The success of an image-guided surgical procedure is dependent on a number of factors; foremost among these is the accuracy with which the positions of surgical tools can be determined relative to the patient. This information can be obtained using a variety of methods however in practice almost all available navigation systems utilize optical tracking. This work presents the validation of custom active tracking markers in combination with a high accuracy tracking system. Two evaluation methodologies are described; a relative positioning test in which the markers are moved in a known pattern throughout the camera workspace examining the positioning accuracy, and a rotation test designed to determine the effects of rotation on the tracked position of the locator. Position testing revealed a mean accuracy 0.019±0.019 mm, with a maximum error of 0.103 mm; rotation testing revealed a maximum deviation of 0.049 mm when rotating about a known axis, through a trackable range of approximately 80°. A maximum angular error 0.096° was noted when rotating about a known axis.
tracking accuracy at large angles as well as defining the trackable range. Finally, an angular test was defined in which the accuracy of the tracking when rotating the marker was examined. Fehlmann AG, Sion, Schweiz, accuracy <0.01 mm) and the camera positioned with the field of view approximately perpendicular to the rigid body face as in Figure 1. The camera was then rigidly fixed on a support connected to the ground. To eliminate problems with movement of the camera or vibration a second rigid body was attached within the camera workspace, stationary relative to the moving XY table of the CNC; all measured positions were taken relative to the reference rigid body. The CNC table was then moved in a plane with distances of 10mm between the points, covering the complete camera workspace. At each position 30 measurements were taken, resulting in a total of 1920 single points recorded in a grid of 64 known positions. A grid of the known positions was then generated in MATLAB (Mathworks, Natick, MA) and the ideal distances between the first point and each subsequent point calculated. The Euclidean distance of each measured point to the initial point was then calculated and compared to the ideal distance. Rotational Positioning Accuracy: Rotational experiments were completed by fixing the marker rigid body to the spindle of a lathe, with the camera rigidly attached above. The spindle was then repeatedly rotated by hand until the rigid body was no longer visible by the camera. A circle was fit to the observed points; the radius of this circle was compared to the known (from CAD) radius of rotation. Errors were calculated based on the Euclidean distance between the fitted circle and observed rigid body positions.
Angular Accuracy: Testing of the angular accuracy of the developed locators was completed as follows: a single marker rigid body was attached to a turn table, with a reference rigid body fixed above. The marker was then rotated in known increments of 2.25° throughout the full range of visibility. Once the marker was no longer visible, the marker was rotated in the opposite direction with the same increment until no longer visible. At each 3.25° step a total of 30 points were taken; the angle observed between subsequent steps was then calculated and compared to the nominal value. 3
The results of both the positioning and rotation experiments are shown in Table 1. Static tests reveal a mean positioning error of 0.019 mm with a standard deviation of 0.018 mm. The maximum observed positioning error was 0.103 mm. Rotational tests revealed an error of 0.021 mm from the observed radius to the known radius of rotation. A maximum deviation of 0.049 mm from the fitted circle was observed. Furthermore, the rigid body was trackable through an angular range of approximately 80°. A mean angular error of 0.003° was observed, with a standard deviation of 0.024° and maximum angular error of 0.096°. Fig. 2 shows the results of the positioning testing in the coordinate system of the CNC X-Y table, as well as the variation of the rigid body position from the fitted circle throughout the rotation. Note that for the rotation, the angle at which the rigid body was first visible was defined as 0°. A number of outliers were noted during the rotation testing, most of which occurred at approximately 12°; the reason for this is currently unknown, however further investigation is currently underway. -10 )-20 m m (-30 n o i it-40 s o P-50 Y
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The positioning test defined within, in which the marker rigid body is tracked throughout the workspace, is designed to be directly applicable to the case of six-dimensional tracking of surgical tools. Although the marker rigid body is not moved throughout the full camera workspace, instead only on a plane within, the observed errors are dominated by those in the axial direction of the camera (approximately the Y-direction of the CNC X-Y table), suggesting that further movements throughout the workspace will lead to minimal changes in the results. The largest positioning errors occur at the rear and edges of the camera workspace; the largest observed error was 0.103 mm. Determination of positioning errors by comparison to the first observed point could potentially introduce additional errors (or lead to reduced errors) due to the noise in the camera system, however this relative positioning accuracy is of most interest in terms of the final application. As all tracking is completed relative to a reference marker, the relative movement i.e. relative distance moved by the marker is of most interest.
Tracking systems which utilize retro-reflective spheres as markers would be expected to be rotationally invariant, i.e. if the rigid body is rotated there should be no loss of accuracy, however the developed tracking markers utilize flat circular points which may be affected by changes in rotation. Additionally, there will be some maximum angle at which the flat points can be tracked. The rotation test described within is designed to examine the change in the position of the rigid body, defined as a point along the axis of the tool, if it is rotated about this axis. In terms of overall tracking accuracy, this means that the rotation of the tool relative to the camera will have little effect on the defined position of that tool. The results of this testing demonstrate that the change in the rigid body position is minimal through an angular range of 80°. Furthermore, angular accuracy testing reveals a maximum angular error of 0.096° when rotated throughout the full visible range. Rotation was completed around the major axis of the marker (i.e. the axis of the tool); due to the design of the markers and the relative inaccuracy in the axial direction of the camera, it can be expected that rotation about this axis would be the least accurate. 5
The accuracy observed after the completion of both static positioning, dynamic rotation and angular accuracy tests is sufficient for the defined application of minimally invasive cochlear access, and is similar to that observed in previous examinations of the tracking system accuracy as well as the manufacturer specifications. 7