A perspective matrix-based seed reconstruction algorithm with applications to C-arm based intra-operative dosimetry

摘要

Currently available seed reconstruction algorithms are based on the assumption that accurate information about the imaging geometry is known. The assumption is valid for isocentric x-ray units such as radiotherapy simulators. However, the large majority of the clinics performing prostate brachytherapy today use C-arms for which imaging parameters such as source to axis distance, image acquisition angles, central axis of the image are not accurately known. We propose a seed reconstruction algorithm that requires no such knowledge of geometry. The new algorithm makes use of perspective projection matrix, which can be easily derived from a set of known reference points. The perspective matrix calculates the transformation of a point in 3D space to the imaging coordinate system. An accurate representation of the imaging geometry can be derived from the generalized projection matrix (GPM) with eleven degrees of freedom. In this paper we show how GPM can be derived given a theoretical minimum number of reference points. We propose an algorithm to compute the line equation that defines the backprojection operation given the GPM. The algorithm can be extended to any ray-tracing based seed reconstruction algorithms. Reconstruction using the GPM does not require calibration of C-arms and the images can be acquired at arbitrary angles. The reconstruction is performed in near real-time. Our simulations show that reconstruction using GPM is robust and accuracy is independent of the source to detector distance and location of the reference points used to generate the GPM. Seed reconstruction from C-arm images acquired at unknown geometry provides a useful tool for intra-operative dosimetry in prostate brachytherapy.