Three-dimensional carpal arch morphology using robot-assisted ultrasonography

Abstract

Objective:

The morphology of the carpal arch implicates the available space for the median nerve within the carpal tunnel. The purposes of this study were to 1) reconstruct the three-dimensional (3D) carpal arch by robot-assisted ultrasonography with a linear array transducer using cadaveric hands, and 2) investigate the 3D morphological properties of the carpal arch.

Methods:

An ultrasound probe with two-dimensional (2D) linear array was integrated on a robotic arm and maneuvered over the cadaveric carpal tunnels to scan the entire transverse carpal ligament and its osseous attachments to carpal bones. The acquired series of 2D ultrasound images together with robot positioning were utilized to reconstruct the 3D carpal arch for morphometric analyses.

Results:

Total carpal arch volume was 1099.4 ± 163.2 mm³ with the distal, middle, and proximal regions contributing 18.2 ± 1.5%, 32.7 ± 1.2%, and 49.1 ± 2.3%, respectively. The ligament surface area was 420.1 ± 63.9 mm². The carpal arch width, height, curvature, length, area, and palmar bowing index progressively increased from the distal to proximal locations within the tunnel (p < 0.01).

Conclusion:

The incorporation of the robot technology with the ultrasound system advanced the applications of traditional 2D ultrasound imaging for a 3D carpal arch reconstruction, allowing for comprehensive morphological assessment of the carpal arch.

Significance:

The developed workflow can be used for the reconstruction and analysis of other anatomical features in vivo.

I. Introduction

THE carpal tunnel has a complex geometry derived from the transverse carpal ligament, intercarpal ligaments, and interconnected carpal bones. The carpal arch formed by the transverse carpal ligament is relevant to compression neuropathy due to the sandwiched location of the median nerve between the ligament and flexor tendons. For instance, palmar bowing of the transverse carpal ligament has been shown to accommodate for enlargement of carpal tunnel contents [1], especially in cases with carpal tunnel syndrome [2]. A less elastic ligament might not be able to palmarly bow adequately to accommodate for the reduction in available space for contents or elevated pressure within the tunnel. Moreover, the ligament compliance is sex-dependent with a stiffer ligament in females [3] possibly leading to a smaller carpal arch and lower structural compliance compared to males [4]. Furthermore, the carpal tunnel has variable cross-sectional configuration, non-uniform thickness in the transverse carpal ligament, and location-dependent tunnel compliance [5]-[7]. However, there is a lack of understanding how the carpal arch varies at various tunnel locations.

A rigorous way to study location-dependent changes in the carpal arch space is to reconstruct the 3D carpal arch, allowing for visualization of spatial relationship among anatomical features and calculation of comprehensive morphometric parameters. Ultrasonography is a suitable method for carpal arch imaging and 3D reconstruction due to the distinct echogenicity differentiation for the relevant tissues. Ultrasonographic recontraction in 3D has been shown to be accurate and is comparable to the magnetic resonance imaging counterpart [8]. The 3D ultrasonography has been applied for volumetric measurement of cervical carcinoma [9], solid breast masses [10], and cadaveric kidneys [11].

Relevant to the carpal tunnel, 3D ultrasonography was used for the assessment of neuropathy (e.g. carpal tunnel syndrome) by reconstructing the median nerve from wrist to the elbow [12]. Recently, Shah and Li (2020) recently used a catheter ultrasound probe to scan the carpal tunnel boundaries by sequentially rotating the probe within the tunnel and demonstrated the utility of the 3D ultrasonography technology for investigating the tunnel structure [13]. However, a more applicable approach to 3D ultrasonography for the carpal tunnel would be to scan the tunnel from the palmar aspect of the wrist using a conventional linear array surface ultrasound transducer.

The purposes of this study were to 1) reconstruct the 3D carpal arch by robot-assisted ultrasonography with a linear array transducer using cadaveric hands, and 2) investigate the 3D morphology of the ligament formed carpal arch. We hypothesized that the size and shape of the carpal arch would be dependent on the locations of the carpal tunnel. Specifically, the bowing of the carpal arch would progressively increase from the distal (outlet) to the proximal (inlet) locations of the carpal tunnel. A 2D linear array ultrasound probe was maneuvered over the cadaveric carpal tunnels to acquire a series of 2D ultrasound images of the carpal arch’s cross-sections with the assistance of a robot. The dorsal boundaries of the ligament were extracted from the individual images to reconstruct the 3D carpal arch for morphometric analyses.

II. Methods

A. Specimen Preparation

Ten freshly frozen male, right cadaveric hand specimens (age 53.8 ± 14.4 years, weight 75.5 ± 10.4 kg, height 1.82 ± 0.09 m, and body mass index 24.2 ± 2.9 kg/m²) were used for this study. Specimens with a history of musculoskeletal disorders related to the wrist were excluded from the study. Each specimen included the hand and mid-forearm. The superficial soft tissues at the wrist were dissected to expose the transverse carpal ligament. The flexor tendons and median nerve were removed from the tunnel. For each specimen the wrist was secured in an anatomically neutral position and the thumb in radial abduction position using a custom-made thermoplastic splint. A medical balloon was inserted into the tunnel and maintained a nominal physiological intra-tunnel pressure of 24 mmHg.

B. Experimental Apparatus

The main experimental setup involves an integration of an ultrasound probe with a robotic arm. An 18L6 HD linear array transducer (Acuson S2000, Siemens Medical Solutions USA, Mountain View, USA) was utilized to capture the ultrasound images. A six degree-of-freedom robot (Denso Corp., Kariya, Aichi, Japan) was used to provide real-time pose information of the ultrasound probe. A custom-made ultrasound probe holder was used to mount the probe to the robot’s end-effector (Fig. 1A). The ultrasound probe was rigidly fixated on the probe holder (Fig. 1B).

Fig. 1.

Experimental setup for robot-assisted ultrasound imaging of cadaveric hands

C. Procedures to Collect Ultrasound Images

For ultrasound imaging, a thin layer of gel was applied to the volar wrist to maintain acoustic transmission while preventing the probe from contacting the skin. Ultrasound scanning was performed pseudo statically to collect multiple cross-sectional images with distinct echogenic visualization of the transverse carpal ligament. The quality of each cross-sectional image was maximized by adjusting the orientation of the probe. The probe was placed transversely to the carpal tunnel and translated in the distal-proximal direction to obtain 40 cross-sectional images per specimen to scan the entire ligament. Similarly, the bony landmarks with the ligament-osseous attachments (i.e. volar aspects of hook of hamate, ridge of trapezium, and tubercles of scaphoid and pisiform) were individually scanned. The probe was rocked and tilted along with the adjustment in orientation to obtain high quality maximum features with hypergenetic bone surfaces. Twenty cross-sectional images per specimen were collected in the distal-proximal tunnel direction for each of the bony landmarks. A teaching pendant was used to maneuver the ultrasound probe with the robotic arm, and a customized LabVIEW code was developed to record the pose of the end effector and collect ultrasound images of the anatomical structures at each probe position.

D. Image Processing

From each ultrasound image the regions of interest corresponding to the individual anatomical features were identified. The dorsal boundary of the transverse carpal ligament and bony landmarks were detected by a custom-made feature extraction algorithm that included thresholding, region growing, and contour detection. The extracted feature points, for each anatomical structure, were outputted to generate an array of interpolated data points distributed along the length of the tunnel.

E. Point Cloud for Carpal Arch and Bony Landmarks

The 2D image coordinates of the ligament and bony landmarks’ boundaries from individual images were spatially assembled to form a 3D point cloud represented in a common local anatomical coordinate system. Any point of interest with a 2D image coordinates (u, v) was converted to 3D coordinates (x, y, z) in an anatomical coordinate system using the following transformation equation:

$$\left\{\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \\ \hfill z\hfill \\ \hfill 1\hfill \end{array}\right\}=[{\mathrm{T}}_{{}_{\text{AR}}}][{\mathrm{T}}_{{}_{\text{RE}}}][{\mathrm{T}}_{{}_{\text{EP}}}][{\mathrm{T}}_{{}_{\text{PI}}}]\left\{\begin{array}{c}\hfill u\hfill \\ \hfill v\hfill \\ \hfill 0\hfill \\ \hfill 1\hfill \end{array}\right\}$$ (1)

where [T_PI], [T_EP], [T_RE], and [T_AR], are homogeneous transformation matrices from the image coordinate system to ultrasound probe coordinate system, from probe coordinate system to robot end-effector coordinate system, from end-effector coordinate system to robot base coordinate system, and from robot coordinate system to local anatomical coordinate system, respectively. [T_PI] was pre-calibrated by digitizing a set of fiducial points in both image and probe coordinate systems. The static relationship between the two sets of point coordinates, for the same set of fiducial points, was obtained by finding the least-squares solution for the rotational and translational matrices based on singular value decomposition [14]. [T_EP] was determined by registering coordinates of the probe control points with respect to the end-effector coordinate system. [T_RE] was established by default end-effector position coordinates with respect to the robot base coordinate system. [T_AR] was defined by the static anatomical configuration with respect to the robot coordinate system. Specifically, the anatomical coordinate system was defined with the origin at the central point of the distal cross section of the arch, the x-axis aligned with the longitudinal central line of the carpal arch, and the positive directions of the x-, y-, and z- axes point proximally, radially and volarly, respectively.

Once the 3D point cloud of the transverse carpal ligament and bony landmarks were assembled in the anatomical coordinate system, the boundaries of the ligament were defined using the ligament-osseous attachment sites. The ligament-osseous attachment points on each bone was determined from the overlapping points between the 3D point clouds of the ligament and bony landmarks. The distal and proximal boundaries of the ligament were determined at the location of the distal ligament-trapezium attachment point and proximal ligament-scaphoid attachment point, respectively. The radial boundary of the ligament was defined by the line passing through the ligament-trapezium and ligament scaphoid attachment points. Similarly, the ulnar boundary of the ligament was established by the line passing through the ligament-hamate and ligament-pisiform attachment points. The subset of the ligament points within the boundaries of the transverse carpal ligament was selected to represent the carpal arch.

F. Data Processing

The carpal arch points were binned into 12 equally spaced slices. To obtain an adequate data set the cloud points within each slice were clubbed together to form a representative carpal arc for the slice. The following carpal arch morphometric parameters were calculated for each slice: carpal arch width (CAW), carpal arch height (CAH), carpal arch curvature (CAC), carpal arch length (CAL), carpal arch area (CAA), and palmar bowing index (PBI). For each slice, the CAW was defined as the distance between the radial and ulnar endpoints of the representative carpal arc, and CAH was obtained as the maximal perpendicular distance of the ligament dorsal boundary points to the line along the arch width. The CAC was determined as the inverse of the radius of the least squares fitted circle to the dorsal boundary points of the ligament. The CAL was calculated as the length of the representative carpal arc for each slice. The CAA was calculated using the integral of the ligament dorsal boundary over the arch width. The PBI was obtained by calculating the ratio of CAH to CAW. Least squares linear regression was performed for each of the above-mentioned morphometric parameters as a function of tunnel slice. Further analysis of the carpal arch point cloud derived the following morphometric parameters: ligament surface area, regional carpal arch volume, and total carpal arch volume. The ligament surface area was calculated by integrating surface areas of all slices (i.e. carpal arch lengths times thickness). The carpal arch cloud points were divided into 3 equal regions to obtain the regional carpal arch volumes at the distal, middle, and proximal regions of the carpal arch. The total carpal arch volume was obtained by summation of the three regional volumes.

G. Statistical Analysis

In addition to descriptive statistics, linear regression analyses were performed for CAW, CAH, CAC, CAL, CAA, and PBI as a function of locations from distal to proximal tunnel. One-sample t-tests were performed for regression slopes to determine whether these morphometric parameters varied with respect to tunnel locations. A one-way repeated measures ANOVA was performed to examine differences in regional (distal, middle, and proximal) carpal arch volume. A post-hoc Holm-Sidak’s test was performed for pairwise comparisons. An α of 0.05 was used for statistical significance level. Statistical analyses were performed with SigmaStat 4.0 (Systat Software Inc, San Jose, CA, USA).

III. Results

The dorsal boundary of the transverse carpal ligament was explicitly identified within the ultrasound image (Fig. 2A). The water inside the balloon was hypoechoic (i.e. lower grayscale values) as compared to the ligament. The contrast in the grayscale values assisted the custom image processing algorithm to extract the ligament dorsal boundary. The volar aspects of the four bony landmarks were displayed in the ultrasound images with the distinct pattern of hyperechoic bone surface followed by a hypoechoic shadow in the dorsal regions (Fig. 2A). A representative 3D reconstruction of the carpal arch and the ligament-osseous attachments on the carpal bones is shown in Fig. 2B. In general, the carpal arch cross sections were non-uniform, changing in size and shape from the outlet (distal) to inlet (proximal) of the tunnel.

Fig. 2.

Representative ultrasound cross-sectional images (A) and 3D reconstruction of the carpal arch and bone landmarks (B). H = hook of hamate, T = ridge of trapezium, S = tubercle of scaphoid, and P = tubercle of pisiform

All carpal arch cross-sectional morphometric parameters increased as location progressed proximally (Fig. 3), which was supported by the positive slopes of linear regression (p < 0.01, Table 1). R-squared values of the linear regression for all carpal arch parameters were greater than 0.85.

Fig. 3.

Carpal arch morphometric parameters from distal to proximal slices of the tunnel. (A) Carpal Arch Width, (B) Carpal Arch Height, (C) Carpal Arch Curvature, (D) Carpal Arch Length, (E) Carpal Arch Area, and (F) Palmar Bowing Index.

TABLE I.

Linear regression results of carpal arch morphometric parameters, Mean (SD)

Parameter	Slope	Intercept	R-squared
Carpal Arch Width	0.45 (0.18)*	19.74 (2.77)	0.86 (0.22)
Carpal Arch Height	0.39 (0.07)*	2.10 (1.19)	0.95 (0.07)
Carpal Arch Curvature	0.004 (0.001)*	0.02 (0.01)	0.98 (0.11)
Carpal Arch Length	0.79 (0.22)*	20.90 (3.69)	0.95 (0.15)
Carpal Arch Area	7.23 (1.81)*	25.61 (2.73)	0.93 (0.13)
Palmar Bowing Index	0.01 (0.003)*	0.07 (0.04)	0.92 (0.09)

^*p < 0.01

The ligament surface area was 420.1 ± 63.9 mm². Total carpal arch volume was 1099.4 ± 163.2 mm³. Regional carpal arch volumes significantly differed from each other (p < 0.001). The distal arch volume (200.1 ± 52.8 mm³) was significantly smaller than the middle arch volume (359.5 ± 96.3 mm³, p < 0.05) and the proximal arch volume (539.8 ± 136.9 mm³, p < 0.05). Similarly, the middle arch volume was significantly smaller than that of the proximal arch volume (p < 0.05). The individual contributions of the distal, middle, and proximal arch volumes to the total arch volume were 18.2 ± 1.5%, 32.7 ± 1.2%, and 49.1 ± 2.3%, respectively.

IV. Discussion

In contrast to the traditional 2D ultrasound imaging, incorporation of the robot with the ultrasound system provides a positional information of the ultrasound probe in space allowing for a 3D reconstruction of an anatomical object of interest. The methodology for robot-assisted ultrasonography established in this study allows for high fidelity 3D reconstruction of the transverse carpal ligament and ligament-osseous attachment sites. Although implemented using cadaveric specimens, the procedures developed in this study can be applied for in vivo reconstruction of the carpal arch. The ultrasonographic imaging of the transverse carpal ligament is commonly performed in a cross-sectional view [15]-[24]. Our methods advance the traditional 2D imaging of the ligament to 3D carpal arch reconstruction for advanced visualization and comprehensive quantification of arch morphometric parameters.

The current study substantiated that the carpal arch size and shape were dependent on the locations within the tunnel. In the past, the carpal arch morphology has been analyzed mainly at the edges of the tunnel to understand the impacts of carpal tunnel syndrome [19], [27], wrist deviations [24], sexes [23], [25], and tunnel locations [23], [25]. Since the material properties of the transverse carpal ligament is dependent on tunnel location [6], [28], the factors affecting the ligament-formed arch space may also demonstrate location-based effects. Hence, an advanced examination of location-based carpal arch morphometric changes will provide an in-depth understanding of the factors reducing the carpal arch space and consequently compressing the median nerve.

The arch morphometric parameters observed in the study agreed well with previous findings. The location dependent arch morphometric parameters revealed that the ligament is relatively flatter with lesser arch space at the distal region of the tunnel compared to the proximal region, which is consistent with the findings from previous studies [13], [23], [25]. In addition to the agreement of the cross-sectional morphometric parameters, the ligament surface area and volume obtained in this study is in good agreement with previous literature [13], [26]. However, the carpal arch volume was underestimated by an average of 9% for the specimen subset shared with the previous study (scanned within the carpal tunnel) [13]. This systematic error is most likely due to how the carpal arch is defined when the images were collected from outside.

For future clinical applications, the developed workflow is applicable to other anatomical features of the human body. A possible use is to reconstruct 3D structure of soft tissues as well as bone surfaces in pathological and trauma conditions. This is valuable for in vivo reconstruction because ultrasound scanning is radiation free and comfortable.

This study has several limitations. First, the ultrasound examination was conducted on cadaveric hands. The developed methods can be applied in vivo as the surface ultrasound transducers are clinically utilized to image the carpal tunnel, although inclusion of soft tissue volar and dorsal to transverse carpal ligament will be more difficult to segment and needs additional development. An additional challenge for human subject is to remain motionless during the scanning. Second, the findings using male hands limit the generalizability to females. Future studies can expand investigation of morphometric properties of carpal arch associated with demographics such as sex, age, and ethnicity.

V. Conclusion

A robot-assisted ultrasonography method was developed for 3D reconstruction of anatomical objects of interest. The method was applied for the reconstruction of the 3D carpal arch formed by the transverse carpal ligament, which provided comprehensive characterization of morphologic properties of the arch structure. The carpal arch size and shape parameters demonstrated progressive palmar bowing of the transverse carpal ligament from the distal to proximal tunnel locations. The observed results suggest that the ligament is relatively flatter with lesser space at the distal region of the tunnel compared to the proximal region. As the median nerve lies close to the ligament, this study provides mechanistic understanding of the propensity of median nerve compression at the distal region. The developed workflow for the robot-assisted ultrasonography along with the calculated outcome parameters can be utilized to explore the pathomorphological changes associated with the carpal arch. In addition, the developed method can be applied to 3D reconstruction and analysis of other anatomical structures.