This is an open access article published by the IET under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/3.0/)
Accurate understanding of surgical tool-tip tracking error is important for decision making in image-guided surgery. In this Letter, the authors present a novel method to estimate/model surgical tool-tip tracking error in which they take pivot calibration uncertainty into consideration. First, a new type of error that is referred to as total target registration error (TTRE) is formally defined in a single-rigid registration. Target localisation error (TLE) in two spaces to be registered is considered in proposed TTRE formulation. With first-order approximation in fiducial localisation error (FLE) or TLE magnitude, TTRE statistics (mean, covariance matrix and root-mean-square (RMS)) are then derived. Second, surgical tool-tip tracking error in optical tracking system (OTS) frame is formulated using TTRE when pivot calibration uncertainty is considered. Finally, TTRE statistics of tool-tip in OTS frame are then propagated relative to a coordinate reference frame (CRF) rigid-body. Monte Carlo simulations are conducted to validate the proposed error model. The percentage passing statistical tests that there is no difference between simulated and theoretical mean and covariance matrix of tool-tip tracking error in CRF space is more than 90% in all test cases. The RMS percentage difference between simulated and theoretical tool-tip tracking error in CRF space is within 5% in all test cases.
References
-
-
1)
-
24. Bruns, T.L., Webster III, R.J.: ‘An image guidance system for positioning robotic cochlear implant insertion tools’. Proc. of SPIE, 2017, 10135, pp. 101350O-1–101350O-6.
-
2)
-
14. West, J.B., Maurer, C.R.: ‘Designing optically tracked instruments for image-guided surgery’, IEEE Trans. Med. Imaging, 2004, 23, (5), pp. 533–545 (doi: 10.1109/TMI.2004.825614).
-
3)
-
1. Yaniv, Z.: ‘Registration for orthopaedic interventions’, In Zheng, G., Li, S. (Eds.): ‘Computational radiology for orthopaedic interventions’ (Springer International Publishing, 2016), pp. 41–70.
-
4)
-
9. Seginer, A.: ‘Rigid-body point-based registration: the distribution of the target registration error when the fiducial registration errors are given’, Med. Image Anal., 2011, 15, (4), pp. 397–413 (doi: 10.1016/j.media.2011.01.001).
-
5)
-
17. Yaniv, Z.: ‘Which pivot calibration?’ SPIE Medical Imaging, 2015, pp. 941527–941527-9.
-
6)
-
12. Datteri, R., Dawant, B.: ‘Estimation and reduction of target registration error’. Medical Image Computing and Computer-Assisted Intervention-MICCAI, 2012, pp. 139–146.
-
7)
-
7. Moghari, M.H., Abolmaesumi, P.: ‘Distribution of target registration error for anisotropic and inhomogeneous fiducial localization error’, IEEE Trans. Med. Imaging, 2009, 28, (6), pp. 799–813 (doi: 10.1109/TMI.2009.2020751).
-
8)
-
20. Simpson, A.L., Dillon, N.P., Miga, M.I., et al: ‘A framework for measuring TRE at the tip of an optically tracked pointing stylus’. SPIE Medical Imaging, 2013, (2013), pp. 867114–867121.
-
9)
-
15. Min, Z., Meng, M.Q.H.: ‘General first-order TRE model when using a coordinate reference frame for rigid point-based registration’. 2017 IEEE 14th Int. Symp. Biomedical Imaging (ISBI 2017), 2017, pp. 169–173.
-
10)
-
8. Ma, B., Moghari, M.H., Ellis, R.E., et al: ‘Estimation of optimal fiducial target registration error in the presence of heteroscedastic noise’, IEEE Trans. Med. Imaging, 2010, 29, (3), pp. 708–723 (doi: 10.1109/TMI.2009.2034296).
-
11)
-
16. Wiles, A.D., Peters, T.M.: ‘Improved statistical TRE model when using a reference frame’. Int. Conf. on Medical Image Computing and Computer-Assisted Intervention, 2007.
-
12)
-
2. Wiles, A.D., Peters, T.M.: ‘Target tracking errors for 5D and 6D spatial measurement systems’, IEEE Trans. Med. Imaging, 2010, 29, (3), pp. 879–894 (doi: 10.1109/TMI.2009.2039344).
-
13)
-
23. Ma, B., Choi, J., Huai, H.M.: ‘Target registration error for rigid shape-based registration with heteroscedastic noise’. SPIE Medical Imaging, 2014, pp. 90360U–90360U.
-
14)
-
22. Balachandran, R., Fitzpatrick, J.M.: ‘Iterative solution for rigid-body point-based registration with anisotropic weighting’. SPIE Medical Imaging, 2009, pp. 72613D–72613D.
-
15)
-
19. Wiles, A.D., Peters, T.M.: ‘Real-time estimation of FLE statistics for 3-D tracking with point-based registration’, IEEE Trans. Med. Imaging, 2009, 28, (9), pp. 1384–1398 (doi: 10.1109/TMI.2009.2016336).
-
16)
-
13. Fitzpatrick, J.M.: ‘Rigid point registration circuits’. SPIE Medical Imaging, 2014, pp. 90362P–90362P.
-
17)
-
3. Fitzpatrick, J.M.: ‘The role of registration in accurate surgical guidance’, Proc. Inst. Mech. Eng. H, J. Eng. Med., 2010, 224, (5), pp. 607–622 (doi: 10.1243/09544119JEIM589).
-
18)
-
4. Simpson, A.L., Ma, B., Vasarhelyi, E.M., et al: ‘Computation and visualization of uncertainty in surgical navigation’, Int. J. Med. Robot. Comput. Assist. Surg., 2014, 10, (3), pp. 332–343 (doi: 10.1002/rcs.1541).
-
19)
-
5. Thompson, S., Penney, G., Dasgupta, P., et al: ‘Improved modelling of tool tracking errors by modelling dependent marker errors’, IEEE Trans. Med. Imaging, 2013, 32, (2), pp. 165–177 (doi: 10.1109/TMI.2012.2216890).
-
20)
-
11. Datteri, R., Dawant, B.M.: ‘Estimation of rigid-body registration quality using registration networks’. SPIE Medical Imaging, 2012, pp. 831419–831419.
-
21)
-
21. Simpson, A.L., Ma, B., Ellis, R.E., et al: ‘Uncertainty propagation and analysis of image-guided surgery’. SPIE Medical Imaging, 2011, pp. 79640H–79640H-7.
-
22)
-
10. Danilchenko, A., Fitzpatrick, J.M.: ‘General approach to first-order error prediction in rigid point registration’, IEEE Trans. Med. Imaging, 2011, 30, (3), pp. 679–693 (doi: 10.1109/TMI.2010.2091513).
-
23)
-
6. Wiles, A.D., Likholyot, A., Frantz, D.D., et al: ‘A statistical model for point-based target registration error with anisotropic fiducial localizer error’, IEEE Trans. Med. Imaging, 2008, 27, (3), pp. 378–390 (doi: 10.1109/TMI.2007.908124).
-
24)
-
25. Dillon, N.P., Siebold, M.A., Mitchell, J.E., et al: ‘Increasing safety of a robotic system for inner ear surgery using probabilistic error modeling near vital anatomy’. SPIE Medical Imaging, 2016, pp. 97861G–97861G.
-
25)
-
18. Ma, B., Banihaveb, N., Choi, J., et al: ‘Is pose-based pivot calibration superior to sphere fitting?’ SPIE Medical Imaging, 2017, pp. 101351U–101351U.
http://iet.metastore.ingenta.com/content/journals/10.1049/htl.2017.0065
Related content
content/journals/10.1049/htl.2017.0065
pub_keyword,iet_inspecKeyword,pub_concept
6
6