Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis

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1 Chinese Journal of Tissue Engineering Research September 28, 217 Vol.21, No.27 Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis Du Chuan-chao, Xiong Ge, Ren Shuang, Rong Qi-guo, Zhang Heng ( Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 135, China; the First Hospital of Tsinghua University, Beijing 116, China; Biomechanical Laboratory of College of Engineering, Peking University, Beijing 1871, China; College of Engineering, Peking University, Beijing 1871, China) Cite this article: Du CC, Xiong G, Ren S, Rong QG, Zhang H. Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis. Zhongguo Zuzhi Gongcheng Yanjiu. 217;21(27): doi:1.3969/j.issn orcid: (Du Chuan-chao) Abstract BACKGROUND: Biomechanical mechanisms are complex, and previous studiers focus on the stress conduction in the carpus. However, the stress distribution and characteristics of trabecula in the carpus are rarely reported. OBJECTIVE: To investigate the stress distribution and deformation characteristics of the normal lunate through a two-dimensional sagittal finite element model. METHODS: A normal cadaveric lunate sample was scanned with Micro-CT and the central sagittal image was chosen for further finite element analysis (FEA). The chosen image was processed and imported into the finite element analysis software (Ansys 14.). A two-dimensional sagittal finite element model of the lunate bone was established. Axial pressure was applied to the model with the wrist held in different positions, and nine regions of interests (ROIs) were identified, for which stress and displacement nephograms were created. These included the first principal stress (S1, the maximum stress in a principal plane), the third principal stress (S3, the minimal stress in a principal plane), shear stress (SXY, the component of stress coplanar with a material cross section), von Mises stress (SEQV, yielding begins when the elastic energy of distortion reaches a critical value) and displacement of each ROI (UY, displacement on the vertical plane of the lunate) which were calculated and compared. RESULTS AND CONCLUSION: (1) The stresses on ROIs located in the proximal and volar cortices of the lunate bone were much higher than those in the distal and dorsal cortices. At the proximal lunate, S1 was less than S3; however at the distal lunate, S1 was greater than S3. The ROIs of the distal and proximal ends of the lunate bone received much higher stress than the ROIs of the middle part. As for axial trabecular displacement, both distal and proximal ROIs were compressed by axial pressure. However, the dorsal and the volar parts of the proximal lunate moved in different directions at different wrist postures. Besides, the stress values and magnitudes of displacement were elevated in wrist flexion and extension compared to neutral position. Furthermore, the stress concentration zones (the proximal volar ROI, the proximal dorsal ROI, the distal volar ROI, and the distal dorsal ROI) had different directions of shear stress and displacement in different wrist postures. (2) These results suggest that when stress is loaded on a normal lunate model, four stress concentration zones, the proximal volar ROI, the proximal dorsal ROI, the distal volar ROI, and the distal dorsal ROI are found. The wrist postures can significantly affect the value and distribution of axial stress on the sagittal lunate. Subject headings: Tissue Engineering; Wrist Joint; Fracture, Bone Funding: the National Clinical Key Construction Project-Hand Surgery, No. (21)35; the High-Level Health Technology Talent Training Program of Beijing Health System, No Du Chuan-chao, Master, Physician, Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 135, China; the First Hospital of Tsinghua University, Beijing 116, China Corresponding author: Xiong Ge, Professor, Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 135, China; Corresponding author: Rong Qi-guo, Professor, College of Engineering, Peking University, Beijing 1871, China Accepted: INTRODUCTION Micro-CT is defined by structural CT image analysis down to the level of the micron [1]. Some properties of bone microstructure (such as, trabecular bone area, trabecular bone thickness, trabecular spacing and trabecular bone number) can be quantitatively analyzed using relevant parameters obtained through associated software. Additionally, the two-dimensional (2D) or three-dimensional (3D) structures of trabecular bone can be reconstructed based on its Micro-CT images. If these data are combined with a finite element model of stress distribution and deformation, the properties of trabecular bone may be investigated [2]. The finite element analysis (FEA) method has already been widely used to study various microstructures and mechanical properties of the diseased bones [3-4]. Lunate injury is commonly seen because of its central location in the wrist joint and huge stresses it bears during stress conduction [5]. Xiao, et al. analyzed the trabecular microstructures and nutrient foramina of normal lunates with Micro-CT, and found the volar and dorsal distal ends have lower subchondral bone plate intensity than those of the distal central part [6]. While few papers ISSN CN /R CODEN: ZLKHAH 4385

2 Table 1 Some anatomic features of the capitolunate and radiolunate joints in different wrist positions Wrist position wrist angle Capitolunate angle The direction of the capitolunate joint Contact area of the radio lunate joint (mm²) Contact area of the capitolunate joint (mm²) ( ) ( ) Neutral position 2.5 Volar angulation Volarflexion Dorsal angulation Dorsal-flexion Volar angulation adress the mechanisms of stress conduction through lunate. Kienbock s disease (KD), aseptic lunate osteonecrosis, results in serious disturbance of wrist joint function, due to end-stage bony deformation, instability and wrist joint arthritis. Previous researches on the pathogenesis of KD have focused on abnormal anatomical factors which increase forces across the lunate such as ulna-negative variance, excessive radial tilt angleand deformation of the lunate s gross spatial structure [8-9]. Although Han compared the micro-structure differences between the normal and KD lunates, the mechanical analysis FEA for lunate has not yet been reparted [1], which may uncover the microstructure mechanical reason for KD. So we established a sagittal 2D FEA model based on the Micro-CT data images of a normal lunate, and analyzed the microstructure and mechanical properties of the normal lunate under axial stress,to investigate the stress distribution and deformation characteristics. MATERIALS AND METHODS Design Biomechanic research of the lunate microstructure based on FEA model experiment of single lunate sample. Time and setting From December 213 to March 214, the experiment was performed at the Trauma Orthopaedic Institute of Beijing Jishuitan Hospital and State Key Biomechanical Laboratory of Peking University. Materials A normal fresh frozen right lunate was obtained from a healthy cadaver (36 years old, male, right upper extremity amputated for destructive injury, Bone Bank of Beijing Jishuitan Hospital, Beijing). The sample was scanned by Micro-CT (Skyscan1172, Belgium) at room temperature. To determine the vector and scale of stress and deformation under different physiological loading positions, a right wrist of a healthy volunteer (male, 29 years old, Beijing) was scanned with a spiral CT (TOSHIBA/Aquili, Japan) in neutral, flexion and extension positions (flexion 62 and extension 71, the largest angle of activity during work). Geomagic-studio (a reverse engineering software) and Materialism s interactive medical image control system (Mimics 1.1, 64bit, Materialise Inc., USA) were used. Methods Loading positions and directions The spiral CT images of the right wrist of the healthy 4386 volunteer were stored as DICOM format and imported into Mimics 1.1 software for 3D reconstruction. The capitolunate angle was measured in the sagittal section. The different wrist positions for the 3D model were neutral, flexion (62 ) and extension (71 ). The contact surfaces of the capitolunate and radiolunate joints were inspected and only the central sagittal lunate section was found to exhibit a high contact area. The precise contact surfaces were chosen as loading positions (Figure 1A). In addition, the direction of load was co-ordinated by application of X, Y and Z-axes (Figure 1B). The same processes were performed in three wrist positions, and the anatomic features of joint were measured (Table 1). Figure 1 Diagrams of joint contiguous contact area of the capitolunate and radiolunate joints Note: (A) Sagittal section of the reconstructed three-dimensional right wrist model in volar-flexion, the contact areas of these joints are shown in the red-circled blue areas. (B) The central sagittal section of the lunate was extracted, and a three-dimensional coordinate Axis was established (on a symmetrical sagittal plane the middle line is denoted the X axis (in red); the line crossing the halfway point of the X axis in the sagittal plane is denoted the Y axis (in green) and the line crossing the halfway point of the X axis perpendicular to the Y axis is denoted the Z axis (in purple). From this and the exact contact surfaces of the capitolunate and radiolunate could be co-ordinated. The lunate scanned with Micro-CT After reduction and compression, the original images of lunate from the Micro-CT were converted into the 3D images. The central sagittal section was extracted with Data Viewer software (Sky Scan, Kontich, Belgium). The chosen image was then converted into a readable format for further finite element analysis. Establishing a sagittal 2D FEA model Derived from Capitolunate Angle (proximal parts of lunate constrained), radiolunate and capitolunate contact surfaces, loading positions and directions on the sagittal lunate finite element model in different wrist positions were determined (Figure 2). P.O. Box 12, Shenyang 1118

3 Du CC, et al. Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis A Figure 2 B C Loading positions, directions and constraints are shown when the Figure 3 The distribution of nine ROIs and right wrist in different positions associated units (colored patches) on the Note: (A) neutral, (B) volar flexion and (C) dorsal flexion. Red lines presented the constraint areas. Yellow lines showed the loading positions. two-dimensional finite element model A Figure 4 B C D Note: Each ROI was marked with Arabic Numbers from 1 to 9. ROIs: regions of interests. E F The stress and displacement nephograms in neutral wrist position are shown when axial stress was applied to the two dimensional finite element model Note: (A) Deformation picture. Dotted areas represent the lunate contour before loading. (B) S1 stress nephogram. (C) S3 stress nephogram. (D) SXY stress nephogram. (E) SEQV stress nephogram. (F) Displacement nephogram on y axis (isotonic pressure zones shown in different colors; blue-low pressure, red-high pressure). In the finite element model, both cortical and cancellous bone were assumed to have isotropic homogeneity and continuous linear elastic properties with an elasticity modulus set at 1 MPa and Poisson s ratio.2. A combination of manual and computerized methods was used, and the 2D FEA image model was divided into units and nodes. Nine regions of interest (ROIs) were chosen, and each region contains 11 units (Figure 3). Under different loading conditions (load position, direction and size,.1 MPa), a finite element analysis was [11] conducted. S1 (the first main stress, the maximum stress in a principal plane), S3 (the third main stress, the minimal stress in a principal plane), SEQV (von Mises stress, yielding begins when the elastic energy of distortion reaches a critical value), SXY (XY shear stress, the component of stress coplanar with a material cross section) and UY (Y axial displacement, displacement on the vertical plane of the lunate) for each unit were calculated with Ansys 14. software. Column diagrams of stresses and displacements at each ROI Although the nephograms could show the feature of the parameters in one positions, the regularities of stress distribution and displacement of the same ROI in different wrist posture were of more significance. Bar charts of stresses (MPa) and displacements (mm) at each ROI of the FE model in different wrist positions were established (Figure 5) to analyze the variation of the parameter alone with the different postures of wrist. RESULTS Each ROI shared more S1 stress (tensile stress) in flexion or extension than that in neutral wrist, in addition, zone 1, 2, 3 and 9 (volar ROIs) got more S1 stressed in extension than those in the flexion, while zone 4, 5, 6, 7 and 8 (dorsal ROIs) got more stressed in flexion. As to S3 (compressive stress), the proximal ROIs got more compressed than the distal ROIs without obvious influence by wrist postures. For the SXY (shear stress), zone 1, 2 and 4 (volar ROIs) shared more shear stress in extension than those in flexion, but the conditions for the zone 3 (volar ROIs) was just the opposite. Besides, the directions of SXY were greatly influenced by the wrist postures. Directions of UY were also different with the change of wrist postures. However, SEQV was little affected by the wrist postures. Stress and displacement nephogram Deformation, the stress nephograms and displacement contours were created using a post-processing module of the Ansys14. software. The nephograms showed the distribution features of the parameters in neutral wrist position (Figure 4). In brief, the ROIs on the volar side shared more stress than those on the dorsal side, but the displacements of the ROIs on the volar side are much less. Besides, the directions of SXY on the volar and dorsal side are different (Figure 6). The procession of experimental data The distribution nephograms and bar charts were used to document and analyze different stresses and their distributions. ISSN CN /R CODEN: ZLKHAH 4387

4 Volar flexion Neutral Dorsal flexion Volar flexion Neutral Dorsal flexion Volar flexion Neutral Dorsal flexion A 1.8 B 6 C D Volar flexion Neutral Dorsal flexion Volar flexion Neutral Dorsal flexion 6 E Figure 5 The stress and displacement column diagrams when the axial stress was applied on the two-dimensional finite element model of a sagittal the lunate Note: From A to E, values on X-axis mean the ROI, while the Y-axis mean the value of pressure in A D, but in E it means displacement in millimeter. (A) S1 stress column diagram is shown; (B) S3 stress column diagram is shown; (C) SXY stress column diagram is shown; (D) SEQV stress column diagram is shown; (E) UY displacement is shown. A B ligaments in tension, thus reducing the blood supply to the lunate bone [13]. Therefore, the volar part of the lunate bone may be vulnerable to be vascular insufficiency in wrist extension [14]. So KD is commonly seen in those doing heavy labour who have to extend or flex their wrists [15-17]. Figure 6 The directions of SXY stress and UY displacement when the axial stress was applied on the two-dimensional finite element model of a sagittal the lunate Note: (A) Directions of SXY (yellow arrows). (B) Directions of UY (red arrows). DISCUSSION Although there are some researches about the stress transmission through wrist and force distributions among the wrist bones [12], the stress distribution in the lunate is still unrevealed, which may contribute to the understanding of the lunate diseases, such as KD. Our research found that the stress transmitted in the lunate changed with different wrist postures, and the stress concentration points were also determined. The tension of the ligaments around the lunate changed with different wrist postures, thus influencing the stress distribution and displacement of the lunate. In flexion, the volar ligaments are flabby while the dorsal ligaments are relatively tight, which would inflict a greater load on dorsal part of the lunate. Furthermore, the force bearing point of the lunate moved volarly in wrist flexion. It also made the stress increased when wrist flexed. In dorsal flexion, the situation was reversed, and there was more stress on the volar part of the lunate. It was reported that the main arteries of the lunate located on the volar side, and would be compressed by the volar 4388 In our study, we found a high consistency between the clinically common broken points of the lunate and stress concentration regions. Among stress concentration regions, the zone 3 and 6 are apt to be injured, because of the single layer of the cortical bone in these two zones and different directions of SXY and UY in different wrist positions. The zone 1 is also easy to be injured because it shares more SXY than zone 3 and 4 in extension, and also because it is the transitional zone from transverse cortical plate to longitudinal bone trabecula in the sagittal plane. However, the central part of the distal sagittal lunate bone consists of multi layers of cortical plates which are intercalated with the trabecula perpendicular to them and thus has very high strength and rigidity [18]. Below the central part, there are some trabecula extended from the distal to the proximal, which is in favor of stress dispersion and maintenance of the lunate height. These trabecula would be lost and broken in the late stages of KD [19]. Zone 1 and 8 are vulnerable to be injured, because they are the stress concentrated ROIs, the junctional zone between transverse trabecula and longitudinal trabecula, and suffered more stress in extension [2]. The dorsal ROIs are easier to be injured in volar flexion at which they share more stress; on the contrary, the volar ROIs are easier to be injured in dorsal flexion. Schiltenwolf et al. came to the consistent conclusion as our finding through measuring the pressures in the lunate bone in different wrist postures [21]. The regularity of stress distribution is consistent to the structure characteristic that there is more trabecula on the volar lunate bone than the dorsal lunate bone, which P.O. Box 12, Shenyang 1118

5 fully embodies the basic theory that structures are always consistent with their functions. With Micro-CT images, the structures at micron level of bonelunate can be firstly investigated as well as their mechanic properties. We provide a new way for studying the failure process of trabecula and may be used to test the well-known theory that stress concentration causes fractures of a few trabecula, and then the capillaries in the fracture site are compressed when bone healing, so newly formed bone become necrosis secondary to reduction of blood supply or fragile to be broken again [21-22]. Histologically, the trabecula become thickened, collapsed, flattened, density increased, fatty changes, trabecula space and anisotropy reduced, which are consistent with the pathological appearance of vascular bone necrosis [23-24]. In the future, we intend to further explore lunates at different stages of KD. Honestly, there are several limitations in our study. Firstly, the 3D finite element model of the lunate bone is impossible to be created by personal computers, because the vast information in those images is impossible to be reconstructed. Therefore, a 2D finite element model of the sagittal lunate bone was created rather than a 3D one which is the real structure of trabecula. Secondly, both the cortical bone and trabecula were assumed as isotropic homogeneity and continuous linear elastic material without considering the differences among trabecula [25]. Additionally, the mechanical model of the lunate bone was simplified in order to simulate the complicated mechanical environment of the lunate bone, which obviously cannot fully reflect the real physical situation around the lunette joints. REFERENCES [1] Kinney JH, Johnson QC, Nichols MC, et al. X-ray micro-tomography X at SSRL. Environ Sci Technol. 1989; 6(7): [2] Neldam CA, Pinholt EM. 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6 Micro-CT ( ). Micro-CT [J] (27): Micro- CT MIMICS Ansys CT Mimics 1.1 Geomagic- studio 212 Ansys : R318 : B : (217) Micro-CT CT CT X X ( ) Micro-CT 9 4 Micro-CT [ (21)35 ] ( ) CNKI 3 3. (Edited by Wang XF, Wang JT/Li JY/Qiu Y) 439 P.O. Box 12, Shenyang 1118