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Published in final edited form as: J Hand Surg Am. 2012 May 26;37(7):1393–1399. doi: 10.1016/j.jhsa.2012.04.025

Elongation of the Dorsal Carpal Ligaments: A Computational Study of In Vivo Carpal Kinematics

Michael J Rainbow 1, Joseph J Crisco 1, Douglas C Moore 1, Robin N Kamal 1, David H Laidlaw 2, Edward Akelman 1, Scott W Wolfe 3
PMCID: PMC3381980  NIHMSID: NIHMS380925  PMID: 22633233

Abstract

Purpose

The dorsal radial carpal (DRC) and dorsal intercarpal (DIC) ligaments play an important role in scapholunate and lunotriquetral stability. The purpose of this study was to compute changes in ligament elongation as a function of wrist position for the DRC and the scaphoid and trapezoidal insertions of the DIC.

Methods

A computational model was developed that incorporated a digital dataset of ligament origin and insertions, bone surfaces models and in vivo 3-D kinematics (n = 28 wrists), and an algorithm for computing ligament fiber path.

Results

The differences between the maximum length and minimum length of the DRC, DIC scaphoid component, and DIC trapezoidal component over the entire range of motion were 5.1 ± 1.5 mm, 2.7 ± 1.5 mm, and 5.9 ± 2.5 mm respectively. The DRC elongated as the wrist moved from ulnar-extension to radial-flexion, and the DIC elongated as the wrist moved from radial deviation to ulnar deviation.

Conclusions

The DRC and DIC lengthened in opposing directions during wrist ulnar and radial deviation. Despite complex carpal bone anatomy and kinematics, computed fiber elongations were found to vary linearly with wrist position. Errors between computed values and model predictions were less than 2.0 mm across all subjects and positions.

Clinical Relevance

The relationships between ligament elongation and wrist position should further our understanding of ligament function, provide insight into the potential effects of dorsal wrist incisions on specific wrist ranges of motion, and serve as a basis for modeling of the wrist.

Keywords: Carpal, Dorsal, In Vivo, Kinematics, Ligaments

INTRODUCTION

The wrist is unique in that the motions of its component carpal bones are determined almost exclusively by cartilage contact and ligament forces rather than by direct muscular attachments. Many surgical interventions attempt to restore ligament function [1–2], yet little is known about the in vivo mechanical behavior of the ligaments. One set of ligaments that has not been extensively studied in vivo is the extrinsic dorsal carpal ligaments. The dorsal carpal ligaments consist of the dorsal intercarpal ligament (DIC) and the dorsal radiocarpal (DRC) ligament [3], which together form a lateral V shape, originating on the triquetrum and inserting on the scaphoid, and originating on the radius and inserting on the triquetrum respectively. Although these ligaments have been characterized as less substantive when compared to their volar counterparts, [4] recent studies have suggested that they play an important role in scapholunate stability and lunotriquetral stability [5–7].

Determining how a ligament elongates as a function of wrist position is a crucial step in understanding ligament function. Much of the previous work on carpal ligaments has focused on mechanical testing and anatomical descriptions of the ligaments and their origin and insertion sites [3–4, 6, 8–9]. Measuring ligament length changes as a function of wrist position in living subjects is a challenge because current imaging modalities are limited in their ability to simultaneously resolve bone surfaces, kinematics, and soft tissue morphology. The current state of the art for in vivo imaging of the carpal ligaments is limited to identification of major ligaments and pathological conditions [10] [11].

Computational models can be powerful tools for evaluating wrist kinematics and ligament function. These models have previously provided insights into pathology of the distal radioulnar joint [12]. Additionally, they have determined which wrist motions are likely to cause the carpal ligaments to become taut [13–14]. The elongation of the DRC and DIC ligaments have been previously studied along specific paths of ulnar-radial deviation [15] and a dart thrower’s path [16] using this approach. The purpose of this study was to determine the relationship between fiber elongation and wrist position of these 2 important dorsal carpal ligaments through the full range of wrist motion.

METHODS

Carpal Bone Surfaces and Kinematics

After institutional review board approval and informed consent, both wrists of 8 healthy men (mean age 24; range 22–26) and 6 healthy women (mean age 25; range 21–28) underwent computed tomographic (CT) imaging in 9 wrist positions as part of another study [17]. Both the right and left wrist were scanned simultaneously using a GE HiSpeed Advantage CT scanner (GE Healthcare Technologies, Waukesha, Wisconsin) with settings of 120kVP and 80mAs, in plane resolution of 0.9 × 0.9 mm2, and slice thickness of 1.0 mm. Digital bone surface models (BSMs) for each subject were obtained via segmentation of the CT volumes (ANALYZE™, Mayo Clinic Foundation, Rochester, MN) and tessellation using GEOMAGIC STUDIO (Raindrop Geomagic, Research Triangle Park, NC). Kinematic transformations from the neutral wrist position to the remaining positions were calculated using a previously-reported markerless bone registration technique [18–19]. Briefly, the technique first identified tissue-classified voxels associated with the segmented point cloud of each carpal bone in the neutral position. Then, the algorithm optimized the fit between the neutral position voxels and voxels in each subsequent scan, computing the change in bone posture with sub-voxel accuracy [19]. Actual wrist position was defined by the position of the capitate with respect to the radius [20]. The targeted wrist positions of neutral, 40° flexion (F), 40° extension (E), 10° radial deviation (R), 30° ulnar deviation (U), and the combined motions of 40° E and 30° U, 40° F and 30° U, 40° E and 10° R, and 40° F and 10° R resulted in a range of wrist motion for all subjects of 34° F to 62° E and 35° U to 27° R. The actual range of wrist motion per subject was 29° ± 6° ulnar-radial deviation (UR) and 69° ± 8.° flexion-extension (FE) [17].

Selection of Ligament Insertion Regions

The DRC and DIC ligaments insert on multiple bones and interdigitate with other ligaments. Only the largest portions of the DRC and DIC ligaments with insertion areas greater than 4 mm2 [21] were modeled in the present study. These included the main band of the DRC ligament, which originates on the dorsal medial ridge of the radius, passes over the lunate, and inserts onto the dorsal pole of the triquetrum. They also included the main bundles of the DIC ligament, which originate on the dorsal pole of the triquetrum and pass over the hamate, lunate, and capitate to insert onto the dorsal ridge of the scaphoid (DICS) and the dorsal aspect of the trapezoid (DICT) [3]. These attachments of the DRC, DICS and DICT ligaments have been reported to be present in 100%, 97%, and 42% of people, respectively [6]. The regions of insertion were mapped to each subject’s BSM using a template created in a previous study via careful digitization of insertion sites on cadaver bones which were then registered to the corresponding BSM [22]. Insertion site mapping was performed manually using GEOMAGIC STUDIO, with both models opened simultaneously for visual comparison (Fig 1).

Figure 1.

Figure 1

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The template [22] insertion BSM (top) with points representing the insertion regions for the dorsal radio carpal ligament: DRC (blue), scaphoid attachment of the dorsal intercarpal ligament: DICS (red), and trapezoidal attachment of the dorsal intercarpal ligament: DICT (green), and a representative subject’s BSM (bottom) with polygons selected to match the template insertion regions. The points on the subject’s triquetrum represent the 3 fibers analyzed: the most proximal point located on the perimeter, the most distal point, and a point in the center of the insertion region.

Ligament Fiber Generation

Fibers for all 3 ligaments (DRC, DICS and DICT) were modeled as paths of points that traversed the shorted possible distance between insertion sites, with the constraint that the BSMs were not penetrated (Fig 2) [23]. Each fiber contained 40 discreet points (39 segments), and the length of each ligament fiber at each wrist position was defined as the distance along its path. A central fiber was defined between the central points of corresponding attachment regions. Two additional fibers were also defined using the most proximal and distal aspects of the triquetrum insertion region. The fibers were roughly parallel to the central fiber based on previous qualitative studies that showed that individual fibers were primarily aligned with the course of the ligament [8, 24]. The paths and lengths of the central, proximal, and distal fibers were computed for each subject in each of the 9 widely distributed wrist positions. The total excursion of each ligament fiber was defined as the difference between its minimum and maximum length across all 9 wrist positions.

Figure 2.

Figure 2

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Right wrist, dorsal view. The proximal, central, and distal fibers of the dorsal radiocarpal ligament: DRC (blue), scaphoid attachment of the dorsal intercarpal ligament: DICS (red), and trapezoidal attachment of the dorsal intercarpal ligament: DICT (green) of a subject in a slightly extended wrist position.

Analysis

The relationship between fiber length and wrist position was evaluated using hierarchical linear modeling (HLM). HLM can be conceptualized as a set of subject-specific best-fit planes fit to the wrist position and fiber length data, with wrist position as the independent variable and fiber length as the dependent variable. The length of each fiber at the neutral position (0° FE and 0° UR) was used to define the intercept of the model. The coefficients of the best-fit model, termed elongation rates, reflect the change in fiber length per change in wrist position. The HLM evaluated the model parameters using a hierarchy of 3 levels. The first level contained the central, proximal, and distal fibers within each ligament, the second contained each ligament within a subject’s wrist, and the third contained all wrists within the study population. The HLM used residual estimation of maximum likelihood to simultaneously evaluate ligament lengths at each level of the hierarchy as well as the interactions between levels and within each level [25].

The fidelity of the HLM was reported in terms of the root mean squared error between the ligament lengths computed from the in vivo data set and the lengths estimated by the HLM. The HLM was used to determine the elongation rate along 4 specific paths of wrist motion: pure FE (with ulnar-radial deviation set to 0°), pure ulnar-radial deviation (with flexion-extension set to 0°), the dart thrower’s path (radial-extension to ulnar-flexion), and the anti-dart thrower’s path (ulnar-extension to radial-flexion). The dart thrower’s and anti-dart throwers paths were oriented 45° to the flexion-extension and ulnar-radial deviation paths and passed through 0° FE and 0° UR. The HLM model tested which paths of wrist motion significantly lengthened each ligament. The HLM determined if the fibers within a ligament had significantly different elongation rates. The threshold for statistical significance was set a priori at P < 0.05. The HLM also predicted which paths of wrist motion minimized the elongation rate. In other words, it identified the paths of wrist motion where the fiber length was constant. These minimal paths were reported for each ligament in terms of degrees of FE per degree of ulnar-radial deviation.

RESULTS

There were no statistically significant differences in elongation rates between the central, distal, or proximal fibers within each ligament as the wrist moved through its range of motion. Therefore, the results presented herein are reported at the ligament level. The mean total excursions were 5.1 ± 1.5 mm for the DRC ligament, 2.7 ± 1.5 mm for the DICS ligament, and 5.9 ± 2.5 mm for the DICT ligament. The average neutral length estimated by the HLM was 16.1 ± 3.7 mm, 21.8 ± 4.2 mm, and 26.0 ± 4.2mm, for the DRC, DICS, and DICT ligament s respectively. Neutral fiber length of each ligament was found to increase significantly (P < 0.05) with an increase in size of the subject's capitate (Fig. 3).

Figure 3.

Figure 3

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Neutral fiber length versus the cube root of the capitate’s volume. The neutral fiber length increased significantly with increasing wrist size as measured by capitate volume (P < 0.05). This size effect is accounted for by the hierarchical linear model, as it models length changes from neutral of each subject.

Fiber length varied linearly with wrist position for the DRC, DICS, and DICT ligaments, as reflected in low root mean squared errors between the computed and HLM-estimated fiber lengths, which were 1.0 mm, 1.8 mm, and 1.2 mm for the DRC, DICS, and DICT ligaments, respectively.

Ulnar-Radial Deviation

The DRC ligament significantly lengthened during radial deviation (P < 0.001), while the DICS, and DICT ligaments significantly lengthened with wrist ulnar deviation (P < 0.001) (Fig 4 a–b). The elongation rate of the DRC ligament was 0.078 ± 0.009 mm/deg (standard error of the mean) of wrist radial deviation, while the elongation rate of the DICS and DICT ligaments were 0.053 ± 0.009 mm/deg and 0.147 ± 0.009mm/deg, of wrist ulnar deviation respectively.

Figure 4.

Figure 4

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Ligament fiber path computed for a representative wrist in a. radial deviation, b. ulnar-deviation, c. flexion, and d. extension.

Flexion Extension

The DRC ligament lengthened significantly (P < 0.001) with flexion, with an elongation rate of 0.051 ± 0.003 mm/deg of wrist flexion (Table 1). Neither wrist flexion nor extension lengthened the DICS ligament (P = 0.37). The DICT ligament lengthened (P < 0.001) with an elongation rate of 0.023 ± 0.03 mm/deg of wrist flexion (Fig 4 c–d).

Table 1.

HLM-predicted ligament elongation rates in the direction of flexion-extension (FE), ulnar radial deviation (UR), the dart thrower’s path (RF to UE), and the anti-dart thrower’s path (UF to RE). The sign of the elongation rate reflects the direction of motion in which the ligament elongates (e.g. a negative value in the U(+) R(−) field indicates ligament elongation in radial deviation.

Neutral Length
(mm (standard error))
Ligament U(+) R(−) F(+) E(−) UF(+) RE(−)

Dart Thrower’s
Path		 RF(−) UE(+)

Anti-Dart Thrower’s
Path
DRC 16.1 (0.7) (−) 0.078 (0.009)* 0.051 (0.003)* (−) 0.04 (0.008)* (−) 0.084 (0.004)*
DICS 22.2 (0.8) 0.053 (0.009)* 0.001 (0.003) 0.045 (0.008)* 0.027 (0.004)*
DICT 25.6 (0.8) 0.147 (0.009)* 0.023 (0.003)* 0.137 (0.008)* 0.058 (0.004)*
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*

P < 0.001

Dart Thrower’s Path (wrist radial-extension to ulnar-flexion)

The DRC ligament lengthened with an elongation rate of 0.040 ± 0.008 mm/deg of wrist motion along a path from ulnar-flexion to radial-extension (P < 0.001), which is the reverse of the dart thrower’s path. The DICS and DICT ligaments lengthened with an elongation rate of 0.045 ± 0.008 mm/deg and 0.137 ± 0.008 mm/deg of wrist motion along the normal dart thrower’s path (P < 0.001).

Anti-Dart Thrower’s Path (ulnar-extension to radial-flexion)

The DRC ligament lengthened with an elongation rate of 0.084 ± 0.004 mm/deg of wrist motion along the anti-dart thrower’s path (P < 0.001)o. Fibers of the DIC ligament lengthened with an elongation rate of 0.027 ± 0.004 mm/deg (DICS ligament) and 0.058 ± 0.004 mm/deg (DICT ligament) of wrist motion along a path from radial-flexion to ulnar-extension (P < 0.001), which is the reverse of the anti-dart thrower’s path.

Paths of Minimal Elongation

The length of the DRC ligament remained constant along a dart thrower’s path that had a coupling ratio of 1.5° of FE for every 1° of UR. The length of the DICS ligament was constant in pure flexion-extension, and the length of the DICT ligament was constant along a path with a couple ratio of 7.1° FE for every 1° UR.

DISCUSSION

The aim of this study was to expand our understanding of dorsal ligament function using a computaional model developed with an in vivo carpal kinematics database. Ligaments may prevent extreme joint motion by functioning as check-reins, and they may guide the carpal bones synchronously through the wrist’s full range of motion. It has been proposed that a ligament that elongates through a range of motion functions as a check-rein, while a ligament that does not lengthen functions as a guide [26]. Our results suggest that the dorsal carpal ligaments may function differentially, as both check-reins and guides, depending on the direction of wrist motion. In our model, the DIC ligament elongates when the wrist moves toward ulnar deviation, while the DRC ligament elongates when the wrist moves toward radial deviation. Accordingly, the DIC and DRC ligaments limit motion at the extremes of ulnar and radial deviation, respectively, acting as check-reins. In contrast, the elongation of the DRC ligament was minimized along a dart thrower’s path that had a coupling ratio of 1.5° of FE for every 1° of ulnoradial deviation. The length of the DICS ligament is essentially constant during pure wrist FE, while elongation of the DICT ligament was minimized along a path of flexion-extension and slight ulnar-radial deviation. These paths of minimal elongation would suggest that if the ligament fibers were strained, they could be functioning to guide the carpal bones through these ranges of motion.

When interpreting these data, it is important to note that the length at which a ligament transitions from being slack to generating tensile loads cannot be definitively determined with our methods. A related limitation is that slack ligament lengths were likely included in the HLM model. However, the inclusion of slack lengths in the model does not affect our elongation results because the carpal ligaments transition between slack and taut states in a linear fashion [27]. One final implication of the linear model is that a ligament fiber that elongates when the wrist is moved in a specific direction will shorten by the same amount when the wrist is moved in the exact opposite direction.

The range of elongation and neutral length of the DIC and DRC ligaments compared well with previous in vitro and in vivo studies despite these limitations and large variability between studies [6, 8–9, 28]. The neutral length of the DRC and DIC ligaments fell within ranges of (14.7 mm to 17.7 mm) and (13.5 mm to 40.9 mm) reported in several cadaver studies [6, 8, 21]. Neutral lengths and elongation of the DRC and DIC ligaments compared well with in vivo studies that used similar techniques to measure elongation in radial and ulnar deviation and the dart thrower’s motion [15–16]. Neutral lengths of the DRC, DICS, and DICT ligaments differed between our study and previous studies by 1.0 mm, 2.8 mm, and 1.4 mm respectively and were within the standard deviations of each other. In a cadaver study, Savelberg et al. [27] injected radio-opaque beads into the carpal bones and selected ligaments and used Roentgen stereophotogrammetry. They found that the DRC ligament lengthened 5.7 ± 5% when the wrist was flexed to 70 ± 15° but did not elongate in radial or ulnar deviation. Beginning in the clinical neutral position (0° FE, and 0° UR), the elongation of the DRC ligament in our study increased to 22% (CI: 21% – 23%) in a position of 70° flexion; however, we found that the DRC ligament also elongated more substantially in positions of radial deviation. Savelberg et. al. reported that the DIC ligament elongated 6 ± 4% when the wrist was ulnarly deviated to 44 ± 7°, but this value was not statistically significant. Our study found a greater elongation of the DIC with values of 10% (CI: 9% – 10%) (DICS) and 23% (CI: 23% –23%) (DICT) at 40° of ulnar deviation. The consistently higher elongation values found in this and other in vivo studies, compared to cadaver studies, could be due to the assumption that neutral length occurs at the neutral wrist position (0 ° FE, and 0 ° UR). This assumption may cause higher percent changes in elongation. While not an outcome of our study, the mean insertion site areas were within 1 standard deviation of those reported in Nagao et al [21]. The average difference between insertion site areas reported in Nagao et al. and those in the present study was 3 mm2.

It has been postulated that the DRC and DIC ligaments work in tandem to support the scaphoid throughout the range of motion [6]. This is possible only if the DRC ligament is taut in the same positions that the DIC ligament is taut. Our study suggests that the ligaments may be complementary; while one ligament is elongating, the other is shortening and possibly moving into a slack state. However, we did not model the lunate attachments of either ligament or their direct interactions with one another. Modeling these attachments may reveal an interaction between the DRC and DIC ligaments that supports the concept that they work in tandem to support the scaphoid. The DIC ligament elongated in ulnar deviation but not in FE, consistent with Macconnail’s description of the “screw-home” mechanism of the wrist and the importance of the dorsal intercarpal ligament to proximal row synchrony [29].

Our results suggest that even limited approaches to the wrist, including the dorsal approach to the scaphoid for nonunion, or TFCC approaches to the ulnocarpal joint, if associated with scarring of the dorsal extrinsic ligaments, would lead to deficits in wrist motion. A dorsal approach that leads to scarring of the DRC ligament, for example, could potentially lead to decreased wrist flexion, radial deviation, and ulnar-flexion, while an approach that leads to scarring of the DIC ligament would lead to decreased ulnar deviation and ulnar-flexion. We postulate that alternative approaches to the wrist, such as arthroscopy, that cause minimal disruption of these ligaments, along with early range of motion may decrease the risk of postoperative wrist stiffness.

We quantified the elongation of the fibers of the DRC and DIC ligaments over all anatomical and oblique planes of active motion. Previous studies have examined length changes in these ligaments along specific motion paths. This study generated a ligament elongation model using multiple directions of wrist motion simultaneously. Computing ligament elongations as a function of wrist position is an important step to determining the function of these ligaments during motion. We identified differing behaviors of the DRC ligament and the scaphoid and trapezoidal attachments of the DIC ligament. An improved understanding of these dynamic relationships will better predict ligament response to injury and repair, and their effects on wrist range of motion.

Acknowledgements

Funded by NIH HD052127 and AR053648. We would like to acknowledge the Division of Biomechanics and Bone Physiology Research at the University of Texas Medical Branch Department of Orthopaedic Surgery and Rehabilitation for their contribution of 3D bone structures with ligament attachment regions.

Footnotes

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