The experimental set-up can be seen in Figs. 1, 2.
Phantom
A plastic skull (Somso, Coburg, Germany) was used for all experiments. Radiolucent markers (X-spot, izi-Kooperation, Beekley Corp., Conn, USA) and MR marker (Donuts, izi-Kooperation, Beekley Corp., Conn., USA) were attached on the skull. For all experiments the plastic skull was fixed on an OR table with a VBH head holder [4]. With the VBH mouthpiece, the skull can be attached at the holder [6]. Dental foam vacuum fixation on the maxilla leads to a stable construction in all experiments. This is a fast and secure non-invasive method to fix a patient during interventions. On the reference element of the VBH mouthpiece, radiolucent markers were attached (see Figs. 3, 4). Those external markers were only used for half of the experiments (see Table 1).
CT images
CT images of the plastic skull were acquired with a Siemens-Sensation-16 (Siemens, Erlangen, Germany), leading to 2 axial datasets. The first dataset was captured with the reference element fixed on the VBH mouthpiece in place and the second one without the reference element. Image parameters were 140 kV, 220 mAs with 1 mm slice thickness.
Navigation system
The SNN navigation system (Fa. SNS, Aalen, Germany) was used for navigation with optical tracking of (flashpoint-3000-system, IGT, Boulder, USA). It comprises classical pointer-based navigation and a navigated microscope with heads-up display capabilities for navigation.
Pointers
Two different pointers were used for registration and navigation on a plastic skull. The probe (135-mm flashpoint) can be optically tracked by the camera with the two LEDs attached to it and is connected with a cable to the navigation system.
The microscope (OPMI 2000, Zeiss, Oberkochen, Germany) can be optically tracked with a DRF attached to it (see Fig. 2). The microscope is factory-calibrated, and thus, the parameters of the camera are known and the position of the point that is in focus can be determined.
Registration
To register the plastic skull to its CT images, four different registration methods were performed with the probe (group A) or the microscope (group B). As a skull has only a few prominent anatomical landmarks that can be defined well both on the patient and in the CT images, different kinds of markers were used as fiducials (but also targets, as can be seen in the next section), to have a sufficient amount of fiducials for each registration method.
The different methods and fiducials used for registration were defined as follows (see also Table 1):
A1 and B1: paired-point registration with 5 anatomical landmarks, 2 donut markers and 3 radiolucent markers
A2 and B2: paired-point registration with 5 anatomical landmarks, 2 donut markers, 3 radiolucent markers and additionally a surface registration with 25 points
A3 and B3: paired-point registration with 3 anatomical landmarks, 1 donut marker and 2 radiolucent markers on the skull and 4 radiolucent markers on the VBH mouthpiece
A4 and B4: paired-point registration with 3 anatomical landmarks, 1 donut marker and 2 radiolucent markers on the skull, 4 radiolucent markers on the VBH mouthpiece and additionally a surface registration with 25 points
The probe and the microscope were both used as pointers to locate a fiducial on the plastic skull. The fiducials were physically located with the tip of the probe. With the microscope, the fiducials were located with maximum magnification. Only when the fiducial of interest was in autofocus and the microscope was not moving anymore, this point was used for registration.
In detail (cf. Figs. 3, 4), the fiducials used for the experiments without VBH mouthpiece are the 2 donut markers on the right parietal bone and the right frontal bone, the 3 radiolucent markers on the frontal bone, the left nasal bone and the left temporal bone. The five anatomical landmarks are the right supraorbital foramen, the right medial cantus, the anterior nasal spine, the ‘saddle point’ on the left frontozygomatic suture, and the left infraorbital foramen.
For the experiments with the VBH mouthpiece, the fiducials in detail are 4 radiolucent markers on the referencing element of the VBH mouthpiece, 1 donut marker at the right parietal bone, 2 radiolucent markers median on the frontal bone and the left temporal bone and the 3 anatomical landmarks on the anterior nasal spine, the left infraorbital foramen and the right supraorbital foramen.
For the surface registration, 25 points were acquired by the probe touching the mid-face, the frontal bone and the orbitae of the skull surface. The same anatomical locations were focused with the microscope with maximum magnification. Again 25 points were selected, when the points were in focus and the microscope was not moving.
TRE measurements
After all different registration methods, the TRE was measured on 10 targets, which were per definition different to the fiducials (c.f. Fig. 3). The targets used were always the same for A1–A4 and B1–B4.
Five anatomical landmarks, 2 radiolucent markers and 3 donut markers were used. In detail, the targets (in ascending order target number 1–10) are the 2 radiolucent markers on the right frontal bone and the right cheek bone, the donut markers on the left frontal bone, near the left coronal suture and the left parietal bone. The 5 anatomical targets are the left supraorbital foramen, the left medial cantus, the bony structure on the left nasal bone, the ‘saddle point’ on the right frontozygomatic suture and the right infraorbital foramen.
Each experiment (registration and TRE measurement) was repeated 10 times. To avoid a learning effect during the experiments, initial experiments were done to get used to the equipment without recording the results.
Each target was located as exactly as possible with the probe. A screenshot of the navigation systems display was taken, when the probe was placed at the target. The same procedure was repeated with the microscope, and each target was located with the maximum magnification and with autofocus.
After finishing the experiments, each screenshot was processed in Adobe Photoshop 5.0. Each image plane was maximally magnified. The difference of real target and projected target (\(\varDelta {x}\), \(\varDelta {y}\), \(\varDelta {z}\)) was measured in each image plane, axial (x–y), sagittal (x–z) and coronal (y–z). So each x-, y- and z direction was measured twice (10 \(\times \) 6 data matrix for each group). Those pixel measurements were converted in mm. The scale is known by measuring the length of the crosshair, which is 1 cm. An example of the TRE measurement is shown in Figs. 5, 6.
It could be possible that the target was not visible in one plane, and thus, the error could only be measured in the other two planes. The missing values were assigned as NaN (not-a-number) and replaced with the corresponding value in x-, y- and z-directions; for example, if the axial x-direction could not be measured, the measurement of the sagittal x- direction was used for both x-values.
Overall 4800 measurements were taken, 600 for each experiment. For each target, the mean of the 10 repetitions in each direction was calculated. Thus, the values (\(\Delta x_{{\textit{ij}}}\), \(\Delta y_{{\textit{ij}}}\), \(\Delta z_{{\textit{ij}}}\)) remained for each target. With these values, the TRE was calculated by
$$\begin{aligned} \mathrm{{TRE}} ({t_{{\textit{ij}}}}) = \sqrt{\Delta x_{{\textit{ij}}}^2 + \Delta y_{{\textit{ij}}}^2 + \Delta z_{{\textit{ij}}}^2}, \end{aligned}$$
which is the TRE for target number i, \(i = 1, {\ldots }, 10\), experiment j, \(j = \hbox {A1},{\ldots }, \hbox {A4}, \hbox {B1},{\ldots }, \hbox {B4}\).
All calculations were done with all measurements of each group in Matlab.
Besides that, a worst-case scenario was analysed, where only the largest values in each x-, y-, and z-directions of each repetition were used for calculations (10 \(\times \) 3 data matrix for each group).
Table 2 TREs with the p values of the Wilcoxon signed-rank test
Evaluation
The aim of this investigation was to find the difference regarding the TRE between registrations via microscope and probe on a plastic skull. Besides that, it was evaluated if surface registration (additionally to paired-point registration) and additional fiducials fixed on the reference element of the VBH mouthpiece improve the TRE. Group A (probe) and group B (microscope) were compared to each other. The overall TRE over all four types of registration was calculated for a first overview, but also the TRE of each registration method was calculated separately. All calculations were done with Matlab R2012a. Statistical tests were done with \(\alpha = 0.05\). An ANOVA was used to find differences in group A or group B. If a statistically significant difference was found, multiple comparisons were done with Bonferroni correction to analyse which experiments were significantly different to each other. For comparing \(\hbox {A}i\) and \(\hbox {B}i\), \(i = 1, {\ldots }, 4\), a Wilcoxon signed-rank test was used.