Analytic Expressions for Fiducial and Surface Target Registration Error

Performance assessment of surgical tracking systems based on statistical process control and longitudinal QA

A system for performance assessment and quality assurance (QA) of surgical trackers is reported based on principles of geometric accuracy and statistical process control (SPC) for routine longitudinal testing. A simple QA test phantom was designed, where the number and distribution of registration fiducials was determined drawing from analytical models for target registration error (TRE). A tracker testbed was configured with open-source software for measurement of a TRE-based accuracy metric ε and Jitter (J ). Six trackers were tested: 2 electromagnetic (EM - Aurora); and 4 infrared (IR - 1 Spectra, 1 Vega, and 2 Vicra) - all NDI (Waterloo, ON). Phase I SPC analysis of Shewhart mean (x ¯ ) and standard deviation (s ) determined system control limits. Phase II involved weekly QA of each system for up to 32 weeks and identified Pass, Note, Alert, and Failure action rules. The process permitted QA in <1 min. Phase I control limits were established for all trackers: EM trackers exhibited higher upper control limits than IR trackers in ε (EM: x ¯ ε   ∼ 2.8-3.3 mm, IR: x ¯ ε   ∼ 1.6-2.0 mm) and Jitter (EM: x ¯ jitter   ∼ 0.30-0.33 mm, IR: x ¯ jitter   ∼ 0.08-0.10 mm), and older trackers showed evidence of degradation - e.g. higher Jitter for the older Vicra (p-value < .05). Phase II longitudinal tests yielded 676 outcomes in which a total of 4 Failures were noted - 3 resolved by intervention (metal interference for EM trackers) - and 1 owing to restrictive control limits for a new system (Vega). Weekly tests also yielded 40 Notes and 16 Alerts - each spontaneously resolved in subsequent monitoring.

Vector field analysis for surface registration in computer-assisted ENT surgery

BACKGROUND

Manual paired-point registration for navigated ENT-surgery is prone to human errors; automatic surface registration is often caught in local minima.

METHODS

Anatomical features of the human occiput are integrated into an algorithm for surface registration. A vector force field is defined between the patient and operating room datasets; registration is facilitated through gradient-based vector field analysis optimization of an energy function. The method is validated exemplarily on patient surface data provided by a mechanically positioned A-mode ultrasound sensor.

RESULTS

Successful registrations were achieved within the entire parameter space, as well as from positions of local minima that were found by the Gaussian fields algorithm for surface registration. Sub-millimetric registration error was measured in clinically relevant anatomical areas on the anterior skull and within the generally accepted margin of 1.5 mm for the entire head.

CONCLUSION

The satisfactory behavior of this approach potentially suggests a wider clinical integration.

Determination of optimal ultrasound planes for the initialisation of image registration during endoscopic ultrasound-guided procedures

PURPOSE

Navigation of endoscopic ultrasound (EUS)-guided procedures of the upper gastrointestinal (GI) system can be technically challenging due to the small fields-of-view of ultrasound and optical devices, as well as the anatomical variability and limited number of orienting landmarks during navigation. Co-registration of an EUS device and a pre-procedure 3D image can enhance the ability to navigate. However, the fidelity of this contextual information depends on the accuracy of registration. The purpose of this study was to develop and test the feasibility of a simulation-based planning method for pre-selecting patient-specific EUS-visible anatomical landmark locations to maximise the accuracy and robustness of a feature-based multimodality registration method.

METHODS

A registration approach was adopted in which landmarks are registered to anatomical structures segmented from the pre-procedure volume. The predicted target registration errors (TREs) of EUS-CT registration were estimated using simulated visible anatomical landmarks and a Monte Carlo simulation of landmark localisation error. The optimal planes were selected based on the 90th percentile of TREs, which provide a robust and more accurate EUS-CT registration initialisation. The method was evaluated by comparing the accuracy and robustness of registrations initialised using optimised planes versus non-optimised planes using manually segmented CT images and simulated ([Formula: see text]) or retrospective clinical ([Formula: see text]) EUS landmarks.

RESULTS

The results show a lower 90th percentile TRE when registration is initialised using the optimised planes compared with a non-optimised initialisation approach (p value [Formula: see text]).

CONCLUSIONS

The proposed simulation-based method to find optimised EUS planes and landmarks for EUS-guided procedures may have the potential to improve registration accuracy. Further work will investigate applying the technique in a clinical setting.

Contact-less stylus for surgical navigation: registration without digitization

PURPOSE

We present a laser-based, contact-less, stylus for the purpose of fiducial registration and digitization in the context of surgical navigation.

METHODS

We augmented a laser pointer with a spatial measurement device and used the laser beam as a means to locate a fiducial in 3D space. We developed a method for calibrating the orientation of the laser beam with respect to its attached tracking target. Digitization of a fiducial was formulated as a line intersection problem, and registration was formulated as a point-to-line registration problem.

RESULTS

We achieved an RMS fiducial localization error of 0.63 mm for 151 measurements of 12 fiducial markers. Mean TRE values of less than 1.5 mm over the entire surface of a lumbar vertebra were achievable using 4 fiducial markers. We found that contact-based rigid registration performed carefully under near-ideal conditions outperforms contact-less registration in terms of TRE.

CONCLUSION

An inexpensive contact-less stylus can be used to obtain accurate fiducial registration, which can be performed without explicit fiducial digitization.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.

Anatomical landmarks for point-matching registration in image-guided neurosurgery

BACKGROUND

Accurate patient to image registration is the core for successful image-guided neurosurgery. While skin adhesive markers (SMs) are widely used in point-matching registration, a proper implementation of anatomical landmarks (ALs) may overcome the inconvenience brought by the use of SMs.

METHODS

Using nine ALs, a set of three configurations of different combinations of them is proposed. These configurations are defined according to the required positioning of the patient's head during surgery and the resulting distribution of the expected target registration error (TRE). These configurations were first evaluated by simulation experiment using the data of 20 patients from two hospitals, and then testing the applicability of them in eight real clinical surgeries of neuronavigation.

RESULTS

The results of the simulation experiment showed that, by incorporating a fiducial registration error (FRE) of 3.5 mm measured in the clinical setting, the expected TRE in the whole skull was less than 2.5 mm, and the expected TRE in the whole brain was less than 1.75 mm when using all the nine ALs. A small TRE could also be achieved in the corresponding surgical field by using the other three configurations with less ALs. In the clinical experiment, the FLE ranges in the image and the patient space were 1.4-3.6 mm and 1.6-5.5 mm, respectively. The measured TRE and FRE were 3.1 ± 0.75 mm and 3.5 ± 0.17 mm, respectively.

CONCLUSIONS

The AL configurations proposed in this investigation provide sufficient registration accuracy and can help to avoid the disadvantages of SMs if used clinically.

Preoperative analysis of the stability of fit of a patient-specific surgical guide

Although the use of patient-specific surgical guides has gained popularity over the past decade, little research has been done to examine in an objective and qualitative way the fit of such instruments. In this study, we have developed a model to predict the stability of a guide designed to fit on a supporting bone surface, thereby providing feedback on the translational and rotational stability of the device. The method was validated by comparing different guide designs with respect to their stability on the contact surface and comparing these results to those measured with a set of experiments. This validation experiment indicates that our stability model can be used to predict the stability of the fit of a surgical guide during the preoperative design process.

[Automatic registration of patients with A-mode ultrasound for computer-assisted surgery. Laboratory proof of concept]

BACKGROUND

The main source of error in 3D navigation is the patient-to-image registration process. Anatomical landmarks or adhesive markers perform sub-optimally. Bone-anchored invasive markers significantly change the clinical workflow of navigated ENT surgery, are invasive and cause patient discomfort. In order to minimize registration errors and to further streamline the clinical use of intraoperative 3D navigation we demonstrate that A-mode ultrasound allows an accurate 3D surface profile of the os occipitale to be created which can be reliably registered on preoperative patient CT data.

METHODS

The transducer is mechanically positioned with sub-millimeter accuracy on the patient's occiput. From the sound echos a 3D surface is generated and registered to the preoperative CT images with the iterative closest point (ICP) algorithm. The evaluation of our setup was performed on three anatomic specimens and one bony skull.

RESULTS

The ultrasound echoes from the occiput allowed the creation of an adequate 3D surface which could be registered to a segmentation of the CT image with an accuracy greater than 1.5 mm. The experiments were evaluated by an intuitive representation of the spatial deviation between CT and ultrasound data as a color-coded map.

CONCLUSION

The approach to scan the posterior skull with A-mode ultrasound enables automatic intraoperative registration and can be integrated into the intraoperative setup.

Target tracking errors for 5D and 6D spatial measurement systems

In recent years, magnetic tracking systems, whose fundamental unit of measurement is a 5D transformation (three translational and two rotational degrees-of-freedom), have become much more popular. Two 5D sensors can be combined to obtain a 6D transformation similar to the ones provided by the point-based registration in optical tracking. However, estimates of the tool tip uncertainty, which we have called the target tracking error (TTE) since no registration is explicitly performed, are not available in the same manner as their optical counterpart. If the systematic bias error can be corrected and estimates of the 5D or 6D fiducial localizer error (FLE) are provided in the form of zero mean normally distributed random variables in [Formula: see text] and [Formula: see text], respectively, then the TTE can be modeled. In this paper, the required expressions that model the TTE as a function of the systematic bias, FLE and target location are derived and then validated using Monte Carlo simulations. We also show that the first order approximation is sufficient beyond the range of errors typically observed during an image-guided surgery (IGS) procedure. Applications of the models are described for a minimally invasive intracardiac surgical guidance system and needle-based therapy systems. Together with the target registration error (TRE) statistical models for point-based registration, the models presented in this article provide the basic framework for estimating the total system measurement uncertainty for an IGS system. Future work includes developing TRE models for commonly used registration methods that do not already have them.

Estimation of optimal fiducial target registration error in the presence of heteroscedastic noise

We study the effect of point dependent (heteroscedastic) and identically distributed anisotropic fiducial localization noise on fiducial target registration error (TRE). We derive an analytic expression, based on the concept of mechanism spatial stiffness, for predicting TRE. The accuracy of the predicted TRE is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm. The predicted values are shown to be contained by the 95% confidence intervals of the root mean square TRE obtained from the simulations.

Distribution of target registration error for anisotropic and inhomogeneous fiducial localization error

In point-based rigid-body registration, target registration error (TRE) is an important measure of the accuracy of the performed registration. The registration's accuracy depends on the fiducial localization error (FLE) which, in turn, is due to the measurement errors in the points (fiducials) used to perform the registration. FLE may have different characteristics and distributions at each point of the registering data sets, and along each orthogonal axis. Previously, the distribution of TRE was estimated based on the assumption that FLE has an independent, identical, and isotropic or anisotropic distribution for each point in the registering data sets. In this article, we present a general solution based on the Maximum Likelihood (ML) algorithm that estimates the distribution of TRE for the cases where FLE has an independent, identical or inhomogeneous, isotropic or anisotropic, distribution at each point in the registering data sets, and when an algorithm is available that is capable of calculating the optimum registration to first order. Mathematically, we show that the proposed algorithm simplifies to the one proposed by Fitzpatrick and West when FLE has an independent, identical, and isotropic distribution in the registering data sets. Furthermore, we use numerical simulations to show that the proposed algorithm accurately estimates the distribution of TRE when FLE has an independent, inhomogeneous, and anisotropic distribution in the registering data sets.

Localization and registration accuracy in image guided neurosurgery: a clinical study

PURPOSE

To measure and compare the clinical localization and registration errors in image-guided neurosurgery, with the purpose of revising current assumptions.

MATERIALS AND METHODS

Twelve patients who underwent brain surgeries with a navigation system were randomly selected. A neurosurgeon localized and correlated the landmarks on preoperative MRI images and on the intraoperative physical anatomy with a tracked pointer. In the laboratory, we generated 612 scenarios in which one landmark pair was defined as the target and the remaining ones were used to compute the registration transformation. Four errors were measured: (1) fiducial localization error (FLE); (2) target registration error (TRE); (3) fiducial registration error (FRE); (4) Fitzpatrick's target registration error estimation (F-TRE). We compared the different errors and computed their correlation.

RESULTS

The image and physical FLE ranges were 0.5-2.0 and 1.6-3.0 mm, respectively. The measured TRE, FRE and F-TRE were 4.1 +/- 1.6, 3.9 +/- 1.2, and 3.7 +/- 2.2 mm, respectively. Low correlations of 0.19 and 0.37 were observed between the FRE and TRE and between the F-TRE and the TRE, respectively. The differences of the FRE and F-TRE from the TRE were 1.3 +/- 1.0 mm (max = 5.5 mm) and 1.3 +/- 1.2 mm (max = 7.3 mm), respectively.

CONCLUSION

Contrary to common belief, the FLE presents significant variations. Moreover, both the FRE and the F-TRE are poor indicators of the TRE in image-to-patient registration.

On fiducial target registration error in the presence of anisotropic noise

We study the effect of anisotropic noise on target registration error (TRE) by using a tracked and calibrated stylus tip as the fiducial registration application. We present a simple, efficient unscented Kalman filter algorithm that is suitable for fiducial registration even with a small number of fiducials. We also derive an equation that predicts TRE under anisotropic noise. The predicted TRE values are shown to closely match the simulated TRE values achieved using our UKF-based algorithm.