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Quantitative error analysis for computer assisted navigation: A feasibility study
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Image of FIG. 1.

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FIG. 1.

Setup used for the experiments. The objects rest on a standard operating table (Brumaba, Germany) on a wood-plexiglass combination to hold hydraulic immobilization arms. The volunteer was resting in a comfortable position directly on the operating table to which he was immobilized with a tape running across the forehead. The active NDI Polaris camera (1) is placed in the optimal working distance from the object. The navigation system's monitor (2) and tracker control unit (3) are placed opposite to the surgeon. The probe used for all experiments (4) is lying on the table. In the example shown, the anatomic specimen (5) is held by two hydraulic arms and the patient tracker (a NDI rigid body, 6), is held separately. Thus a rigid mechanical setup could be achieved.

Image of FIG. 2.

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FIG. 2.

Setup with overlay of optimal working zone. The active Polaris tracker was placed 1400 mm away from the zone of maximum precision, a silo-type volume made up by a cylinder of 1000 mm height and diameter, covered by a semisphere of radius of 500 mm. All numbers in the figures are given in millimeters. Object placement within the ideal measurement zone was verified with a custom application used for centering patient tracker and tracked probe as seen by the tracker within this volume specified by the manufacturer. The dot on the cameras' center marks the origin of the camera coordinate system. Down to the right the coordinate axes are shown.

Image of FIG. 3.

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FIG. 3.

Schematic drawing of the positions selected for the DRF-DRF tracker calibration within the measurement volume. The dark dots were selected on the outer border; bright dots show positions at the border of the optimal measurement volume.

Image of FIG. 4.

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FIG. 4.

Photograph of the DRF-DRF assembly used for tracker calibration. The dark structure protruding downwards is a carbon holder. The origins of the DRF coordinate systems are marked in the centers of the LEDs in the fourth quadrant of each DRF; distances were obtained with a microcalliper; all dimensions are given in millimeters.

Image of FIG. 5.

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FIG. 5.

Active tracked probe used for the experiments, front and top view with dimensions (in millimeters). The origin is located on the most distal LED (the crossed circle).

Image of FIG. 6.

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FIG. 6.

(a) Plastic skull with landmarks used for registration (crosses) and targets (circles) on which the system accuracy was tested. The skull is placed on a base plate to hold the mechanical immobilization on base of the VBH headholder's mouthpiece (Ref. 67 ). (b) Anatomic specimen with landmarks used for registration (crosses) and targets (circles) on which the system accuracy was tested. The specimen was cut to allow accessing various anatomical structures. (c) Volunteer (3D model) with landmarks used for registration (crosses) and targets (circles) on which the system accuracy was tested. Surface reconstruction of the CT-data, thresholded to skin.

Image of FIG. 7.

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FIG. 7.

(a) Definitions of the coordinate systems for the experiments: image, DRF, and tracker. (b) The probe coordinate system associated with the navigated probe.

Image of FIG. 8.

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FIG. 8.

Correlation plots for (a) plastic skull, (b) anatomic specimen, and (c) volunteer for TLE with TRE from the experimental data.

Image of FIG. 9.

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FIG. 9.

Experimental TTEs for the three specimens, right column, and predictions of the TTE with the isotropic model (Ref. 25 ), left column.

Image of FIG. 10.

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FIG. 10.

Experimental TTEs for the three specimens, right column, and predictions of the TTE with the anisotropic model (Ref. 27 ), left column.

Image of FIG. 11.

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FIG. 11.

Experimental TTEs for the three specimens, right column, and predictions of the TRE with the isotropic model (Ref. 25 ), left column.

Image of FIG. 12.

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FIG. 12.

Experimental TTEs for the three specimens, right column, and predictions of the TRE with the anisotropic model (Ref. 27 ), left column.


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Test for normal distribution of measurements for all measured objects, fiducials and targets, used in the experiments. Testing was done with the Shapiro-Wilk for α = 0.05. Deviations from normal distribution of data are given in image coordinates.

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Measured values for ⟨FLE image 2⟩, ⟨FLE tracker 2⟩, ⟨FLE probe_calib 2⟩, and ⟨TFLE 2⟩ from the experiments with nine registration points for plastic skull, anatomic specimen and volunteer, all values in millimeters. ⟨FLE 2 tracker⟩ and ⟨FLE 2 probe_calib⟩ were obtained from the tracker measurements and probe calibration, respectively. Values are given in mm2.

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The measured covariance matrices of a DRF, the probe-DRF assembly, and the probe-tip-DRF calibration measurements as required for calculation of ΣTRE.

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Covariance matrices for defining features in image and tracker space, respectively, with the computer mouse and tracked probe for plastic skull and anatomic specimen from experimental data.

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ULE 2⟩ from Eqs. (13) and (14) for all sets of registration points (3, 5, 7, and 9) and objects (anatomic specimen, plastic skull, and volunteer) studied; the average over all fiducials is given. All values are given in mm2.


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The benefit of computer-assisted navigation depends on the registration process, at which patient features are correlated to some preoperative imagery. The operator-induced uncertainty in localizing patient features—the user localization error (ULE)—is unknown and most likely dominating the application accuracy. This initial feasibility study aims at providing first data for ULE with a research navigation system.


Active optical navigation was done in CT-images of a plastic skull, an anatomic specimen (both with implanted fiducials), and a volunteer with anatomical landmarks exclusively. Each object was registered ten times with 3, 5, 7, and 9 registration points. Measurements were taken at 10 (anatomic specimen and volunteer) and 11 targets (plastic skull). The active NDI Polaris system was used under ideal working conditions (tracking accuracy 0.23 mm root-mean-square, RMS; probe tip calibration was 0.18 mm RMS). Variances of tracking along the principal directions were measured as 0.18 mm2, 0.32 mm2, and 0.42 mm2. ULE was calculated from predicted application accuracy with isotropic and anisotropic models and from experimental variances, respectively.


The ULE was determined from the variances as 0.45 mm (plastic skull), 0.60 mm (anatomic specimen), and 4.96 mm (volunteer). The predicted application accuracy did not yield consistent values for the ULE.


Quantitative data of application accuracy could be tested against prediction models with iso- and anisotropic noise models and revealed some discrepancies. This could potentially be due to the facts that navigation and one prediction model wrongly assume isotropic noise (tracking is anisotropic), while the anisotropic noise prediction model assumes an anisotropic registration strategy (registration is isotropic in typical navigation systems). The ULE data are presumably the first quantitative values for the precision of localizing anatomical landmarks and implanted fiducials. Submillimetric localization is possible for implanted screws; anatomic landmarks are not suitable for high-precision clinical navigation.


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Scitation: Quantitative error analysis for computer assisted navigation: A feasibility study