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Expected versus observed error in a computer-aided navigation system for spine surgery
International Congress Series 1230 (2001) 112 – 116
Expected versus observed error in a computer-aided navigation system for spine surgery H. Holza,*, D. Russakoff a, H. Abbasia, D. Kimb, G. Steinbergb, R. Shahidia a
Image Guidance Laboratories, Stanford University, 300 Pasteur Dr. Stanford, CA 94305, USA Department of Neurosurgery, Stanford University, 300 Pasteur Dr. Stanford, CA 94305, USA
b
Abstract Error analysis of surgical navigation is extremely important in systems intended for clinical use. Knowledge of the overall clinical accuracy is vital for physicians during the preoperative planning process. Recent results in error analysis give us an idea of the expected impact of fiducial placement on overall clinical error (IEEE Trans. Med. Imaging 17 (1998)). We discuss this impact with respect to an end-to-end system for image-guided spine surgery. We show that fiducial placements have a definite effect on the clinical accuracy of our spine surgery system. Our results agree with the prediction that areas outside of the ‘‘bounding box’’ of fiducials are subject to greater clinical error. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Expected error; Observed error; Spine surgery
1. Introduction Characteristics of the expected error and observed error in a computer-aided surgical navigation system using preoperative computerized tomography (CT) and intraoperative fluoroscopy for spine are described. Error analysis of computer-aided surgical navigation is important for a variety of reasons: The clinician must know the overall clinical accuracy of the navigational system in order to make informed decisions about pre-operative plans versus actual surgery; developers use error measurements to make improvements in overall system accuracy; and researchers use data about expected error to assess applications and prioritize potential areas of focus. *
Corresponding author. Tel.: +1-650-498-7958; fax: +1-650-724-4846. E-mail address: hilary _ [email protected] (H. Holz).
0531-5131/01/$ – see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 5 3 1 - 5 1 3 1 ( 0 1 ) 0 0 0 2 6 - 7
H. Holz et al. / International Congress Series 1230 (2001) 112–116
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Calculating the transformation between the coordinate system of the surgical instrument and the coordinate system of the computerized tomography (CT) study requires a number of steps. Each of these individual components has an expected error based on theoretical or experimental models. The expected error of many of the components is theoretically independent of the surgical application, for our purposes spine surgery. The fact that individual vertebrae are rigid offers an opportunity for the use of rigid-body transformation techniques. Spine surgery, however, presents a number of unique challenges, including the choice of pattern and number of fiducials for a complex shape and the extraction of fiducials in the fluoroscopic images. Since the spine is a deformable body with individual rigid components (vertebra), fiducial placement must be balanced between bounding the surgical area and attachment to the vertebra of interest. The use of fiducials for calculating the transformation between the fluoroscopic images and the CT study should eliminate or minimize the importance of the image content. Relying on fiducials, however, is difficult without a clear understanding of how their placement affects error. We present experimental results confirming predictions that fiducial configurations can indeed have an impact on target registration error (TRE) [3].
Fig. 1. Configuration of fiducials (squares) and targets (pluses) used in our experiments. This is a view looking down on a spine phantom which, in this case, is oriented along the positive y-axis. All values are in millimeters. Experiment 1 compares the relative error between the average RMS of targets 1 and 2 versus that of targets 3, 4, 5, 6, and 7. The error is expected to be greater for the latter targets as they are outside of the bounding box of fiducials.
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H. Holz et al. / International Congress Series 1230 (2001) 112–116
2. Methods We have developed a navigation system for minimally invasive spine surgery [2]. Using fiducials, our system registers pre-operative CT data with the intraoperative location of the surgical instrument through analysis of two fluoroscopic X-ray images. Before the CT study is done, five small fiducials are embedded adjacent to the vertebra of interest. The location of the fiducials in the two image modalities is used to register and compare the intraoperative location of the surgical instrument against the preoperative study. We examine the differences between the expected error and the observed error in our navigational system using a precision spine phantom. Tests have been constructed with known error bias for the individual components. Multiple measurements are used in order to minimize bias effects. We measure TRE by digitizing the locations of seven nonfiducial targets on the spine phantom, projecting the targets into the CT space, and measuring the error between the projected and known locations over 10 different trials. See Fig. 1 for the initial configuration of fiducials. In the following trials, we analyze the relative error between different targets in different configurations with respect to the fiducials. Our assumption here is that the Target Localization Error (TLE) is consistent over each of the non-fiducial targets, an assumption we verified experimentally before proceeding. We calculate the TRE using the average root-mean-squared (RMS) error over all of the trials.
3. Results We performed three experiments:
Experiment 1: We take the average RMS error over all trials for the targets inside the bounding box of the fiducials and compare it with that of the targets outside (Fig. 1).
Fig. 2. Fiducial/target configurations for experiment #2. (a) The bounding box of four fiducials does not enclose either target. (b) The bounding box of four fiducials encloses both targets. Again, theoretical results predict that the resulting RMS error will be greater for the former configuration.
H. Holz et al. / International Congress Series 1230 (2001) 112–116
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Table 1 Results from experiments 1, 2, and 3. In #2, the error increase is measured by comparing the results for the two targets in the box with the results for the same two targets outside of the box Experiment
Inside bounding box
Outside
Error increase (%)
1 2 3
Targets 1,2 Targets 0 or 1,2 Target 1
Targets 3,4,5,6,7 Targets 1,2 or 0 Target 2
22.5 10.2 2.65
Experiment 2: Taking four fiducials at a time, we compare the average RMS error for two targets within a bounding box of fiducials with a configuration which has the same two targets outside of a bounding box of fiducials (Fig. 2). Experiment 3: Again using four fiducials at a time, we perform the same experiment as in #2 except isolating only one fiducial in the bounding box and one outside. The results of these experiments are summarized in Table 1. In each experiment, particularly the first two, relative TRE rises for targets which are not surrounded by fiducials.
4. Discussion Measuring overall system error in a navigation system for spine surgery in a clinically meaningful way is very difficult. The surgeon’s concern is accuracy in the three-dimensional space occupied by the surgical instrument. Measures of error in the fluoroscopic two-dimensional image plane do not measure overall system error. We measured overall system error by digitizing the locations of non-fiducial targets on the spine phantom, projecting the targets into the CT space, and measuring the error between the projected and known locations. However, error is introduced into the accuracy measurement by the tracking system used for digitization, extraction of the target locations in the CT, and human error in conducting the experiment. While each of these errors can be estimated, the precision of the overall system accuracy measurement is limited. Measures of error in other individual components are likewise limited. Nonetheless, our experience supports recent results produced by Fitzpatrick et al. [1] of Vanderbilt University that proved that fiducial configuration is very important to registration accuracy. When the rigid body which the fiducials are being used to bound is a vertebra, finding a fiducial configuration which produces good results is challenging. The magnitude of the effects of the fiducial configuration is determined by the inaccuracy of the extracted fiducial locations. Extracting the fiducial locations in the fluoroscopic images is made problematic by the need for camera calibration and image dewarping. Thus, the interactions between the various components of the navigational system are significant. It is also important to note that, in particular, the study of fiducial placements and the errors they generate will always be relevant. The rise in popularity of intensity-based registration algorithms notwithstanding [4], situations will always arise that require a fiducial-based fall back. A few examples include procedures involving obese patients or
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patients who cannot be exposed to large doses of radiation and procedures which require a high degree of accuracy. Application-independent analysis of the components that may be used in a surgical navigation system is useful to researchers who develop computer aided surgical systems. Understanding the relationship between expected error and observed error in a particular application not only aids further development within application areas, but demonstrates the impact of the assumptions underlying the predictors of error. Error analysis in clinical end-to-end systems advances the accuracy of predicted error in the individual components and aids surgeons in evaluating how advances in individual components may impact clinical use.
References [1] J.M. Fitzpatrick, J.B. West, C.R. Maurer, Predicting error in rigid-body, point-based image registration, IEEE Trans. Med. Imaging 17 (4) (1998) 694 – 702. [2] R. Grzeszczuk, S. Chin, R. Fahrig, H. Abbasi, H. Holz, D. Kim, J. Adler, R. Shahidi, A fluoroscopic Xray registration process for three-dimensional surgical navigation, in: S. Delp, A. DiGioia, B. Jaramaz (Eds.), Medical Image Computing and Computer-Assisted Intervention 2000, Springer-Verlag, Berlin, 2000, pp. 551 – 556. [3] J.M. Fitzpatrick, J.B. West, C.R. Maurer Jr., Derivation of expected registration error for rigid-body, pointbased, image registration, Proc. SPIE Medical Imaging 98, San Diego, CA, vol. 3338, 1998, pp. 16 – 27. [4] G.P. Penney, J. Weese, J.L. Little, P. Desmedt, D.L.G. Hill, D.J. Hawkes, A comparison of similarity measures for use in 2D-3D image registration, IEEE Trans. Med. Imaging 17 (4) (1998) 586 – 595.
Expected versus observed error in a computer-aided navigation system for spine surgery H. Holza,*, D. Russakoff a, H. Abbasia, D. Kimb, G. Steinbergb, R. Shahidia a
Image Guidance Laboratories, Stanford University, 300 Pasteur Dr. Stanford, CA 94305, USA Department of Neurosurgery, Stanford University, 300 Pasteur Dr. Stanford, CA 94305, USA
b
Abstract Error analysis of surgical navigation is extremely important in systems intended for clinical use. Knowledge of the overall clinical accuracy is vital for physicians during the preoperative planning process. Recent results in error analysis give us an idea of the expected impact of fiducial placement on overall clinical error (IEEE Trans. Med. Imaging 17 (1998)). We discuss this impact with respect to an end-to-end system for image-guided spine surgery. We show that fiducial placements have a definite effect on the clinical accuracy of our spine surgery system. Our results agree with the prediction that areas outside of the ‘‘bounding box’’ of fiducials are subject to greater clinical error. D 2001 Elsevier Science B.V. All rights reserved. Keywords: Expected error; Observed error; Spine surgery
1. Introduction Characteristics of the expected error and observed error in a computer-aided surgical navigation system using preoperative computerized tomography (CT) and intraoperative fluoroscopy for spine are described. Error analysis of computer-aided surgical navigation is important for a variety of reasons: The clinician must know the overall clinical accuracy of the navigational system in order to make informed decisions about pre-operative plans versus actual surgery; developers use error measurements to make improvements in overall system accuracy; and researchers use data about expected error to assess applications and prioritize potential areas of focus. *
Corresponding author. Tel.: +1-650-498-7958; fax: +1-650-724-4846. E-mail address: hilary _ [email protected] (H. Holz).
0531-5131/01/$ – see front matter D 2001 Elsevier Science B.V. All rights reserved. PII: S 0 5 3 1 - 5 1 3 1 ( 0 1 ) 0 0 0 2 6 - 7
H. Holz et al. / International Congress Series 1230 (2001) 112–116
113
Calculating the transformation between the coordinate system of the surgical instrument and the coordinate system of the computerized tomography (CT) study requires a number of steps. Each of these individual components has an expected error based on theoretical or experimental models. The expected error of many of the components is theoretically independent of the surgical application, for our purposes spine surgery. The fact that individual vertebrae are rigid offers an opportunity for the use of rigid-body transformation techniques. Spine surgery, however, presents a number of unique challenges, including the choice of pattern and number of fiducials for a complex shape and the extraction of fiducials in the fluoroscopic images. Since the spine is a deformable body with individual rigid components (vertebra), fiducial placement must be balanced between bounding the surgical area and attachment to the vertebra of interest. The use of fiducials for calculating the transformation between the fluoroscopic images and the CT study should eliminate or minimize the importance of the image content. Relying on fiducials, however, is difficult without a clear understanding of how their placement affects error. We present experimental results confirming predictions that fiducial configurations can indeed have an impact on target registration error (TRE) [3].
Fig. 1. Configuration of fiducials (squares) and targets (pluses) used in our experiments. This is a view looking down on a spine phantom which, in this case, is oriented along the positive y-axis. All values are in millimeters. Experiment 1 compares the relative error between the average RMS of targets 1 and 2 versus that of targets 3, 4, 5, 6, and 7. The error is expected to be greater for the latter targets as they are outside of the bounding box of fiducials.
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H. Holz et al. / International Congress Series 1230 (2001) 112–116
2. Methods We have developed a navigation system for minimally invasive spine surgery [2]. Using fiducials, our system registers pre-operative CT data with the intraoperative location of the surgical instrument through analysis of two fluoroscopic X-ray images. Before the CT study is done, five small fiducials are embedded adjacent to the vertebra of interest. The location of the fiducials in the two image modalities is used to register and compare the intraoperative location of the surgical instrument against the preoperative study. We examine the differences between the expected error and the observed error in our navigational system using a precision spine phantom. Tests have been constructed with known error bias for the individual components. Multiple measurements are used in order to minimize bias effects. We measure TRE by digitizing the locations of seven nonfiducial targets on the spine phantom, projecting the targets into the CT space, and measuring the error between the projected and known locations over 10 different trials. See Fig. 1 for the initial configuration of fiducials. In the following trials, we analyze the relative error between different targets in different configurations with respect to the fiducials. Our assumption here is that the Target Localization Error (TLE) is consistent over each of the non-fiducial targets, an assumption we verified experimentally before proceeding. We calculate the TRE using the average root-mean-squared (RMS) error over all of the trials.
3. Results We performed three experiments:
Experiment 1: We take the average RMS error over all trials for the targets inside the bounding box of the fiducials and compare it with that of the targets outside (Fig. 1).
Fig. 2. Fiducial/target configurations for experiment #2. (a) The bounding box of four fiducials does not enclose either target. (b) The bounding box of four fiducials encloses both targets. Again, theoretical results predict that the resulting RMS error will be greater for the former configuration.
H. Holz et al. / International Congress Series 1230 (2001) 112–116
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Table 1 Results from experiments 1, 2, and 3. In #2, the error increase is measured by comparing the results for the two targets in the box with the results for the same two targets outside of the box Experiment
Inside bounding box
Outside
Error increase (%)
1 2 3
Targets 1,2 Targets 0 or 1,2 Target 1
Targets 3,4,5,6,7 Targets 1,2 or 0 Target 2
22.5 10.2 2.65
Experiment 2: Taking four fiducials at a time, we compare the average RMS error for two targets within a bounding box of fiducials with a configuration which has the same two targets outside of a bounding box of fiducials (Fig. 2). Experiment 3: Again using four fiducials at a time, we perform the same experiment as in #2 except isolating only one fiducial in the bounding box and one outside. The results of these experiments are summarized in Table 1. In each experiment, particularly the first two, relative TRE rises for targets which are not surrounded by fiducials.
4. Discussion Measuring overall system error in a navigation system for spine surgery in a clinically meaningful way is very difficult. The surgeon’s concern is accuracy in the three-dimensional space occupied by the surgical instrument. Measures of error in the fluoroscopic two-dimensional image plane do not measure overall system error. We measured overall system error by digitizing the locations of non-fiducial targets on the spine phantom, projecting the targets into the CT space, and measuring the error between the projected and known locations. However, error is introduced into the accuracy measurement by the tracking system used for digitization, extraction of the target locations in the CT, and human error in conducting the experiment. While each of these errors can be estimated, the precision of the overall system accuracy measurement is limited. Measures of error in other individual components are likewise limited. Nonetheless, our experience supports recent results produced by Fitzpatrick et al. [1] of Vanderbilt University that proved that fiducial configuration is very important to registration accuracy. When the rigid body which the fiducials are being used to bound is a vertebra, finding a fiducial configuration which produces good results is challenging. The magnitude of the effects of the fiducial configuration is determined by the inaccuracy of the extracted fiducial locations. Extracting the fiducial locations in the fluoroscopic images is made problematic by the need for camera calibration and image dewarping. Thus, the interactions between the various components of the navigational system are significant. It is also important to note that, in particular, the study of fiducial placements and the errors they generate will always be relevant. The rise in popularity of intensity-based registration algorithms notwithstanding [4], situations will always arise that require a fiducial-based fall back. A few examples include procedures involving obese patients or
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H. Holz et al. / International Congress Series 1230 (2001) 112–116
patients who cannot be exposed to large doses of radiation and procedures which require a high degree of accuracy. Application-independent analysis of the components that may be used in a surgical navigation system is useful to researchers who develop computer aided surgical systems. Understanding the relationship between expected error and observed error in a particular application not only aids further development within application areas, but demonstrates the impact of the assumptions underlying the predictors of error. Error analysis in clinical end-to-end systems advances the accuracy of predicted error in the individual components and aids surgeons in evaluating how advances in individual components may impact clinical use.
References [1] J.M. Fitzpatrick, J.B. West, C.R. Maurer, Predicting error in rigid-body, point-based image registration, IEEE Trans. Med. Imaging 17 (4) (1998) 694 – 702. [2] R. Grzeszczuk, S. Chin, R. Fahrig, H. Abbasi, H. Holz, D. Kim, J. Adler, R. Shahidi, A fluoroscopic Xray registration process for three-dimensional surgical navigation, in: S. Delp, A. DiGioia, B. Jaramaz (Eds.), Medical Image Computing and Computer-Assisted Intervention 2000, Springer-Verlag, Berlin, 2000, pp. 551 – 556. [3] J.M. Fitzpatrick, J.B. West, C.R. Maurer Jr., Derivation of expected registration error for rigid-body, pointbased, image registration, Proc. SPIE Medical Imaging 98, San Diego, CA, vol. 3338, 1998, pp. 16 – 27. [4] G.P. Penney, J. Weese, J.L. Little, P. Desmedt, D.L.G. Hill, D.J. Hawkes, A comparison of similarity measures for use in 2D-3D image registration, IEEE Trans. Med. Imaging 17 (4) (1998) 586 – 595.