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Modelling individual geometric variation based on dominant eigenmodes of organ deformation: implementation and evaluation

M Söhn1, M Birkner1, D Yan2 and M Alber1

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We present a method of modelling inter-fractional organ deformation and correlated motion of adjacent organ structures in terms of so-called eigenmodes. The method is based on a principal component analysis (PCA) of organ shapes and allows for reducing the large dimensionality of geometry information from multiple CT studies to a few-parametric statistical model of organ motion and deformation. Eigenmodes are 3D vectorfields of correlated displacements of the organ surface points and can be seen as fundamental 'modes' of the patient's geometric variability. The amount of variability represented by the eigenmodes is quantified in terms of corresponding eigenvalues. Weighted sums of eigenmodes describe organ displacements/deformations and can be used to generate new organ geometries. We applied the method to four patient datasets of prostate/rectum/bladder with N = 15–18 CTs to assess interfractional geometric variation. The spectrum of eigenvalues was found to be dominated by only few values, indicating that the geometric variability of prostate/bladder/rectum is governed by only few patient specific eigenmodes. We evaluated the capability of this approach to represent the measured organ samples by calculating the residual errors for the organ surface points, using a varying number of eigenmodes. The distribution of residual errors shows fast convergence with the number of eigenmodes. Using 4 dominating modes, the range of residual errors for the four patients was 1.3–2.0 mm (prostate), 1.4–1.9 mm (rectum) and 1.5–1.9 mm (bladder). Thus, individual geometric variation taken from multiple imaging data can be described accurately by few dominating eigenmodes, thereby providing the most important factors to characterize deformable organ motion, which can assist adaptive radiotherapy planning.


PACS

87.55.-x Treatment strategy

02.50.-r Probability theory, stochastic processes, and statistics

02.10.Ud Linear algebra

87.59.bd Computed radiography

Subjects

Mathematical physics

Computational physics

Medical physics

Dates

Issue 24 (21 December 2005)

Received 14 June 2005, in final form 18 October 2005

Published 7 December 2005



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