Probe calibration for freehand 3-D ultrasound

Coplanarity Constrained Ultrasound Probe Calibration Based on N-Wire Phantom

OBJECTIVE

N-wire phantom-based ultrasound probe calibration has been used widely in many freehand tracked ultrasound imaging systems. The calibration matrix is obtained by registering the coplanar point cloud in ultrasound space and non-coplanar point cloud in tracking sensor space based on the least squares method. This method is sensitive to outliers and loses the coplanar information of the fiducial points. In this article, we describe a coplanarity-constrained calibration algorithm focusing on these issues.

METHODS

We verified that the out-of-plane error along the oblique wire in the N-wire phantom followed a normal distribution and used it to remove the experimental outliers and fit the plane with the Levenberg-Marquardt algorithm. Then, we projected the points to the plane along the oblique wire. Coplanarity-constrained point cloud registration was used to calculate the transformation matrix.

RESULTS

Compared with the other two commonly used methods, our method had the best calibration precision and achieved 25% and 36% improvement of the mean calibration accuracy than the closed-form solution and in-plane error method respectively at depth 16. Experiments at different depths revealed that our algorithm had better performance in our setup.

CONCLUSION

Our proposed coplanarity-constrained calibration algorithm achieved significant improvement in both precision and accuracy compared with existing algorithms with the same N-wire phantom. It is expected that calibration accuracy will improve when the algorithm is applied to all other N-wire phantom-based calibration procedures.

Automatic spatial calibration of freehand ultrasound probe with a multilayer N-wire phantom

The classic N-wire phantom has been widely used in the calibration of freehand ultrasound probes. One of the main challenges of the phantom is accurately identifying N-fiducials in ultrasound images, especially with multiple N-wire structures. In this study, a method using a multilayer N-wire phantom for the automatic spatial calibration of ultrasound images is proposed. All dots in the ultrasound image are segmented, scored, and classified according to the unique geometric features of the multilayer N-wire phantom. A recognition method for identifying N-fiducials from the dots is proposed for calibrating the spatial transformation of the ultrasound probe. At depths of 9, 11, 13, and 15 cm, the reconstruction error of 50 points is 1.24 ± 0.16, 1.09 ± 0.06, 0.95 ± 0.08, 1.02 ± 0.05 mm, respectively. The reconstruction mockup test shows that the distance accuracy is 1.11 ± 0.82 mm at a depth of 15 cm.

Ultrasound Probe and Hand-Eye Calibrations for Robot-Assisted Needle Biopsy

In robot-assisted ultrasound-guided needle biopsy, it is essential to conduct calibration of the ultrasound probe and to perform hand-eye calibration of the robot in order to establish a link between intra-operatively acquired ultrasound images and robot-assisted needle insertion. Based on a high-precision optical tracking system, novel methods for ultrasound probe and robot hand-eye calibration are proposed. Specifically, we first fix optically trackable markers to the ultrasound probe and to the robot, respectively. We then design a five-wire phantom to calibrate the ultrasound probe. Finally, an effective method taking advantage of steady movement of the robot but without an additional calibration frame or the need to solve the AX=XB equation is proposed for hand-eye calibration. After calibrations, our system allows for in situ definition of target lesions and aiming trajectories from intra-operatively acquired ultrasound images in order to align the robot for precise needle biopsy. Comprehensive experiments were conducted to evaluate accuracy of different components of our system as well as the overall system accuracy. Experiment results demonstrated the efficacy of the proposed methods.

A Novel Ultrasound Probe Spatial Calibration Method Using a Combined Phantom and Stylus

Intra-operative ultrasound (US) is a popular imaging modality for its non-radiative and real-time advantages. However, it is still challenging to perform an interventional procedure under two-dimensional (2-D) US image guidance. Accordingly, the trend has been to perform three-dimensional (3-D) US image guidance by equipping the US probe with a spatial position tracking device, which requires accurate probe calibration for determining the spatial position between the B-scan image and the tracked probe. In this report, we propose a novel probe spatial calibration method by developing a calibration phantom combined with the tracking stylus. The calibration phantom is custom-designed to simplify the alignment between the stylus tip and the B-scan image plane. The spatial position of the stylus tip is tracked in real time, and its 2-D image pixel location is extracted and collected simultaneously. Gaussian distribution is used to model the spatial position of the stylus tip and the iterative closest point-based optimization algorithm is used to estimate the spatial transformation that matches these two point sets. Once the probe is calibrated, its trajectory and the B-scan image are collected and used for the volume reconstruction in our freehand 3-D US imaging system. Experimental results demonstrate that the probe calibration approach results in less than 1-mm mean point reconstruction accuracy. It requires less than 5 min for an inexperienced user to complete the probe calibration procedure with minimal training. The mockup test shows that the 3-D images are geometrically correct with 0.28°-angle accuracy and 0.40-mm distance accuracy.

Automated 3D geometry segmentation of the healthy and diseased carotid artery in free-hand, probe tracked ultrasound images

PURPOSE

Rupture of an arterosclerotic plaque in the carotid artery is a major cause of stroke. Biomechanical analysis of plaques is under development aiming to aid the clinician in the assessment of plaque vulnerability. Patient-specific three-dimensional (3D) geometry assessment of the carotid artery, including the bifurcation, is required as input for these biomechanical models. This requires a high-resolution, 3D, noninvasive imaging modality such as ultrasound (US). In this study, a high-resolution two-dimensional (2D) linear array in combination with a magnetic probe tracking device and automatic segmentation method was used to assess the geometry of the carotid artery. The advantages of using this system over a 3D ultrasound probe are its higher resolution (spatial and temporal) and its larger field of view.

METHODS

A slow sweep (v = ± 5 mm/s) was made over the subject's neck so that the full geometry of the bifurcated geometry of the carotid artery is captured. An automated segmentation pipeline was developed. First, the Star-Kalman method was used to approximate the center and size of the vessels for every frame. Images were filtered with a Gaussian high-pass filter before conversion into the 2D monogenic signals, and multiscale asymmetry features were extracted from these data, enhancing low lateral wall-lumen contrast. These images, in combination with the initial ellipse contours, were used for an active deformable contour model to segment the vessel lumen. To segment the lumen-plaque boundary, Otsu's automatic thresholding method was used. Distension of the wall due to the change in blood pressure was removed using a filter approach. Finally, the contours were converted into a 3D hexahedral mesh for a patient-specific solid mechanics model of the complete arterial wall.

RESULTS

The method was tested on 19 healthy volunteers and on 3 patients. The results were compared to manual segmentation performed by three experienced observers. Results showed an average Hausdorff distance of 0.86 mm and an average similarity index of 0.91 for the common carotid artery (CCA) and 0.88 for the internal and external carotid artery. For the total algorithm, the success rate was 89%, in 4 out of 38 datasets the ICA and ECA were not sufficient visible in the US images. Accurate 3D hexahedral meshes were successfully generated from the segmented images .

CONCLUSIONS

With this method, a subject-specific biomechanical model can be constructed directly from a hand-held 2D US measurement, within 10 min, with a minimal user input. The performance of the proposed segmentation algorithm is comparable to or better than algorithms previously described in literature. Moreover, the algorithm is able to segment the CCA, ICA, and ECA including the carotid bifurcation in transverse B-mode images in both healthy and diseased arteries.

Ultrasound Based Planning and Navigation for Non-Anatomical Liver Resections – An Ex-Vivo Study

Goal: Non-anatomical resections of liver tumors can be very challenging as the surgeon cannot use anatomical landmarks on the liver surface or in the ultrasound image for guidance. This makes it difficult to achieve negative resection margins (R0) and still preserve as much healthy liver tissue as possible. Even though image-guided surgery systems have been introduced to overcome this challenge, they are still rarely used due to their inaccuracy, time-effort and complexity in usage and setup. Methods: We have developed a novel approach, which allows us to create an intra-operative resection plan using navigated ultrasound. First, the surface is scanned using a navigated ultrasound, followed by tumor segmentation on a midsection ultrasound image. Based on this information, the navigation system calculates an optimal resection strategy and displays it along with the tracked surgical instruments. In this study, this approach was evaluated by three experienced hepatobiliary surgeons on ex-vivo porcine models. Results: Using this technique, an R0 resection could be achieved in 22 out of 23 (95.7% R0 resection rate) cases with a median resection margin of 5.9 mm (IQR 3.5–7.7 mm). The resection margin between operators 1, 2 and 3 was 7.8 mm, 4.15 mm and 5.1 mm respectively (p = 0.054). Conclusions: This approach could represent a useful tool for intra-operative guidance in non-anatomical resection alongside conventional ultrasound guidance. However, instructions and training are essential especially if the operator has not used an image-guidance system before.

A Novel Design of N-Fiducial Phantom for Automatic Ultrasound Calibration

Background:

Freehand ultrasound (US) is a technique used to acquire three-dimensional (3D) US images using a tracked 2D US probe. Calibrating the probe with a proper calibration phantom improves the precision of the technique and allows several applications in computer-assisted surgery. N-fiducial phantom is widely used due to the robustness of precise fabrication and convenience of use. In principle, the design supports single-frame calibration by providing at least three noncollinear points in 3D space at once. Due to this requirement, most designs contain multiple N-fiducials in unpatterned and noncollinear arrangements. The unpatterned multiple N-fiducials appearing as scattered dots in the US image are difficult to extract, and the extracted data are usually contaminated with noise. In practice, the extraction mostly relied on manual interventions, and calibration with N-fiducial phantom has not yet achieved high accuracy with single or few frame calibrations due to noise contamination.

Aims:

In this article, we propose a novel design of the N-fiducial US calibration phantom to enable automatic feature extraction with comparable accuracy to multiple frame calibration.

Materials and Methods:

Along with the design, the Random Sample Consensus (RANSAC) algorithm was used for feature extraction with both 2D and 3D models estimation. The RANSAC feature extraction algorithm was equipped with a closed-form calibration method to achieve automatic calibration.

Results:

The accuracy, precision, and shape reconstruction errors of the calibration acquired from the experiment were significantly matched with the previous literature reports.

Conclusions:

The results showed that our proposed method has a high efficiency to perform automatic feature extraction compared to conventional extraction performed by humans.

Actuator-Assisted Calibration of Freehand 3D Ultrasound System

Freehand three-dimensional (3D) ultrasound has been used independently of other technologies to analyze complex geometries or registered with other imaging modalities to aid surgical and radiotherapy planning. A fundamental requirement for all freehand 3D ultrasound systems is probe calibration. The purpose of this study was to develop an actuator-assisted approach to facilitate freehand 3D ultrasound calibration using point-based phantoms. We modified the mathematical formulation of the calibration problem to eliminate the need of imaging the point targets at different viewing angles and developed an actuator-assisted approach/setup to facilitate quick and consistent collection of point targets spanning the entire image field of view. The actuator-assisted approach was applied to a commonly used cross wire phantom as well as two custom-made point-based phantoms (original and modified), each containing 7 collinear point targets, and compared the results with the traditional freehand cross wire phantom calibration in terms of calibration reproducibility, point reconstruction precision, point reconstruction accuracy, distance reconstruction accuracy, and data acquisition time. Results demonstrated that the actuator-assisted single cross wire phantom calibration significantly improved the calibration reproducibility and offered similar point reconstruction precision, point reconstruction accuracy, distance reconstruction accuracy, and data acquisition time with respect to the freehand cross wire phantom calibration. On the other hand, the actuator-assisted modified “collinear point target” phantom calibration offered similar precision and accuracy when compared to the freehand cross wire phantom calibration, but it reduced the data acquisition time by 57%. It appears that both actuator-assisted cross wire phantom and modified collinear point target phantom calibration approaches are viable options for freehand 3D ultrasound calibration.

Freehand three-dimensional ultrasound imaging of carotid artery using motion tracking technology

Ultrasound imaging has been extensively used for determining the severity of carotid atherosclerotic stenosis. In particular, the morphological characterization of carotid plaques can be performed for risk stratification of patients. However, using 2D ultrasound imaging for detecting morphological changes in plaques has several limitations. Due to the scan was performed on a single longitudinal cross-section, the selected 2D image is difficult to represent the entire morphology and volume of plaque and vessel lumen. In addition, the precise positions of 2D ultrasound images highly depend on the radiologists' experience, it makes the serial long-term exams of anti-atherosclerotic therapies are difficult to relocate the same corresponding planes by using 2D B-mode images. This has led to the recent development of three-dimensional (3D) ultrasound imaging, which offers improved visualization and quantification of complex morphologies of carotid plaques. In the present study, a freehand 3D ultrasound imaging technique based on optical motion tracking technology is proposed. Unlike other optical tracking systems, the marker is a small rigid body that is attached to the ultrasound probe and is tracked by eight high-performance digital cameras. The probe positions in 3D space coordinates are then calibrated at spatial and temporal resolutions of 10μm and 0.01s, respectively. The image segmentation procedure involves Otsu's and the active contour model algorithms and accurately detects the contours of the carotid arteries. The proposed imaging technique was verified using normal artery and atherosclerotic stenosis phantoms. Human experiments involving freehand scanning of the carotid artery of a volunteer were also performed. The results indicated that compared with manual segmentation, the lowest percentage errors of the proposed segmentation procedure were 7.8% and 9.1% for the external and internal carotid arteries, respectively. Finally, the effect of handshaking was calibrated using the optical tracking system for reconstructing a 3D image.

User-friendly freehand ultrasound calibration using Lego bricks and automatic registration

PURPOSE

As an inexpensive, noninvasive, and portable clinical imaging modality, ultrasound (US) has been widely employed in many interventional procedures for monitoring potential tissue deformation, surgical tool placement, and locating surgical targets. The application requires the spatial mapping between 2D US images and 3D coordinates of the patient. Although positions of the devices (i.e., ultrasound transducer) and the patient can be easily recorded by a motion tracking system, the spatial relationship between the US image and the tracker attached to the US transducer needs to be estimated through an US calibration procedure. Previously, various calibration techniques have been proposed, where a spatial transformation is computed to match the coordinates of corresponding features in a physical phantom and those seen in the US scans. However, most of these methods are difficult to use for novel users.

METHODS

We proposed an ultrasound calibration method by constructing a phantom from simple Lego bricks and applying an automated multi-slice 2D-3D registration scheme without volumetric reconstruction. The method was validated for its calibration accuracy and reproducibility.

RESULTS

Our method yields a calibration accuracy of [Formula: see text] mm and a calibration reproducibility of 1.29 mm.

CONCLUSION

We have proposed a robust, inexpensive, and easy-to-use ultrasound calibration method.

A Robotic Ultrasound Scanner for Automatic Vessel Tracking and Three-Dimensional Reconstruction of B-Mode Images

Locating and evaluating the length and severity of a stenosis is very important for planning adequate treatment of peripheral arterial disease (PAD). Conventional ultrasound (US) examination cannot provide maps of entire lower limb arteries in 3-D. We propose a prototype 3D-US robotic system with B-mode images, which is nonionizing, noninvasive, and is able to track and reconstruct a continuous segment of the lower limb arterial tree between the groin and the knee. From an initialized cross-sectional view of the vessel, automatic tracking was conducted followed by 3D-US reconstructions evaluated using Hausdorff distance, cross-sectional area, and stenosis severity in comparison with 3-D reconstructions with computed tomography angiography (CTA). A mean Hausdorff distance of 0.97 ± 0.46 mm was found in vitro for 3D-US compared with 3D-CTA vessel representations. To evaluate the stenosis severity in vitro, 3D-US reconstructions gave errors of 3%-6% when compared with designed dimensions of the phantom, which are comparable to 3D-CTA reconstructions, with 4%-13% errors. The in vivo system's feasibility to reconstruct a normal femoral artery segment of a volunteer was also investigated. These results encourage further ergonomic developments to increase the robot's capacity to represent lower limb vessels in the clinical context.

Reconstruction of specular reflectors by iterative image source localization

A method is presented to reconstruct the geometry of specular reflectors with an ultrasonic array based on the image source principle. The ultrasonic beam is focused at a point in space emulating a point source within the medium. The transmitted wave interacts with the specular reflector and propagates back to the array as if it were generated by an image source. The reflected wave is analyzed with a sound source localization algorithm to estimate the image source location, and the reflector geometry is extracted using the mirror equation for spherical reflectors. The method is validated experimentally and its accuracy is studied. Under ideal conditions the method provides an accurate reconstruction of the position, orientation, and radius of curvature of specular reflectors, with errors Δr < 0.2 mm, Δα < 3°, and ΔR/R0 < 0.2, respectively. The method performs very well in the presence of high levels of thermal and speckle noise, with no degradation of the reconstruction as long as SNR(th) > -3 dB (signal-to-thermal-noise ratio) and SNR(sp) > 7 dB (signal-to-speckle-noise ratio). An iterative scheme based on the proposed method is presented to reconstruct the geometry of arbitrary reflectors by subdividing the reflector boundary into smaller segments. The iterative scheme is demonstrated both numerically and experimentally.

Panorama Ultrasound for Navigation and Guidance of Epidural Anesthesia

Despite the common use of epidural anesthesia in obstetrics and surgery, the procedure can be challenging, especially for obese patients. We propose the use of an ultrasound guidance system employing a transducer-mounted camera to create 3-D panorama ultrasound volumes of the spine, thereby allowing identification of vertebrae and selection of puncture site, needle trajectory and depth of insertion. The camera achieves absolute position estimation of the transducer with respect to the patient using a specialized marker strip attached to the skin surface. The guidance system is validated first on a phantom against a commercial optical tracking system and then in vivo by comparing panorama images from human subjects against independent measurements by an experienced sonographer. The results for measuring depth to the epidural space, intervertebral spacing and registration of interspinous gaps to the skin prove the potential of the system for improving guidance of epidural anesthesia. The tracking and visualization are implemented in real time using the 3D Slicer software package.

A closed-form differential formulation for ultrasound spatial calibration: single wall phantom

Calibration is essential in freehand 3-D ultrasound to find the spatial transformation from the image coordinates to the sensor coordinate system. Ease of use, simplicity, precision and accuracy are among the most important factors in ultrasound calibration, especially when aiming to make calibration more reliable for day-to-day clinical use. We introduce a new mathematical framework for the simple and popular single-wall calibration phantom with a plane equation pre-determination step and the use of differential measurements to obtain accurate measurements. The proposed method provides a novel solution for ultrasound calibration that is accurate and easy to perform. This method is applicable to both radiofrequency (RF) and B-mode data, and both linear and curvilinear transducers. For a linear L14-5 transducer, the point reconstruction accuracy (PRA) of reconstructing 370 points is 0.73 ± 0.23 mm using 100 RF images, whereas the triple N-wire PRA is 0.67 ± 0.20 mm using 100 B-mode images. For a curvilinear C5-2 transducer, the PRA using the proposed method is 0.86 ± 0.28 mm on 400 points using 100 RF images, whereas N-wire calibration gives a PRA of 0.80 ± 0.46 mm using 100 B-mode images. Therefore, the accuracy of the proposed variation of the single-wall method using RF data is practically similar to the N-wire method while offering a simpler phantom with no need for accurate design and construction.

Metrological Evaluation of a Novel Medical Robot and Its Kinematic Calibration

The vessels are twisted in a longitudinal 3D space in the lower limbs of humans. Thus, it is difficult to perform an ultrasound scanning examination in this area. In this paper, a new medical parallel robot is introduced to effectively diagnose vessel disease in the lower limbs. The robot's position repeatability and accuracy are evaluated. Furthermore, the robot's accuracy is improved through a calibration process in which the kinematic parameters are identified through a simple identification approach.

A closed-form differential formulation for ultrasound spatial calibration: multi-wedge phantom

Calibration is essential in freehand 3-D ultrasound to find the spatial transformation from the image coordinates to the sensor coordinate system. Calibration accuracy has significant impact on image-guided interventions. We introduce a new mathematical framework that uses differential measurements to achieve high calibration accuracy. Accurate measurements of axial differences in ultrasound images of a multi-wedge phantom are used to calculate the calibration matrix with a closed-form solution. The multi-wedge phantom has been designed based on the proposed differential framework and can be mass-produced inexpensively using a 3-D printer. The proposed method enables easy, fast and highly accurate ultrasound calibration, which is essential for most current ultrasound-guided applications and also widens the range of new applications. The precision of the method using only a single image of the phantom is comparable to that of the standard N-wire method using 50 images. The method can also directly take advantage of the fine sampling rate of radiofrequency ultrasound data to achieve very high calibration accuracy. With 100 radiofrequency ultrasound images, the method achieves a point reconstruction error of 0.09 ± 0.39 mm.

Intra-operative correction of brain-shift

BACKGROUND

Brain-shift is a major source of error in neuronavigation systems based on pre-operative images. In this paper, we present intra-operative correction of brain-shift using 3D ultrasound.

METHODS

The method is based on image registration of vessels extracted from pre-operative MRA and intra-operative power Doppler-based ultrasound and is fully integrated in the neuronavigation software.

RESULTS

We have performed correction of brain-shift in the operating room during surgery and provided the surgeon with updated information. Here, we present data from seven clinical cases with qualitative and quantitative error measures.

CONCLUSION

The registration algorithm is fast enough to provide the surgeon with updated information within minutes and accounts for large portions of the experienced shift. Correction of brain-shift can make pre-operative data like fMRI and DTI reliable for a longer period of time and increase the usefulness of the MR data as a supplement to intra-operative 3D ultrasound in terms of overview and interpretation.

Neck tumor dissection improved with 3-dimensional ultrasound image guidance: technical case report

BACKGROUND AND IMPORTANCE

Three-dimensional ultrasound navigation has been performed to assist in resection of cranial and spinal tumors, but to the best of our knowledge, no one has described the use of real-time 3-dimensional ultrasound navigation in the resection of neck tumors beyond biopsy.

CLINICAL PRESENTATION

This case report describes the use of 3-dimensional ultrasonic navigation in assisting with resection of a large neck paraganglioma. The 3-dimensional ultrasonic navigation improved real-time visualization of the carotid arteries, the trachea, and other vital structures.

CONCLUSION

The use of 3-dimensional ultrasound navigation should be considered in aiding resection of large neck tumors because it can allow more efficient and safer tumor resection.

Intra-operative 2-D ultrasound and dynamic 3-D aortic model registration for magnetic navigation of transcatheter aortic valve implantation

We propose a navigation system for transcatheter aortic valve implantation that employs a magnetic tracking system (MTS) along with a dynamic aortic model and intra-operative ultrasound (US) images. This work is motivated by the desire of our cardiology and cardiac surgical colleagues to minimize or eliminate the use of radiation in the interventional suite or operating room. The dynamic 3-D aortic model is constructed from a preoperative 4-D computed tomography dataset that is animated in synchrony with the real time electrocardiograph input of patient, and then preoperative planning is performed to determine the target position of the aortic valve prosthesis. The contours of the aortic root are extracted automatically from short axis US images in real-time for registering the 2-D intra-operative US image to the preoperative dynamic aortic model. The augmented MTS guides the interventionist during positioning and deployment of the aortic valve prosthesis to the target. The results of the aortic root segmentation algorithm demonstrate an error of 0.92±0.85 mm with a computational time of 36.13±6.26 ms. The navigation approach was validated in porcine studies, yielding fiducial localization errors, target registration errors, deployment distance, and tilting errors of 3.02±0.39 mm, 3.31±1.55 mm, 3.23±0.94 mm, and 5.85±3.06(°) , respectively.

Automatic 3D ultrasound calibration for image guided therapy using intramodality image registration

Many real time ultrasound (US) guided therapies can benefit from management of motion-induced anatomical changes with respect to a previously acquired computerized anatomy model. Spatial calibration is a prerequisite to transforming US image information to the reference frame of the anatomy model. We present a new method for calibrating 3D US volumes using intramodality image registration, derived from the 'hand-eye' calibration technique. The method is fully automated by implementing data rejection based on sensor displacements, automatic registration over overlapping image regions, and a self-consistency error metric evaluated continuously during calibration. We also present a novel method for validating US calibrations based on measurement of physical phantom displacements within US images. Both calibration and validation can be performed on arbitrary phantoms. Results indicate that normalized mutual information and localized cross correlation produce the most accurate 3D US registrations for calibration. Volumetric image alignment is more accurate and reproducible than point selection for validating the calibrations, yielding <1.5 mm root mean square error, a significant improvement relative to previously reported hand-eye US calibration results. Comparison of two different phantoms for calibration and for validation revealed significant differences for validation (p = 0.003) but not for calibration (p = 0.795).

Improving N-wire phantom-based freehand ultrasound calibration

PURPOSE

   Freehand tracked ultrasound imaging is an inexpensive non-invasive technique used in several guided interventions. This technique requires spatial calibration between the tracker and the ultrasound image plane. Several calibration devices (a.k.a. phantoms) use N-wires that are convenient for automatic procedures since the segmentation of fiducials in the images and the localization of the middle wires in space are straightforward and can be performed in real time. The procedures reported in literature consider only the spatial position of the middle wire. We investigate if better results can be achieved if the information of all the wires is equally taken into account. We also evaluated the precision and accuracy of the implemented methods to allow comparison with other methods.

METHODS

   We consider a cost function based on the in-plane errors between the intersection of all the wires with the image plane and their respective segmented points in the image. This cost function is minimized iteratively starting from a seed computed with a closed-form solution based on the middle wires.

RESULTS

   Mean calibration precision achieved with the N-wire phantom was about 0.5 mm using a shallow probe, and mean accuracy was around 1.4 mm with all implemented methods. Precision was about 2.0 mm using a deep probe.

CONCLUSIONS

   Precision and accuracy achieved with the N-wire phantom and a shallow probe are at least comparable to that obtained with other methods traditionally considered more precise. Calibration using N-wires can be done more consistently if the parameters are optimized with the proposed cost function.

A pilot study on magnetic navigation for transcatheter aortic valve implantation using dynamic aortic model and US image guidance

PURPOSE

In this paper, we propose a pilot study for transcatheter aortic valve implantation guided by an augmented magnetic tracking system (MTS) with a dynamic aortic model and intra-operative ultrasound (US) images.

METHODS

The dynamic 3D aortic model is constructed from the preoperative 4D computed tomography, which is animated according to the real-time electrocardiograph (ECG) input of patient. Before the procedure, the US probe calibration is performed to map the US image coordinate to the tracked device coordinate. A temporal alignment is performed to synchronize the ECG signals, the intra-operative US image and the tracking information. Thereafter, with the assistance of synchronized ECG signals, the spatial registration is performed by using a feature-based registration. Then the augmented MTS guides the surgeon to confidently position and deploy the transcatheter aortic valve prosthesis to the target.

RESULTS

The approach was validated by US probe calibration evaluation and animal study. The US calibration accuracy achieved [Formula: see text], whereas in the animal study on three porcine subjects, fiducial, target, deployment distance and tilting errors reached [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], respectively.

CONCLUSION

Our pilot study has revealed that the proposed approach is feasible and accurate for delivery and deployment of transcatheter aortic valve prosthesis.

Registration of 3D ultrasound through an air-tissue boundary

In this study we evaluated a new method for registering three-dimensional ultrasound (3DUS) data to external coordinate systems. First, 3DUS was registered to the stereo endoscope of a da Vinci Surgical System by placing a registration tool against an air-tissue boundary so that the 3DUS could image ultrasound fiducials while the stereo endoscope could image camera markers on the same tool. The common points were used to solve the registration between the 3DUS and camera coordinate systems. The target registration error (TRE) when imaging through a PVC tissue phantom ranged from 3.85 1.76 mm to 1.82 1.03 mm using one to four registration tool positions. TRE when imaging through an ex-vivo liver tissue sample ranged from 2.36 1.01 mm to 1.51 0.70 mm using one to four registration tool positions. Second, using a similar method, 3DUS was registered to the kinematic coordinate system of a da Vinci Surgical System by using the da Vinci surgical manipulators to identify common points on an air-tissue boundary. TRE when imaging through a PVC tissue phantom was 0.95 0.38 mm. This registration method is simpler and potentially more accurate than methods using commercial motion tracking systems. This method may be useful in the future in augmented reality systems for laparoscopic and robotic-assisted surgery.

Magnetic navigation for thoracic aortic stent-graft deployment using ultrasound image guidance

We propose a system for thoracic aortic stent-graft deployment that employs a magnetic tracking system (MTS) and intraoperative ultrasound (US). A preoperative plan is first performed using a general public utilities-accelerated cardiac modeling method to determine the target position of the stent-graft. During the surgery, an MTS is employed to track sensors embedded in the catheter, cannula, and the US probe, while a fiducial landmark based registration is used to map the patient's coordinate to the image coordinate. The surgical target is tracked in real time via a calibrated intraoperative US image. Under the guidance of the MTS integrated with the real-time US images, the stent-graft can be deployed to the target position without the use of ionizing radiation. This navigation approach was validated using both phantom and animal studies. In the phantom study, we demonstrate a US calibration accuracy of 1.5 ± 0.47 mm, and a deployment error of 1.4 ± 0.16 mm. In the animal study, we performed experiments on five porcine subjects and recorded fiducial, target, and deployment errors of 2.5 ± 0.32, 4.2 ± 0.78, and 2.43 ± 0.69 mm, respectively. These results demonstrate that delivery and deployment of thoracic stent-graft under MTS-guided navigation using US imaging is feasible and appropriate for clinical application.

Passive markers for tracking surgical instruments in real-time 3-D ultrasound imaging

A family of passive echogenic markers is presented by which the position and orientation of a surgical instrument can be determined in a 3-D ultrasound volume, using simple image processing. Markers are attached near the distal end of the instrument so that they appear in the ultrasound volume along with the instrument tip. They are detected and measured within the ultrasound image, thus requiring no external tracking device. This approach facilitates imaging instruments and tissue simultaneously in ultrasound-guided interventions. Marker-based estimates of instrument pose can be used in augmented reality displays or for image-based servoing. Design principles for marker shapes are presented that ensure imaging system and measurement uniqueness constraints are met. An error analysis is included that can be used to guide marker design and which also establishes a lower bound on measurement uncertainty. Finally, examples of marker measurement and tracking algorithms are presented along with experimental validation of the concepts.

Automated intraoperative calibration for prostate cancer brachytherapy

PURPOSE

Prostate cancer brachytherapy relies on an accurate spatial registration between the implant needles and the TRUS image, called "calibration". The authors propose a new device and a fast, automatic method to calibrate the brachytherapy system in the operating room, with instant error feedback.

METHODS

A device was CAD-designed and precision-engineered, which mechanically couples a calibration phantom with an exact replica of the standard brachytherapy template. From real-time TRUS images acquired from the calibration device and processed by the calibration system, the coordinate transformation between the brachytherapy template and the TRUS images was computed automatically. The system instantly generated a report of the target reconstruction accuracy based on the current calibration outcome.

RESULTS

Four types of validation tests were conducted. First, 50 independent, real-time calibration trials yielded an average of 0.57 ± 0.13 mm line reconstruction error (LRE) relative to ground truth. Second, the averaged LRE was 0.37 ± 0.25 mm relative to ground truth in tests with six different commercial TRUS scanners operating at similar imaging settings. Furthermore, testing with five different commercial stepper systems yielded an average of 0.29 ± 0.16 mm LRE relative to ground truth. Finally, the system achieved an average of 0.56 ± 0.27 mm target registration error (TRE) relative to ground truth in needle insertion tests through the template in a water tank.

CONCLUSIONS

The proposed automatic, intraoperative calibration system for prostate cancer brachytherapy has achieved high accuracy, precision, and robustness.

Navigated laparoscopic ultrasound in abdominal soft tissue surgery: technological overview and perspectives

PURPOSE

Two-dimensinal laparoscopic ultrasound (LUS) is commonly used for many laparoscopic procedures, but 3D LUS and navigation technology are not conventional tools in the clinic. Navigated LUS can help the user understand and interpret the ultrasound images in relation to the laparoscopic view and preoperative images. When combined with information from MRI or CT, navigated LUS has the potential to provide information about anatomic shifts during the procedure. In this paper, we present an overview of the ongoing technological research and development related to LUS combined with navigation technology, The purpose of this overview is threefold: (1) an introduction for those new to the field of navigated LUS; (2) an overview for those working in the field and; and (3) as a reference for those searching for literature on technological developments related to navigation in ultrasound-guided laparoscopic surgery.

METHODS

Databases were searched to identify relevant publications from the last 10 years.

RESULTS

We were able to identify 18 key papers in the area of navigated LUS for the abdomen, originating from about 10-11 groups. We present the literature overview, including descriptions of our own experience in the field, and a discussion of the important clinical and technological aspects related to navigated LUS.

CONCLUSIONS

LUS integrated with miniaturized tracking technology is likely to play an important role in guiding future laparoscopic surgery.

Three-dimensional ultrasound scanning

The past two decades have witnessed developments of new imaging techniques that provide three-dimensional images about the interior of the human body in a manner never before available. Ultrasound (US) imaging is an important cost-effective technique used routinely in the management of a number of diseases. However, two-dimensional viewing of three-dimensional anatomy, using conventional two-dimensional US, limits our ability to quantify and visualize the anatomy and guide therapy, because multiple two-dimensional images must be integrated mentally. This practice is inefficient, and may lead to variability and incorrect diagnoses. Investigators and companies have addressed these limitations by developing three-dimensional US techniques. Thus, in this paper, we review the various techniques that are in current use in three-dimensional US imaging systems, with a particular emphasis placed on the geometric accuracy of the generation of three-dimensional images. The principles involved in three-dimensional US imaging are then illustrated with a diagnostic and an interventional application: (i) three-dimensional carotid US imaging for quantification and monitoring of carotid atherosclerosis and (ii) three-dimensional US-guided prostate biopsy.

Improvement of freehand ultrasound calibration accuracy using the elevation beamwidth profile

This article presents a novel approach that incorporates an ultrasound slice-thickness profile into a filtered, weighted-least-square framework to improve the reconstruction accuracy of a real-time freehand calibration system. An important part of the system is a slice-thickness calibration device that aids in the extraction of the slice thickness across a wide range of imaging depths. Extensive experiments were conducted on a 10,000-image dataset to evaluate the effects of the framework on the calibration accuracy. The results showed that three-dimensional (3-D) reconstruction errors were significantly reduced in every experiment (p < 0.001). Real-time testing showed that the proposed method worked effectively with a small number of input images, suggesting great potential for intraoperative use where only a limited number of data may be available. This new framework can enable efficient quality control of calibration accuracy in real-time operating-room use.

Alignment and calibration of dual ultrasound transducers using a wedge phantom

We present a novel method of aligning two orthogonal ultrasound transducers into a coincident scan plane. A wedge phantom design provides visual feedback to the user to facilitate alignment. Calibration provides the transformation from one transducer to the other as well as a measure of the residual error in alignment. Mean alignment error is shown to be under 1° in the rotation axes and 1 mm in translation after repeated manual alignments. The repeatability of wedge based calibration has similar results compared with N-fiducial based calibration. The accuracy of the calibration for mapping points from one transducer to the other is found to have a mean error of 1.6 mm. The dual transducer system is well suited to imaging anatomy such as the breast and may be used for spatial compounding for improving B-mode images and motion estimation compounding for improving elastography results.

Tandem-robot assisted laparoscopic radical prostatectomy to improve the neurovascular bundle visualization: a feasibility study

OBJECTIVES

To examine the feasibility of image-guided navigation using transrectal ultrasound (TRUS) to visualize the neurovascular bundle (NVB) during robot-assisted laparoscopic radical prostatectomy (RALP). The preservation of the NVB during radical prostatectomy improves the postoperative recovery of sexual potency. The accompanying blood vessels in the NVB can serve as a macroscopic landmark to localize the microscopic cavernous nerves in the NVB.

METHODS

A novel, robotic transrectal ultrasound probe manipulator (TRUS Robot) and three-dimensional (3-D) reconstruction software were developed and used concurrently with the daVinci surgical robot (Intuitive Surgical, Inc., Sunnyvale, CA) in a tandem-robot assisted laparoscopic radical prostatectomy (T-RALP).

RESULTS

After appropriate approval and informed consent were obtained, 3 subjects underwent T-RALP without associated complications. The TRUS Robot allowed a steady handling and remote manipulation of the TRUS probe during T-RALP. It also tracked the TRUS probe position accurately and allowed 3-D image reconstruction of the prostate and surrounding structures. Image navigation was performed by observing the tips of the daVinci surgical instruments in the live TRUS image. Blood vessels in the NVB were visualized using Doppler ultrasound.

CONCLUSIONS

Intraoperative 3-D image-guided navigation in T-RALP is feasible. The use of TRUS during radical prostatectomy can potentially improve the visualization and preservation of the NVB. Further studies are needed to assess the clinical benefit of T-RALP.

New prototype neuronavigation system based on preoperative imaging and intraoperative freehand ultrasound: system description and validation

PURPOSE

The aim of this report is to present IBIS (Interactive Brain Imaging System) NeuroNav, a new prototype neuronavigation system that has been developed in our research laboratory over the past decade that uses tracked intraoperative ultrasound to address surgical navigation issues related to brain shift. The unique feature of the system is its ability, when needed, to improve the initial patient-to-preoperative image alignment based on the intraoperative ultrasound data. Parts of IBIS Neuronav source code are now publicly available on-line.

METHODS

Four aspects of the system are characterized in this paper: the ultrasound probe calibration, the temporal calibration, the patient-to-image registration and the MRI-ultrasound registration. In order to characterize its real clinical precision and accuracy, the system was tested in a series of adult brain tumor cases.

RESULTS

Three metrics were computed to evaluate the precision and accuracy of the ultrasound calibration. 1) Reproducibility: 1.77 mm and 1.65 mm for the bottom corners of the ultrasound image, 2) point reconstruction precision 0.62-0.90 mm: and 3) point reconstruction accuracy: 0.49-0.74 mm. The temporal calibration error was estimated to be 0.82 ms. The mean fiducial registration error (FRE) of the homologous-point-based patient-to-MRI registration for our clinical data is 4.9 ± 1.1 mm. After the skin landmark-based registration, the mean misalignment between the ultrasound and MR images in the tumor region is 6.1 ± 3.4 mm.

CONCLUSIONS

The components and functionality of a new prototype system are described and its precision and accuracy evaluated. It was found to have an accuracy similar to other comparable systems in the literature.

Ultrasound guided robotic biopsy using augmented reality and human-robot cooperative control

Ultrasound-guided biopsy is a proficient mininvasive approach for tumors staging but requires very long training and particular manual and 3D space perception abilities of the physician, for the planning of the needle trajectory and the execution of the procedure. In order to simplify this difficult task, we have developed an integrated system that provides the clinician two types of assistance: an augmented reality visualization allows accurate and easy planning of needle trajectory and target reaching verification; a robot arm with a six-degree-of-freedom force sensor allows the precise positioning of the needle holder and allows the clinician to adjust the planned trajectory (cooperative control) to overcome needle deflection and target motion. Preliminary tests have been executed on an ultrasound phantom showing high precision of the system in static conditions and the utility and usability of the cooperative control in simulated no-rigid conditions.

Blood flow imaging: an angle-independent ultrasound modality for intraoperative assessment of flow dynamics in neurovascular surgery

OBJECTIVE

The objective of this study was to investigate the clinical applicability of navigated blood flow imaging (BFI) in neurovascular applications. BFI is a new 2-dimensional ultrasound modality that offers angle-independent visualization of flow. When integrated with 3-dimensional (3D) navigation technology, BFI can be considered as a first step toward the ideal tool for surgical needs: a real-time, high-resolution, 3D visualization that properly portrays both vessel geometry and flow direction.

METHODS

A 3D model of the vascular tree was extracted from preoperative magnetic resonance angiographic data and used as a reference for intraoperative any-plane guided ultrasound acquisitions. A high-end ultrasound scanner was interconnected, and synchronized recordings of BFI and 3D navigation scenes were acquired. The potential of BFI as an intraoperative tool for flow visualization was evaluated in 3 cerebral aneurysms and 3 arteriovenous malformations.

RESULTS

The neurovascular flow direction was properly visualized in all cases using BFI. Navigation technology allowed for identification of the vessels of interest, despite the presence of brain shift. The surgeon found BFI to be very intuitive compared with conventional color Doppler methods. BFI allowed for quality control of sufficient flow in all distal arteries during aneurysm surgery and made it easier to discern between feeding arteries and draining veins during surgery for arteriovenous malformations.

CONCLUSION

BFI seems to be a promising modality for neurovascular flow visualization that may provide the neurosurgeon with a valuable tool for safer surgical interventions. However, further work is needed to establish the clinical usefulness of the proposed imaging setup.

Navigated ultrasound in laparoscopic surgery

Laparoscopic surgery is performed through small incisions that limit free sight and possibility to palpate organs. Although endoscopes provide an overview of organs inside the body, information beyond the surface of the organs is missing. Ultrasound can provide real-time essential information of inside organs, which is valuable for increased safety and accuracy in guidance of procedures. We have tested the use of 2D and 3D ultrasound combined with 3D CT data in a prototype navigation system. In our laboratory, micro-positioning sensors were integrated into a flexible intraoperative ultrasound probe, making it possible to measure the position and orientation of the real-time 2D ultrasound image as well as to perform freehand 3D ultrasound acquisitions. Furthermore, we also present a setup with the probe optically tracked from the shaft with the flexible part locked in one position. We evaluated the accuracy of the 3D laparoscopic ultrasound solution and obtained average values ranging from 1.6% to 3.6% volume deviation from the phantom specifications. Furthermore, we investigated the use of an electromagnetic tracking in the operating room. The results showed that the operating room setup disturbs the electromagnetic tracking signal by increasing the root mean square (RMS) distance error from 0.3 mm to 2.3 mm in the center of the measurement volume, but the surgical instruments and the ultrasound probe added no further inaccuracies. Tracked surgical tools, such as endoscopes, pointers, and probes, allowed surgeons to interactively control the display of both registered preoperative medical images, as well as intraoperatively acquired 3D ultrasound data, and have potential to increase the safety of guidance of surgical procedures.

A real-time freehand ultrasound calibration system with automatic accuracy feedback and control

This article describes a fully automatic, real-time, freehand ultrasound calibration system. The system was designed to be simple and sterilizable, intended for operating-room usage. The calibration system employed an automatic-error-retrieval and accuracy-control mechanism based on a set of ground-truth data. Extensive validations were conducted on a data set of 10,000 images in 50 independent calibration trials to thoroughly investigate the accuracy, robustness, and performance of the calibration system. On average, the calibration accuracy (measured in three-dimensional reconstruction error against a known ground truth) of all 50 trials was 0.66 mm. In addition, the calibration errors converged to submillimeter in 98% of all trials within 12.5 s on average. Overall, the calibration system was able to consistently, efficiently and robustly achieve high calibration accuracy with real-time performance.

Comparison of freehand 3-D ultrasound calibration techniques using a stylus

In a freehand 3-D ultrasound system, a probe calibration is required to find the rigid body transformation from the corner of the B-scan to the electrical center of the position sensor. The most intuitive way to perform such a calibration is by locating fiducial points in the scan plane directly with a stylus. The main problem of this approach is the difficulty in aligning the tip of the stylus with the scan plane. The thick beamwidth makes the tip of the stylus visible in the B-scan, even if the tip is not exactly at the elevational center of the scan plane. We present a novel stylus and phantom that simplify the alignment process for more accurate probe calibration. We also compare our calibration techniques with a range of styli. We show that our stylus and cone phantom are both simple in design and can achieve a point reconstruction accuracy of 2.2 mm and 1.8 mm, respectively, an improvement from 3.2 mm and 3.6 mm with the sharp and spherical stylus. The performance of our cone stylus and phantom lie between the state-of-the-art Z-phantom and Cambridge phantom, where accuracies of 2.5 mm and 1.7 mm are achieved.

Navigation in laparoscopy--prototype research platform for improved image-guided surgery

The manipulation of the surgical field in laparoscopic surgery, through small incisions with rigid instruments, reduces free sight, dexterity, and tactile feedback. To help overcome some of these drawbacks, we present a prototype research and development platform, CustusX, for navigation in minimally invasive therapy. The system can also be used for planning and follow-up studies. With this platform we can import and display a range of medical images, also real-time data such as ultrasound and X-ray, during surgery. Tracked surgical tools, such as pointers, video laparoscopes, graspers, and various probes, allow surgeons to interactively control the display of medical images during the procedure. This paper introduces navigation technologies and methods for laparoscopic therapy, and presents our software and hardware research platform. Furthermore, we illustrate the use of the system with examples from two pilots performed during laparoscopic therapy. We also present new developments that are currently being integrated into the system for future use in the operating room. Our initial results from pilot studies using this technology with preoperative images and guidance in the retroperitoneum during laparoscopy are promising. Finally, we shortly describe an ongoing multicenter study using this surgical navigation system platform.

Real-time freehand 3D ultrasound calibration

Z-fiducial phantoms allow three-dimensional ultrasound probe calibration with a single B-scan. One of the main difficulties in using this phantom is the need for reliable segmentation of the wires in the ultrasound images, which necessitates manual intervention. In this article, we have shown how we can solve this problem by mounting a thin rubber membrane on top of the phantom. The membrane is segmented automatically and the wires can be easily located as they are at known positions relative to the membrane. This enables us to segment the wires automatically at the full PAL frame rate of 25 Hz, to produce calibrations in real-time, while achieving accuracies similar to those reported in the literature. We have also devised a technique to improve the estimation of the elevational offset (calibration parameter) by capturing a few images of the planar membrane. If spatial calibration is known, fully automatic wire segmentation allows the fiducials to be tracked in real-time. This also enables temporal calibration to be performed in real-time as the probe is moved away from the phantom. We have evaluated the performance of our phantom by calibrating a probe at 8 cm and 15 cm depth. The precision of the calibrations are 0.7 mm and 1.2 mm, respectively. The point reconstruction accuracies of fiducial points provided by the same Z-phantom are slightly below 1.5 mm. The point reconstruction accuracies obtained by scanning the end of a wire tip are 2.5 mm and 3.0 mm. These results match the accuracies achieved in the literature. It takes approximately 2 min to set up the experiment, submerge the phantom in the water bath, locate the phantom in space with a pointer and capture six images of the planar membrane. After this, spatial calibration can be performed in less than a second. Temporal calibration can be completed in approximately 3 s.

Calibration of an orientation sensor for freehand 3D ultrasound and its use in a hybrid acquisition system

BACKGROUND

Freehand 3D ultrasound is a powerful imaging modality with many potential applications. However, its reliance on add-on position sensors, which can be expensive, obtrusive and difficult to calibrate, is a major drawback. Alternatively, freehand 3D ultrasound can be acquired without a position sensor using image-based techniques. Sensorless reconstructions exhibit good fine scale detail but are prone to tracking drift, resulting in large scale geometrical distortions.

METHOD

We investigate an alternative position sensor, the Xsens MT9-B, which is relatively unobtrusive but measures orientation only. We describe a straightforward approach to calibrating the sensor, and we measure the calibration precision (by repeated calibrations) and the orientation accuracy (using independent orientation measurements). We introduce algorithms that allow the MT9-B potentially to correct both linear and angular drift in sensorless reconstructions.

RESULTS

The MT9-B can be calibrated to a precision of around 1 degrees . Reconstruction accuracy is also around 1 degrees . The MT9-B was able to eliminate angular drift in sensorless reconstructions, though it had little impact on linear drift. In comparison, six degree-of-freedom drift correction was shown to produce excellent reconstructions.

CONCLUSION

Gold standard freehand 3D ultrasound acquisition requires the synthesis of image-based techniques, for good fine scale detail, and position sensors, for good large scale geometrical accuracy. A hybrid system incorporating the MT9-B offers an attractive compromise between quality and ease of use. The position sensor is unobtrusive and the system is capable of faithful acquisition, with the one exception of linear drift in the elevational direction.

GPU based real-time instrument tracking with three-dimensional ultrasound

Real-time three-dimensional ultrasound enables new intracardiac surgical procedures, but the distorted appearance of instruments in ultrasound poses a challenge to surgeons. This paper presents a detection technique that identifies the position of the instrument within the ultrasound volume. The algorithm uses a form of the generalized Radon transform to search for long straight objects in the ultrasound image, a feature characteristic of instruments and not found in cardiac tissue. When combined with passive markers placed on the instrument shaft, the full position and orientation of the instrument is found in 3D space. This detection technique is amenable to rapid execution on the current generation of personal computer graphics processor units (GPU). Our GPU implementation detected a surgical instrument in 31 ms, sufficient for real-time tracking at the 25 volumes per second rate of the ultrasound machine. A water tank experiment found instrument orientation errors of 1.1 degrees and tip position errors of less than 1.8mm. Finally, an in vivo study demonstrated successful instrument tracking inside a beating porcine heart.

Sensorless reconstruction of unconstrained freehand 3D ultrasound data

Freehand 3D ultrasound can be acquired without a position sensor by finding the separations of pairs of frames using information in the images themselves. Previous work has not considered how to reconstruct entirely freehand data, which can exhibit irregularly spaced frames, intersecting frames, nonmonotonic out-of-plane probe motion and significant in-plane motion. This paper presents reconstruction methods that overcome these limitations and are able to robustly reconstruct unconstrained freehand data. The methods are assessed on freehand data sets and compared with reconstructions obtained with a position sensor.

Tracking a 3-D ultrasound probe with constantly visible fiducials

A new method is presented for tracking a 3-D ultrasound (US) probe in space. The key is to use small fiducials that create point features in the US volume near the probe face and which are connected rigidly to the tracker on the probe. In this way, fiducials appear in every US volume and are used to calculate the position and orientation of the volume with respect to a fixed base. The main novelty is the elimination of a separate calibration device because calibration can be considered to be performed on every volume. After acquisition, the user simply marks the locations of the fiducials in the volume and solves a single equation to convert volume coordinates to the base. The point accuracy of the new method is slightly lower than those of conventional methods mainly because of the suboptimal appearance of the fiducials near the top of the image and little data averaging, but ease of use is improved.