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Finite-element analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures
J Orthop Sci (2007) 12:354–360 DOI 10.1007/s00776-007-1144-z
Original article Finite-element analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures Taizo Hato1, Norio Kawahara1, Katsuro Tomita1, Hideki Murakami1, Tomoyuki Akamaru1, Daisuke Tawara2, Jiro Sakamoto2, Juhachi Oda2, and Shigenori Tanaka3 1 2 3
Department of Orthopaedic Surgery, Kanazawa University, 13-1 Takaramachi, Kanazawa 920-8641, Japan Department of Human and Mechanical System Engineering, Faculty of Engineering, Kanazawa University, Kanazawa, Japan Department of Anatomy and Neuroembryology, Kanazawa University, Kanazawa, Japan
Abstract Background. Closing-opening correction (COC) osteotomy is a useful procedure for severe angular kyphosis. However, there is no previous research on the reconstructed vertebrae with kyphotic malalignment in the presence of osteoporosis. Finite-element (FE) analysis was performed to estimate the biomechanical stress with both osteoporotic grades and corrective kyphotic angles during COC osteotomy for osteoporotic angular kyphosis. Methods. FE models of COC osteotomy were created by changing three major parameters: (1) grade of osteoporosis; (2) kyphotic angle; and (3) compensated posture when standing still. Osteoporosis was graded at four levels: A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middlegrade osteoporosis; D, high-grade osteoporosis. The kyphotic angle ranged from 0° as normal to 15° and 30° as moderate and severe kyphosis, respectively. FE analyses were performed with and without assumed compensated posture in kyphotic models of 15° and 30°. Along each calculated axis of gravity, a 427.4-N load was applied to evaluate the maximum compressive principal stress (CPS) for each model. Results. The CPS values for the vertebral element were the highest at the anterior element of T10 in all FE models. The maximum CPS at T10 increased based on the increases in both the grade of osteoporosis and the kyphotic angle. Compensated posture made the maximum CPS value decrease in the 15° and 30° kyphotic models. The highest CPS value was 40.6 MPa in the high-grade osteoporosis (group D) model with a kyphotic angle of 30°. With the normal (nonosteoporotic) group A, the maximum CPS at T10 was relatively low. With middle- and high-grade osteoporosis (groups C and D, respectively), the maximum CPS at T10 was relatively high with or without compensated posture, except for the 0° model. Conclusions. Lack of correction in osteoporotic kyphosis leads to an increase in CPS. This biomechanical study proved the advantage of correcting the kyphotic angle to as close as
Offprint requests to: T. Hato Received: August 7, 2006 / Accepted: March 12, 2007
possible to physiological alignment in the thoracolumbar spine, especially in patients with high-grade osteoporosis.
Introduction Osteoporotic vertebral fractures often develop a persistent spinal kyphotic deformity on sagittal alignment, leading to severe low back pain and even delayed paralysis on occasion. In such cases, surgery is often necessary. Various surgical procedures have been reported for such cases. Kaneda et al.1 noted that anterior decompression and reconstruction using the Kaneda device was effective in osteoporotic posttraumatic vertebral collapse. Saita et al.2 reported that posterior spinal shortening for delayed paraplegia after an osteoporotic vertebral fracture was performed by resecting the wedging spine and producing a short vertebra. However, in the case of a severe kyphotic deformity, it is difficult to correct the deformity completely. Furthermore, postoperative failures, such as additional vertebral collapse generally at the edge of the surgically treated segment, are often problematic in the presence of osteoporosis.3 Kawahara et al.4 noted that closing-opening correction (COC) osteotomy enabled satisfactory spinal correction and reconstruction for severe angular kyphosis. However, there is no previous biomechanical research examining the outcome of correction for severe spinal kyphosis due to osteoporosis. In the present study, we constructed threedimensional finite-element (FE) models of COC osteotomy with four types of osteoporosis and three types of corrected kyphosis. The compressive principal stress (CPS) in each FE model was evaluated to compare the completely corrected thoracolumbar spine with the incompletely corrected spine according to the osteoporotic grade.
T. Hato et al.: Closing-opening correction osteotomy
Materials and methods Construction of the FE basic model for COC osteotomy A basic FE model for COC osteotomy was created by modifying the FE model for total en bloc spondylectomy (TES).5,6 Verification of the TES model had already been performed using compressive load testing.5 The segmental levels of the model were T9-L2, and the apex level was T12 because osteoporotic compression fractures often occur at the thoracolumbar level. The thoracolumbar spine (T9-L2), harvested from a formalinized human cadaver (a 90-year-old man with no spinal disease), was used to create the basic outline of the FE model. After the total spinal segment of T12 was completely resected, including the upper and lower levels of discs, a Harms titanium mesh cage (25 mm diameter × 10 mm height) (DePuy, AcroMed, Raynham, MA, USA) filled with grafting cancellous bone was used at T12 for anterior reconstruction. Impacted cancellous bone chips were used to fill the gap in the dead space between T11 and L1. For posterior instrumentation, pedicle screws (Moss Miami System; DePuy, AcroMed) were inserted into both sides of the T10, T11, L1, and L2 pedicles — 6.0 mm diameter polyaxial pedicle screws, 40 mm in length at T10 and T11 and 45 mm in length at L1 and L2. Two 5.5 mm diameter rods were attached to the pedicle screws, and two posterior cross-link transverse units were connected between T11 and L1. In the basic FE model, the kyphotic angle at T10 was set to 0°, which was physiological spinal alignment in T12.7 All spinal instrumentation systems were made of titanium. This research was faithfully based on the national law of human macroscopic anatomy in Japan. That is, it was
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executed under supervision of the Professor of Macroscopic Anatomy, School of Medicine, Kanazawa University, for the purpose of elucidating more advanced human gross anatomy from a viewpoint of clinical medicine. The results of this research were employed for high-grade medical education, and it was lectured to medical students in our institution as a part of their high-grade anatomy practice (March 2004). The specimen from the cadaver used in this research, with great dignity and respect, was returned to the bereaved family in an official ceremony. The basic outline of the three-dimensional FE model was reconstructed from the computed tomography (CT) value for the cadaver specimen after COC osteotomy. In this FE model, the materials consisted of cortical bone, cancellous bone, intervertebral discs, facet joint cartilage, and paravertebral ligaments (anterior and posterior longitudinal ligament, supraspinous ligament, interspinous ligament, capsular ligament, ligamentum flavum); each material was assumed to be isotropic and homogeneous. At the facet joints, one layer of cartilage was in contact with another layer on both sides of T9/10, T10/11 and L1/2. On the lower endplate of T9, a onelayer rounded surface was attached for loading. The FE modeling and analysis were carried out by MARC and MENTAT analyses (MARC Analysis, Tokyo, Japan) (Fig. 1). This was a linear elastic model and consisted of 11 524 elements and 13 799 nodes. The input parameters for each material (except the cortical and cancellous bone) were according to Yamamoto et al.8 (Table 1). Next, three major parameters of the model were established: (1) the grade of osteoporosis; (2) the kyphotic angle; and (c) with or without assumed compensated posture while standing still.
Fig. 1. Finite-element (FE) modeling of reconstructive closing-opening correction (COC) osteotomy. Anterior reconstruction was done with a titanium mesh cage and impacted cancellous bone. Posterior instrumentation was performed
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Table 1. Material properties in the basic FE model for COC osteotomy Tissue
Young’s modulus
Poisson’s ratio
Grafting bone Instrument Titanium cage Disc Cartilage
E = 1000 (MPa) E = 110 (GPa) E = 35 (GPa) E = 7.5 (MPa) E = 0.6 (MPa)
υ = 0.2 υ = 0.3 υ = 0.3 υ = 0.4 υ = 0.49
Ligaments (ALL, PLL) Ligaments (SSL, ISL, LF, CL)
E = 20 (MPa) E = 10 (MPa)
υ = 0.4 υ = 0.3
FE, finite-element; COC, closing-opening correction; ALL, anterior longitudinal ligament; PLL, posterior longitudinal ligament; SSL, supraspinous ligament; ISL, interspinous ligament; CL, capsular ligament; LF, ligamentum flavum
Table 2. Four grades of osteoporosis and material properties of cortical and cancellous bone Cortical bonea Osteoporosis grade Normal (nonosteoporotic) Low grade Middle grade High grade a b
Properties
Thickness (mm)
Cancellous boneb properties
E = 10 000 MPa, υ = 0.3 E = 5000 MPa, υ = 0.3 E = 2500 MPa, υ = 0.3 E = 1250 MPa, υ = 0.3
0.8 0.6 0.4 0.2
E = 750 MPa, υ = 0.2 E = 300 MPa, υ = 0.2 E = 100 MPa, υ = 0.2 E = 75 MPa, υ = 0.2
The properties and thickness of the cortical shell were quoted according to Silva et al.9 The values of Young’s modulus were decided referring to Kopperdahl et al.10
Fig. 2. Variations of the corrected kyphotic angle by FE modeling. Simulated fusion angles were 0° (basic model) (a), 15° (b), and 30° (c). The kyphotic angle at T12 was defined as the angle from the lower surface of T11 to the upper surface of L1, an index of the extent of correction
Variation of the grade of osteoporosis by FE modeling
Variation of the kyphotic angle by FE modeling
Four grades of osteoporosis — A, normal (nonosteoporotic); B, low-grade osteoporosis, C, middle-grade osteoporosis; D, high-grade osteoporosis — were established by altering the material properties of the bone: the thickness and Young’s modulus of the cortical shell and Young’s modulus of the cancellous bone. The material properties of the cortical shell were according to Silva et al.,9 and Young’s modulus of cancellous bone were according to Kopperdahl et al.10 (Table 2).
The compressive apex of T12, the location of angular kyphosis, was completely resected and then corrected with titanium mesh and impacted cancellous bone during a COC osteotomy. Therefore, the kyphotic angle at T12 was defined as the angle from the lower surface of T11 to the upper surface of L1 as the extent of correction. Three types of kyphotic angle at T12 were produced: 0° as normal in the thoracolumbar spine7 and 15° and 30° as moderate and severe kyphosis, respectively (Fig. 2).
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Table 3. Condition of compressive load with or without compensation Length of moment arm (cm)a Kyphotic angle (°) 0 15 30 a b
Tilt angle (°)b
Without compensation
With compensation
Without compensation
With compensation
4.5 9.7 12.7
— 7.8 8.9
95 80 65
— 91 90
The distance from the axis of gravity to the anterior edge of T9 Tilt angle from the axis of gravity to the lower surface of T9
Fig. 3. Standing with or without compensated posture. a, b 0° and 15° without compensation, respectively; c 30° without compensation; d 15° with compensation; e 30° with compensation. Tilt angle means the angle from the axis of gravity to the lower surface of T9; the length of the moment arm means the distance from the axis of gravity to the anterior edge of T9
FE analysis without compensated posture In the case of spinal kyphosis, the loading condition of gravity is different because the axis of gravity in the human body varies according to the degree of kyphosis.11 Therefore, it was necessary to determine the loading condition when the weight of the human upper body was transferred to the reconstructed thoracolumbar spine. According to the method for the center of gravity,12 we assumed that the area center of gravity of a human body is the approximate center of gravity. First, the figure from a silhouette of a woman who had undergone COC osteotomy at T12 to physiological spinal alignment of 0° in the sagittal plane was produced. Her height and body weight were 158 cm and 52 kg, respectively, which approximated the mean values among the female patients who had undergone COC osteotomy.13 In addition, an illustration was produced in a standing posture with the lower body fixed straight and the upper body flexed along each level of kyphosis; they were prepared for reconstructed models with 0°, 15°, and 30° kyphosis at T12 without compensated posture. The area center of gravity of the upper body was calculated as the approximate center of gravity, and a perpendicular line from the point was assumed to be the axis of gravity in each figure. Next, the figure for the FE model was projected onto the illustration at the thoracolumbar area for each kyphotic angle after the
thoracic and lumbar spinal body of the woman was projected. The distance from the axis of gravity to the anterior edge of T9 (identified as the moment lever arm) and the tilt angle from the axis of gravity to the surface for loading at the lower endplate of T9 were calculated for each model (Fig. 3). The results are summarized in Table 3 (without compensation). The point of intersection was chosen as the loading point in each kyphotic model. Finite-element analysis was performed to evaluate the CPS on the reconstructed vertebrae. A 424.7-N load, assumed from the calculation of lumbar disc pressure measurements,14 was applied along the axis of gravity on each loading point of the lower surface of T9, with L2 fixed at the bottom. This analysis was performed for each of the four osteoporotic grades, and the CPS of each model was calculated. FE analysis with compensated posture In patients with spinal kyphotic deformity, the patient commonly straightens up by posteriorly tilting the pelvis, hip extension, and knee flexion to make the axis of gravity close to the trunk, as well as the compensation of other healthy spinal segments.11,15 Kiefer and ShiraziAdl at al.16 noted that the sagittal position of the T1-S1 line is aligned vertically in a neutral position to generate the least L5-S1 disc compressive stress. Therefore, to
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consider the axis of gravity and determine the loading condition for compensated posture, the figures of 15° and 30° without compensated posture (Fig. 3b,c), were modified to figures with compensated posture (Fig. 3d,e) by posteriorly rotating the upper half of the body, focusing on S1, as the T1-S1 lines became almost perpendicular.17 In this study, compensation by other healthy spinal segments was ignored. In the same way as without the compensated posture, the distance and the tilted angle from the axis of gravity were also calculated for each kyphosis for the loading point (Table 3, with compensation). A 424.7-N load was applied to each loading point along the axis of gravity, as previously described, with L2 fixed at the bottom; the CPS on each model was then calculated.
Results The CPS value of vertebral element was highest at T10, which was the superior segment of the reconstructed vertebrae. The maximum values of the CPS at T10 vertebra are shown in Table 4. The CPS values at T10 increased according to increases in both the grade of osteoporosis and the kyphotic angle at T12 (Figs. 4, 5a–c). The compensated posture caused the maximum CPS value to decrease in the kyphotic models at 15° and 30° (Table 4, Fig. 5d,e). With posterior instrumentation, the stress values were maximum at the rods directly under the L1 pedicle screws in all models. The minimum value was 39 MPa in the model at 0° kyphotic angle in group A, and the maximum was 119 MPa in the model at 30° kyphotic angle in group D without compensated posture (Figs. 4, 5).
Discussion Finite-element modeling is a useful biomechanical simulation to obtain clinical evidence by allowing integrated measurement of mechanical behavior in a model.18 In
the current study, there were some limitations for FE modeling and analysis. First, we did not analyze the primary osteoporotic fracture, so the analysis was not absolute, but relative. Therefore, this discussion was limited to verification of the relative comparison about the grade of osteoporosis and the reconstructed kyphosis. Second, determining the loading condition in this model was extremely difficult because the exact loading condition during daily activities was unclear. Therefore, we tried to introduce the approximate axis of gravity as the loading axis using a figure of the human body for each kyphosis. By assuming the loading condition for this model with the compensated posture, we could compare the CPS values among various levels of stress when standing still. Third, we assumed that the area center of gravity was the approximate center of gravity by selecting a woman who had an average body shape, so the loading point could be calculated according to each kyphosis. The same woman’s silhouette was used to unify the area center of gravity from the shape of the same upper half of the body. In this study, various setup conditions were needed for the FE modeling and analysis. The development of simplified, detailed software to unify these various conditions is needed to achieve a more realistic analysis in the future. Some authors have suggested the importance of maintaining normal spinal alignment in the sagittal plane. Panjabi and colleagues,19,20 in a biomechanical analysis, noted that abnormal thoracic kyphosis caused a mechanical response that further increased thoracic kyphosis in a chain reaction and that an abnormal thoracic configuration created a vicious cycle of abnormal tissue loading. Keller et al.,17 in a biomechanical analysis of thoracic hyperkyphosis at T7, noted that anterior translation of the skull and upper thoracic column caused increased compressive loads, resulting in lumbar compression fractures solely from weight bearing. They noted that it is important to reduce thoracic hyperkyphosis.
Table 4. Maximum values of compressive principal stress at the anterior element of T10 Compressive principle stress (MPa) Osteoporosis grade
0°a
15°a
30°a
15°b
30°b
Normal (nonosteoporotic) Low grade Middle grade High grade
6.1 8.1 11.8 15.1
12.5 16.4 23.9 31.3
16.3 21.3 31.0 40.6
9.5 12.5 18.3 24.0
11.4 16.1 21.8 28.5
a b
Kyphotic angle without compensation Kyphotic angle with compensation
T. Hato et al.: Closing-opening correction osteotomy
a
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Fig. 4. a FE analysis in the model with a kyphotic angle of 0° without compensated posture. A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middle-grade osteoporosis; D, high-grade osteoporosis. A 424.7-N force was applied along the z-axis to each loading point of the figure. b FE analysis in the model of kyphotic angle of 0° without compensated posture. A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middle-grade osteoporosis; D, high-grade osteoporosis. A 424.7-N force was applied along the z-axis to each loading point of the figure
b
Fig. 5. FE analysis in high-grade osteoporotic group D. The angles of kyphosis were as follows: 0° and 15° (a and b, respectively); 30° without compensation (c); and 15° and 30° with compensation (d and e, respectively). A 424.7-N force was applied along the z-axis to each loading point
Vertebral collapse at the edge of reconstructed vertebrae is often clinically problematic during spinal reconstruction.3 In this study, the CPS was highest at T10, which was the top of the reconstructed vertebrae. The study showed that the CPS values at T10 increased according to increases in both the grade of osteoporosis and kyphosis (Table 4; Figs. 4, 5). Therefore, the grade of osteoporosis and the kyphotic angle are thought to be important factors in spinal correction and reconstruction of the thoracolumbar spine. Because the FE
analysis was performed under the restrictive condition that L2 was fixed as the lower edge of the model in this study, the biggest increase in CPS occurred on the upper vertebra of the model, which received the most distortion via a hinge that received the momentum. Depending on the loading condition, a large increase in CPS may also arise on the lower edge. The highest vertebral CPS value in this study was 40.6 MPa, which was almost half of the yield stress of human compact bone (83 MPa),21 in the high-grade
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osteoporotic group D model (30° without compensated posture). Nachemson noted in the study of disc pressure measurement that the pressure on lumbar discs during light manual labor was about five times greater than when standing still.22 Therefore, this linear elastic analysis showed that vertebral collapse could occur at the top of the reconstructed vertebrae if a further massive load was experienced during daily living activities other than standing still, especially in osteoporotic malaligned vertebrae. On the other hand, with posterior instrumentation it was not a marked stress increase that led to metal breakage when the yield stress of the titanium alloy (860 MPa)23 was considered, although the stress value increased owing to the reconstructed kyphotic malalignment. (Fig. 4, 5) However, in the long run, instrument failure may arise due to metal fatigue.
Conclusions We concluded that it is biomechanically reasonable to correct osteoporotic angular kyphosis to as close as possible to physiological spinal alignment in the thoracolumbar spine, especially in the presence of high-grade osteoporosis, to prevent clinical complications such as vertebral collapse and to obtain better clinical results. Careful analysis of individual patients is necessary prior to surgery. Acknowledgment. The authors give special thanks to Tsuyoshi Kamio, Graduate School of Engineering, Kanazawa University, for invaluable assistance. The authors did not receive and will not receive any benefits or funding from any commercial party related directly or indirectly to the subject of the article.
References 1. Kaneda K, Asano S, Hashimoto T, Satoh S, Fujiya M. The treatment of osteoporotic-posttraumatic vertebral collapse using the Kaneda device and a bioactive ceramic vertebral prosthesis. Spine 1992;17:S295–303. 2. Saita K, Hoshino Y, Kikkawa I, Nakamura H. Posterior spinal shortening for paraplegia after vertebral collapse caused by osteoporosis. Spine 2000;25:2832–5. 3. Inaoka M, Tada K, Yonanobu K. Problems of posterior lumbar interbody fusion (PLIF) for the rheumatoid spondylitis of the lumbar spine. Arch Orthop Trauma Surg 2002;122:73–9.
T. Hato et al.: Closing-opening correction osteotomy 4. Kawahara N, Tomita K, Baba H, Kobayashi T, Fujita T, Murakami H. Closing-opening wedge osteotomy to correct angular kyphotic deformity by a single posterior approach. Spine 2001;26:391– 402. 5. Akamaru T, Kawahara N, Sakamoto J, Yoshida A, Murakami H, Tomita K, et al. The transmission of stress to grafted bone inside a titanium mesh cage used in anterior column reconstruction after total spondylectomy: a finite-element analysis. Spine 2005;30: 2783–7. 6. Tomita K, Kawahara N, Baba H, Tsuchiya H, Fujita T, Toribatake Y. Total en bloc spondylectomy: a new surgical technique for primary malignant vertebral tumors. Spine 1997;22:324–33. 7. Bernhardt M, Bridwell KH. Segmental analysis of the sagittal plane alignment of the normal thoracic and lumbar spines and thoracolumbar junction. Spine 1989;14:717–21. 8. Yamamoto S, Tanaka E, Mihara K, Inoue H, Ohmori K. Finiteelement evaluation of spondylolysis taking account of nonlinear mechanical properties of ligaments and annulus fibrosus. JSME Int J 1999;42(series C):521–31. 9. Silva MJ, Keaveny TM, Hayes WC. Load sharing between the shell and centrum in the lumbar vertebral body. Spine 1997;22: 140–50. 10. Kopperdahl DL, Morgan EF, Keaveny TM. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. J Orthop Res 2002;20:801–5. 11. Itoi E. Roentgenographic analysis of posture in spinal osteoporotics. Spine 1991;16:750–6. 12. Lafond D, Duarte M, Prince F. Comparison of three methods to estimate the center of mass during balance assessment. J Biomech 2004;37:1421–6. 13. Kawahara N, Tomita K, Murakami H, Demura S, Hato T. Closingopening correction (COC) for kyphotic deformity due to osteoporotic vertebral fracture. Kotsu Kansetsu Jintai (J Musculoskeletal Syst) 2006;19:645–52 (in Japanese). 14. Nachemson A, Elfström G. Intravital dynamic pressure measurements in lumbar disc: a study of common movements, maneuvers and exercises. Scand J Rehabil Med Suppl 1970;1:1–40. 15. Harrison DE, Janik TJ, Harrison DD, Cailliet R, Harmon SF. Can the thoracic kyphosis be modeled with a simple geometric shape? The results of circular and elliptical modeling in 80 asymptomatic subjects. J Spinal Disord 2002;15:213–20. 16. Kiefer A, Shirazi-Adl A, Parnianpour M. Synergy of the human spine in neutral postures. Eur Spine J 1998;7:471–9. 17. Keller TS, Harrison DE, Colloca CJ, Harrison DD, Janik TJ. Prediction of osteoporotic spinal deformity. Spine 2003;28: 445–62. 18. Liebschner MAK, Kopperdahl DL, Rosenberg WS, Keaveny TM. Finite-element modeling of human thoracolumbar spine. Spine 2003;28:559–65. 19. Panjabi MM. Biomechanical evaluation of spinal fixation devices. I. A conceptual framework. Spine 1988;13:1129–34. 20. Panjabi MM, Abumi K, Duranceau J, Crisco JJ. Biomechanical evaluation of spinal fixation devices. II. Stability provided by eight internal fixation devices. Spine 1988;13:1135–40. 21. Evans FG. Mechanical properties of bone. Springfield, IL: Charles C Thomas; 1973. p. 10–121. 22. Nachemson AL. Disc pressure measurements. Spine 1981;6: 93–7. 23. Murakami H, Kawahara N, Tomita K, Sakamoto J, Oda J. Biomechanical evaluation of reconstructed lumbosacral spine after total sacrectomy. J Orthop Sci 2002;7:658–64.
Original article Finite-element analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures Taizo Hato1, Norio Kawahara1, Katsuro Tomita1, Hideki Murakami1, Tomoyuki Akamaru1, Daisuke Tawara2, Jiro Sakamoto2, Juhachi Oda2, and Shigenori Tanaka3 1 2 3
Department of Orthopaedic Surgery, Kanazawa University, 13-1 Takaramachi, Kanazawa 920-8641, Japan Department of Human and Mechanical System Engineering, Faculty of Engineering, Kanazawa University, Kanazawa, Japan Department of Anatomy and Neuroembryology, Kanazawa University, Kanazawa, Japan
Abstract Background. Closing-opening correction (COC) osteotomy is a useful procedure for severe angular kyphosis. However, there is no previous research on the reconstructed vertebrae with kyphotic malalignment in the presence of osteoporosis. Finite-element (FE) analysis was performed to estimate the biomechanical stress with both osteoporotic grades and corrective kyphotic angles during COC osteotomy for osteoporotic angular kyphosis. Methods. FE models of COC osteotomy were created by changing three major parameters: (1) grade of osteoporosis; (2) kyphotic angle; and (3) compensated posture when standing still. Osteoporosis was graded at four levels: A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middlegrade osteoporosis; D, high-grade osteoporosis. The kyphotic angle ranged from 0° as normal to 15° and 30° as moderate and severe kyphosis, respectively. FE analyses were performed with and without assumed compensated posture in kyphotic models of 15° and 30°. Along each calculated axis of gravity, a 427.4-N load was applied to evaluate the maximum compressive principal stress (CPS) for each model. Results. The CPS values for the vertebral element were the highest at the anterior element of T10 in all FE models. The maximum CPS at T10 increased based on the increases in both the grade of osteoporosis and the kyphotic angle. Compensated posture made the maximum CPS value decrease in the 15° and 30° kyphotic models. The highest CPS value was 40.6 MPa in the high-grade osteoporosis (group D) model with a kyphotic angle of 30°. With the normal (nonosteoporotic) group A, the maximum CPS at T10 was relatively low. With middle- and high-grade osteoporosis (groups C and D, respectively), the maximum CPS at T10 was relatively high with or without compensated posture, except for the 0° model. Conclusions. Lack of correction in osteoporotic kyphosis leads to an increase in CPS. This biomechanical study proved the advantage of correcting the kyphotic angle to as close as
Offprint requests to: T. Hato Received: August 7, 2006 / Accepted: March 12, 2007
possible to physiological alignment in the thoracolumbar spine, especially in patients with high-grade osteoporosis.
Introduction Osteoporotic vertebral fractures often develop a persistent spinal kyphotic deformity on sagittal alignment, leading to severe low back pain and even delayed paralysis on occasion. In such cases, surgery is often necessary. Various surgical procedures have been reported for such cases. Kaneda et al.1 noted that anterior decompression and reconstruction using the Kaneda device was effective in osteoporotic posttraumatic vertebral collapse. Saita et al.2 reported that posterior spinal shortening for delayed paraplegia after an osteoporotic vertebral fracture was performed by resecting the wedging spine and producing a short vertebra. However, in the case of a severe kyphotic deformity, it is difficult to correct the deformity completely. Furthermore, postoperative failures, such as additional vertebral collapse generally at the edge of the surgically treated segment, are often problematic in the presence of osteoporosis.3 Kawahara et al.4 noted that closing-opening correction (COC) osteotomy enabled satisfactory spinal correction and reconstruction for severe angular kyphosis. However, there is no previous biomechanical research examining the outcome of correction for severe spinal kyphosis due to osteoporosis. In the present study, we constructed threedimensional finite-element (FE) models of COC osteotomy with four types of osteoporosis and three types of corrected kyphosis. The compressive principal stress (CPS) in each FE model was evaluated to compare the completely corrected thoracolumbar spine with the incompletely corrected spine according to the osteoporotic grade.
T. Hato et al.: Closing-opening correction osteotomy
Materials and methods Construction of the FE basic model for COC osteotomy A basic FE model for COC osteotomy was created by modifying the FE model for total en bloc spondylectomy (TES).5,6 Verification of the TES model had already been performed using compressive load testing.5 The segmental levels of the model were T9-L2, and the apex level was T12 because osteoporotic compression fractures often occur at the thoracolumbar level. The thoracolumbar spine (T9-L2), harvested from a formalinized human cadaver (a 90-year-old man with no spinal disease), was used to create the basic outline of the FE model. After the total spinal segment of T12 was completely resected, including the upper and lower levels of discs, a Harms titanium mesh cage (25 mm diameter × 10 mm height) (DePuy, AcroMed, Raynham, MA, USA) filled with grafting cancellous bone was used at T12 for anterior reconstruction. Impacted cancellous bone chips were used to fill the gap in the dead space between T11 and L1. For posterior instrumentation, pedicle screws (Moss Miami System; DePuy, AcroMed) were inserted into both sides of the T10, T11, L1, and L2 pedicles — 6.0 mm diameter polyaxial pedicle screws, 40 mm in length at T10 and T11 and 45 mm in length at L1 and L2. Two 5.5 mm diameter rods were attached to the pedicle screws, and two posterior cross-link transverse units were connected between T11 and L1. In the basic FE model, the kyphotic angle at T10 was set to 0°, which was physiological spinal alignment in T12.7 All spinal instrumentation systems were made of titanium. This research was faithfully based on the national law of human macroscopic anatomy in Japan. That is, it was
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executed under supervision of the Professor of Macroscopic Anatomy, School of Medicine, Kanazawa University, for the purpose of elucidating more advanced human gross anatomy from a viewpoint of clinical medicine. The results of this research were employed for high-grade medical education, and it was lectured to medical students in our institution as a part of their high-grade anatomy practice (March 2004). The specimen from the cadaver used in this research, with great dignity and respect, was returned to the bereaved family in an official ceremony. The basic outline of the three-dimensional FE model was reconstructed from the computed tomography (CT) value for the cadaver specimen after COC osteotomy. In this FE model, the materials consisted of cortical bone, cancellous bone, intervertebral discs, facet joint cartilage, and paravertebral ligaments (anterior and posterior longitudinal ligament, supraspinous ligament, interspinous ligament, capsular ligament, ligamentum flavum); each material was assumed to be isotropic and homogeneous. At the facet joints, one layer of cartilage was in contact with another layer on both sides of T9/10, T10/11 and L1/2. On the lower endplate of T9, a onelayer rounded surface was attached for loading. The FE modeling and analysis were carried out by MARC and MENTAT analyses (MARC Analysis, Tokyo, Japan) (Fig. 1). This was a linear elastic model and consisted of 11 524 elements and 13 799 nodes. The input parameters for each material (except the cortical and cancellous bone) were according to Yamamoto et al.8 (Table 1). Next, three major parameters of the model were established: (1) the grade of osteoporosis; (2) the kyphotic angle; and (c) with or without assumed compensated posture while standing still.
Fig. 1. Finite-element (FE) modeling of reconstructive closing-opening correction (COC) osteotomy. Anterior reconstruction was done with a titanium mesh cage and impacted cancellous bone. Posterior instrumentation was performed
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Table 1. Material properties in the basic FE model for COC osteotomy Tissue
Young’s modulus
Poisson’s ratio
Grafting bone Instrument Titanium cage Disc Cartilage
E = 1000 (MPa) E = 110 (GPa) E = 35 (GPa) E = 7.5 (MPa) E = 0.6 (MPa)
υ = 0.2 υ = 0.3 υ = 0.3 υ = 0.4 υ = 0.49
Ligaments (ALL, PLL) Ligaments (SSL, ISL, LF, CL)
E = 20 (MPa) E = 10 (MPa)
υ = 0.4 υ = 0.3
FE, finite-element; COC, closing-opening correction; ALL, anterior longitudinal ligament; PLL, posterior longitudinal ligament; SSL, supraspinous ligament; ISL, interspinous ligament; CL, capsular ligament; LF, ligamentum flavum
Table 2. Four grades of osteoporosis and material properties of cortical and cancellous bone Cortical bonea Osteoporosis grade Normal (nonosteoporotic) Low grade Middle grade High grade a b
Properties
Thickness (mm)
Cancellous boneb properties
E = 10 000 MPa, υ = 0.3 E = 5000 MPa, υ = 0.3 E = 2500 MPa, υ = 0.3 E = 1250 MPa, υ = 0.3
0.8 0.6 0.4 0.2
E = 750 MPa, υ = 0.2 E = 300 MPa, υ = 0.2 E = 100 MPa, υ = 0.2 E = 75 MPa, υ = 0.2
The properties and thickness of the cortical shell were quoted according to Silva et al.9 The values of Young’s modulus were decided referring to Kopperdahl et al.10
Fig. 2. Variations of the corrected kyphotic angle by FE modeling. Simulated fusion angles were 0° (basic model) (a), 15° (b), and 30° (c). The kyphotic angle at T12 was defined as the angle from the lower surface of T11 to the upper surface of L1, an index of the extent of correction
Variation of the grade of osteoporosis by FE modeling
Variation of the kyphotic angle by FE modeling
Four grades of osteoporosis — A, normal (nonosteoporotic); B, low-grade osteoporosis, C, middle-grade osteoporosis; D, high-grade osteoporosis — were established by altering the material properties of the bone: the thickness and Young’s modulus of the cortical shell and Young’s modulus of the cancellous bone. The material properties of the cortical shell were according to Silva et al.,9 and Young’s modulus of cancellous bone were according to Kopperdahl et al.10 (Table 2).
The compressive apex of T12, the location of angular kyphosis, was completely resected and then corrected with titanium mesh and impacted cancellous bone during a COC osteotomy. Therefore, the kyphotic angle at T12 was defined as the angle from the lower surface of T11 to the upper surface of L1 as the extent of correction. Three types of kyphotic angle at T12 were produced: 0° as normal in the thoracolumbar spine7 and 15° and 30° as moderate and severe kyphosis, respectively (Fig. 2).
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Table 3. Condition of compressive load with or without compensation Length of moment arm (cm)a Kyphotic angle (°) 0 15 30 a b
Tilt angle (°)b
Without compensation
With compensation
Without compensation
With compensation
4.5 9.7 12.7
— 7.8 8.9
95 80 65
— 91 90
The distance from the axis of gravity to the anterior edge of T9 Tilt angle from the axis of gravity to the lower surface of T9
Fig. 3. Standing with or without compensated posture. a, b 0° and 15° without compensation, respectively; c 30° without compensation; d 15° with compensation; e 30° with compensation. Tilt angle means the angle from the axis of gravity to the lower surface of T9; the length of the moment arm means the distance from the axis of gravity to the anterior edge of T9
FE analysis without compensated posture In the case of spinal kyphosis, the loading condition of gravity is different because the axis of gravity in the human body varies according to the degree of kyphosis.11 Therefore, it was necessary to determine the loading condition when the weight of the human upper body was transferred to the reconstructed thoracolumbar spine. According to the method for the center of gravity,12 we assumed that the area center of gravity of a human body is the approximate center of gravity. First, the figure from a silhouette of a woman who had undergone COC osteotomy at T12 to physiological spinal alignment of 0° in the sagittal plane was produced. Her height and body weight were 158 cm and 52 kg, respectively, which approximated the mean values among the female patients who had undergone COC osteotomy.13 In addition, an illustration was produced in a standing posture with the lower body fixed straight and the upper body flexed along each level of kyphosis; they were prepared for reconstructed models with 0°, 15°, and 30° kyphosis at T12 without compensated posture. The area center of gravity of the upper body was calculated as the approximate center of gravity, and a perpendicular line from the point was assumed to be the axis of gravity in each figure. Next, the figure for the FE model was projected onto the illustration at the thoracolumbar area for each kyphotic angle after the
thoracic and lumbar spinal body of the woman was projected. The distance from the axis of gravity to the anterior edge of T9 (identified as the moment lever arm) and the tilt angle from the axis of gravity to the surface for loading at the lower endplate of T9 were calculated for each model (Fig. 3). The results are summarized in Table 3 (without compensation). The point of intersection was chosen as the loading point in each kyphotic model. Finite-element analysis was performed to evaluate the CPS on the reconstructed vertebrae. A 424.7-N load, assumed from the calculation of lumbar disc pressure measurements,14 was applied along the axis of gravity on each loading point of the lower surface of T9, with L2 fixed at the bottom. This analysis was performed for each of the four osteoporotic grades, and the CPS of each model was calculated. FE analysis with compensated posture In patients with spinal kyphotic deformity, the patient commonly straightens up by posteriorly tilting the pelvis, hip extension, and knee flexion to make the axis of gravity close to the trunk, as well as the compensation of other healthy spinal segments.11,15 Kiefer and ShiraziAdl at al.16 noted that the sagittal position of the T1-S1 line is aligned vertically in a neutral position to generate the least L5-S1 disc compressive stress. Therefore, to
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consider the axis of gravity and determine the loading condition for compensated posture, the figures of 15° and 30° without compensated posture (Fig. 3b,c), were modified to figures with compensated posture (Fig. 3d,e) by posteriorly rotating the upper half of the body, focusing on S1, as the T1-S1 lines became almost perpendicular.17 In this study, compensation by other healthy spinal segments was ignored. In the same way as without the compensated posture, the distance and the tilted angle from the axis of gravity were also calculated for each kyphosis for the loading point (Table 3, with compensation). A 424.7-N load was applied to each loading point along the axis of gravity, as previously described, with L2 fixed at the bottom; the CPS on each model was then calculated.
Results The CPS value of vertebral element was highest at T10, which was the superior segment of the reconstructed vertebrae. The maximum values of the CPS at T10 vertebra are shown in Table 4. The CPS values at T10 increased according to increases in both the grade of osteoporosis and the kyphotic angle at T12 (Figs. 4, 5a–c). The compensated posture caused the maximum CPS value to decrease in the kyphotic models at 15° and 30° (Table 4, Fig. 5d,e). With posterior instrumentation, the stress values were maximum at the rods directly under the L1 pedicle screws in all models. The minimum value was 39 MPa in the model at 0° kyphotic angle in group A, and the maximum was 119 MPa in the model at 30° kyphotic angle in group D without compensated posture (Figs. 4, 5).
Discussion Finite-element modeling is a useful biomechanical simulation to obtain clinical evidence by allowing integrated measurement of mechanical behavior in a model.18 In
the current study, there were some limitations for FE modeling and analysis. First, we did not analyze the primary osteoporotic fracture, so the analysis was not absolute, but relative. Therefore, this discussion was limited to verification of the relative comparison about the grade of osteoporosis and the reconstructed kyphosis. Second, determining the loading condition in this model was extremely difficult because the exact loading condition during daily activities was unclear. Therefore, we tried to introduce the approximate axis of gravity as the loading axis using a figure of the human body for each kyphosis. By assuming the loading condition for this model with the compensated posture, we could compare the CPS values among various levels of stress when standing still. Third, we assumed that the area center of gravity was the approximate center of gravity by selecting a woman who had an average body shape, so the loading point could be calculated according to each kyphosis. The same woman’s silhouette was used to unify the area center of gravity from the shape of the same upper half of the body. In this study, various setup conditions were needed for the FE modeling and analysis. The development of simplified, detailed software to unify these various conditions is needed to achieve a more realistic analysis in the future. Some authors have suggested the importance of maintaining normal spinal alignment in the sagittal plane. Panjabi and colleagues,19,20 in a biomechanical analysis, noted that abnormal thoracic kyphosis caused a mechanical response that further increased thoracic kyphosis in a chain reaction and that an abnormal thoracic configuration created a vicious cycle of abnormal tissue loading. Keller et al.,17 in a biomechanical analysis of thoracic hyperkyphosis at T7, noted that anterior translation of the skull and upper thoracic column caused increased compressive loads, resulting in lumbar compression fractures solely from weight bearing. They noted that it is important to reduce thoracic hyperkyphosis.
Table 4. Maximum values of compressive principal stress at the anterior element of T10 Compressive principle stress (MPa) Osteoporosis grade
0°a
15°a
30°a
15°b
30°b
Normal (nonosteoporotic) Low grade Middle grade High grade
6.1 8.1 11.8 15.1
12.5 16.4 23.9 31.3
16.3 21.3 31.0 40.6
9.5 12.5 18.3 24.0
11.4 16.1 21.8 28.5
a b
Kyphotic angle without compensation Kyphotic angle with compensation
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a
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Fig. 4. a FE analysis in the model with a kyphotic angle of 0° without compensated posture. A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middle-grade osteoporosis; D, high-grade osteoporosis. A 424.7-N force was applied along the z-axis to each loading point of the figure. b FE analysis in the model of kyphotic angle of 0° without compensated posture. A, normal (nonosteoporotic); B, low-grade osteoporosis; C, middle-grade osteoporosis; D, high-grade osteoporosis. A 424.7-N force was applied along the z-axis to each loading point of the figure
b
Fig. 5. FE analysis in high-grade osteoporotic group D. The angles of kyphosis were as follows: 0° and 15° (a and b, respectively); 30° without compensation (c); and 15° and 30° with compensation (d and e, respectively). A 424.7-N force was applied along the z-axis to each loading point
Vertebral collapse at the edge of reconstructed vertebrae is often clinically problematic during spinal reconstruction.3 In this study, the CPS was highest at T10, which was the top of the reconstructed vertebrae. The study showed that the CPS values at T10 increased according to increases in both the grade of osteoporosis and kyphosis (Table 4; Figs. 4, 5). Therefore, the grade of osteoporosis and the kyphotic angle are thought to be important factors in spinal correction and reconstruction of the thoracolumbar spine. Because the FE
analysis was performed under the restrictive condition that L2 was fixed as the lower edge of the model in this study, the biggest increase in CPS occurred on the upper vertebra of the model, which received the most distortion via a hinge that received the momentum. Depending on the loading condition, a large increase in CPS may also arise on the lower edge. The highest vertebral CPS value in this study was 40.6 MPa, which was almost half of the yield stress of human compact bone (83 MPa),21 in the high-grade
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osteoporotic group D model (30° without compensated posture). Nachemson noted in the study of disc pressure measurement that the pressure on lumbar discs during light manual labor was about five times greater than when standing still.22 Therefore, this linear elastic analysis showed that vertebral collapse could occur at the top of the reconstructed vertebrae if a further massive load was experienced during daily living activities other than standing still, especially in osteoporotic malaligned vertebrae. On the other hand, with posterior instrumentation it was not a marked stress increase that led to metal breakage when the yield stress of the titanium alloy (860 MPa)23 was considered, although the stress value increased owing to the reconstructed kyphotic malalignment. (Fig. 4, 5) However, in the long run, instrument failure may arise due to metal fatigue.
Conclusions We concluded that it is biomechanically reasonable to correct osteoporotic angular kyphosis to as close as possible to physiological spinal alignment in the thoracolumbar spine, especially in the presence of high-grade osteoporosis, to prevent clinical complications such as vertebral collapse and to obtain better clinical results. Careful analysis of individual patients is necessary prior to surgery. Acknowledgment. The authors give special thanks to Tsuyoshi Kamio, Graduate School of Engineering, Kanazawa University, for invaluable assistance. The authors did not receive and will not receive any benefits or funding from any commercial party related directly or indirectly to the subject of the article.
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