A Preliminary Model of the Wrist Midcarpal Joint

Abstract

Background  A challenge to deciphering the effect of structure on function in the wrist involves difficulty in obtaining in-vivo information. To provide a platform to study wrist mechanics using in vivo acquired forces, we developed a model of the midcarpal joint based on computed tomography (CT) scans of normal wrists. Finite element analysis (FEA) can enable application of in vivo collected information to an ex vivo model.

Objectives  The objectives of this study are to (1) create a three-dimensional model of the midcarpal joint of the wrist based on CT scans and (2) generate separate models for the midcarpal joint based on two distinct wrist types and perform a pilot loading of the model.

Methods  CT scans from a normal patient database were converted to three-dimensional standard template library (STL) files using OsiriX software. Five type 1 and five type 2 wrists were used for modeling. A simulated load was applied to the carpometacarpal joints in a distal-to-proximal direction, and FEA was used to predict force transfer in the wrist.

Results  There were 33% type 1 and 67% type 2 wrists. The midcarpal joint dimensional measurements estimated from the model had intermediate agreement between wrist type as measured on CT scan and as predicted by the model: 56% Cohen's kappa (95% confidence interval) = 0.221 (0.05–0.5). Surface stress on the carpometacarpal joints is different in type 1 and type 2 wrists. On loading the neutral wrist, the capitolunate angle was 90 degrees in type 1 wrists and 107 degrees in type 2 wrists ( p  < 0.0001).

Conclusions  The model predicted differences in movement and force transfer through the midcarpal joint dependent on structural type. This knowledge can improve our understanding of the development of disparate patterns of degeneration in the wrist.

Introduction

Structural variability affects the mechanics of distinctive wrists. ¹ This fact, coupled with difficulties in accruing in vivo data, precludes the relatively simple “one size fits all” approach to wrist mechanics. In an attempt to provide a platform for the study of wrist mechanics using in vivo acquired forces, but allowing for processing and analysis in vitro, we built a model of the midcarpal joint based on computed tomography (CT) scans of normal wrists. Modeling using finite element analysis can enable the application of in vivo collected information to an ex vivo model. ^{2 3}

The structure of the midcarpal joint has been divided into two structural patterns: a type 1 wrist that has a lunate type 1 and spherical proximal capitate, and a type 2 wrist with a type 2 lunate and flat proximal capitate. ^{4 5} This variation has been shown to affect load transfer in between the ulna and radius. ⁶ Assuming that these structural disparities will affect load transfer through the midcarpal joint, the purpose of this study was to:

• Provide a three-dimensional (3D) model of the midcarpal joint of the wrist based on CT scans of normal wrists.

• Generate separate models for the midcarpal joint based on two distinct wrist types (type 1 and type 2) and to perform a pilot loading of the model.

• To compare measurements and evaluation of bone shape within the midcarpal joints based on the model, with different methods of measurement based on plain radiographs and CT scans.

We hypothesized the load as predicted by the model will be transferred differently in the different wrist types within the midcarpal joint.

Methods

Thirty-seven distinct CT scans (.dicom files, anonymized, 2 mm/slice resolution) were randomly selected from a normal patient database. These scans had been accrued retrospectively and read by the radiologist as normal. To ensure image quality to produce the 3D models, we used only CTs with a complete 2 mm/slice interval across the entire scan. Hundreds of CT scans from a clinical database were evaluated and only 5% were eligible for modeling.

The CT measurements were performed on the coronal cuts of the wrist. To compare radiographs and CT scan measurements to the measurements as predicted by the model, and since the scans had not been done as part of a research protocol, the cuts that demonstrated the relevant joint were grouped together for measurement. All measurements were made using the PACS Carestream Version 11.0 computer program, and two hand surgeons performed the measurements on the CT scans.

The measurements that were performed included:

• Lunate type was classified according to the shape of the lunate in the midcarpal articulation. The definition does not rely on the amount of contact between the hamate and the lunate but is rather a categorical variable of contact versus no contact ⁵ :

  • Type 1 was defined as a lunate without a facet for the hamate bone.

  • Type 2 was defined as a lunate with a clear facet for the hamate bone.

• Capitate type was defined according to the shape of the proximal capitate in the midcarpal joint. ⁷ They were divided into spherical- and flat-type capitates.

• Wrist type 1 and 2: Wrist type 1 includes a type 1 lunate with spherical-type capitate and wrist type 2 includes a lunate type 2 with a flat-type capitate.

• The circumference of the capitate was measured using the outer cortical surface. In the model, the circumference of the capitate bone was predicted around the main axis, on the surface of the bone.

• Percent of the circumference of the distal capitate facet that articulates with the lunate is measured.

• Percent (capitate circumference) that comes in contact with the scapholunate ligament is measured.

• Percent (capitate circumference) that articulates with the scaphoid is measured.

• Percent (capitate circumference) that articulates with the hamate is measured.

• Percent (capitate circumference) that articulates with the trapezoid is measured.

• Percent (capitate circumference) that articulates with the base of the index and middle and ring metacarpal bones is measured. The measurements were based on previous studies ^{4 8}

The second part consists of generating a 3D model of the wrist midcarpal joint using finite element analysis, as follows.

Ten different CT scans were selected from our patient database, anonymized and converted into 3D files. To allow the image processing and computational work using these images, we exported these images to 3D .stl files using OsiriX software (version 9, 2016, GNU LGPL), keeping the maximum resolution available in the original files. These files are compatible with multiple 3D modeling and finite element analysis software.

The resulting .stl files were reviewed and processed to remove soft-tissue images and multiple elements not related to the analysis, such as names, labels, soft tissue, and other elements, using the software MeshLab (v. 2016.12, Pablo Cignoni, Visual Computing Laboratory) and optimized (correction of errors, closing gaps, and removal of orphan elements) using Meshmixer (v. 3.4.35, Autodesk). This allowed us to obtain clean 3D models of every specific wrist.

Once the files were optimized, we removed the phalanges, and the remaining bones were saved individually to keep their mechanical role and position, using 123Design software (v. 14.2.2, Autodesk 2015). Once we had all the wrist bones individually available (radius, ulna, lunate, scaphoid, trapezium, trapezoid, capitate, hamate, triquetrum, pisiform), they were imported into a COMSOL file, reconstructing the wrist as initially available in the CT scans. Once all the resulting structures are imported to COMSOL, the following geometry parameters were selected: length unit, centimeters; angular unit, degrees; and default relative repair tolerance, 1e-6; and these were configured to form an assembly with the same relative repair tolerance. These settings are selected to keep the highest fidelity possible with the original images.

Using the materials library available in the software, we assigned the mechanical properties of cortical bone to the elements in our simulations. The specific material properties are listed in Table 1 , which contains the material properties assigned to cortical bone to calculate a realistic material response in the simulation. These properties are available in the software materials library, and they are consistent with the literature and other publications using finite element analysis. ⁹

Table 1. The bony properties imported into the model.

Property	Value	Unit
Density	1,908	kg/cm 3
Young's (elastic) modulus	1.5	GPa
Poisson's ratio	0.56	–
Heat capacity at pressure	1,313	J/(kg × K)

We selected a solid mechanics study, in stationary conditions (no movement), using the COMSOL library for such conditions. The mechanical reference for the simulation of forces, ulna, and radial surfaces was assigned as the fixed boundary for the simulation.

Similarly, the simulated loads were applied in the most distal articular surface of the model with the wrists in neutral flexion/extension. We applied a load of 200 N onto the distal articular surfaces, in a distal-to-proximal direction, in the same fashion as a frontal fist punch to simulate the wrist load while generating a fist frontal load.

This load is aligned with the axial axis of the model (z-axis) and its magnitude is as detected in normal wrist studies. This load was based on a study evaluating force transfer to the wrist during performance of a pushup. ¹⁰

The software then constructed a finite mesh, with a triangular configuration. The finite element analysis software creates a mesh with triangular elements over our 3D model to be calculated individually and consequently extrapolates the final, general solution. These meshes can be built with triangular or sometimes hexagonal elements. We preferred triangular elements, since they were more versatile when completing our irregular model.

Calculations of forces were performed individually on each triangle of this mesh, and then extrapolated to represent the complete system. For these models, we used a high-resolution and high-quality setting, to predict more accurately the von Mises (surface) stresses occurring in the wrists.

We created stationary models for all of our simulations. The models were divided into two wrist types (type 1 and 2) based on our findings: specifically using the configurations that we found in the lunate and capitate angle. We had five models of type 1 wrist and five models of type 2 wrist.

Subsequently, we recreated the same stationary simulations into a multibody dynamic simulation, using the same settings as before, to predict directly (generating the predicted structure movement) the effects of the applied forces into the simulations.

Statistical Analysis

Statistical analysis was performed utilizing Wizard software (Evan Miller, v. 1.9.41). Data were checked for distribution normality and uniformity, and given the non-normal distribution of the data, analysis was performed using Shapiro–Wilk test, with a 95% confidence.

Results

In our modeling cohort, there were 33% type 1 wrists and 67% type 2 wrists. The midcarpal joint measurement of wrist type (including lunate and capitate type) estimated from the model had intermediate agreement with the CT scan measurements: 56% Cohen's kappa (95% confidence interval) = 0.221 (0.05–0.5).

In our model, the capitolunate angle was 90 degrees in type 1 wrists and 106.815 degrees in type 2 wrists, p  < 0.0001 ( Fig. 1 ) When loads are applied in our wrist models, von Mises (surface) stresses were 1.408 GPa (standard deviation [SD], 1.6) on average for type 1 wrists, while type 2 wrists showed an average stress of 7.1 GPa (SD, 5.5). This difference is statistically significant ( p  = 0.046; Table 2 and Fig. 2 ).

Fig. 1.

The difference in capitolunate angle between a type 1 and type 2 wrist.

Table 2. Surface (von Mises) stresses on the carpometacarpal joints.

Type 1	von Mises stress (GPa)	Type 2	von Mises stress (GPa)
1	0.22	1	1.26
2	3.74	2	5.26
3	0.0002	3	12.1
4	1.28	4	2.94
5	0.00012	5	13.6
Mean	1.05	Mean	7.03
SD	1.59	SD	5.52

Note: There are significant differences between the midcarpal joint type and surface force application at the carpometacarpal joints ( t -test, p  = 0.046).

Fig. 2.

The von Mises stresses in type 1 and type 2 wrists.

In the multibody dynamic models (as described in the methods), we found a qualitative difference: type 1 wrists showed broader movement predictions, in which the lunate, capitate, trapezium, and scaphoid may be displaced (or moved) by the applied forces. However, in type 2 wrists, the predicted movements showed a centralized behavior, involving only the hamate, lunate, and capitate bones. The average predicted displacement magnitudes (1620.4 cm [SD, 921.469] for type 1 wrists and 990.2 cm [SD, 199.99] for type 2 wrists) are not statistically different, and these numbers consider the displacement of a whole structure and not a single point in the model. However, although the t -test did not find a significant difference, it qualitatively revealed a more centralized behavior for type 2 wrists.

Discussion

Attempts at modeling of the wrist joint have been challenged by structural complexity, individual variation in structure, and functional intricacy that includes individual differences in the performance of tasks. A recent study evaluated robotic technology for in vitro testing to better understand the wrist joint biomechanics. ¹¹ Sandow et al have provided a “unifying kinetic theory of wrist motion based on isometric constraints and rules-based motion.” ² Our approach was to produce a preliminary model that accounts for structural variation in the wrist. Specifically, this preliminary study has started with evaluation of described variants of the midcarpal joint. The model demonstrated disparate force transfer and likely differential displacement dependent on the structural variation of this joint.

Our model predicted that a different angle between the capitate and lunate between a type 1 and type 2 wrist may transfer forces broadly through the wrist (to more bones), while a type 2 wrist transfers forces preferentially more centrally, toward the capitate–lunate joint. It is possible that the angle in the midcarpal joint acts to “modify” the transfer of forces, possibly dampening the increased force in a type 2 wrist. In a cadaver study, Wollstein et al found similarly that a type 1 wrist transferred more force ulnarly in the radiocarpal joint than a type 2 wrist. ⁶ This finding is counterintuitive in that we expect the type 2 midcarpal joint to be more stable due to the lunate hamate articulation and therefore to transfer forces more ulnarly, i.e., less toward the scapholunate joint. A kinetic in vivo study by Abe et al found more triquetral motion and lunate–triquetrum motion with increased shearing forces to the lunotriquetral interosseous ligament, as well as increased hamate lunate shear in type 2 lunates. This was found mainly in ulnar deviation of the wrist. This would seem to support more ulnarly translated forces in type 2 lunate wrists. ¹² However, this more “stable” column, while transferring compression to the triquetrohamate joint, may actually cause shear forces to be transmitted to the area of least resistance, i.e., more radially, into the more mobile scapholunate interosseous ligament (SLIL) area. Furthermore, the forces may differ in the different wrist positions, and while most of the load is transferred ulnarly in ulnar deviation of a type 2 wrist, this may differ in radial or neutral deviation. Since certain tasks require different wrist positions, and particular injuries occur with the wrist in different positions, the pathology that ultimately develops in any given wrist (such as Kienbock's disease, triquetrohamate degeneration, or a specific fracture pattern) may depend not only on the anatomy of the wrist but also on the direction and manner of the applied load.

Rhee et al found that in the presence of documented scapholunate injury, a type 1 wrist developed radioscaphoid dorsal intercalated segmental instability more often than a type 2 midcarpal joint. ¹³ Perhaps, the “locking” of the capitate into the lunate, in the presence of SLIL tear and loss of its restraint, affects the lunate more profoundly than when the lunate is also locked into the hamate and the ulnar carpal column. This would also support the “protective effect” of a type 2 lunate in Kienbock's disease as opposed to a type 1 wrist, where the forces are transferred almost exclusively to the lunate. ¹⁴ Bain et al found significantly greater motion at the radiocarpal joint during flexion/extension in type 1 wrists than in type 2 wrists. They also found that the relative contributions of the midcarpal and radiocarpal joints differed between the radial, the central, and the ulnar columns and that during wrist flexion and extension, these contributions were determined by the lunate morphology. The midcarpal articulations were relatively restricted during flexion and extension of a type 2 wrist. However, during radial–ulnar deviation, the midcarpal joint of the central column became the dominant articulation. ¹⁵ McLean et al looked at the association between midcarpal joint structure and scaphotrapeziotrapezoidal (STT) joint arthritis. They postulated that type 2 lunates cause STT joint osteoarthritis, though the association found does not support a cause-and-effect conclusion. ¹⁶

When taking our results, together with the literature, to understand the development of pathology, we should account for the following:

• The proximal carpal row (scaphoid, lunate, and triquetrum) behaves as an intercalated segment, and since there are no tendon insertions into these bones, their movement will be dependent on the forces applied through the distal carpal row and therefore the capitolunate angle (found to differ between wrist types in our model) will affect their movement. This row was found to move differently dependent on wrist type in the study by Abe et al. ¹²

• The anatomy and biomechanical significance of the ligamentous structural restraints.

• The effect of other related joints, such as the STT joint, lunotriquetral, and the carpometacarpal joints.

We had one-third type 1 wrists and two-thirds type 2 wrists. The actual distribution of type 1 and type 2 wrists in the normal population is unknown and may vary between different populations. ¹⁷ One study found an equal amount of type 1 and type 2 wrists. ⁸ Viegas studied 61 cadaver specimens and found type 1 lunates in 39.3% (no medial hamate facet was present) and type 2 lunates in 60.7%, similar to our numbers. ⁵ In another study of 165 dissected specimens, Viegas et al found 34.5% type1 and 65.5% type 2 wrists. ¹⁸

The development of degeneration will be dependent on the type of forces applied (whether traumatic or repetitive) and the underlying structure of the wrist. Our findings may be significant in understanding the development of degenerative changes in different individuals since structural wrist type and the resulting mechanics may predispose to specific osteoarthritic changes—either the typical scapholunate advanced collapse wrist, where the forces are concentrated on the relatively weak scapholunate joint, or onto the lunate, where either Kienbock's disease or midcarpal joint arthritis may develop preferentially. This information may also be helpful to understand the mechanism of injury in different wrists. Further study will incorporate adjacent joints as well as additional input to refine the model as well as to ultimately transfer forces gleaned in vivo during performance of different tasks.