This work introduces a laser guidance system for improving the performance of surgical navigation. It consists of a laser pointer mounted on a pan-tilt platform calibrated with the tracking system from the navigation platform. With two pan-tilt rotation axes, the laser beam of a green laser pointer can reach any location in 3D space. The calibration between the pan-tilt platform and the tracking system is done by using Levenberg-Marquardt and Least-Squares Estimation of Transformation algorithms. The registration between organ and 3D virtual model is obtained by the tracking system and therefore, the laser is also implicitly registered. Therefore, important points or the resection path of the 3D model can be projected precisely on the surface of the organ with the laser pointer.
The transformation matrix between the laser pointer and the mounting plate is calculated using the following method (explained in figure2): Rotate the pan-tilt axes so that the laser beam points at the grid board and record the coordinates of this point with respect to the base of the pan-tilt platform, after which the coordinates of this point with respect to the mounting plate can be calculated using the rotation angles. The tracking system is used to measure the distance between the pointer outlet and the point on the board, and the distance can represent the coordinates of this point in the laser coordinate system. In the same way, acquire coordinates of four points in both coordinate systems. Thereafter, using the least-squares estimation of transformation algorithm [4], the transformation matrix between the laser pointer and the mounting plate on the pan-tilt platform can be calculated. After modeling, the whole pan-tilt platform will be mounted on the navigation system.
At the beginning of the process, the registration between the tracking system and the 3D model is achieved by matching two point patterns acquired in both coordinate systems.
To acquire the transformation matrix between the tracking system and the pan-tilt platform, the coordinates of four points in both coordinate systems should be obtained. The key problem of this project is to calculate the coordinates of four points in the pan-tilt coordinate system.
The solution is this: The laser pointer points at four arbitrary points one by one (showed in figure 4); the angles of two rotation axes with respect to each point are received from the pan-tilt platform. Simultaneously, use the tracking instrument to acquire the coordinates of each point with respect to the tracking coordinate system. Then the distances of any two points can be calculated using the acquired coordinates.
Knowing the distances and angles, six equations with four variables {KA, KB, KC, KD} can be formulated. To solve this nonlinear over-determined equation set, the Levenberg-Marquardt algorithm is used [5]. After calculating {KA, KB, KC, KD}, the coordinates of these four points with respect to the pan-tilt base can be calculated using angle information again.
Finally, as the coordinates of these four points in both coordinate systems are available, the calibration of pan-tilt platform and tracking system is achieved by using the least-squares estimation of transformation algorithm. Registration of
tracking system and 3D
model
Laser beam points at 4 points one by
one
Tracking system reads the coordinate
Get the rotation angles of pan-tilt platform
Calculate distances between any two points
Apply LevenbergMarquardt method
The coordinates of 4 points in pan-tilt platform
Calibration of pan-tilt platform and tracking system To evaluate the calibration, a millimetre grid board and a tracking instrument are used.
The evaluation method is explained in figure 5: Put the tracking instrument on the cross of a millimetre board and make the laser beam follow the instrument tip. Due to inaccuracy in modeling, calibration error, and resolution limits of the pan-tilt platform, the laser beam will be shifted a slight amount from the instrument tip. The distance between the instrument tip and the laser beam is defined as the error. Altogether, 144 measurements were recorded, for which six calibrations were done. In each of the four predefined regions on the millimetre board, six errors were measured.
The total average mean and variance of the 144 measurements are 1.21 mm and 0.045 mm2; however, the laser mark has an elliptic size of 5 x 3 mm, which is much larger than the error. So, a better laser pointer will be used in the future development to match the accuracy of the calibration. 4
The proposed laser guidance system offers a meaningful improvement of navigation systems, in that the user can easily see the critical points on the organ. The surgeon can choose a point on the 3D virtual model, for which the laser pointer will efficiently display that point. Furthermore, the pointer can slowly follow a line marked on the virtual model, e.g., resection line, which gives seamless guidance for the surgeon. Also, visually assessing the registration error could fit well in overall workflow: A visible organ landmark can be targeted with the laser pointer.
Compared to a projector, the laser guidance system is not capable of showing the anatomy of the organ in detail. However, it can compete with the brightness of the light in the operating room. From another point of view, the laser system can complement a projector.
Another open issue is the organ motion, which is often present in navigated surgery. Until now, only static models were used in the lab environment. Further development of this system would take organ motion into account. If the motion is known or measurable, registration could be updated in real time. In this way, the laser beam will synchronise with the organ’s motion and continuously point at the defined target. 5