Association of Lunate Facet Inclination Angle and Interfacet Angle With Kienböck Disease: A Biomechanical Study

Abstract

Purpose

Kienböck disease is a rare but severe disorder that causes avascular necrosis of the lunate, resulting in wrist pain, functional disability, and early onset arthritis. Although the exact cause remains unknown, changing biomechanical stresses on the lunate have been linked. The purpose of this study was to investigate the association between lunate facet inclination (LFI) angle, interfacet angle (IFA), scaphoid facet inclination (SFI), and stress distribution on the lunate in order to better understand biomechanical risk factors for Kienböck disease.

Methods

This was an experimental study in which a 3-dimensional model was generated from CT images of a healthy wrist, and LFI, SFI, and IFA were changed by simulated osteotomies. A finite element analysis was used to determine stress on the lunate in various situations. Nine different wrist models were tested to determine changes in LFI, SFI, and IFA, as well as the loads placed on the lunate's articulations with the scaphoid, radius, triquetrum, and capitate during flexion and extension.

Results

Our investigation found a strong negative correlation between LFI and lunocapitate joint stress. This suggests that a flatter LFI increases mechanical stress on the lunate. In contrast, higher LFI angles were associated with increased scapholunate stress. The findings imply that LFI could have a direct influence on stress patterns within the lunate, shading light on how these angles may contribute to disease development.

Conclusions

This study shows that LFI is a significant biomechanical element affecting lunate stress in Kienböck disease. Our findings could support the inclusion of these criteria, in addition to ulnar variance and radial inclination, in diagnostic and surgical considerations for Kienböck disease therapy.

Type of study/level of evidence

III.

Kienböck disease is a condition in which lunate undergoes necrosis, which leads to early arthritis and painful degenerative changes.¹ Although Kienböck disease is categorized as a rare condition with a prevalence of less than 0.3%, it can severely deteriorate occupational activities of the patients.2, 3, 4 The patients commonly complain from a variety of severity of wrist pain, painful grip, dorsal wrist swelling, and limited range of motion in different stages of this disease.⁵ Because of the low prevalence of this disease and limited studies regarding this condition, the precise etiology of this disease is yet to be discovered. However, repeated microtrauma and increased load to the lunate have been implicated to be influential in pathogenesis.⁶ Moreover, few studies have evaluated the risk factors for the severity of Kienböck disease such as family history of this condition, as well as prolonged alcohol, tobacco, and corticosteroid consumption.⁷

Plain radiography is used in diagnosis of Kienböck disease, which is usually unremarkable in early stages. However, this modality can rule out other causes for wrist pain and can be used in follow-up of disease progression⁵ Although MRI is the gold standard of diagnosis for this condition in early stages, CT scans can be used for better evaluation of patients suspected for Kienböck disease.⁸

Radiographic studies have found that the morphology of lunate is associated with the severity of Kienböck disease; for instance, lunate bones without medial facet are more likely to have more severe course compared to lunate without this landmark.⁹ Radial inclination and palmar tilt were also associated with the development of Kienböck disease.¹⁰ Increased interfacet angle (IFA) and shallower lunate facet inclination (LFI) angle were risk factors for this disease.¹¹ However, because of the lack of appraised evidence, in this study, we aimed to assess the relationship between IFA and LFI angle with the forces imposed on lunate in Kienböck disease. The main hypothesis associated with this study was that any alternations in interface angle and LFI angle influence the stress applied on lunate in Kienböck disease. This is one of the first studies that evaluated the relationship between LFI angle and IFA with Kienböck disease based on a biomechanical study.

Methods and Materials

In this study, the wrist CT scan of a normal male subject (37 years old) with normal skeletal maturation and normal bone densitometry and without any degenerative disorder or fracture was used. An ethical approval was obtained from Shiraz University of Medical Sciences ethical committee. Materialize Mimics software (developed by Materialize NV) was used to create 3-dimensional model of wrist bones. The CT scan was obtained with the wrist in neutral position, shoulder in a 90° abduction, and elbow in 90° flexion. The CT scan slices had 0.98 mm thickness. The CT images were imported into Mimics version 19.0, and the 3-dimensional model of the wrist with Kienböck disease was made using these steps: First, a mask was created based on the Hounsfield units of the CT images, the masks were edited, the separate parts were divided using the “region growing” feature, the 3-dimensional model was created based on the region masks, and finally, the tiles were converted to a format compatible with 3Mat software (developed by Materialize NV) by the use of “re-mesh” option.

It should be noted that wrist bones, metacarpals, ulna, and radius were created separately in Mimics software. Various steps were performed to prepare the final models, including removing intersects, smoothing, and remeshing. The size of the mesh varied between 0.5 for carpal and 1 mm for radius and ulna. In the next step, the format of the mesh was changed from surface to volume mesh, in 3Mat software. The models of the bones were exported from 3mat software to Mimics software to assign the material. The material properties of bone (bone mineral density and young modulus of elasticity) were assigned to the models. It was performed based on the number of pixels in CT scan images by use of the following equations. In the next stage, the files were exported to Abaqus software and were assembled on each other. The following equations were used to calculate the bone density and young modulus of elasticity from gray level¹²:

$$\mathrm{\rho }=-13.4\pm 1017\text{GV}$$

$$\mathrm{E}=-388.8+5925\mathrm{\rho }$$

In which, E was Young modulus of elasticity, ρ was appearance bone density, and GV was gray value.¹²

The supportive ligaments of wrist joint, carpometacarpal joint, intercarpal joints, and supportive capsule were modeled as spring element. The stiffness of the ligaments was obtained from the available literature.^13,14 An external force of 50 N was applied on metacarpals equally (10 N force was applied on each metacarpal). The interaction between articular surfaces was considered as friction less. The proximal part of radius and ulna was considered as boundary condition.¹⁴

The validation of the models was also evaluated in this study. The validation of the models was performed based on the following procedures^14,15:

• 1.Comparison of the alignment of bones in the model with CT scan images: There was no change in the alignment of bones between the models and CT scan images in natural position.
• 2.Evaluation of mechanical properties of the models’ structures with available literature.
• 3.Comparison between the range of motion of the wrist joint in normal model with the outputs of the studies from the literature. There was a high agreement between the outputs of our model with literature.¹⁴

To measure the LFI angle, a line was drawn from the most distal ulnar edge of the lunate facet to the interfacet ridge. The angle between the aforementioned line and the line perpendicular to the radial axis was named LFI angle. The scaphoid facet inclination (SFI) angle was measured as the angle between the line perpendicular to the radial axis and the line connecting the interfacet ridge to the most distal part of the radial styloid process. The IFA was calculated by subtracting LFI angle from SFI angle.¹¹

After 3-dimensional modeling of the wrist of the normal subject in neutral position, the LFI angle and the IFA were altered by wedge osteotomy 2cm above the articular surface of distal radius to measure the load imposed on lunate especially its articulating surface with scaphoid, capitate, triquetrum, and radius bones in each two positions. Medial based closing wedge osteotomies (2.5°, 5°, and 7.5°), lateral based closing wedge osteotomies (2.5°, 5°, and 7.5°) and excision of bone from both medial and lateral side (1, 2, and 3 mm) were performed to change the aforementioned angles.

Medial wedging was performed in condition 1 (2.5°), condition 2 (5°), and condition 3 (7.5°). Lateral wedging was performed in condition 4 (2.5°), condition 5 (5°), and condition 6 (7.5°). Resection of 1 mm bone equally from medial and lateral side of distal radius was performed in condition 7, 2 mm in condition 8, and 3 mm in condition 9. The Figure 1 sorts some of the models used in this study. Totally, 10 conditions were evaluated in this study. It should be noted that the resection of radius based on above-mentioned conditions was performed in 3Mat software.

Figure 1.

The 3-dimensional model of wrist joint in 3Mat software: A Condition 1. B Condition 2. C Condition 4.

The LFI, SFI, and the IFAs were determined. Models of wrist joint of aforementioned conditions were exported to Abaqus software. A force of flexion (5 kg external force) and extension were applied on the models. The force was applied equally on each finger. The change of LFI, SFI, and IFAs were determined for each condition. Stress applied on lunate (von Mises stress) in scapholunate, radiolunate, lunotriquetral, and lunocapitate were evaluated in this study for each condition.

The data were entered into IBM SPSS version 26.0. The correlation between the stress applied on the lunate in aforementioned conditions and the angles were determined by Pearson correlation analysis.

Results

The mean values of LFI, SFI, and IFAs are shown in the Table 1. As demonstrated in this table, the LFI, SFI and IFAs in normal condition were 17°, 35.5°, and 18.6°, respectively. The LFI angle varied from 10° (condition 3) to 24° (condition 4). The SFI angle differed from 7° (condition 7) and 33.5° (condition 3). The minimum and maximum values of IFA were 7° in condition 7 and 23.5° in condition 3.

Table 1.

Stress Applied on Lunate in Wrist Flexion

Conditions	LFI (°)	SFI (°)	IFA (°)	LS-Stress (MPa)	LR-Stress (MPa)	LT-Stress (MPa)	LC-Stress (MPa)
Normal	17	35.5	18.5	1.6	1.6	12	12
Condition 1	11.5	28	16.5	5	5.69	6.49	6.49
Condition 2	13	25.5	12.5	13	4.4	4.4	13
Condition 3	10	33.5	23.5	4.9	14.7	4.9	14.7
Condition 4	24	37	13	27.3	18	0.7	0.27
Condition 5	14.5	27	12.5	7.8	15.6	3.9	15.6
Condition 6	13	22	9	8.99	17.9	4.49	13.4
Condition 7	14	7	7	3.17	12.7	12.6	12.6
Condition 8	11	25	14	4.82	1.6	9.6	12.8
Condition 9	16	32.6	16.6	4.26	4.26	7.14	9.99

IFA, interfacet angle; LC, lunocapitate; LFI, lunate facet inclination; LR, lunoradius; LS, lunoscaphoid; LT, lunotriquetral; MPa, megapascal; SFI, scaphoid facet inclination.

The stress applied on the lunate in its articulation with scaphoid, radius, triquetrum, and capitate bones are shown in Table 1 for flexion and Table 2 for extension. The stress of lunoscaphoid in normal condition was 1.6 MPa, compared to 3.17 MPa in condition 7 and 27.3 MPa in condition 4 in flexion of wrist joint. The stress of radiolunate articular surface in condition 8 was the same as that in normal condition. The maximum value of stress applied on lunate in radiolunate surface in condition 4 followed by condition 6 and condition 5 in flexion of wrist joint. The stress of lunate in lunotriquetral surface in all conditions was less than that in normal condition (the stress of lunatetriquetral was 12 MPa in normal condition). The stress of lunate in lunocapitate surface in normal condition was 12 MPa, compared to 6.5, 13, 14, 7, 0.27, 15.6, 13.4, 12.6, 12.8, and 9.99 in conditions 1−9, respectively (Table 1).

Table 2.

Stress Applied on Lunate in Wrist Extension

Conditions	LFI (°)	SFI (°)	IFA (°)	LS-Stress (MPa)	LR-Stress (MPa)	LT-Stress (MPa)	LC-Stress (MPa)
Normal	17	35.5	18.5	55	55	386	55
Condition 1	11.5	28	16.5	13	13	34	27
Condition 2	13	25.5	12.5	120	490	180	61.7
Condition 3	10	33.5	23.5	463	463	154	51
Condition 4	24	37	13	6.65	8.9	17.8	17.8
Condition 5	14.5	27	12.5	98	29.4	98	98.1
Condition 6	13	22	9	89	119	119	119
Condition 7	14	7	7	20	12.7	12.6	12.6
Condition 8	11	25	14	4.82	20	83	83
Condition 9	16	32.6	16.6	29.9	29.9	149	29.9

IFA, interfacet angle; LC, lunocapitate; LFI, lunate facet inclination; LR, lunoradius; LS, lunoscaphoid; LT, lunotriquetral; MPa, megapascal; SFI, scaphoid facet inclination.

The stress applied on lunate in its articulation with scaphoid, radius, capitate, and triquetrum in extension of wrist joint is shown in Table 2. As can be seen from this table, the stress of lunate in its articulation with scaphoid was 55 MPa in normal condition. However, the stress in conditions 2, 3, 5, and 6 was more than normal condition. In contrast, in other conditions the stress was less than normal condition.

The stress of lunate in radiolunate surface in conditions 2 and 3 was more than that in normal condition. However, in other conditions, the stress decreased considerably. The stress of lunotriquetral surface in extension of wrist joint was also evaluated in this study. The interesting point was that the stress of lunotriquetral surface in normal condition was more than that of other conditions (in normal condition was 385 MPa). The stress of lunate in lunocapitate surface was 55 MPa in normal condition, 61.7 MPa in condition 2, 98.1 MPa in condition 5, 83 MPa in condition 7, and 119 MPa in condition 6. In contrast, in other conditions, the stress was less than normal condition (Table 2).

Pearson correlation analysis was also performed in this research study. As can be seen from Table 3, the Pearson correlation between LFI angle and stress applied on lunocapitate surface of lunate were 0.713 and −0.292 for flexion and extension, respectively. There was a high negative correlation between LFI and stress applied on lunate in lunocapitate surface articulation in flexion of wrist. The Pearson correlation between LFI and stress applied on lunoscaphoid surface of lunate was 0.7. There was a high positive correlation between LFI and stress applied on scapholunate articulation of lunate in flexion of wrist joint (Table 3). Figures 2, 3, and 4 shows the LFI angle, SFI angle and IFA, respectively.

Table 3.

Pearson Correlation Between Angles and Applied Stress on Articulating Surface of Lunate

	LFI	P	SFI	P	IFA	P
Wrist flexion
LS-stress	0.7	.024∗	0.3	.37	−0.2	.52
LR-stress	0.2	.45	−0.1	.76	−0.3	.42
LT-stress	−0.2	.40	−0.4	.19	−0.6	.87
LC-stress	−0.7	.03∗	−0.3	.32	0.03	.97
Wrist extension
LS-stress	−0.4	.21	0.2	.53	0.6	.6
LR-stress	−0.3	.26	0.1	.76	0.3	.3
LT-stress	0.04	.90	0.2	.43	0.4	.3
LC-stress	−0.2	.43	−0.5	.11	−0.5	.14

IFA, interfacet angle; LC, lunocapitate; LFI, lunate facet inclination; LR, lunoradius; LS, lunoscaphoid; LT, lunotriquetral; MPa, megapascal; SFI, scaphoid facet inclination.

^∗Statically significant.

Figure 2.

Lunate facet inclination angle in normal and other conditions.

Figure 3.

Scaphoid facet inclination angle in normal and other conditions.

Figure 4.

Interfacet angle in normal and other conditions.

Discussion

The pathoetiology of Kienböck disease is not clear. In the literature, various causes such as trauma, vascular impairments, hereditary, and metabolic have been suggested. Moreover, the complex anatomy of the wrist joint has been explored and various mechanical etiologies have been hypothesized.^1,5 Several mechanical factors have been proposed to elucidate the etiology of Kienböck disease. The factors arising from structures adjacent to the lunate are classified as “extrinsic” factors. These include ulnar variance (UV), radial inclination, and radiolunate coverage.¹⁶ Most of the studies on Kienböck disease are focused on radial inclination and UV. Yet, limited numbers of studies have evaluated the role of LFI, SFI, and IFA in pathogenesis of Kienböck disease.

In this biomechanical study of the wrist joint in Kienböck disease, we have evaluated the association of the stress in lunate articulations with alterations in the LFI, SFI, and IFA. We observed a significant negative correlation between LFI and lunocapitate joint stress. Moreover, scapholunate joint stress elevated with increase in LFI.

The lunate is an important component of the carpus, responsible for conducting stress and different forces across the wrist joint. The unique anatomical position of the lunate and its articulations with adjacent bones, particularly the capitate, highlight its vulnerability to avascular necrosis in Kienböck disease. High lunocapitate joint stress, as demonstrated in our study, leads to greater mechanical load on the lunate causing progression of the Kienböck disease. On the other hand, a greater LFI appears to reduce the stress transmitted through the lunocapitate joint, potentially offering a protective biomechanical effect.

Our findings coincide with Yildirim et al¹¹ study of 82 wrists with Kienböck disease. They reported the association of decreased LFI with Kienböck disease. The angle between the curvature of distal radius and development of Kienböck disease was evaluated in their study. The results of their study showed that IFA was considerably higher than normal value in Kienböck disease. An increase in IFA increases the stress on lunate.¹¹ However, it should be noted that the study by Yildirim et al¹¹ was performed on x-ray of the subjects with Kienböck disease. In contrast, the current study was performed based on 3-dimensional modeling of a normal subject.

Classically, researches on Kienböck disease have been focused on UV and radial inclination. There is a consensus that negative UV is a risk factor for Kienböck disease and UV plays an important role in decision making and planning for operative treatments. In early stages that the lunate has not collapsed, in the setting of ulnar negative wrist, joint leveling procedures such as radial shortening is performed, whereas, in wrists with ulnar positive or ulnar neutral, other joint leveling procedures such as capitate shortening is performed to off-load the lunate.^17,18

Variations in lunate morphology are recognized to be associated with changes in carpal kinematics and load transfer to the lunate. Three classifications of lunate bones based on their morphology and trabecular angulation have been documented in scholarly literature. The Zapico type 1 lunate exhibits a trapezoidal shape, with intraosseous trabecular angulation surpassing 135° and with a negative UV.¹⁹ It has been postulated that this inherently weaker trabecular architecture renders the lunate more vulnerable to the development of Kienböck disease.²⁰

Yet, the role of radial inclination has been a matter of debate. Decreasing the radial inclination by 5° to 15° by wedge osteotomies are a suggested operation in the management of Kienböck disease.21, 22, 23, 24 Garcia-Elias et al²⁵ and Watanabe et al²⁶ reported that the reduction of radial tilt through wedge osteotomies leads to a decrease in the axial load across the lunate, and resulting in an increased contact area in the radiolunate region. Long-term follow-ups have also exhibited acceptable clinical outcomes by these techniques.21, 22, 23, 24, 25, 26 On the other hand, early studies suggested that a low radial inclination increases the load on lunate, leading to Kienböck disease.27, 28, 29 Palmer et al²⁹ proposed a concept indicating that the load on the lunate fossa diminishes as the inclination of the distal radius increases. This concept is further supported by evidence suggesting that a flat distal radius may predispose individuals to Kienböck disease.²⁹ Mirabello et al²⁷ reported that flattened radial inclinations are associated with smaller lunates, which exhibit a higher predisposition to Kienböck disease compared to those with a steeper inclination. We believe that inconsistency with findings in the literature regarding the radial inclination is because of the fact that in most of these studies LFI have not been taken into account. As shown in Yildirim et al¹¹ study, despite having same radial inclination, patients might have different LFI.¹¹

The IFA and LFI may serve as valuable radiological parameters for preoperative planning to determine the necessity of performing a wedge osteotomy alongside a radial shortening osteotomy. The optimal corrective angle for the wedge osteotomy, aimed at enhancing the radiolunate surface contact and reducing load transmission across the joint, remains a subject of ongoing debate. A large lateral wedge osteotomy has the potential to increase load transmission on the radiolunate joint because of the resulting excessive ulnar deviation of the carpus.³⁰ Yang et al³¹ conducted a study on the variations in stress distribution on the lunate by employing different radial inclination models. Their findings indicated that the stress value experienced a significant reduction following a 10° wedge osteotomy of the wrist with an elevated radial inclination.

The biomechanical nature of our study is its main limitation. Carpals and ligaments have a complex anatomy and relations. While biomechanical studies provide valuable insights into the forces and stresses acting on joints and bones, their findings do not always directly correlate with the real in vivo conditions of the human body. Moreover, patient specific factors such as ligamentous laxity and anatomical variations have not been taken into account. These factors should be further studied for better understanding the etiology of Kienböck. Further research should also focus on the application of LFI in the management of Kienböck disease. This point should be considered that the current study is a case study. Therefore, the outputs of this study should be used with caution.

Our study clearly shows that decrease in LFI considerably increases stress in lunocapitate joint suggesting a biomechanical role in the pathogenesis of the Kienböck disease. In addition, a positive correlation was observed between LFI and scapholunate joint stress. Our study suggests that besides UV and radial inclination, other distal radial parameters such as LFI must be taken into consideration in the management of the Kienböck disease.

Conflicts of Interest

No benefits in any form have been received or will be received related directly to this article.