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Actuator-Assisted Calibration of Freehand 3D Ultrasound System

Actuator-Assisted Calibration of Freehand 3D Ultrasound System Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 9314626, 10 pages https://doi.org/10.1155/2018/9314626 Research Article Terry K. Koo and Nathaniel Silvia Foot Levelers Biomechanics Research Laboratory, New York Chiropractic College, Seneca Falls, NY, USA Correspondence should be addressed to Terry K. Koo; tkoo@nycc.edu Received 3 January 2018; Revised 21 March 2018; Accepted 11 April 2018; Published 2 May 2018 Academic Editor: Vincenzo Positano Copyright © 2018 Terry K. Koo and Nathaniel Silvia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction coordinate system (W), not the image plane with respect to (W), a probe calibration is required to obtain the rigid body transformation from the coordinate system of the ultrasound Freehand three-dimensional (3D) ultrasound is a technique for acquiring 3D ultrasonic data of an anatomical feature of image to that of the probe ( T ) (Figure 1). interest using a conventional two-dimensional (2D) ultra- Probe calibration can be accomplished by scanning an sound scanner. It has been used directly, or registered with object with known geometric dimensions called a phantom. other imaging modalities such as MRI and CT, to provide The principle is to image the phantom, identify its features 3D visualization of the body for clinical volume measure- on the ultrasound images, and optimize the unknown trans- ment [1], analysis of complex geometries [2, 3], biomechan- formation parameters that minimize the residual error ical analysis [4], surgical planning [5, 6], and radiotherapy between the sets of features identified in the images and on planning [7, 8]. Briefly, freehand 3D ultrasound is accom- the phantom. Although several categories of calibration plished by simultaneously acquiring 2D ultrasound images phantoms have been proposed (e.g., Z-fiducial [9, 10] and and tracking the position and orientation of an ultrasound plane [11, 12] phantoms), point-based phantoms are still probe using a mechanical, optical, or magnetic tracking sys- one of the most widely used [13–15], mainly because they tem. Given that the tracking system can only record the posi- are easy to build, accurate, and precise. However, probe cali- tion and orientation of the probe with respect to a world bration using point-based phantoms can be tedious and 2 Journal of Healthcare Engineering reconstruction accuracy, and data acquisition time between Probe (P) the actuator-assisted and freehand cross wire phantom cali- P P T brations. To take advantage of the actuator-assisted calibra- tion setup, we also constructed two phantoms with multiple Image (I) point targets that could greatly simplify the alignment pro- World cess of the point targets on the image plane, yet provide con- (W) sistent collection of multiple target points that cover the Ultrasound pixel entire image FOV in a timely manner. These new calibration W P approaches were also compared with the cross wire phantom v = T · T v W P I· I calibrations in terms of precision, accuracy, and calibration time to evaluate their potential values for routine use. 2. Materials and Methods 2.1. Mathematical Formulation of the Calibration Problem. Figure 1: Principle of freehand 3D ultrasound. Each ultrasound We measured the true coordinates of each point target i pixel of an ultrasound image (v ) can be expressed with respect to (where i = 1,2,3,… , n; n is the number of target points used the world coordinate system (v ) by multiplying two for the calibration) with respect to the phantom coordinate W P W P transformation matrixes ( T and T ): v = T ⋅ T ⋅ v , W I P I P I system [10] using a digitizing probe (North Digital Inc.) with P W where T and T are 4 × 4 transformation matrix relating the I P an accuracy of 0.1 mm in each direction and defined the true image coordinate system to the probe coordinate system and the coordinates (x ⋅ y , z ) as the average of 20 repeated Ph Ph Ph probe coordinate system to the world coordinate system, i i i measurements. Each point target i identified in the image respectively. Although T can be determined from the tracking P coordinate system (x , y , 0) can be mapped to the phantom system, T needs to be obtained through probe calibration. I I i i coordinate system (x ⋅ y , z )by Ph Ph Ph i i i time-consuming. Point-based phantoms can either compose of single or multiple point targets made of bead, pin head, or x s x Ph x I i i intersecting wires. Among them, the single cross wire phan- tom has been commonly used as a reference standard to vali- y s y Ph y I i Ph W P i = T ⋅ T ⋅ T ⋅ , 1 date other calibration methods [12, 16], thanks to its excellent W P I z 0 Ph precision and accuracy. Traditionally, the single cross wire phantom requires an operator to repeatedly image the inter- 1 1 secting point in a freehand fashion [12, 17]. Transformation parameters from the coordinate system of the ultrasound where s and s are scaling factors in millimeters per pixel, x y image to that of the probe are then found iteratively without which can be directly obtained by using the distance mea- knowing the intersecting point locations [12, 18]. However, surement tool provided by the ultrasound machine; this approach requires the point targets to be scanned in mul- Ph W T and T are 4 × 4 transformation matrix relating W i P i tiple viewing angles [12]. Otherwise, the transformation the world coordinate system to the phantom coordinate sys- parameters can be highly unconstrained by the optimization tem and the probe coordinate system to the world coordinate process and likely to be inaccurate [17]. It has also been sug- system, respectively, and are given by the optical tracking sys- gested that a good cross wire phantom calibration requires tem; and T is a transformation matrix relating the image the intersecting point to be imaged in all regions within the coordinate system to probe coordinate system, which is an field of view (FOV) of the image plane [17]. Failure to do so unknown calibration matrix governed by 6 independent may substantially deteriorate the precision and accuracy of parameters (3 rotations and 3 translations). the calibration. It is quite obvious that these “viewing angle” Hence, T can be found by minimizing the residual error and “FOV” requirements make the traditional freehand cross I (D) using nonlinear optimization among the n point tar- wire phantom calibration highly skill dependent, and they gets 1, 2, 3,… , n: may not be easily achieved in a timely manner. The objective of this study was to refine the traditional x s x freehand cross wire phantom calibration method by modify- Ph x I i i ing the mathematical formulation of the calibration problem y s y Ph y I to eliminate the need of imaging the intersecting point at dif- i Ph W P i 〠 − T ⋅ T ⋅ T ⋅ i=1 W P I i i ferent viewing angles and developing an actuator-assisted z 0 Ph approach to facilitate quick and consistent collection of inter- 1 1 secting points spanning the entire image FOV. We hypothe- D = , sized that such refinements would enhance the precision and accuracy of the single cross wire phantom calibration and 2 streamline its implementation. This hypothesis was tested by comparing the calibration reproducibility, point recon- where ⋅ denotes the Euclidean distance between each corre- struction precision, point reconstruction accuracy, distance sponding point pair x ⋅ y , z , x ⋅ y , z . Ph Ph Ph Ph Ph Ph i i i i i i Journal of Healthcare Engineering 3 This mathematical formulation of the calibration prob- Articulated arm with lem allows for the calibration to be conducted with the 7 degrees of freedom probe positioned in one viewing angle only, which is a prerequisite of the actuator-assisted calibration as dis- cussed in the next section. Quick 2.2. Setup for Actuator-Assisted Calibration. The purpose of release lock actuator-assisted calibration was to facilitate imaging of mul- tiple point targets over the entire image region in a systematic Stand and time-efficient way. To accomplish this, a setup that con- sisted of a rigid stand, an articulated arm, a computer- controlled linear actuator, and a probe clamp was constructed Linear to help position and hold the ultrasound probe perpendicular actuator Ultrasound to point target(s) (Figure 2). Specifically, the articulated arm probe (Model 143, Manfrotto, Italy) possessed multiple degrees of Probe freedom joints and a quick release lock to facilitate precise Probe clamp positioning and quick locking of the ultrasound probe. The coordinate articulated arm was rigidly connected to the stand at one systme A phantom end and the body of a linear actuator (T-NA08A50, Zaber submerged Technologies, Canada) at the other end. A probe clamp was Phantom in a water coordinate custom-made to allow for the probe to be mounted with its tank system footprint perpendicular to the actuator shaft. During actuator-assisted calibration, a phantom was Figure 2: The setup for implementing the actuator-assisted first placed in a container that was filled with water at calibration. room temperature as a coupling media (Figure 2). With the shaft of the linear actuator at its fully extended posi- on the ultrasound probe as well as on each phantom to tion, the ultrasound probe was adjusted by unlocking the keep track of the probe and phantom’s pose with respect articular arm until (1) the lowest point of the footprint to the world coordinate system, and a personal computer with a frame grabber and a data acquisition card installed of the ultrasound probe was ~10 mm from the point tar- get(s) of a phantom and (2) the image plane of the ultra- for capturing ultrasound images. Although 3 noncollinear sound probe is perpendicular to the point target(s) of a diodes are sufficient to track the pose of a rigid body, phantom (which was accomplished by aligning the spirit the use of 5 IR diodes increases the accuracy of the pose level on the probe clamp with the spirit level on the phan- estimation because of the inherent averaging of individual IR diode position errors when the corresponding poses are tom base). Given that the linear actuator used in this study has a travel distance of 50 mm, the step (1) determined [20]. Given that the phantom coordinate sys- described above facilitated the point targets to be imaged tem (Ph) of each phantom could be arbitrarily defined over the entire FOV, whereas the step (2) allowed for for the purpose of probe calibration, three of the 5 IR point target(s) identified at one depth level to be imaged diodes were arbitrarily selected to establish a phantom coordinate system (Ph) for each phantom (Figure 2). First, at other depth levels without the need of readjusting the probe orientation. Figure 3 shows images of a phantom an IR diode was selected as the origin. Second, we defined captured by the ultrasound probe following the alignment the x-axis as the unit vector from the origin to the 2nd IR process. In most cases, the alignment process took less diode. Third, a temporary axis was defined as the unit vec- than a minute to accomplish. tor from the origin to the 3rd IR diode. Fourth, z-axis was defined as the cross product of the temporary axis and the 2.3. Implementation of Actuator-Assisted Calibration. In this x-axis. Finally, the y-axis was defined as the cross product study, actuator-assisted calibration was implemented on of the z-axis and the x-axis. A probe coordinate system (P) three point-based phantoms: (1) single cross wire phan- was also established in a similar way by mounting 5 IR diodes tom, (2) original collinear point target phantom, and (3) on the lateral surface of the probe (Figure 2). Thanks to actuator-assisted calibration setup, both of the ultrasound modified collinear point target phantom. To facilitate a direct comparison of the precision and accuracy among probe and the phantom are stationary after alignment pro- phantoms, calibrations of all phantoms were based on 40 cess, and hence ultrasound images and pose data can be point targets using the same freehand 3D ultrasound sys- acquired independently without the need of synchronization. tem [4, 19] with depth and frequency settings of 90 mm and 4 MHz, respectively. The freehand 3D ultrasound sys- 2.3.1. Cross Wire Phantom. The cross wire phantom con- tem used in this study consisted of an ultrasound scanner sisted of two coplanar nylon wires attached at the top of a (Ultramark 400c; ATL Ultrasound Inc., Bothell, WA) with plastic box (100 × 100 × 80 mm) with their intersection (i.e., a curvilinear probe (CLA 3.5/40), an optical tracking sys- the point target) located at the center of the box opening. tem (Optotrak 3020, Northern Digital Inc., Waterloo, During the actuator-assisted calibration, the probe was posi- Canada) with 5 noncoplanar infrared (IR) diodes attached tioned at 6 different depth levels by the linear actuator, each 4 Journal of Healthcare Engineering Figure 3: Ultrasound images of a collinear point target phantom after the one-time alignment process of the point targets. The top left image was captured with the linear actuator fully extended. The arrow indicates the lowest point of the footprint of the ultrasound probe, which is ~10 mm above the point targets (i.e., between the two parallel lines). The probe was retracted at 10 mm increment to cover the entire image field of view at 6 depth levels. Due to the curvilinear nature of the ultrasound probe used in this study, all of the 7 point targets can be clearly visualized at each depth level except for the most superficial level; only 5 screw heads can be visualized. separated by 10 mm. To ensure that the 40 point targets cov- properly positioned perpendicular to the phantom with the ered the entire image region, the intersecting point was point targets at ~40 mm depth, the phantom was carefully imaged at 7 different locations along the lateral dimension adjusted until all 7 target points were clearly seen in the B- mode image. Ultrasound images and pose data of the phan- of an image plane at each depth level, except for the most superficial level. Only 5 locations were imaged at this level tom and probe were then acquired at 6 different depth levels, due to its smaller lateral dimension. each separated by 10 mm. Altogether, 40 point targets were To better understand the potential benefits of actuator- imaged in 6 images (7 point targets at each depth level except based calibration, the ultrasound probe was also calibrated for the most superficial level, where only 5 point targets could with the same cross wire phantom but using a traditional be visualized) (Figure 3). freehand cross wire phantom calibration approach [12]. 2.3.3. Modified Collinear Point Target Phantom. The modified Given that the ultrasound probe cannot be regarded as sta- collinear point target phantom also consisted of 7 collinear tionary during freehand cross wire phantom calibration, screws. However, it was built differently to facilitate alignment images and pose data were synchronized by aligning a 5 V of the image plane with the 7 point targets in a more system- pulse that was sent to both of the ultrasound and Optotrak atic and time-efficient manner. It comprised a base plexiglass computers. In addition, actuator-assisted cross wire phantom plate (152.4 mm × 177.8 mm) with a screw mounted at its cen- calibration was conducted with all target points localized ter, a top plexiglass plate of the same dimension with a central along the center region of the image FOV to explicitly evalu- hole of 2 mm diameter and 6 screws (3 on each side of the cen- ate the effects of point target distribution on calibration accu- tral hole), and they were stacked together as in Figure 4(b). racy and precision. Again, 40 point targets were imaged for This design allowed for the top plate to rotate about the cen- each trial to allow for a direct comparison of the precision tral screw yet maintained the collinearity among the 7 screws, and accuracy with the actuator-based calibration. facilitating independent adjustment of the translational and rotational degrees of freedom during the alignment process 2.3.2. Original Collinear Point Target Phantom. The original of the point targets. We anticipated that this design would collinear point target phantom comprised 7 collinear screws improve the precision and accuracy of the calibration. Like (diameter: 2 mm, interscrew distance: ~15 mm) mounted the original collinear point target phantom, we acquired perpendicular to an aluminum plate with the screw heads ultrasound images and pose data at 6 depth levels. serving as point targets (Figure 4(a)). This arrangement elim- inated the need to move the phantom laterally during a cali- 2.4. Segmentation and Speed Correction. All point targets bration, as the entire lateral dimension of the image plane (x, y) were manually segmented using ImageJ (NIH, was well covered by the point targets. The alignment process Bethesda) by a research assistant, who was blinded to the cal- ibration results. The coordinates of each point target were of the point targets was as follows: after the probe was Journal of Healthcare Engineering 5 (a) (b) Figure 4: (a) The original collinear point target phantom; (b) the modified collinear point target phantom. The top plate of the modified collinear point target phantom is slightly rotated about the central screw to better illustrate the phantom design. also corrected for speed of sound distortion (δx, δy) based Data acquisition time was recorded for each calibration trial. The probe alignment process was performed for each on the ray model proposed by Goldstein [21] such that the corrected coordinates of each point target became (x + δx, actuator-assisted calibration trial to allow for a more realistic y − δy). Specifically, we measured water temperature after evaluation of the actuator-assisted approaches. each calibration trial and plugged it into a fifth-order poly- For each calibration trial, we optimized 6 independent nomial equation [22] to calculate the actual speed of sound calibration parameters (α, β, γ, x, y, and z)of T . Although (c ) for each calibration trial. Assuming the footprint of the probe coordinate system could be arbitrarily defined for the curvilinear probe is a circular arc, we calculated its the purpose of probe calibration, we strategically attached radius of curvature (R) and origin location. This allowed the 5 IR diodes and defined the probe coordinate system such us to calculate the shift in lateral (δx) and axial (δy) direc- that its x-, y-, z-axis approximated the elevation, lateral, and tions as follows: axial directions of the ultrasound beam, respectively, to facil- itate our interpretation of the sources of uncertainty for c different calibration approaches. Hence, (α, β, and γ) could δx = D − R 1 − sin θ, im be interpreted as the Euler angles in z-y-x (or axial-lateral- cal elevation) sequence that specified the orientation of the image coordinate system with respect to the probe coordinate δy = D − R 1 − cos θ, im system, and (x, y, and z) could be interpreted as the transla- cal tions along the elevation, lateral, and axial directions of the where D is the distance between the origin and the seg- ultrasound beam, respectively, that located the origin of the im mented point target within the image plane, c = 1540 m/s image coordinate system with respect to the probe coordinate cal is the assumed speed of sound used by the ultrasound system. To this end, we reported the standard deviation of machine, and θ is the angle between a line from the origin each calibration parameter among the 10 calibration trials to the segmented point target and a line along the axial direc- for each calibration approach. tion. θ is positive if the segmented point target is located at the left half of the image and vice versa. 2.5.1. Precision. Precision refers to how close measurements 2.5. Performance Evaluation. Altogether, 5 calibration are to each other. In this study, we quantified precision using approaches were compared in this study: (1) freehand cross two widely used parameters: calibration reproducibility [12] wire phantom calibration, (2) actuator-assisted cross wire and point reconstruction precision [12]. To quantify the cal- phantom calibration, (3) actuator-assisted cross wire phan- ibration reproducibility, we transformed the 4 corners and tom calibration based on point targets at the central region, the middle of the image [23] from the image to the probe space using the calibration parameters of each of the 10 cali- (4) actuator-assisted calibration using an original collinear point target phantom, and (5) actuator-assisted calibration bration trials, calculated the Euclidean distance between all using a modified collinear point target phantom. Ten calibra- possible pairs of the 10 possible calibration trials (i.e., tion trials were conducted for each calibration approach. C = 45 pairs) for each point, and reported the mean, 10 2 6 Journal of Healthcare Engineering standard deviation, maximum, and minimum of the pooled true locations after optimization. It provides an indication of data of the 5 points (i.e., 225 observations). To calculate point self-consistency of the calibration. It was noted that the free- reconstruction precision, we fixed a different point phantom hand cross wire phantom calibration resulted in the largest to the world space. This point phantom consisted of a plastic residual error (1.35 ± 0.21 mm), followed by the actuator- base with a single pin, 2 mm in diameter, affixed to the base. assisted cross wire phantom calibration (0.80 ± 0.11 mm), We imaged the pin head 50 times at different viewing angles and the actuator-assisted cross wire phantom calibration and locations within the entire image FOV and derived the based on point targets at the central region had the smallest world coordinates of the pin head from different views and residual error (0.40 ± 0.09 mm). The residual errors of both calibration matrix combinations. From there, we further cal- original (0.55 ± 0.04 mm) and modified (0.47 ± 0.08 mm) col- culated the Euclidean distance between all possible pairs of linear point target phantom calibrations were also very small. views (i.e., Tables 1 and 2 summarize the calibration reproducibility C = 1225 pairs) for each calibration parameter 50 2 set and reported the mean, standard deviation, maximum, and point reconstruction precision, respectively, for each cal- and minimum of the pooled data of the 10 calibrations (i.e., ibration approach. We found that the actuator-assisted cross 12,250 observations). This was done for each of the 5 calibra- wire phantom calibration was the most precise among all cal- tion approaches. Detailed mathematical formulations of both ibration approaches. However, if point targets were only precision parameters can be found elsewhere [12]. imaged at the central region of the image FOV, its precision deteriorated tremendously. In addition, modified collinear 2.5.2. Accuracy. Accuracy refers to how close measurements point target phantom appears to be slightly better than the are to the “true” value. For each calibration approach, we original collinear point target phantom in terms of both quantified reconstruction accuracy using both point-based precision measures. and distance-based measures. For the point reconstruction Tables 3 and 4 summarize the point and distance accuracy [24], we compared the world coordinates of the reconstruction accuracy of each calibration approach, pin head derived from each view and calibration matrix com- respectively. As expected, the accuracy of the actuator- bination (obtained from the “point reconstruction precision” assisted cross wire phantom calibration was poor if the experiment described above) with the true world coordinates point targets were imaged at the central region of the (measured by the digitizing probe based on the average of 20 image FOV only. All other calibration approaches appear measurements) and reported their differences in terms of to have excellent but similar accuracy. mean, standard deviation, maximum, and minimum among To help elucidate the sources of uncertainty for each 500 observations (i.e., 50 views × 10 calibration trials). An calibration approach, standard deviations of the translational additional validation experiment was conducted using a (x, y, and z) and rotational calibration parameters (α, β, and “two-point” phantom (i.e., a plastic base with two pins, γ) for each calibration approach are also plotted as separate 2 mm in diameter, affixed to the base) to quantify distance stacked columns (Figure 5). reconstruction accuracy [10, 12, 18]. This involved (1) digi- Table 5 summarizes the data acquisition time for each tizing each point target 20 times to calculate the true 3D dis- calibration approach. Results revealed that actuator-assisted tance between the two point targets, (2) imaging each point calibration was particularly time-efficient if it was imple- target 50 times at random viewing angles and locations that mented with collinear point target phantoms. However, sim- covered the entire image FOV in a qualitative manner, (3) ilar data acquisition time was recorded for both freehand and deriving the “imaged” 3D distance between the two point tar- actuator-assisted cross wire phantom calibration approaches. gets based on each image pair (50 × 50 = 2500 image pairs) and calibration matrix (10 calibration trials) combinations, 4. Discussion and (4) calculating the difference between the true and imaged 3D distances in terms of mean, standard deviation, Our accuracy and precision data (Tables 1–4) compared maximum, and minimum among 25,000 observations. favorably with other calibration methods reported in the lit- erature [17, 25]. However, because of difference in the quality 2.5.3. Statistical Analysis. For each parameter (i.e., calibration of ultrasound system, probe frequency and configuration, reproducibility, point reconstruction precision, point recon- depth settings, number of target points, accuracy of the struction accuracy, distance reconstruction accuracy, and data tracking system and segmentation, and so on, accuracy and acquisition time), one-way analysis of variance (ANOVA) precision data must be interpreted with extreme caution. was employed to test whether there was a significant differ- We overcame this difficulty by using the traditional freehand ence among the 5 calibration approaches. Post hoc compar- cross wire phantom calibration as a reference standard in isons were based on the Scheffe’s method. All statistical this study. Among the four calibration approaches tested tests were done using SPSS statistical package version 24 in this study (i.e., freehand cross wire phantom calibration, (SPSS, Chicago, IL). A confidence level of 0.05 was chosen actuator-assisted cross wire phantom calibration, actuator- for all analyses. assisted collinear point target phantom calibration, and actuator-assisted modified collinear point target phantom calibration), the actuator-assisted single cross wire phantom 3. Results calibration significantly outperformed the other calibration Residual error indicates the proximity of the locations of the approaches in terms of calibration reproducibility (Table 1) 40 point targets used for each calibration with respect to their and appeared to perform slightly better in terms of point Journal of Healthcare Engineering 7 Table 1: Comparison of calibration reproducibility among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) ∗ # 0.84 (0.57) Mean (SD) 1.50 (1.08) 1.72 (1.20) 1.50 (0.95) 4.91 (3.99) Maximum 5.29 2.85 5.10 4.99 15.94 Minimum 0.043 0.042 0.13 0.077 0.14 For each approach, calibration reproducibility was calculated from 225 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that calibration reproducibility of the actuator-assisted cross wire phantom calibration was significantly better than that of the traditional freehand cross wire phantom calibration (p =0 015). However, if actuator-assisted cross wire phantom calibration was only focused on the central region, it was significantly poorer than the traditional freehand cross wire phantom calibration (p <0 0001). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 2: Comparison of point reconstruction precision among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) Mean (SD) 1.69 (1.04) 1.44 (0.83) 1.68 (1.13) 1.49 (0.92) 2.86 (2.46) Maximum 6.03 4.63 7.85 5.91 17.38 Minimum 0.035 0.045 0.037 0.046 0.039 For each approach, point reconstruction precision was calculated from 12,250 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, point reconstruction precision was significantly poorer than the traditional freehand cross wire phantom calibration (p =0 009). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 3: Comparison of point reconstruction accuracy among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) 2.61 (1.59) Mean (SD) 1.44 (0.82) 1.33 (0.74) 1.65 (0.80) 1.35 (0.75) Maximum 3.84 3.64 4.59 4.17 9.89 Minimum 0.14 0.11 0.21 0.12 0.32 For each approach, point reconstruction precision was calculated from 500 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, point reconstruction accuracy was significantly poorer than the traditional freehand cross wire phantom calibration (p <0 0001). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 4: Comparison of distance reconstruction accuracy among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) Mean (SD) 0.19 (0.47) 0.19 (0.46) 0.21 (0.48) 0.21 (0.48) 0.244 (0.74) Maximum 1.88 1.79 1.90 1.82 4.70 Minimum −1.62 −1.64 −1.61 −1.56 −2.37 For each approach, point reconstruction precision was calculated from 25,000 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, distance reconstruction accuracy was significantly poorer than the traditional freehand cross wire phantom calibration (p =0 024). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. reconstruction precision and accuracy (Tables 2 and 3) but parameters, but point reconstruction precision, point recon- similar to the other calibration approaches in terms distance struction accuracy, and distance reconstruction accuracy reconstruction accuracy (Table 4). Figure 5 further revealed depend on both the calibration parameters and errors associ- that actuator-assisted single cross wire phantom calibra- ated with reconstruction (e.g., segmentation and tracking tion substantially improved the consistency of both trans- errors). That may explain why point reconstruction preci- lational and rotational calibration parameters, especially sion, point reconstruction accuracy, and distance reconstruc- the translational parameters. It is worth noting that cali- tion accuracy were less distinctive between calibration approaches. Nonetheless, one could comfortably conclude bration reproducibility depends only on the calibration 8 Journal of Healthcare Engineering Variation of translational calibration parameters 1.6 Freehand Actuator assisted 1.4 1.2 0.8 0.6 0.4 0.2 Cross wire Cross wire Collinear point Modified Cross wire targets collinear point (central region targets only) Elevation Lateral Axial (a) Variation of rotational calibration parameters Freehand Actuator assisted Cross wire Cross wire Collinear point Modified Cross wire targets collinear point (central region targets only) Alpha Beta Gamma (b) Figure 5: Variation of (a) translational and (b) rotational calibration parameters among the 5 calibration approaches evaluated in this study. Table 5: Comparison of data acquisition time among calibration approaches. Actuator assisted cross Actuator assisted collinear Actuator assisted modified Freehand cross wire wire point targets collinear point targets ∗ ∗ Mean (SD) (minutes) 26.2 (5.1) 26.0 (4.0) 12.8 (3.4) 11.1 (3.7) For each approach, mean (SD) was based on 10 calibration trials. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that data acquisition time for both actuator-based collinear point targets and modified collinear point target phantom calibrations was significantly shorter than that for the traditional freehand cross wire phantom calibration (p <0 0001 for each paired comparison). There was no significant difference in data acquisition time between freehand and actuator-assisted cross wire phantom calibration. that the overall performance of the actuator-assisted cross resulting in tremendous deterioration of precision (Tables 1 wire phantom calibration is the best among all calibration and 2) and accuracy (Tables 3 and 4). approaches tested in this study. We successfully modified the mathematical formulation It has been suggested that probe calibration using point- of the calibration problem to eliminate the need of imaging based phantom should ensure that the point targets be the point targets at different viewing angles. Although this imaged in all regions within the FOV [17]. The results of this modification would benefit the traditional freehand cross study not only confirmed this notion but also elucidated the wire phantom calibration, it offers additional benefits to the reason behind that. We demonstrated that if the point targets actuator-assisted cross wire phantom calibration. First, with were only imaged at the central region of the image FOV dur- the probe held by a probe clamp instead of by hand, the inter- ing cross wire phantom calibration, even though the residual secting points can be more precisely located within the ultra- error of the calibration was among the smallest (likely due sound midplane (reflected by a smaller variation of the to better image quality at the center of the FOV), the rota- translational calibration parameter along the elevation direc- tional calibration parameters (especially rotation about the tion (Figure 5(a))). Second, given that both of the probe and axial direction) became highly unconstrained (Figure 5(b)), the phantom are stationary during imaging, there is no need Standard deviation (mm) Standard deviation (Deg) Journal of Healthcare Engineering 9 precision or accuracy, and hence it should not be directly to synchronize the pose data with the ultrasound images. Third, with the ultrasound probe connected to a linear actu- compared between calibration approaches. ator in the actuator-based calibration, we can easily fulfill the The actuator-assisted calibration approach developed in this study is not without limitation. First, due to the fact that FOV requirement by systematically adjusting the actuator’s positions to cover the entire FOV of ultrasound image. our current setup is mainly composed of metal parts (e.g., lin- In this study, we developed 2 phantoms with collinear ear actuator, probe clamp, stand, and articulated arm), the point targets to take advantage of the actuator-assisted calibra- optical tracking system may not be replaced by magnetic tion setup. Like the cross wire phantom, phantoms with collin- tracking device. This makes our current setup less portable. Further development should focus on replacing the metal ear point targets can be easily constructed in a nonengineering setting. Our results revealed that their precision and accuracy components by plastic components. Second, unlike the tradi- were comparable to those of the traditional freehand cross tional approach, our approach requires the use of specific wire phantom calibration yet significantly reduced the calibra- components such as digitizing pointer and linear actuator, tion time from 26.2 minutes to 11.1 minutes. Based on the val- which may not be commonly found in some scenarios, especially in clinical settings. Third, we only evaluated our idation data of the original collinear point target phantom, we had already identified that the rotational component about the actuator-assisted calibration approach on 3 point-based axial direction and the translational component along the phantoms; its applicability to other point-based phantoms elevation direction were the main sources of uncertainty is largely unknown. It will be a topic of future study. (Figure 5). In fact, these components are primarily governed by the alignment process of the point targets. Hence, we 5. Conclusion intended to develop the modified collinear point target phan- In conclusion, we successfully developed an actuator-assisted tom to improve the alignment process of the point targets. As approach to make the freehand 3D ultrasound calibration expected, the new alignment mechanism improved the rota- less skill dependent, applied it to a single cross wire phantom tional precision about the axial direction (Figure 5(b)), but and two collinear point targets phantoms, and evaluated their surprisingly, it degraded the translational precision along the precision and accuracy by comparing with the traditional elevation direction (Figure 5(a)). This is likely because the freehand cross wire phantom calibration approach. Results modified collinear point target phantom only relied on the demonstrated that the actuator-assisted single cross wire central screw head to guide the translational alignment phantom calibration significantly improved the calibration whereas the original collinear point target phantom used all reproducibility and offered similar point reconstruction pre- the 7 screw heads. Nonetheless, side-by-side comparison of cision, point reconstruction accuracy, distance reconstruc- each precision (Tables 1 and 2) and accuracy (Tables 3 and tion accuracy, and data acquisition time with respect to the 4) parameter as well as the data acquisition time revealed that freehand cross wire phantom calibration. On the other hand, the modified collinear point target phantom appears to be the actuator-assisted modified collinear point target phan- slightly better than the original collinear point target phantom. tom calibration was found to have similar precision and Due to differences in phantom design, the implementa- accuracy when compared to the freehand cross wire phan- tion of the actuator-assisted calibration requires repeated tom calibration, but it reduced the data acquisition time by alignment of each of the 40 point targets with the image plane 57%. It appears that both actuator-assisted approaches are for the single cross wire phantom, whereas the collinear point viable options for freehand 3D ultrasound calibration. target phantoms only require one alignment for all the 40 point targets. In the first glance, one may think that collinear Conflicts of Interest point target phantoms are more attractive choices for the implementation of actuator-assisted calibration. However, The authors declare that there is no conflict of interest the “single” alignment approach of collinear point target regarding the publication of this paper. phantoms could introduce a systematic error to all the 40 point targets. Given that the amplitude and direction of this Acknowledgments systematic error may vary substantially among calibration trials (due to the subjective nature of visual alignment), its The authors would like to thank Amy Lin, Darren Koo, precision is likely to be compromised. Conversely, the and Preya Patel for their assistance in data collection. This “repeated” alignment requirement of the single cross wire work was supported by an intramural fund of New York phantom would lead to a random error to each point target, Chiropractic College. and hence the calibration should be less sensitive to point tar- get alignment error. 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Actuator-Assisted Calibration of Freehand 3D Ultrasound System

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Hindawi Publishing Corporation
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Copyright © 2018 Terry K. Koo and Nathaniel Silvia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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2040-2295
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2040-2309
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10.1155/2018/9314626
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Abstract

Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 9314626, 10 pages https://doi.org/10.1155/2018/9314626 Research Article Terry K. Koo and Nathaniel Silvia Foot Levelers Biomechanics Research Laboratory, New York Chiropractic College, Seneca Falls, NY, USA Correspondence should be addressed to Terry K. Koo; tkoo@nycc.edu Received 3 January 2018; Revised 21 March 2018; Accepted 11 April 2018; Published 2 May 2018 Academic Editor: Vincenzo Positano Copyright © 2018 Terry K. Koo and Nathaniel Silvia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction coordinate system (W), not the image plane with respect to (W), a probe calibration is required to obtain the rigid body transformation from the coordinate system of the ultrasound Freehand three-dimensional (3D) ultrasound is a technique for acquiring 3D ultrasonic data of an anatomical feature of image to that of the probe ( T ) (Figure 1). interest using a conventional two-dimensional (2D) ultra- Probe calibration can be accomplished by scanning an sound scanner. It has been used directly, or registered with object with known geometric dimensions called a phantom. other imaging modalities such as MRI and CT, to provide The principle is to image the phantom, identify its features 3D visualization of the body for clinical volume measure- on the ultrasound images, and optimize the unknown trans- ment [1], analysis of complex geometries [2, 3], biomechan- formation parameters that minimize the residual error ical analysis [4], surgical planning [5, 6], and radiotherapy between the sets of features identified in the images and on planning [7, 8]. Briefly, freehand 3D ultrasound is accom- the phantom. Although several categories of calibration plished by simultaneously acquiring 2D ultrasound images phantoms have been proposed (e.g., Z-fiducial [9, 10] and and tracking the position and orientation of an ultrasound plane [11, 12] phantoms), point-based phantoms are still probe using a mechanical, optical, or magnetic tracking sys- one of the most widely used [13–15], mainly because they tem. Given that the tracking system can only record the posi- are easy to build, accurate, and precise. However, probe cali- tion and orientation of the probe with respect to a world bration using point-based phantoms can be tedious and 2 Journal of Healthcare Engineering reconstruction accuracy, and data acquisition time between Probe (P) the actuator-assisted and freehand cross wire phantom cali- P P T brations. To take advantage of the actuator-assisted calibra- tion setup, we also constructed two phantoms with multiple Image (I) point targets that could greatly simplify the alignment pro- World cess of the point targets on the image plane, yet provide con- (W) sistent collection of multiple target points that cover the Ultrasound pixel entire image FOV in a timely manner. These new calibration W P approaches were also compared with the cross wire phantom v = T · T v W P I· I calibrations in terms of precision, accuracy, and calibration time to evaluate their potential values for routine use. 2. Materials and Methods 2.1. Mathematical Formulation of the Calibration Problem. Figure 1: Principle of freehand 3D ultrasound. Each ultrasound We measured the true coordinates of each point target i pixel of an ultrasound image (v ) can be expressed with respect to (where i = 1,2,3,… , n; n is the number of target points used the world coordinate system (v ) by multiplying two for the calibration) with respect to the phantom coordinate W P W P transformation matrixes ( T and T ): v = T ⋅ T ⋅ v , W I P I P I system [10] using a digitizing probe (North Digital Inc.) with P W where T and T are 4 × 4 transformation matrix relating the I P an accuracy of 0.1 mm in each direction and defined the true image coordinate system to the probe coordinate system and the coordinates (x ⋅ y , z ) as the average of 20 repeated Ph Ph Ph probe coordinate system to the world coordinate system, i i i measurements. Each point target i identified in the image respectively. Although T can be determined from the tracking P coordinate system (x , y , 0) can be mapped to the phantom system, T needs to be obtained through probe calibration. I I i i coordinate system (x ⋅ y , z )by Ph Ph Ph i i i time-consuming. Point-based phantoms can either compose of single or multiple point targets made of bead, pin head, or x s x Ph x I i i intersecting wires. Among them, the single cross wire phan- tom has been commonly used as a reference standard to vali- y s y Ph y I i Ph W P i = T ⋅ T ⋅ T ⋅ , 1 date other calibration methods [12, 16], thanks to its excellent W P I z 0 Ph precision and accuracy. Traditionally, the single cross wire phantom requires an operator to repeatedly image the inter- 1 1 secting point in a freehand fashion [12, 17]. Transformation parameters from the coordinate system of the ultrasound where s and s are scaling factors in millimeters per pixel, x y image to that of the probe are then found iteratively without which can be directly obtained by using the distance mea- knowing the intersecting point locations [12, 18]. However, surement tool provided by the ultrasound machine; this approach requires the point targets to be scanned in mul- Ph W T and T are 4 × 4 transformation matrix relating W i P i tiple viewing angles [12]. Otherwise, the transformation the world coordinate system to the phantom coordinate sys- parameters can be highly unconstrained by the optimization tem and the probe coordinate system to the world coordinate process and likely to be inaccurate [17]. It has also been sug- system, respectively, and are given by the optical tracking sys- gested that a good cross wire phantom calibration requires tem; and T is a transformation matrix relating the image the intersecting point to be imaged in all regions within the coordinate system to probe coordinate system, which is an field of view (FOV) of the image plane [17]. Failure to do so unknown calibration matrix governed by 6 independent may substantially deteriorate the precision and accuracy of parameters (3 rotations and 3 translations). the calibration. It is quite obvious that these “viewing angle” Hence, T can be found by minimizing the residual error and “FOV” requirements make the traditional freehand cross I (D) using nonlinear optimization among the n point tar- wire phantom calibration highly skill dependent, and they gets 1, 2, 3,… , n: may not be easily achieved in a timely manner. The objective of this study was to refine the traditional x s x freehand cross wire phantom calibration method by modify- Ph x I i i ing the mathematical formulation of the calibration problem y s y Ph y I to eliminate the need of imaging the intersecting point at dif- i Ph W P i 〠 − T ⋅ T ⋅ T ⋅ i=1 W P I i i ferent viewing angles and developing an actuator-assisted z 0 Ph approach to facilitate quick and consistent collection of inter- 1 1 secting points spanning the entire image FOV. We hypothe- D = , sized that such refinements would enhance the precision and accuracy of the single cross wire phantom calibration and 2 streamline its implementation. This hypothesis was tested by comparing the calibration reproducibility, point recon- where ⋅ denotes the Euclidean distance between each corre- struction precision, point reconstruction accuracy, distance sponding point pair x ⋅ y , z , x ⋅ y , z . Ph Ph Ph Ph Ph Ph i i i i i i Journal of Healthcare Engineering 3 This mathematical formulation of the calibration prob- Articulated arm with lem allows for the calibration to be conducted with the 7 degrees of freedom probe positioned in one viewing angle only, which is a prerequisite of the actuator-assisted calibration as dis- cussed in the next section. Quick 2.2. Setup for Actuator-Assisted Calibration. The purpose of release lock actuator-assisted calibration was to facilitate imaging of mul- tiple point targets over the entire image region in a systematic Stand and time-efficient way. To accomplish this, a setup that con- sisted of a rigid stand, an articulated arm, a computer- controlled linear actuator, and a probe clamp was constructed Linear to help position and hold the ultrasound probe perpendicular actuator Ultrasound to point target(s) (Figure 2). Specifically, the articulated arm probe (Model 143, Manfrotto, Italy) possessed multiple degrees of Probe freedom joints and a quick release lock to facilitate precise Probe clamp positioning and quick locking of the ultrasound probe. The coordinate articulated arm was rigidly connected to the stand at one systme A phantom end and the body of a linear actuator (T-NA08A50, Zaber submerged Technologies, Canada) at the other end. A probe clamp was Phantom in a water coordinate custom-made to allow for the probe to be mounted with its tank system footprint perpendicular to the actuator shaft. During actuator-assisted calibration, a phantom was Figure 2: The setup for implementing the actuator-assisted first placed in a container that was filled with water at calibration. room temperature as a coupling media (Figure 2). With the shaft of the linear actuator at its fully extended posi- on the ultrasound probe as well as on each phantom to tion, the ultrasound probe was adjusted by unlocking the keep track of the probe and phantom’s pose with respect articular arm until (1) the lowest point of the footprint to the world coordinate system, and a personal computer with a frame grabber and a data acquisition card installed of the ultrasound probe was ~10 mm from the point tar- get(s) of a phantom and (2) the image plane of the ultra- for capturing ultrasound images. Although 3 noncollinear sound probe is perpendicular to the point target(s) of a diodes are sufficient to track the pose of a rigid body, phantom (which was accomplished by aligning the spirit the use of 5 IR diodes increases the accuracy of the pose level on the probe clamp with the spirit level on the phan- estimation because of the inherent averaging of individual IR diode position errors when the corresponding poses are tom base). Given that the linear actuator used in this study has a travel distance of 50 mm, the step (1) determined [20]. Given that the phantom coordinate sys- described above facilitated the point targets to be imaged tem (Ph) of each phantom could be arbitrarily defined over the entire FOV, whereas the step (2) allowed for for the purpose of probe calibration, three of the 5 IR point target(s) identified at one depth level to be imaged diodes were arbitrarily selected to establish a phantom coordinate system (Ph) for each phantom (Figure 2). First, at other depth levels without the need of readjusting the probe orientation. Figure 3 shows images of a phantom an IR diode was selected as the origin. Second, we defined captured by the ultrasound probe following the alignment the x-axis as the unit vector from the origin to the 2nd IR process. In most cases, the alignment process took less diode. Third, a temporary axis was defined as the unit vec- than a minute to accomplish. tor from the origin to the 3rd IR diode. Fourth, z-axis was defined as the cross product of the temporary axis and the 2.3. Implementation of Actuator-Assisted Calibration. In this x-axis. Finally, the y-axis was defined as the cross product study, actuator-assisted calibration was implemented on of the z-axis and the x-axis. A probe coordinate system (P) three point-based phantoms: (1) single cross wire phan- was also established in a similar way by mounting 5 IR diodes tom, (2) original collinear point target phantom, and (3) on the lateral surface of the probe (Figure 2). Thanks to actuator-assisted calibration setup, both of the ultrasound modified collinear point target phantom. To facilitate a direct comparison of the precision and accuracy among probe and the phantom are stationary after alignment pro- phantoms, calibrations of all phantoms were based on 40 cess, and hence ultrasound images and pose data can be point targets using the same freehand 3D ultrasound sys- acquired independently without the need of synchronization. tem [4, 19] with depth and frequency settings of 90 mm and 4 MHz, respectively. The freehand 3D ultrasound sys- 2.3.1. Cross Wire Phantom. The cross wire phantom con- tem used in this study consisted of an ultrasound scanner sisted of two coplanar nylon wires attached at the top of a (Ultramark 400c; ATL Ultrasound Inc., Bothell, WA) with plastic box (100 × 100 × 80 mm) with their intersection (i.e., a curvilinear probe (CLA 3.5/40), an optical tracking sys- the point target) located at the center of the box opening. tem (Optotrak 3020, Northern Digital Inc., Waterloo, During the actuator-assisted calibration, the probe was posi- Canada) with 5 noncoplanar infrared (IR) diodes attached tioned at 6 different depth levels by the linear actuator, each 4 Journal of Healthcare Engineering Figure 3: Ultrasound images of a collinear point target phantom after the one-time alignment process of the point targets. The top left image was captured with the linear actuator fully extended. The arrow indicates the lowest point of the footprint of the ultrasound probe, which is ~10 mm above the point targets (i.e., between the two parallel lines). The probe was retracted at 10 mm increment to cover the entire image field of view at 6 depth levels. Due to the curvilinear nature of the ultrasound probe used in this study, all of the 7 point targets can be clearly visualized at each depth level except for the most superficial level; only 5 screw heads can be visualized. separated by 10 mm. To ensure that the 40 point targets cov- properly positioned perpendicular to the phantom with the ered the entire image region, the intersecting point was point targets at ~40 mm depth, the phantom was carefully imaged at 7 different locations along the lateral dimension adjusted until all 7 target points were clearly seen in the B- mode image. Ultrasound images and pose data of the phan- of an image plane at each depth level, except for the most superficial level. Only 5 locations were imaged at this level tom and probe were then acquired at 6 different depth levels, due to its smaller lateral dimension. each separated by 10 mm. Altogether, 40 point targets were To better understand the potential benefits of actuator- imaged in 6 images (7 point targets at each depth level except based calibration, the ultrasound probe was also calibrated for the most superficial level, where only 5 point targets could with the same cross wire phantom but using a traditional be visualized) (Figure 3). freehand cross wire phantom calibration approach [12]. 2.3.3. Modified Collinear Point Target Phantom. The modified Given that the ultrasound probe cannot be regarded as sta- collinear point target phantom also consisted of 7 collinear tionary during freehand cross wire phantom calibration, screws. However, it was built differently to facilitate alignment images and pose data were synchronized by aligning a 5 V of the image plane with the 7 point targets in a more system- pulse that was sent to both of the ultrasound and Optotrak atic and time-efficient manner. It comprised a base plexiglass computers. In addition, actuator-assisted cross wire phantom plate (152.4 mm × 177.8 mm) with a screw mounted at its cen- calibration was conducted with all target points localized ter, a top plexiglass plate of the same dimension with a central along the center region of the image FOV to explicitly evalu- hole of 2 mm diameter and 6 screws (3 on each side of the cen- ate the effects of point target distribution on calibration accu- tral hole), and they were stacked together as in Figure 4(b). racy and precision. Again, 40 point targets were imaged for This design allowed for the top plate to rotate about the cen- each trial to allow for a direct comparison of the precision tral screw yet maintained the collinearity among the 7 screws, and accuracy with the actuator-based calibration. facilitating independent adjustment of the translational and rotational degrees of freedom during the alignment process 2.3.2. Original Collinear Point Target Phantom. The original of the point targets. We anticipated that this design would collinear point target phantom comprised 7 collinear screws improve the precision and accuracy of the calibration. Like (diameter: 2 mm, interscrew distance: ~15 mm) mounted the original collinear point target phantom, we acquired perpendicular to an aluminum plate with the screw heads ultrasound images and pose data at 6 depth levels. serving as point targets (Figure 4(a)). This arrangement elim- inated the need to move the phantom laterally during a cali- 2.4. Segmentation and Speed Correction. All point targets bration, as the entire lateral dimension of the image plane (x, y) were manually segmented using ImageJ (NIH, was well covered by the point targets. The alignment process Bethesda) by a research assistant, who was blinded to the cal- ibration results. The coordinates of each point target were of the point targets was as follows: after the probe was Journal of Healthcare Engineering 5 (a) (b) Figure 4: (a) The original collinear point target phantom; (b) the modified collinear point target phantom. The top plate of the modified collinear point target phantom is slightly rotated about the central screw to better illustrate the phantom design. also corrected for speed of sound distortion (δx, δy) based Data acquisition time was recorded for each calibration trial. The probe alignment process was performed for each on the ray model proposed by Goldstein [21] such that the corrected coordinates of each point target became (x + δx, actuator-assisted calibration trial to allow for a more realistic y − δy). Specifically, we measured water temperature after evaluation of the actuator-assisted approaches. each calibration trial and plugged it into a fifth-order poly- For each calibration trial, we optimized 6 independent nomial equation [22] to calculate the actual speed of sound calibration parameters (α, β, γ, x, y, and z)of T . Although (c ) for each calibration trial. Assuming the footprint of the probe coordinate system could be arbitrarily defined for the curvilinear probe is a circular arc, we calculated its the purpose of probe calibration, we strategically attached radius of curvature (R) and origin location. This allowed the 5 IR diodes and defined the probe coordinate system such us to calculate the shift in lateral (δx) and axial (δy) direc- that its x-, y-, z-axis approximated the elevation, lateral, and tions as follows: axial directions of the ultrasound beam, respectively, to facil- itate our interpretation of the sources of uncertainty for c different calibration approaches. Hence, (α, β, and γ) could δx = D − R 1 − sin θ, im be interpreted as the Euler angles in z-y-x (or axial-lateral- cal elevation) sequence that specified the orientation of the image coordinate system with respect to the probe coordinate δy = D − R 1 − cos θ, im system, and (x, y, and z) could be interpreted as the transla- cal tions along the elevation, lateral, and axial directions of the where D is the distance between the origin and the seg- ultrasound beam, respectively, that located the origin of the im mented point target within the image plane, c = 1540 m/s image coordinate system with respect to the probe coordinate cal is the assumed speed of sound used by the ultrasound system. To this end, we reported the standard deviation of machine, and θ is the angle between a line from the origin each calibration parameter among the 10 calibration trials to the segmented point target and a line along the axial direc- for each calibration approach. tion. θ is positive if the segmented point target is located at the left half of the image and vice versa. 2.5.1. Precision. Precision refers to how close measurements 2.5. Performance Evaluation. Altogether, 5 calibration are to each other. In this study, we quantified precision using approaches were compared in this study: (1) freehand cross two widely used parameters: calibration reproducibility [12] wire phantom calibration, (2) actuator-assisted cross wire and point reconstruction precision [12]. To quantify the cal- phantom calibration, (3) actuator-assisted cross wire phan- ibration reproducibility, we transformed the 4 corners and tom calibration based on point targets at the central region, the middle of the image [23] from the image to the probe space using the calibration parameters of each of the 10 cali- (4) actuator-assisted calibration using an original collinear point target phantom, and (5) actuator-assisted calibration bration trials, calculated the Euclidean distance between all using a modified collinear point target phantom. Ten calibra- possible pairs of the 10 possible calibration trials (i.e., tion trials were conducted for each calibration approach. C = 45 pairs) for each point, and reported the mean, 10 2 6 Journal of Healthcare Engineering standard deviation, maximum, and minimum of the pooled true locations after optimization. It provides an indication of data of the 5 points (i.e., 225 observations). To calculate point self-consistency of the calibration. It was noted that the free- reconstruction precision, we fixed a different point phantom hand cross wire phantom calibration resulted in the largest to the world space. This point phantom consisted of a plastic residual error (1.35 ± 0.21 mm), followed by the actuator- base with a single pin, 2 mm in diameter, affixed to the base. assisted cross wire phantom calibration (0.80 ± 0.11 mm), We imaged the pin head 50 times at different viewing angles and the actuator-assisted cross wire phantom calibration and locations within the entire image FOV and derived the based on point targets at the central region had the smallest world coordinates of the pin head from different views and residual error (0.40 ± 0.09 mm). The residual errors of both calibration matrix combinations. From there, we further cal- original (0.55 ± 0.04 mm) and modified (0.47 ± 0.08 mm) col- culated the Euclidean distance between all possible pairs of linear point target phantom calibrations were also very small. views (i.e., Tables 1 and 2 summarize the calibration reproducibility C = 1225 pairs) for each calibration parameter 50 2 set and reported the mean, standard deviation, maximum, and point reconstruction precision, respectively, for each cal- and minimum of the pooled data of the 10 calibrations (i.e., ibration approach. We found that the actuator-assisted cross 12,250 observations). This was done for each of the 5 calibra- wire phantom calibration was the most precise among all cal- tion approaches. Detailed mathematical formulations of both ibration approaches. However, if point targets were only precision parameters can be found elsewhere [12]. imaged at the central region of the image FOV, its precision deteriorated tremendously. In addition, modified collinear 2.5.2. Accuracy. Accuracy refers to how close measurements point target phantom appears to be slightly better than the are to the “true” value. For each calibration approach, we original collinear point target phantom in terms of both quantified reconstruction accuracy using both point-based precision measures. and distance-based measures. For the point reconstruction Tables 3 and 4 summarize the point and distance accuracy [24], we compared the world coordinates of the reconstruction accuracy of each calibration approach, pin head derived from each view and calibration matrix com- respectively. As expected, the accuracy of the actuator- bination (obtained from the “point reconstruction precision” assisted cross wire phantom calibration was poor if the experiment described above) with the true world coordinates point targets were imaged at the central region of the (measured by the digitizing probe based on the average of 20 image FOV only. All other calibration approaches appear measurements) and reported their differences in terms of to have excellent but similar accuracy. mean, standard deviation, maximum, and minimum among To help elucidate the sources of uncertainty for each 500 observations (i.e., 50 views × 10 calibration trials). An calibration approach, standard deviations of the translational additional validation experiment was conducted using a (x, y, and z) and rotational calibration parameters (α, β, and “two-point” phantom (i.e., a plastic base with two pins, γ) for each calibration approach are also plotted as separate 2 mm in diameter, affixed to the base) to quantify distance stacked columns (Figure 5). reconstruction accuracy [10, 12, 18]. This involved (1) digi- Table 5 summarizes the data acquisition time for each tizing each point target 20 times to calculate the true 3D dis- calibration approach. Results revealed that actuator-assisted tance between the two point targets, (2) imaging each point calibration was particularly time-efficient if it was imple- target 50 times at random viewing angles and locations that mented with collinear point target phantoms. However, sim- covered the entire image FOV in a qualitative manner, (3) ilar data acquisition time was recorded for both freehand and deriving the “imaged” 3D distance between the two point tar- actuator-assisted cross wire phantom calibration approaches. gets based on each image pair (50 × 50 = 2500 image pairs) and calibration matrix (10 calibration trials) combinations, 4. Discussion and (4) calculating the difference between the true and imaged 3D distances in terms of mean, standard deviation, Our accuracy and precision data (Tables 1–4) compared maximum, and minimum among 25,000 observations. favorably with other calibration methods reported in the lit- erature [17, 25]. However, because of difference in the quality 2.5.3. Statistical Analysis. For each parameter (i.e., calibration of ultrasound system, probe frequency and configuration, reproducibility, point reconstruction precision, point recon- depth settings, number of target points, accuracy of the struction accuracy, distance reconstruction accuracy, and data tracking system and segmentation, and so on, accuracy and acquisition time), one-way analysis of variance (ANOVA) precision data must be interpreted with extreme caution. was employed to test whether there was a significant differ- We overcame this difficulty by using the traditional freehand ence among the 5 calibration approaches. Post hoc compar- cross wire phantom calibration as a reference standard in isons were based on the Scheffe’s method. All statistical this study. Among the four calibration approaches tested tests were done using SPSS statistical package version 24 in this study (i.e., freehand cross wire phantom calibration, (SPSS, Chicago, IL). A confidence level of 0.05 was chosen actuator-assisted cross wire phantom calibration, actuator- for all analyses. assisted collinear point target phantom calibration, and actuator-assisted modified collinear point target phantom calibration), the actuator-assisted single cross wire phantom 3. Results calibration significantly outperformed the other calibration Residual error indicates the proximity of the locations of the approaches in terms of calibration reproducibility (Table 1) 40 point targets used for each calibration with respect to their and appeared to perform slightly better in terms of point Journal of Healthcare Engineering 7 Table 1: Comparison of calibration reproducibility among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) ∗ # 0.84 (0.57) Mean (SD) 1.50 (1.08) 1.72 (1.20) 1.50 (0.95) 4.91 (3.99) Maximum 5.29 2.85 5.10 4.99 15.94 Minimum 0.043 0.042 0.13 0.077 0.14 For each approach, calibration reproducibility was calculated from 225 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that calibration reproducibility of the actuator-assisted cross wire phantom calibration was significantly better than that of the traditional freehand cross wire phantom calibration (p =0 015). However, if actuator-assisted cross wire phantom calibration was only focused on the central region, it was significantly poorer than the traditional freehand cross wire phantom calibration (p <0 0001). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 2: Comparison of point reconstruction precision among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) Mean (SD) 1.69 (1.04) 1.44 (0.83) 1.68 (1.13) 1.49 (0.92) 2.86 (2.46) Maximum 6.03 4.63 7.85 5.91 17.38 Minimum 0.035 0.045 0.037 0.046 0.039 For each approach, point reconstruction precision was calculated from 12,250 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, point reconstruction precision was significantly poorer than the traditional freehand cross wire phantom calibration (p =0 009). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 3: Comparison of point reconstruction accuracy among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) 2.61 (1.59) Mean (SD) 1.44 (0.82) 1.33 (0.74) 1.65 (0.80) 1.35 (0.75) Maximum 3.84 3.64 4.59 4.17 9.89 Minimum 0.14 0.11 0.21 0.12 0.32 For each approach, point reconstruction precision was calculated from 500 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, point reconstruction accuracy was significantly poorer than the traditional freehand cross wire phantom calibration (p <0 0001). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. Table 4: Comparison of distance reconstruction accuracy among calibration approaches. Freehand cross Actuator assisted cross Actuator assisted Actuator assisted modified Acutator assisted cross wire wire collinear point targets collinear point targets wire (central region only) Mean (SD) 0.19 (0.47) 0.19 (0.46) 0.21 (0.48) 0.21 (0.48) 0.244 (0.74) Maximum 1.88 1.79 1.90 1.82 4.70 Minimum −1.62 −1.64 −1.61 −1.56 −2.37 For each approach, point reconstruction precision was calculated from 25,000 observations. All data in mm. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that if actuator-assisted cross wire phantom calibration was only focused on the central region, distance reconstruction accuracy was significantly poorer than the traditional freehand cross wire phantom calibration (p =0 024). Other actuator-based calibration approaches were not significantly different from the traditional freehand cross wire phantom calibration. reconstruction precision and accuracy (Tables 2 and 3) but parameters, but point reconstruction precision, point recon- similar to the other calibration approaches in terms distance struction accuracy, and distance reconstruction accuracy reconstruction accuracy (Table 4). Figure 5 further revealed depend on both the calibration parameters and errors associ- that actuator-assisted single cross wire phantom calibra- ated with reconstruction (e.g., segmentation and tracking tion substantially improved the consistency of both trans- errors). That may explain why point reconstruction preci- lational and rotational calibration parameters, especially sion, point reconstruction accuracy, and distance reconstruc- the translational parameters. It is worth noting that cali- tion accuracy were less distinctive between calibration approaches. Nonetheless, one could comfortably conclude bration reproducibility depends only on the calibration 8 Journal of Healthcare Engineering Variation of translational calibration parameters 1.6 Freehand Actuator assisted 1.4 1.2 0.8 0.6 0.4 0.2 Cross wire Cross wire Collinear point Modified Cross wire targets collinear point (central region targets only) Elevation Lateral Axial (a) Variation of rotational calibration parameters Freehand Actuator assisted Cross wire Cross wire Collinear point Modified Cross wire targets collinear point (central region targets only) Alpha Beta Gamma (b) Figure 5: Variation of (a) translational and (b) rotational calibration parameters among the 5 calibration approaches evaluated in this study. Table 5: Comparison of data acquisition time among calibration approaches. Actuator assisted cross Actuator assisted collinear Actuator assisted modified Freehand cross wire wire point targets collinear point targets ∗ ∗ Mean (SD) (minutes) 26.2 (5.1) 26.0 (4.0) 12.8 (3.4) 11.1 (3.7) For each approach, mean (SD) was based on 10 calibration trials. One-way ANOVA revealed a significant difference among calibration approaches. Post hoc analysis further revealed that data acquisition time for both actuator-based collinear point targets and modified collinear point target phantom calibrations was significantly shorter than that for the traditional freehand cross wire phantom calibration (p <0 0001 for each paired comparison). There was no significant difference in data acquisition time between freehand and actuator-assisted cross wire phantom calibration. that the overall performance of the actuator-assisted cross resulting in tremendous deterioration of precision (Tables 1 wire phantom calibration is the best among all calibration and 2) and accuracy (Tables 3 and 4). approaches tested in this study. We successfully modified the mathematical formulation It has been suggested that probe calibration using point- of the calibration problem to eliminate the need of imaging based phantom should ensure that the point targets be the point targets at different viewing angles. Although this imaged in all regions within the FOV [17]. The results of this modification would benefit the traditional freehand cross study not only confirmed this notion but also elucidated the wire phantom calibration, it offers additional benefits to the reason behind that. We demonstrated that if the point targets actuator-assisted cross wire phantom calibration. First, with were only imaged at the central region of the image FOV dur- the probe held by a probe clamp instead of by hand, the inter- ing cross wire phantom calibration, even though the residual secting points can be more precisely located within the ultra- error of the calibration was among the smallest (likely due sound midplane (reflected by a smaller variation of the to better image quality at the center of the FOV), the rota- translational calibration parameter along the elevation direc- tional calibration parameters (especially rotation about the tion (Figure 5(a))). Second, given that both of the probe and axial direction) became highly unconstrained (Figure 5(b)), the phantom are stationary during imaging, there is no need Standard deviation (mm) Standard deviation (Deg) Journal of Healthcare Engineering 9 precision or accuracy, and hence it should not be directly to synchronize the pose data with the ultrasound images. Third, with the ultrasound probe connected to a linear actu- compared between calibration approaches. ator in the actuator-based calibration, we can easily fulfill the The actuator-assisted calibration approach developed in this study is not without limitation. First, due to the fact that FOV requirement by systematically adjusting the actuator’s positions to cover the entire FOV of ultrasound image. our current setup is mainly composed of metal parts (e.g., lin- In this study, we developed 2 phantoms with collinear ear actuator, probe clamp, stand, and articulated arm), the point targets to take advantage of the actuator-assisted calibra- optical tracking system may not be replaced by magnetic tion setup. Like the cross wire phantom, phantoms with collin- tracking device. This makes our current setup less portable. Further development should focus on replacing the metal ear point targets can be easily constructed in a nonengineering setting. Our results revealed that their precision and accuracy components by plastic components. Second, unlike the tradi- were comparable to those of the traditional freehand cross tional approach, our approach requires the use of specific wire phantom calibration yet significantly reduced the calibra- components such as digitizing pointer and linear actuator, tion time from 26.2 minutes to 11.1 minutes. Based on the val- which may not be commonly found in some scenarios, especially in clinical settings. Third, we only evaluated our idation data of the original collinear point target phantom, we had already identified that the rotational component about the actuator-assisted calibration approach on 3 point-based axial direction and the translational component along the phantoms; its applicability to other point-based phantoms elevation direction were the main sources of uncertainty is largely unknown. It will be a topic of future study. (Figure 5). In fact, these components are primarily governed by the alignment process of the point targets. Hence, we 5. Conclusion intended to develop the modified collinear point target phan- In conclusion, we successfully developed an actuator-assisted tom to improve the alignment process of the point targets. As approach to make the freehand 3D ultrasound calibration expected, the new alignment mechanism improved the rota- less skill dependent, applied it to a single cross wire phantom tional precision about the axial direction (Figure 5(b)), but and two collinear point targets phantoms, and evaluated their surprisingly, it degraded the translational precision along the precision and accuracy by comparing with the traditional elevation direction (Figure 5(a)). This is likely because the freehand cross wire phantom calibration approach. Results modified collinear point target phantom only relied on the demonstrated that the actuator-assisted single cross wire central screw head to guide the translational alignment phantom calibration significantly improved the calibration whereas the original collinear point target phantom used all reproducibility and offered similar point reconstruction pre- the 7 screw heads. Nonetheless, side-by-side comparison of cision, point reconstruction accuracy, distance reconstruc- each precision (Tables 1 and 2) and accuracy (Tables 3 and tion accuracy, and data acquisition time with respect to the 4) parameter as well as the data acquisition time revealed that freehand cross wire phantom calibration. On the other hand, the modified collinear point target phantom appears to be the actuator-assisted modified collinear point target phan- slightly better than the original collinear point target phantom. tom calibration was found to have similar precision and Due to differences in phantom design, the implementa- accuracy when compared to the freehand cross wire phan- tion of the actuator-assisted calibration requires repeated tom calibration, but it reduced the data acquisition time by alignment of each of the 40 point targets with the image plane 57%. It appears that both actuator-assisted approaches are for the single cross wire phantom, whereas the collinear point viable options for freehand 3D ultrasound calibration. target phantoms only require one alignment for all the 40 point targets. In the first glance, one may think that collinear Conflicts of Interest point target phantoms are more attractive choices for the implementation of actuator-assisted calibration. However, The authors declare that there is no conflict of interest the “single” alignment approach of collinear point target regarding the publication of this paper. phantoms could introduce a systematic error to all the 40 point targets. Given that the amplitude and direction of this Acknowledgments systematic error may vary substantially among calibration trials (due to the subjective nature of visual alignment), its The authors would like to thank Amy Lin, Darren Koo, precision is likely to be compromised. Conversely, the and Preya Patel for their assistance in data collection. This “repeated” alignment requirement of the single cross wire work was supported by an intramural fund of New York phantom would lead to a random error to each point target, Chiropractic College. and hence the calibration should be less sensitive to point tar- get alignment error. 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