Experimental evaluation of needle deflection estimation for brachytherapy
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Purpose Needle placement is commonly employed in clinical procedures for diagnostic or therapeutic purposes, such as prostate biopsy and brachytherapy. In these interventions accurate needle placement is required to carry out the desired diagnosis or therapy. However, complex needle behavior within tissue poses a major challenge, particularly when needle deflection exacerbates the targeting error. Accurate needle deflection estimation can help compensate for needle bending before and during insertion. Numerous mechanical models have been proposed for needle deflection estimation in soft tissue [1, 2]. The majority of techniques demand precise a priori quantification of deflection model parameters and in actual clinical settings they suffer from errors inherent in such quantification. Through extensive simulation studies [3], it has been observed that this error can be significantly reduced by integrating additional measurements taken directly from the needle tip. Accordingly, a needle deflection method has been proposed that combines a kinematic deflection model with data collected from two electromagnetic (EM) trackers located at the needle tip and base using Kalman filters. This paper presents experimental validation of the simulation results. Methods The experimental method evaluates the effectiveness of the proposed fusion approach [3] in estimating needle deflection that occurs during brachytherapy needle insertion procedures performed on prostate phantoms. As shown in Fig. 1, a total of 21 needles (beveled tip, 18 Gauge, 200 mm length) were manually inserted through a template, and towards different targets distributed within three prostate phantoms made from polyvinyl chloride (PVC) of varying stiffness. The needle deflection was modeled as a kinematic quadratic polynomial. Parameters of the deflection model were identified and perturbed by 50 % to simulate uncertainties in model parameters. An external 8 mm EM tracker and an internal 0.55 mm EM tracker were attached to the needle base and tip, respectively, to provide observations of their positions. These measurements were then fused recursively with the deflection model using a Kalman filter (KF) and an extended Kalman filter (EKF) to improve on the needle tip position estimation accuracy. C-arm fluoroscopy was subsequently used to obtain the ground truth deflection, and assess the performance of the proposed fusion technique. To quantify the estimation error, two metrics were used: the direct linear tip position estimation error and the cumulative deflection error (CDE). The former is the Euclidean distance between the estimated tip position and the ground truth tip position observed at a specific insertion depth, and the latter is the integral of the linear error over a range of insertion depths. Results Needle deflection during the procedure ranged from 2 to 8 mm at an insertion depth of 76 mm. As illustrated in Fig. 2, our experiments validated the simulation results shown in [3]. Compared to the estimations relying exclusively on a deflection model, the method reduced the direct linear needle tip position estimation error by 52 ± 17 %, and the CDE by 57 ± 19 %. While the KF was effective only in situations where the extent of deflection was limited, the EKF was efficient in the majority of cases and proved to be robust to model uncertainties as its formulation included a deflection model. The EKF, however, required more processing time due to the additional states, the nonlinearity of the process equations, and the computation of Jacobian matrices. Still, the recursive structure of both filters still enabled real-time implementation on a single core of an Intel Core Quad 2.4 GHz CPU. Conclusion In general, estimation methods based exclusively on needle deflection models normally include some degree of uncertainty due to the error in the model parameter quantification. Similarly, direct observations of the needle tip contain some degree of uncertainty due to the measurement noise. As a result, statistical sensor fusion techniques, such as Kalman filters can help improve the estimation accuracy. In this work, we tested the usability of our proposed fusion approach [3] during simulated brachytherapy procedures performed on prostate phantoms. The results demonstrated significant improvement compared to the methods relying entirely on model-based estimations or solely on direct tip position measurements. We will continue to examine the performance of this method using alternative needle deflection models and expand the experimental validation to a wider range of clinical applications. References [1] Goksel O, Dehghan E, Salcudean S (2009) Modeling and simulation of flexible needles. Medical Engineering & Physics [2] Webster R, Kim J, Cowan N, Chirikjian G, Okamura A (2006) Nonholonomic modeling of needle steering. International Journal of Robotics Research [3] Sadjadi H, Hashtrudi-Zaad K, Fichtinger G (2012) Needle deflection estimation using fusion of electromagnetic trackers. Fig. 1 Experimental setup for needle deflection measurement in prostate brachytherapy Fig. 2 Comparison of needle deflection estimation errors at various insertion depths, with the measurement data down-sampled for clarity Int J CARS (2013) 8 (Suppl 1):S337–S395 S391
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