performance was suboptimal with a threshold limit of only 20 N (5 mm deformation) beyond which the average marker error was $\geq$ 3 mm. DIR performance improved significantly with the addition of only one marker for the intensity based MIM algorithm. In contrast, the Velocity B-spline algorithm showed reduced sensitivity to the number of markers introduced in both the source and target images. Conclusions: The limits of applicability of DIR are strongly dependent on the magnitude of deformation. There is a threshold limit beyond which the accuracy of DIR fails in uniform low contrast anatomy. The sensitivity of the DIR performance to the number of fiducial markers present indicates that if DIR performance is solely assessed with the contrast rich features present in clinical anatomy, the results may not be reflective of the true DIR performance in uniform low contrast anatomy.
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