Cross-sectional Changes of the Distal Carpal Tunnel with Simulated Carpal Bone Rotation

Abstract

This study simulated the cross-sectional changes in the distal carpal tunnel resulting from inward rotations of the hamate and trapezium. Rotations which decreased the carpal arch width, increased the carpal arch area. For example, simultaneous rotation of 5 degrees around the hamate and trapezium centroids decreased the carpal arch width by 1.69 ± 0.17 mm and increased the carpal arch area by 6.83 ± 0.68 mm². Although the bone arch area decreased, decompression of the median nerve would likely occur due to the adjacent location of the nerve near the transverse carpal ligament.

Introduction

Carpal tunnel syndrome is a peripheral nerve entrapment syndrome affecting a large portion of the general (Atroshi et al. 1999) and working populations (Luckhaupt et al. 2012; Dale et al. 2013). The most common treatment for carpal tunnel syndrome is to undergo carpal tunnel release surgery, whereby pressure at the median nerve is relieved by transecting the transverse carpal ligament (TCL) (Badger et al. 2008; Rodner and Katarincic 2008). Regarding various patient outcome measurables, surgical treatment shows preferred results, as compared to those for therapeutic options such as splinting (Gerritsen et al. 2002), non-steroidal anti-inflammatory drugs (Jarvik et al. 2009) and steroid injections (Hui et al. 2005). Although surgery is more effective, the invasive nature of the procedure does present the risk of complications, albeit rare (Karl et al. 2016). Such risks are minimal with noninvasive physical therapeutics. These options, which can include splinting (Huisstede et al. 2010) and carpal bone mobilization (Huisstede et al. 2010), often involve force application at or near the radiocarpal or midcarpal joint. These force applications are likely to induce relative motion of the carpal bones.

Physical therapeutics which act to decompress the median nerve by increasing the carpal arch area have been demonstrated. A mechanism for increasing the carpal arch area has been exhibited by narrowing the carpal arch width (Li et al. 2009; Li et al. 2011; Li et al. 2013). The increase in carpal arch area resulting from carpal arch width narrowing has been demonstrated to occur with respect to in-vivo thenar muscle contraction (Shen and Li 2013) and with radioulnar compressive forces applied at the wrist in-vitro (Li et al. 2013) and in-vivo (Marquardt et al. 2015). A negative correlation between the change in carpal arch width with respect to the change in carpal arch height and area was identified in these studies, where average changes in these respective morphological features were measured to be approximately −1 mm, +0.4 mm and +4 mm² (Li et al. 2013; Marquardt et al. 2015).

The effect of increasing the carpal arch area on the decompression of the median nerve has been demonstrated with ultrasonically measured increases in nerve circularity and decreases in flattening ratio, resulting from pneumatically applied compressive forces at the wrist (Marquardt et al. 2015). Segmentation of the median nerve at the distal, middle and proximal tunnel levels showed increases in longitudinal nerve mobility in patients with carpal tunnel syndrome (Yao et al. 2018). The increases in nerve circularity and mobility demonstrated by these studies suggest that the nerve became less compressed. Because of the TCL insertions at the hook of hamate and ride of trapezium, the narrowing of the carpal arch width for the purpose of median nerve compression relief is also likely to involve some relative motion of the carpal bones.

Given the effectiveness of these therapeutic options and the understanding of how changes in the carpal tunnel cross-section can serve to relieve median nerve compression, it is of interest to understand how the carpal tunnel cross-section is affected by the motion of the carpal bones. To investigate this, a computational model was developed to measure changes in the distal carpal tunnel cross-section resulting from internal hamate and trapezium rotation. The specific morphological parameters of interest were the carpal arch width (CAW), carpal arch area (CAA), carpal arch height (CAH), bone arch area (BAA), bone arch height (BAH) and total cross-sectional area (CSA).

Materials and Methods

Ten cadaveric hands were used for the study. The palmar surface of each specimen was dissected to expose the TCL. The carpal tunnel contents were evacuated, leaving only the carpal bones and intact TCL. A medical balloon was inserted into the tunnel and pressurized to 10 mm Hg using a solution of water and computed tomography contrast agent. A clinical computed tomography scanner (InReach, CurveBeam, Hatfield, PA) was used to scan each specimen from the distal radius to the distal phalanges. The DICOM image files were uploaded into an image segmentation software platform ITK-SNAP (Yushkevich et al. 2006), where a single distal slice containing the hook of hamate and ridge of trapezium was identified for analysis (Figure 1). In Figure 1, the total carpal tunnel cross-sectional area is outlined in black.

Figure 1.

Distal carpal tunnel cross-section with manually identified landmarks and morphological variables of interest

The individual bones were manually segmented and the local coordinate data was stored. Several landmarks were manually identified including the TCL vertex (a), TCL hamate insertion (b), capitate volar apex (c) and the TCL trapezium insertion (d). The distal insertion points of the TCL at the hook of hamate and ridge of trapezium were identified by the intersection of the balloon with the surface of the bones. The CAW was identified as the distance between points b and d. The areas volar and dorsal to the carpal width line were identified as the CAA and BAA, respectively. The CAH was identified as the distance between the carpal width line and the TCL vertex. The base of the bone arch was identified as a point on the volar capitate surface colinear with the TCL vertex. The bone arch height was identified as the distance between this point and the carpal width line.

The coordinate data of the segmented cross-section was imported into MATLAB (MathWorks, Natick, MA), where a custom script was employed for analysis. The coordinate data of each bone was used to generate polygon shapes. The location of the centroid (C) of the hamate and trapezium polygons was determined, along with four additional points on the centroidal x and y-axes for each bone. These points were one each on the centroid-volar (CV), centroid-dorsal (CD), centroid-radial (CR) and centroid-ulnar (CU) boundaries of the hamate and trapezium cross-sections (Figure 2).

Figure 2.

Distal carpal tunnel segmentation with modeled transverse carpal ligament and bone rotation around different points (C, CD, CV, CR and CU)

The TCL was modeled as a second order polynomial with three constants to be determined. For any prescribed rotation θ, the original model coordinates moved from $\left(\mathrm{x},\mathrm{y}\right)\mathrm{to}({\mathrm{x}}^{\prime },{\mathrm{y}}^{\prime })$. The post-rotation coordinates of the hamate and trapezium TCL insertions, $\left({\mathrm{x}}_1^{\prime },{\mathrm{y}}_1^{\prime }\right)\mathrm{and}({\mathrm{x}}_3^{\prime },{\mathrm{y}}_3^{\prime })$, were known. The post-rotation coordinates of the TCL vertex $\left({\mathrm{x}}_2^{\prime },{\mathrm{y}}_2^{\prime }\right)$, were unknown. An unconstrained optimization routine, subject to two assumptions, was written in MATLAB to determine the post-rotation TCL vertex coordinates. These assumptions were that the TCL arc length remained constant across rotations and that the change in CAA was proportional to the change in CAW (Li et al. 2013).

The TCL arc length was calculated using the integral of equation (1), where ${\mathrm{c}}_1$ and ${\mathrm{c}}_2$ were polynomial coefficients. For any prescribed rotation, evaluation of equation (1) resulted in the post-rotation arc length ${\mathrm{S}}^{\prime }$ (Equation 2), where ${\mathrm{c}}_1^{\prime }$ and ${\mathrm{c}}_2^{\prime }$ were the post-rotation polynomial coefficients. $\mathrm{\varphi }\mathrm{and}\mathrm{\psi }$ (Equations 3–4), were the respective integration limits. The objective function W, to be minimized was given by Equation (5), where ${\mathrm{S}}_{\mathrm{o}}$ was the original TCL arc length, $\mathrm{\Delta }\mathrm{C}\mathrm{A}\mathrm{W}$ was the change in the carpal arch width, ${\mathrm{C}\mathrm{A}\mathrm{A}}^{\prime }$ was the post-rotation carpal arch area, ${\mathrm{C}\mathrm{A}\mathrm{A}}_{\mathrm{o}}$ was the original carpal arch area and $\mathrm{\alpha }$ was a proportionality constant relating the change in CAW to the change in CAA (Li et al. 2013).

$$\text{S}={\int }_{{\text{y}}_1}^{{\text{y}}_3}\sqrt{1+{\left(2{\text{c}}_1\text{y}+{\text{c}}_2\right)}^2}\text{dy}$$ (1)

$${\text{S}}^{\prime }=\frac{1}{{4{\text{c}}_1}^{\prime }}\left[\text{secϕtanϕ}-\text{secψtanψ}+\text{ln}\left|\text{secϕ}+\text{tanϕ}\right|-\text{ln}\left|\text{secψ}+\text{tanψ}\right|\right]$$ (2)

$$\text{ϕ}={\tan }^{-1}(2{\text{c}}_1^{\prime }{\text{y}}_3^{\prime }+{\text{c}}_2^{\prime })$$ (3)

$$\text{ψ}={\tan }^{-1}(2{\text{c}}_1^{\prime }{\text{y}}_1^{\prime }+{\text{c}}_2^{\prime })$$ (4)

$$\text{W}={\left(1-\frac{{\text{S}}^{\prime }}{{\text{S}}_{\text{o}}}\right)}^2+{\left(1-\frac{\text{α}\left(\text{ΔCAW}\right)+{\text{CAA}}_{\text{o}}}{{\text{CAA}}^{\prime }}\right)}^2$$ (5)

Inward rotations about each of the five rotation points, up to a maximum of 5 °, were applied to the hamate and trapezium in intervals of 1 °. A maximum angle of 5 ° was chosen in order to obtain an appreciable data set, without extending the simulation outside the range of previously observed results; specifically, the magnitude of CAW narrowing. There were three rotation cases: hamate rotation only, trapezium rotation only and simultaneous rotation.

For each rotation, those morphological parameters associated with the optimized TCL polynomial curve were calculated as follows. The CAA was calculated as the area between the optimized carpal arch polynomial curve and the carpal width line. The CAH was calculated as the distance between the optimized carpal arc vertex location and a point on the x-axis that lies on the carpal width line. The BAH was calculated as the distance between a point on the volar capitate surface and a point on the carpal width line lying on the x-axis of the original TCL vertex. The total area was calculated as the sum of the CAA and BAA. All other morphological parameters were calculated as previously described.

Results

Figure 3 shows the continuous changes in the interested carpal tunnel morphological parameters for a representative specimen under simultaneous rotation. Figure 4 shows the average results for the ten specimens. The average initial CAW, CAH and CAA were 27.01 ± 2.37 mm, 3.52 ± 0.70 mm and 37.81 ± 20.05 mm². Rotations about C, CD, CR and CU decreased the CAW, increased the CAH and increased the CAA for all bone rotations. Simultaneous rotation produced the largest average changes in CAW (−1.69 ± 0.17, −3.53 ± 0.32, −1.76 ± 0.18 and −1.61 ± 0.16 mm), CAH (+0.92 ± 0.16, +2.02 ± 0.36, +0.93 ± 0.17 and +0.91 ± 0.15 mm) and CAA (+6.83 ± 0.68, +14.27 ± 1.30, +7.09 ± 0.73 and +6.51 ± 0.66 mm²) for rotations about C, CD, CR, and CU, respectively. Rotations about CV increased the CAW, which decreased the CAH and decreased the CAA for hamate, trapezium and simultaneous rotations. The average changes for simultaneous rotation were +0.12 ± 0.07 mm, −0.06 ± 0.04 mm and −0.49 ± 0.26 mm² for the CAW, CAH and CAA, respectively.

Figure 3.

Representative specimen results for continuous change in carpal tunnel morphological variables: (A) bone arch area, (B) carpal arch area, (C) total cross-sectional area, (D) carpal arch width, (E) bone arch height and (F) carpal arch height

Figure 4.

Change in carpal tunnel morphological variables (mean ± standard deviation) for 5 ° inward rotation: (A) bone arch area, (B) carpal arch area, (C) total cross-sectional area, (D) carpal arch width, (E) bone arch height and (F) carpal arch height

The average initial BAA and BAH were 152.29 ± 27.62 mm² and 9.16 ± 1.34 mm. The average BAA decreased for every rotation combination, excluding hamate rotation about CV. The largest changes occurred for simultaneous rotation, where the greatest average decrease was −22.08 ± 4.38 mm² for rotation about CD. The BAH decreased for every rotation combination except for rotations about CR. The largest change in BAH was −1.38 ± 0.19 mm and occurred for simultaneous rotation about CU.

The average total CSA was 190.10 ± 45.27 mm². The total CSA decreased for every bone rotation combination, excluding rotations about CR. The largest average changes in total CSA occurred for simultaneous rotation. These changes were −5.58 ± 2.87 mm² for rotation about C, −7.81 ± 4.34 mm² for rotation about CD, −2.69 ± 2.44 mm² for rotation about CV, +3.15 ± 1.53 mm² for rotation about CR and −13.81 ± 4.99 mm² for rotation about CU.

Figure 5 shows the carpal arch behavior for a representative specimen across all rotation combinations. The algorithm for finding the optimal TCL vertex position while minimizing the deviation in TCL arc length and the deviation in correlated CAA performed well. The effectiveness of the optimization routine utilizing several different objective functions is represented by Figure 6, where W1 was an objective function describing the deviation in TCL arc length, W2 described the deviation in CAA with respect to the CAW correlation (Li et al. 2013) and W3 described a combination of W1 and W2 (Equation 5). The average initial arc length of the modeled TCL was 28.26 ± 2.49 mm. For simultaneous rotation, the average deviation from the original TCL arc length was −0.84 ± 0.18 mm for rotation about C, −1.28 ± 0.42 mm for rotation about CD, 0.07 ± 0.042 mm for rotation about CV, −0.87 ± 0.19 mm for rotation about CR and −0.81 ± 0.18 mm for rotation about CU.

Figure 5.

Carpal arch behavior with rotation around point C, CD, CV, CR and CU for hamate, trapezium and simultaneous rotation

Figure 6.

Optimization of (A) transverse carpal ligament arc length and (B) carpal arch area

Discussion

This study simulated the cross-sectional changes of the distal carpal tunnel due to inward rotations of the trapezium and hamate about multiple rotation points. The locations of the points were selected with respect to the centroid of the bone cross-sections in order to provide a standardized means of point selection between specimens. Key takeaways from the work include the greater degree of cross-sectional changes that occurred for simultaneous bone rotation; the propensity for hamate and trapezium rotation to increase the CAH and CAA; and that rotations about dorsally located rotation points produced the greatest degree of increase in CAA.

Morphological variables including CAA, CAH, CAW, total CSA and TCL arc length were within the range of previously reported values (Pacek et al. 2009; Li et al. 2011; Li et al. 2013; Bueno-Gracia et al. 2017). Changes in the morphological variables associated with the carpal arch were well correlated with the results of previous studies. Where a decrease in CAW was observed, there was a corresponding increase in CAA and CAH. Conversely, an increase in CAW resulted in a decrease in CAH and CAA. This relationship served to corroborate the physical coherency of the model, as well as the agreement with previous studies, where the narrowing of the CAW in cadaveric hands showed a negative correlation with CAA and CAH (Li et al. 2013). This relationship was also shown in-vivo with the application of radio-ulnar wrist compression (Marquardt et al. 2015).

The rotation points which caused the average CAA to increase were C, CD, CR and CU. The location of these axes, with respect to the TCL insertion points, dictated that the displacement of the insertion points be directed toward the tunnel space during rotation. This motion of the insertion points narrowed the CAW, which increased the CAH and CAA. Rotation about CV moved the insertion points away from the tunnel space, which lengthened the CAW and decreased the CAH and CAA. With the internal rotation of the hamate and trapezium, it was expected that the internal boundary of the bone arch would move both radially and ulnarly, as the volar and dorsal surfaces of the bones moved in opposition. This simultaneous narrowing and expanding of the boundary made the net BAA change intuitively ambiguous. The decrease of the BAA for the majority of the rotation combinations suggests that the narrowing portion of the boundary had a greater effect than the expanding portion.

The model was geometrical. Any physical effects, such as those from the surrounding tissue and any loading that would result from the bone motion, were not explicitly included. Instead, these effects were implicitly incorporated by the minimization of the objective function (Equation 5) which enforced physical limitations on the model results. The assumptions made for the optimization were based on the results from physical TCL measurements. The assumption regarding constant TCL arc length was derived from a cadaveric study, where palmarly directed forces between 10-200 N were applied to the exposed TCL and no significant changes in TCL arc length were observed (Li et al. 2009). The constant of proportionality (α = −4.033) used to optimize the CAA was derived from a previous study, where the CAW was progressively narrowed and ultrasound imaging was used to measure the changes in CAW and CAA (Li et al. 2013). The presented model was idealized with a smooth TCL arc. With the TCL maintaining a relatively constant arc length during wrist compression and, given the comparable morphological measurements of the model with respect to previous works, it was assumed that any warping of the TCL would not considerably affect the nature of the results.

The changes of the carpal tunnel cross-section have been studied with respect to carpal bone motion. In a cadaveric study, wrist forces were applied to cadaveric hand specimens and the carpal tunnel cross-section was digitally imaged and analyzed (Bueno-Gracia et al. 2018a). In an in-vivo study, external forces were manually applied to participant wrists and the resulting changes in carpal tunnel morphology were measured via ultrasound (Bueno-Gracia et al. 2018b). These studies showed that the application of wrist forces causing carpal bone motion can increase the cross-sectional area, increase the anterior-posterior diameter and decrease the transverse diameter. Analogous comparisons to the current study can be made regarding the total CSA, which was observed to decrease for all rotation axes excluding CR. Differences can potentially be explained in the bone mobilization method. The external mobilization method employed by Bueno-Gracia et al. (Bueno-Gracia et al. 2018a, 2018b) may have involved bone translation and rotation, as well as the motion of additional carpal bones, aside from just the hamate and trapezium.

Carpal bone mobilization is a therapeutic technique where the carpal bones are manipulated through multidirectional glide or distraction at the radiocarpal and midcarpal joint. When used in conjunction with wrist splinting, these techniques have shown improvement in carpal tunnel syndrome symptom severity (Huisstede et al. 2010). Previous studies suggest that physical methods which apply forces at or near the carpal bones may serve to decompress the median nerve by increasing the CAA (Marquardt et al. 2015) or total CSA (Bueno-Gracia et al. 2018a, 2018b). The results of this study support these previous findings which show how carpal bone motion can increase the carpal tunnel space near the median nerve. Additionally, the results of this study suggest that carpal bone mobilization techniques which induce inward rotation of the hamate and trapezium may act to increase the CAA, thus relieving the pressure at the median nerve and alleviating the associated carpal tunnel syndrome symptoms.

Limitations with this study include the relative motion of the capitate and trapezoid, as well as the articulating bone surfaces, which were not accounted for in the simulation. Given the location of the median nerve with respect to the TCL, it was assumed that the motion of the insertion sites at the hamate and trapezium would have a greater effect of increasing the carpal arch area where the median nerve locates. Second, the effect of the surrounding tissue which would restrict the motion of the bones and TCL was not explicitly accounted for. Future studies would seek to provide validation by employing a method to monitor and measure the bone rotation and cross-sectional changes in-vivo. Third, the manual identification of the distal TCL insertion points was selected from a small area of the bone attachments. However, this geometric representation is unlikely to affect the main findings of the study, as the results are due to the carpal arch width change.