The lunate bone is a carpal bone in the human hand. Kienbock’s disease is the osteonecrosis of the lunate bone [1]. This disease was firstly termed by Robert Kienböck, an Austrian radiologist, in 1910 and was believed to be the consequence of the surrounding soft tissue trauma [2] [3]. Nowadays, although the aetiology and the progression history of the disease still remain unclear, the disease seems to be more frequently related to a biological vascular issue for blood flow affecting the lunate [1]. It might be affected by many factors such as morphological variations of carpus bones and trauma. It has been observed relatively more frequently in labor-intensive people and young individuals [4]-[8]. It was also reported that the disease could be caused by abnormal internal stresses on the lunate [9].

As for the treatment of the Kienbock’s disease, many surgical options have been reported including ulna lengthening or radial shortening, capitate shortening, lunate resection, and radial wedge osteotomy [10] [11]. The short-term effect has been studied experimentally and analytically, and the long-term effect has been studied with following-up studies [9] [10] [12] [13]. Although many researchers have conducted various studies on the effectiveness of treatments, the conclusion of which one is the most effective is still controversial. Among all the treatments, radial closing wedge osteotomy, as shown in Figure 1, is one of the most frequently used treatment options, which has been reported with better long term results than some other treatments by some researchers [2] [14]-[20]. The operation is to cut a wedge on the radius to change the inclination angle of the radius bone. However, the results about the treatment are still controversial in some literatures and some key mechanisms are still not clear. While it was showed the load on lunate could be relieved by the operation by some researchers [21], some other researchers reported increased load on the lunate after the operation [22]. To resolve the conflict, Kam et al. measured the load on lunate with strain gauge [23]. However, their results also showed increased strain with the wedge cut angle. They couldn’t explain the satisfactory clinical results. As for the angle of the wedge cut on the radial bone. Tsumura et al. (1984) recommended cutting the distal radius by an approximately 15-degree wedge, but Kojima et al. recommended 5 degrees [19] [24].

Based on the literature review, it seems that there is no consistent conclusion on the effectiveness of the osteotomy treatment and on the optimum angle of the wedge that should be cut on the radial bone. Therefore, the objective of the current work is to study how the stress distribution changes on the lunate bone and the surrounding cartilages with the radial inclination. Finite element models were developed in the study to demonstrate how the stress distributions were affected by various factors.

To obtain the full field solution of the stress distribution of the lunate bone, two-di- mensional finite element models were developed using software ANSYS [25]. The geometry of the model was created by tracing an anteriorposterior X-ray of the carpal joint. This geometry development method was used by Ledoux et al. in 2001 and 2008 to study the biomechanics mechanism of the Kienbock’s disease and fracture of the scaphoid bone [26] [27]. The X-ray picture, as shown in Figure 2(a), and CT scan model as shown in Figure 2(b), were obtained from a right carpal joint of a 19 years old man without Kienbock’s disease.

To simplify the extremely complicated carpal joint structure, only the scaphoid, lunate, ulna and radius bones were used in the model and the lunate bone contacts with radius and ulna bones with cartilages. It was believed the abnormal radial inclination, uncovering of the lunate, and the relative position of the lunate could be the factors that lead to the disease [1]. Therefore, three (types of) FE models were developed as shown in Figure 3. The geometry of the first model (model 1) in Figure 3(a) was created based on healthy carpal joint in Figure 2(a). The second model (model 2), as shown in Figure 3(b), was created off the healthy model (model 1) by tilting the lunate bone 15 degrees counterclockwise to simulate the abnormal radial inclination. The third model (model 3) was developed by shifting the lunate bone in the second model horizontally to the right by 1.5 mm, 3 mm, and 4.5 mm. This model is based on one x-ray picture of a patient with Kienbock’s disease in [28]. The one with 3 mm shift is shown in Figure 3(c). The third model is to simulate different covering and relative position of the lunate. The effect of radial inclination (wedge cut) was studied using the first two models. It was assumed that the radial bone has a wedge cut of 0˚, 5˚, 10˚, and 15˚ to simulate the operation. The first variation was with no cut in the radius bone to simulate a control model. The radius inclination angle for the control models is 22˚ for both the models.

For all the models, cartilages were assumed to be bonded between the contact surfaces of the four bones. Fixed boundary conditions were applied at the bottom of radius and ulna bones to constrain the model. Forces of 40N and 60N were applied in the downward direction on the top of the scaphoid and lunate bone, respectively. The lunate, radius, ulna, and scaphoid bones were simulated as homogenous elastic cancellous material with Young’s modulus of 18,000 MPa and Poisson’s ratio of 0.2 [26] [27]. The cartilage has a Young’s modulus of 10 MPa with the Poisson’s ratio of 0.49 to assume the near non-compressibility of the cartilage [29]. Mesh convergence was verified based on results.

Yang, G., Partridge, K.A., Abdel-Mohti, A., McMullen, A.J. and Shen, H. (2016) Finite Element Analysis of Osteotomy Treatment for Kienbock’s Disease. J. Biomedical Science and Engineering, 9, 161-170. http://dx.doi.org/10.4236/jbise.2016.910B021