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

Development and validation of a gel wax phantom to evaluate geometric accuracy and measurement of a hyperechoic target diameter in diagnostic ultrasound imaging

Diagnostic ultrasound (US) scanners are generally evaluated using proprietary quality assurance (QA) phantoms, but their prohibitively high cost may prevent organizations to perform the necessary tests. This study aimed to develop a low-cost gel wax phantom with targets to determine the lateral and axial resolution and diameter of a hyperechoic target in an US scanner. The acoustic property (AP) of gel wax, which includes the speed of sound (cus), acoustic impedance (Z), and attenuation coefficient (µ), were determined for multiple transducers operating at 2.25, 5, 10, 15, and 30 MHz. These results were compared to the AP of soft tissue. Two polytetrafluoroethylene (PTFE) rectangular frames with holes separated by 5, 10, and 20 mm were constructed. Nylon filaments and stainless-steel disc (SS disc) (diameter = 16.8 mm) were threaded through the frames and suitably placed in gel wax to obtain orthogonal targets in the phantom. The target dimensions obtained from computerized tomography (CT) and US images of the phantom were compared for phantom validation. The average cus=1431.4 m/s, mass density ρ = 0.87 g/cm3, Z = 1.24 MRayls, and µ ranged from 0.7 to 0.98 dB/cm/MHz for gel wax at 22 °C. The US image measurement exhibited a maximum error in determining the diameter of the SS disc, resulting in a value of 18 mm instead of its actual value of 16.8 mm. The phantom volume decreased by 1.8% in 62 weeks. The present phantom is affordable, stable, customizable, and can be used to evaluate diagnostic US scanners across multiple centers.

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.

Calibration method for a breast intervention robot based on four-dimensional ultrasound image guidance

In breast interventional ultrasound therapy, it is difficult to directly diagnose the location of a tumor in 2-D ultrasound images. To assist surgeons in treatment more intuitively, a four-dimensional ultrasound image-guided breast intervention robot is proposed. The calibration approach of the ultrasonic image for the robot is one of the main contents of the research. This method is based on the establishment of a complete coordinate system conversion model, and it uses the ORB (oriented FAST and rotated BRIEF) feature extraction method to obtain and record the real-time image marker pixel positions, calculate the unknown parameters of the coordinate system conversion matrix, and establish a complete calibration system. This article demonstrates the feasibility of the calibration approach through experiments in our developed US-guided robotic system. Additional experimental and parametrical comparisons of the proposed method with state-of-the-art methods were conducted to thoroughly evaluate the outperformance of the proposed method.

A novel ultrasound probe calibration method for multimodal image guidance of needle placement in cervical cancer brachytherapy

PURPOSE

Interstitial needles placement is a critical component of combined intracavitary/interstitial (IC/IS) brachytherapy (BT). To ensure precise placement of interstitial needles, we proposed a novel ultrasonic (US) probe calibration method to accurately register the US image in the magnetic resonance imaging (MRI) image and provide multimodal image guidance for needle placement.

METHODS

A wire-based calibration phantom combined with the stylus was developed for the calibration of US probe. The calibration phantom helps to quickly align the imaging plane of the US probe with the fiducial points to obtain US images of these points. The coordinates of fiducial points in US images were located automatically by feature extraction algorithms and were further corrected by the proposed correction method. Ingenious structures were designed on both sides of the calibration phantom to accurately obtain the coordinates of the fiducial points relative to the tracking device. Marker validation and pelvic phantom study were performed to evaluate the accuracy of the proposed calibration method.

RESULTS

In the marker validation, the US probe calibration method with corrected transformation achieves a registration accuracy of 0.694 ± 0.014 mm, and the uncorrected one is 0.746 ± 0.018 mm. In the pelvic phantom study, the needle tip difference was 1.096 ± 0.225 mm and trajectory difference was 1.416 ± 0.284 degrees.

CONCLUSION

The proposed US probe calibration method is helpful to achieve more accurate multimodality image guidance for needle placement.

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.

Evaluation of Scoliosis With a Commercially Available Ultrasound System

OBJECTIVES

Currently, radiography with measurement of the Cobb angle is still considered the reference standard for diagnosing scoliosis. However, the ionizing radiation hazard is drawing wide attention. Can 3-dimensional (3D) ultrasound (US) be an alternative modality for diagnosing and monitoring patients with scoliosis? The aim of our study was to assess the reliability and validity of 3D US imaging in the evaluation of scoliosis.

METHODS

A commercially available ultrasound system with a magnetic tracking system was selected for long-distance 3D US imaging. Straight phantoms and curved phantoms were scanned with the imaging system to evaluate the stability of the system for curvature measurements. Eight healthy adult volunteers and 28 patients with scoliosis were recruited for long-distance 3D US imaging. The intraclass correlation coefficient was used to test the reproducibility of the interobserver and intraobserver measurements for both the healthy adults and patients with scoliosis. A linear regression analysis and Bland-Altman plot were used to analyze the correlation and to determine the extent of agreement between the angles measured on US images and the Cobb angles measured on conventional radiographs.

RESULTS

The 28 patients with scoliosis included 10 male and 18 female patients aged 8 to 37 years (mean age ± SD, 17.7 ± 1.4 years; body mass index, <25 kg/m² ). In the phantom study, there was no statistically significant difference between the angles measured by the 3D US imaging system and those measured by an angle gauge (P > 0.05). In the clinical study, there was very good interobserver and intraobserver reliability (intraclass correlation coefficients, >0.90) for the US imaging system, with a high correlation (r² = 0.92) and agreement between the US and radiographic methods.

CONCLUSIONS

The long-distance 3D US imaging system offers a viable modality for diagnosing and monitoring scoliosis without radiation.

Coherent Multi-Transducer Ultrasound Imaging

This work extends the effective aperture size by coherently compounding the received radio frequency data from multiple transducers. As a result, it is possible to obtain an improved image, with enhanced resolution, an extended field of view (FoV), and high-acquisition frame rates. A framework is developed in which an ultrasound imaging system consisting of N synchronized matrix arrays, each with partly shared FoV, take turns to transmit plane waves (PWs). Only one individual transducer transmits at each time while all N transducers simultaneously receive. The subwavelength localization accuracy required to combine information from multiple transducers is achieved without the use of any external tracking device. The method developed in this study is based on the study of the backscattered echoes received by the same transducer and resulting from a targeted scatterer point in the medium insonated by the multiple ultrasound probes of the system. The current transducer locations along with the speed of sound in the medium are deduced by optimizing the cross correlation between these echoes. The method is demonstrated experimentally in 2-D for two linear arrays using point targets and anechoic lesion phantoms. The first demonstration of a free-hand experiment is also shown. Results demonstrate that the coherent multi-transducer ultrasound imaging method has the potential to improve ultrasound image quality, improving resolution, and target detectability. Compared with coherent PW compounding using a single probe, lateral resolution improved from 1.56 to 0.71 mm in the coherent multi-transducer imaging method without acquisition frame rate sacrifice (acquisition frame rate 5350 Hz).

Phantomless Auto-Calibration and Online Calibration Assessment for a Tracked Freehand 2-D Ultrasound Probe

This paper presents a method for automatically calibrating and assessing the calibration quality of an externally tracked 2-D ultrasound (US) probe by scanning arbitrary, natural tissues, as opposed a specialized calibration phantom as is the typical practice. A generative topic model quantifies the posterior probability of calibration parameters conditioned on local 2-D image features arising from a generic underlying substrate. Auto-calibration is achieved by identifying the maximum a-posteriori image-to-probe transform, and calibration quality is assessed online in terms of the posterior probability of the current image-to-probe transform. Both are closely linked to the 3-D point reconstruction error (PRE) in aligning feature observations arising from the same underlying physical structure in different US images. The method is of practical importance in that it operates simply by scanning arbitrary textured echogenic structures, e.g., in-vivo tissues in the context of the US-guided procedures, without requiring specialized calibration procedures or equipment. Observed data take the form of local scale-invariant features that can be extracted and fit to the model in near real-time. Experiments demonstrate the method on a public data set of in vivo human brain scans of 14 unique subjects acquired in the context of neurosurgery. Online calibration assessment can be performed at approximately 3 Hz for the US images of pixels. Auto-calibration achieves an internal mean PRE of 1.2 mm and a discrepancy of [2 mm, 6 mm] in comparison to the calibration via a standard phantom-based method.

A computationally efficient method for hand-eye calibration

Purpose

Surgical robots with cooperative control and semiautonomous features have shown increasing clinical potential, particularly for repetitive tasks under imaging and vision guidance. Effective performance of an autonomous task requires accurate hand–eye calibration so that the transformation between the robot coordinate frame and the camera coordinates is well defined. In practice, due to changes in surgical instruments, online hand–eye calibration must be performed regularly. In order to ensure seamless execution of the surgical procedure without affecting the normal surgical workflow, it is important to derive fast and efficient hand–eye calibration methods.

Methods

We present a computationally efficient iterative method for hand–eye calibration. In this method, dual quaternion is introduced to represent the rigid transformation, and a two-step iterative method is proposed to recover the real and dual parts of the dual quaternion simultaneously, and thus the estimation of rotation and translation of the transformation.

Results

The proposed method was applied to determine the rigid transformation between the stereo laparoscope and the robot manipulator. Promising experimental and simulation results have shown significant convergence speed improvement to 3 iterations from larger than 30 with regard to standard optimization method, which illustrates the effectiveness and efficiency of the proposed method.

Spatial calibration of a 2D/3D ultrasound using a tracked needle

Purpose

Spatial calibration between a 2D/3D ultrasound and a pose tracking system requires a complex and time-consuming procedure. Simplifying this procedure without compromising the calibration accuracy is still a challenging problem.

Method

We propose a new calibration method for both 2D and 3D ultrasound probes that involves scanning an arbitrary region of a tracked needle in different poses. This approach is easier to perform than most alternative methods that require a precise alignment between US scans and a calibration phantom.

Results

Our calibration method provides an average accuracy of 2.49 mm for a 2D US probe with 107 mm scanning depth, and an average accuracy of 2.39 mm for a 3D US with 107 mm scanning depth.

Conclusion

Our method proposes a unified calibration framework for 2D and 3D probes using the same phantom object, work-flow, and algorithm. Our method significantly improves the accuracy of needle-based methods for 2D US probes as well as extends its use for 3D US probes.

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 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.