Title. Author(s)Salmingo, Remel; Tadano, Shigeru; Fujisaki, Kazuhiro. CitationClinical Biomechanics, 27(6): Issue Date Doc URL.

Transcription

1 Ttle Correctve force analyss for scoloss from mplant Author(s)Salmngo, Remel; Tadano, Shgeru; Fujsak, Kazuhro CtatonClncal Bomechancs, 27(6): Issue Date Doc URL Type artcle (author verson) Fle Informaton CB27_ pdf Instructons for use Hokkado Unversty Collecton of Scholarly and Aca

2 Correctve force analyss for scoloss from mplant rod deformaton Remel Salmngo, MEng a, Shgeru Tadano, PhD b,*, Kazuhro Fujsak, PhD b, Yuchro Abe, MD, PhD c, Manabu Ito, MD, PhD c a Dvson of Human Mechancal Systems and Desgn, Graduate School of Engneerng, Hokkado Unversty, North 13 West 8 Kta-ku, Sapporo, Japan b Dvson of Human Mechancal Systems and Desgn, Faculty of Engneerng, Hokkado Unversty, North 13 West 8 Kta-ku, Sapporo, Japan c Department of Orthopaedc Surgery, Graduate School of Medcne, Hokkado Unversty, North 15 West 7 Kta-ku, Sapporo, Japan * Correspondng Author Shgeru Tadano, e-mal: tadano@eng.hokuda.ac.jp tel: fax: The total number of words of the man text excludng references: 3171 The number of words of the abstract: 245 The number of fgures: 7 The number of table: 1

3 ABSTRACT Background: Scoloss s a serous dsease n whch a human spne s abnormally deformed n three dmensons wth vertebral rotaton. Surgcal treatment s attaned when the scolotc spne s corrected nto ts normal shape by mplant rods and screws fxed nto the vertebrae. The three-dmensonal correctve forces actng at the screws deformed the mplant rod durng the surgcal treatment of scoloss. The objectve of ths study was to propose a method to analyze the three-dmensonal forces actng at the rod usng the changes of mplant rod geometry before and after the surgcal treatment. Methods: An nverse method based on Fnte Element Analyss s proposed. The geometres of mplant rod before and after the surgcal treatment were measured three-dmensonally. The mplant rod before the surgcal treatment was reconstructed usng an elasto-plastc fnte element model. The three-dmensonal forces were appled teratvely to the rod through the screws such that the rod s deformed the same after the surgcal treatment of scoloss. Fndngs: The maxmum force actng at the screw of each patent ranged from 198 N to 439 N. The magntude of forces were clncally acceptable. The maxmum forces occurred at the lowest fxaton level of vertebra of each patent. Interpretaton: The three-dmensonal forces dstrbuton that deformed the rod can be evaluated usng the changes of mplant geometry. Although the current clncal cases are stll few, ths study demonstrated the feasblty of measurng the forces that deformed the mplant rod after the surgcal treatment of scoloss. KEYWORDS Bomechancs, scoloss, rod deformaton, fnte element analyss

4 1. Introducton Scoloss s characterzed as a three-dmensonal (3D) deformty of the spne wth axal rotaton of the vertebrae. The degree of severty of the scolotc deformty s evaluated usng the value of Cobb angle. The Cobb angle s defned as the maxmum angle between two lnes drawn parallel to the endplates of scolotc vertebrae at the frontal plane. The Cobb angle can be also expressed threedmensonally (3D) usng the method of (Kanayama et al., 1996). When the Cobb angle s greater than 50 degrees, surgcal treatment usng mplant fxaton s used. Surgcal treatment of severe scoloss requres fxaton of mplantable devces such as rods, screws, hooks and wres accomplshed usng surgcal technques. Varous rod rotaton technques have evolved and became more sophstcated n applyng the forces requred to correct the three-dmensonal scolotc deformty. These surgcal technques are rod rotaton technques or popularly known as Cotrel-Dubousset (CD) technque, Smultaneous Double Rod Rotaton Technque (SDRRT) and other rod derotaton technques (Dubousset et al., 1988; Ito et al., 2010; Zelke, 1982; Cheng et al., 2008; Gudera et al., 1993, Mc Lan et al., 1993; Schlenk et al., 2003). The three-dmensonal surgcal correcton of scoloss s prmarly dependent to the chosen surgcal technque or procedure. The SDRRT procedure was used to correct the scoloss deformty. In SDRRT, two pre-bent rods were nserted nto the polyaxal screw heads. The polyaxal screw heads remaned untghtened untl the rod rotaton was completed (.e. rod can rotate and translate freely nsde the screw head durng rod rotaton maneuver). A rod rotatng devce was used to hold and rotate the rod. A torque was appled to the rod rotatng devce to rotate the rod (approx. 90 ) at the same tme to create correctve forces on rods through the screws to deform the spne nto normal shape. Scoloss correcton was attaned, however, the correctve

5 forces actng on screws were hgh enough that deformed the mplant rod after the surgcal treatment of scoloss. Thus, nvestgaton of the bomechancal changes (.e. ncludng forces that caused the deformaton of mplant rod n vvo) after the surgcal procedure s mportant to understand the bomechancs of scoloss correcton. Understandng the bomechancs of scoloss correcton could help avod clncal complcatons and obtan optmal surgcal correcton. Several authors have nvestgated the bomechancs of scoloss correcton usng patent-specfc fnte element models (Lafon et al., 2009; Wang et al., 2011). These studes were successful n analyzng the forces occurrng at the mplant rod-vertebra connecton. However, the magntude of forces obtaned mght not be so realstc because the analyses were focused only on the elastc deformaton of rod. Elasto-plastc deformaton analyss should have been consdered. Furthermore, the rod geometry acquston methods were lmted because they dd not measure the actual ntal geometry of rod and the n vvo three-dmensonal shape of the rod was just approxmated from the postoperatve radographs and vdeos. Thus, t was not possble to obtan the real ntal and fnal three-dmensonal geometry of rod and consequently the forces usng ther methods. The objectve of ths study was to propose a method to analyze the threedmensonal forces actng at each screw from the changes of mplant geometry after scoloss surgery usng SDRRT. These forces could be the correctve forces developed at the screws transferred to rod due to the resstance of spne durng the rod rotaton maneuver. The method s based on FEA. The three-dmensonal geometry of the mplant rod was measured before and after surgery. The threedmensonal forces that deformed the rod could be obtaned usng just the geometry of rod before and after the surgcal treatment of three scoloss patents.

6 2. Methods 2.1 Force Analyss Fgure 1(left) shows the CT mage of the spne after the surgcal treatment n the posteror vew. Fgure 1(rght) also shows the three-dmensonal mplant geometry of rod at the concave sde before and after surgery. To standardze the use of the three-dmensonal geometry of rod, the coordnate system proposed by the Scoloss Research Socety was used n ths study (Yeung et al., 2003). The postve x-axs s drected anterorly, the postve y-axs s drected toward the left lateral sde and the postve z-axs s drected toward the superor drecton. From a mechancal pont of vew, when a rod made from metal s deformed, forces occur n accordance to the deformaton. Ths fgure also shows that the mplant rod at the concave sde was deformed after surgery. It mples that there are forces actng at the mplant rod after the surgcal treatment of scoloss. Fgure 2 s a schematc dagram showng mplant rod deformaton before and after surgery. The orgn (0,0,0) was set at the nferor end of the rod. The three-dmensonal force F actng at the screw (-th from bottom) whch dsplaced the poston of screw before surgery p 0 nto after surgery p * s requred n the analyss. Intally, zero force s appled to the screw p on the rod geometry before 0 surgery. The dsplacement p s calculated usng FEA. To search for the forces actng at the deformed rod after surgery, the dfference e whch s defned as the dstance between the screw locaton p * on the rod geometry after surgery and dsplaced locaton p s used n the teraton process. The drecton of the threedmensonal force F created from the x-z plane s defned as the angle. The

7 drecton of force along y-z plane was neglected because CT acquston could not accurately depct deformaton along ths plane. Fgure 3 shows the procedure to calculate the forces from mplant rod deformaton. Here, the three-dmensonal rod geometres before and after surgery are already obtaned. The rod dameter was 6mm and the rod length dffers wth each patent. The fnte element model of the rod was made by ANSYS 11.0 software (ANSYS, Inc., Pennsylvana, USA) usng a 10 node tetrahedral sold elements. The boundary condton was set consderng the manner of rod fxaton durng the surgcal treatment. The screws coordnates were reorented such that the most superor screw concdes wth the z-axs (.e. on top of the most nferor screw) because each patent has dfferent mplant rod orentaton and fxaton levels. The most nferor screw at the end of rod was fxed n all translatons but free to rotate. The most superor screw was also fxed except that t was free to move along the superor drecton only. As the loadng condton, Forces F were set wth ntal values. An elasto-plastc analyss was conducted snce the mplant rod was made from ttanum alloy (JIS T ), a typcal elasto-plastc materal. The deformaton behavor of the rod n unaxal tensle loadng s shown n Fg. 4. In the elastc regon 0 ), the stress-stran relaton and E as the elastc modulus s ( Y expressed n Eq. (1) E (1) The stress-stran relatonshp n the plastc regon ( ) s expressed n Eq. (2). ε Y s the yeld stran ndcatng the start of plastc deformaton. E ) (2) Y H( Y Y

8 Materal propertes of ths rod are Young s Modulus (E), yeld stress (σ Y ), yeld stran (ε Y ) and hardenng coeffcent (H) equal to 105 GPa, 900 MPa, 8.57x10-3 and 2.41 GPa, respectvely. In three-dmensonal FE analyss, the von Mses stress was adopted to evaluate the stress dstrbuton along the rod. The dsplacements from elasto-plastc deformaton p were analyzed usng FEA. The dfference e at each screw locaton was calculated from the screw locaton after surgery p. The evaluatng functon whch was defned as the sum * of the squares of dfferences on each screw s expressed n Eq. (3). n 1 e 2 α (3) If the evaluatng functon s greater than α (where α 0.5), the value of the appled forces F are replaced usng Eq. (4) and terated for the next step. F F e The constant coeffcent n Eq. (4) s ntroduced n every teraton step so as to attan smooth and rapd convergence. The constant coeffcent s equal to 0.5 N mm. The process was terated untl the value of Eq. (3) s less than α. The forces at ths teraton step are consdered to be optmal. These forces could be the result of correctve forces transferred to the spne snce the rod s drectly attached to t through the screws. Furthermore, the stress or stran dstrbutons n the deformed mplant rod caused by the forces F were obtaned n ths study. 2.2 Clncal Geometry Measurements The ntal geometry of mplant rod was measured from the actual rod used before surgery. The mplant rod geometry after surgery was obtaned a week after the surgcal operaton usng Aqulon 64 CT scanner (Toshba Medcal Systems Corporaton, Tochg, Japan). The slce thckness was 0.5mm. The mages were (4)

9 mported nto CAD software Soldworks 2010 (Dassault Systemes, Massachusetts, USA) to measure the 3D geometry and deformaton. The procedure was approved by the ethcs commttee of Graduate School of Medcne. A proper nformed consent was obtaned for all patents. All patents were classfed as severe Adolescent Idopathc Scoloss (AIS) that s wth hgh Cobb angle whch requres surgcal treatment. The USS II 6 mm dameter rods and polyaxal pedcle screws (Synthes GmbH, Oberdorf, Swtzerland) were mplanted usng the SDRRT surgcal technque. The clncal data of the patents used n ths study s lsted n Table 1. In SDRRT, two mplant rods were used. However, n all patents, the rod geometry mages show that the rod at the convex sde was not deformed (.e. mnmum and rod deformaton cannot be detected by CT magng) after the surgcal treatment of scoloss. Ths mples that the correctve force actng on the rod at the convex sde was neglgble. On the other hand, the rod at the concave sde was sgnfcantly deformed. The three-dmensonal changes of rod geometry at the concave sde of the three patents were used to analyze the forces actng at the rod after the surgcal treatment of scoloss. 3. Results 3.1 Forces Analyss The teraton process was stopped when the objectve functon was less than α. The appled forces at ths teraton step s referred to as the optmal forces F. Fgure 5(top) shows the magntude of three-dmensonal forces actng at the vertebrae of Patent 1. The drecton of the three dmensonal forces at each level of vertebra along the x-z plane s defned by angle. The drecton of forces along the y-z plane was neglected snce the rod was not deformed along that

10 plane. Fgure 5(bottom) shows the magntude of forces that deformed the rod for Patent 2 and Patent 3. The maxmum forces obtaned were 248 N, 198 N and 439 N for Patent 1, Patent 2 and Patent 3 respectvely. 3.2 Stress Dstrbuton To dentfy the possble locaton of rod breakage, the von Mses stress dstrbutons were also obtaned usng FEA. Fgure 6 shows the von Mses stress dstrbutons when the mplant rod was deformed after the surgcal treatment of scoloss. The maxmum von Mses stresses were 726 MPa, 241 MPa, 905 MPa located at T10 for Patent 1, T11 for Patent 2, T11 for Patent 3 respectvely. 4. Dscusson The forces actng at each screw were calculated usng just the changes of mplant rod geometry before and after surgery usng SDRRT. The current maxmum values obtaned n ths study were at the lumbar regon 248 N, 198 N and 439 N for Patent 1, Patent 2 and Patent 3 respectvely. These forces occurred at each screw when the scolotc spne ressts the rotaton of rod. As a result, the forces deformed the rod after the surgcal treatment of scoloss. These forces could be the result of correctve forces transferred to the rod and vertebrae of spne snce t s attached nto the screws. The present method could be used also to analyze the post-operatve correctve forces from the changes of mplant rod geometry after many months or years. These could be done by takng CT mages of mplant rod. Post-operatve daly lvng actvtes such as standng, bendng, walkng and etc. may change the rod shape as well as the correctve forces actng on t. These actvtes may cause correctve forces to ncrease or decrease whch may affect the stablty of the fxaton. Furthermore, these actvtes could also develop hgh correctve forces

11 whch mght be unsafe to the patent. Thus, the present method wll be appled to nvestgate the magntude of post-operatve correctve forces from the changes of mplant rod geometry durng future patent follow ups. The objectve of scoloss correcton s to deform and fx the scolotc spne nto ts normal shape wthout damagng deformatons and neurologcal complcatons. Ths could be attaned by applyng sutable correctve forces to the spne through mplant rods and screws. The correctve forces requred to correct the deformty must be suffcent n order to acheve the requred correcton. Lou et al. attached stran gages to the rod rotatng devce. They montored the correctve force appled by surgeon at the rotatng devce durng the CD derotaton maneuver. The measured correctve force ranged from N (Lou et al., 2002). Although patents were lmted, an ncreasng trend was found between the appled force and degree of correcton. However, the correctve forces actng at each screw were dffcult to measure snce the rotatng devce s attached only to the mplant rod. The magntude of forces occurrng at each screw s also mportant because overloadng due to the rod rotaton maneuver mght occur (Lttle and Adam, 2010). Another mportant ssue durng the rod rotaton maneuver s the loss of feelng of the surgeon to feel the resstance of each corrected level (.e. located at each screw). Ths s because the rod rotatng devce s attached to the rod at a sngle locaton only. The correctve forces occurrng at each screw mght be excessve (Lou et al., 2002). 15 cases of pedcle fractures were reported durng the rod rotaton maneuver due to excessve correctve forces (D Slvestre et al., 2007). Although t s dffcult, however, t wll be more meanngful for future studes f we can drectly establsh the relaton of the requred torque to rotate the rod and the forces actng on each screw or vce versa. From ths, the surgeons can

12 decde ntraoperatvely whether the appled torque durng the rotaton maneuver s safe or not. Some cases of broken mplant rods were reported durng CD nstrumentaton (Gudera et al., 1993). The breakage rsk was nvestgated usng von Mses stress. The von Mses stress dstrbuton along the entre length of the deformed rod was obtaned. The possble locatons of rod breakage can be located. Ths also demonstrates the usefulness of the current method to locate possble locatons of mplant rod fracture by checkng the stresses dstrbuton after the surgcal treatment of scoloss. Accurate measurement of mplant rod geometry before the surgcal treatment s mportant to attan more accurate results. Currently, the surgeons manually traced the contoured rods usng the actual mplant rod used before surgery. The traced geometry was scanned and reconstructed as an mage fle. The CT magng can be used also to measure the rod geometry before surgery. Although ths has not been done yet, we have to consder ts vablty n the clncal settng. Furthermore, a precse 3D geometry measurement method can be developed usng laser dsplacement sensors. Laser dsplacement sensor s useful clncally because t can measure the shape of the rod wthout contact. The scoloss cases presented here shows that the screws were not nserted at all vertebral levels. The forces mght change f more or lesser screws were used. Thus, there can be varous screw placement confguratons applcable for a certan scoloss case. Some authors nvestgated the dfferent screw placement confguratons n anteror spne nstrumentaton usng a bomechancal model (Desroches et al., 2007). They were successful n fndng the optmal screw placement confguratons before surgery as confrmed by ther post operatve results. Lkewse, some screw placement confguratons were not recommended

13 because ther calculated correctve forces exceeded the publshed pullout forces. Ther study ntroduces the possblty to perform preoperatve plannng usng the anteror approach. Further study consderng not only the deformaton of rod but also the effect of varous screw placement confguraton to the correctve forces n SDRRT surgcal technque shall be further nvestgated (e.g. optmal number of screws and placement of screws). The current method presented here calculated the correctve forces actng at the mplant rod after the surgcal treatment of scoloss. Lou et al., 2002 strengthened that too much hgh correctve forces can cause mplant breakage or bone fracture whch may lead to pullout of screws from the vertebra. Thus, the magntude of correctve forces s crtcal durng surgery. Lljenqvst et al., 2001 performed bomechancal pullout tests of pedcle screws usng nne human cadaverc thoracc spnes. The measured pullout strengths of the pedcle screws ranged from 532 N to 808 N (Lljenqvst et al., 2001). Although ths value seems to be unsafe because t s close to the maxmum calculated value of our study (.e. 439 N), mplant dfferences as well as specmen (osteoporotc vs. normal, age, sex) need to be consdered for better comparson. The closest pullout experment that can be compared to our results was conducted by Seller et al., They performed pullout test usng calf vertebrae and the same mplant screw used n our study (.e. USS II posteror screw). The average pullout force was 2413 N that was approxmately 5.5 tmes hgher than the maxmum calculated force of our study (2413 N / 439 N 5.5). Ths suggests that the forces actng on the screws of the current scoloss cases are stll safely below the pullout force threshold. Although dfferences n bone qualty and mplant confguratons such as mplant nserton depth mght affect the comparson, actual pullout

14 experments shall be conducted to valdate these fndngs. Nevertheless, problems nvolvng screw pullout dd not occur as confrmed by the surgeons. In the current treatment, two rods were used for each case. The geometry of rod attached n the concave and convex sde of Patent 1 s shown n Fgure 7. The rod geometry of all patents at the convex sde was not deformed after the surgcal treatment. Although the current numbers of cases were few, further nvestgaton must be made n order to elucdate the mechansm of these fndngs. Conversely, the rod at the concave sde ndcates that t has a sgnfcant mechancal role durng the SDRRT. In surgcally treated scolotc patents, the mplant rod and screw are fxed nto the spne for a long perod of tme. The bone of the spne s contnuously remodelng or adaptng ts structure durng the fxaton perod. At ths tme, the forces actng on the rod mght change due to adaptaton of spne. The changes of rod geometry wll be further nvestgated usng CT magng durng future followups. 5. Concluson In ths study, the dstrbutons of forces that deformed the mplant rod were analyzed usng just the rod geometry before and after the surgcal treatment. These forces could be assocated wth the correctve forces actng at the vertebrae of the spne snce the rod s drectly attached to t through the screws. The work presented here helps to understand the magntude of correctve forces actng at the vertebrae of spne durng scoloss correcton surgery. Future studes nvolvng larger number of patents wll elucdate the relatonshp between the correctve forces actng at the rod and scoloss correcton mechansm.

15 References Cheng, J., Lebow, R., Schmdt, M., Spooner, J., Rod derotaton technques for thoracolumbar spnal deformty. Neurosurgery. 63, Cotrel, Y., Dubousset, J., Gullaumat, M., New unversal nstrumentaton n spnal surgery. Cln. Orthop. 227, Desroches, G., Aubn, C., Sucato, D., Rvard, C., Smulaton of an anteror spne nstrumentaton n adolescent dopathc scoloss usng a flexble multbody model. Med. Bo. Eng. Comput. 45, D Slvestre, M., Parsn, P., Loll, F., Bakalouds, G., Complcatons of thoracc pedcle screws n scoloss treatment. Spne. 32, Gudera, K., Hooten, J., Weatherly, W., Hghhouse, M., Castellv, A., Ogden, J., Pug, L., Cook, S., Cotrel-Dubousset nstrumentaton: results n 52 patents. Spne. 18, Ito, M., Abum, K., Kotan, Y., Takahata, M., Sudo, H., Hojo, Y., Mnam, A., Smultaneous double rod rotaton technque n posteror nstrumentaton surgery for correcton of adolescent dopathc scoloss. J. Neurosurg. Spne. 12, Kanayama, M., Tadano, S., Kaneda, K., Uka, T., Abum, K., A mathematcal expresson of three-dmensonal confguraton of the scolotc spne. J. Bomech. Eng. 118, Lafon, Y., Lafage, V., Dubousset, J., Skall, W., Intraoperatve threedmensonal correcton durng rod rotaton technque. Spne. 34, Lljenqvst, U., Hackenberg, L., Lnk, T., Halm, H., Pullout strength of pedcle screws versus pedcle and lamnar hooks n the thoracc spne. Acta Orthopaedca Belgca. 67,

16 Lttle, J., Adam, C., Development of a computer smulaton tool for applcaton n adolescent spnal deformty surgery. Lecture Notes n Computer Scence. 5958, Lou, E., Hll, D., Raso, J., Moreau, M., Mahood, J., Instrumented rod rotator system for spnal surgery. Med. Bol. Eng. Comput. 40, McLan, R.F., Sparlng, E., Benson, D.R., Early falure of short-segment pedcle nstrumentaton for thoracolumbar fractures. A prelmnary report. J. Bone Jont Surg. Am. 75, Schlenk, R.P., Kowalsk, R.J., Benzel, E.C., Bomechancs of spnal deformty. Neurosurg. Focus. 14, 1-6. Seller, K., Wahl, D., Wld, A., Krasupe, R., Schneder, E., Lnke, B., Pullout strength of anteror spnal nstrumentaton: a product comparson of seven screws n calf vertebral bodes. Eur. Spne J. 16, Wang, X., Aubn, C., Crandall, D., Labelle, H., Bomechancal modelng and analyss of a drect ncremental segmental translaton system for the nstrumentaton of scolotc deformtes. Cln. Bomech. 26, Yeung, A., Ottavano, D., Lee, D., Haher T., Spne testng modaltes, n: DeWald, R., Arlet, V., Carl, A., O'Bren, M., (Eds.), Spnal deformtes the comprehensve text, Theme Medcal Publshers Inc., New York, pp Zelke, K., Ventral derotaton spondylodess. Results of treatment of cases of dopathc lumbar scoloss. Z. Orthop. Ihre. Grenzgeb. 120,

17 Lst of Tables Table 1 Clncal data of the three scolotc patents Lst of Fgures Fgure 1 Image showng 3D mplant rod deformaton before and after the surgcal treatment Fgure 2 Schematc dagram of 3D rod geometry before and after surgery Fgure 3 Procedure for 3D force analyss Fgure 4 Blnear elasto-plastc materal model Fgure 5 Magntude of 3D forces actng at each screw calculated from mplant rod deformaton Fgure 6 von Mses stress dstrbuton of deformed rod after the surgcal treatment Fgure 7 Rod geometres n the concave and convex sde before and after the surgcal treatment of Patent 1

18 Fgure 1 Image showng 3D mplant rod deformaton before and after the surgcal treatment Implant rod (concave sde) Thoracc Vertebrae (T1-T12) T5 T6 T7 T10 Before Surgery After Surgery T11 Implant rod (convex sde) Lumbar Vertebrae (L1-L5) z z T12 L1 L2 Screw Head F y x CT mage of the spne and rods fxed by the screws 3D geometry of deformed rod and force at fxaton pont shown n frontal and sagttal vew

19 Fgure 2 Schematc dagram of 3D rod geometry before and after surgery 0 p p * p Rod Geometry After Surgery F e p * p Rod Geometry Before Surgery y z (0,0,0) x

20 Fgure 3 Procedure for 3D force analyss 3D Geometry FE Modelng Boundary Condton Inverse Calculaton For Optmzng Force Loadng Condton Apply Force F (gven) Elasto-plastc Analyss F F e Dsplacement p e Dfference p * p NO n 1 e 2 α YES Optmal Forces F 3D Forces F Stress/Stran Dstrbuton /

21 Fgure 4 Blnear elasto-plastc materal model σ H σ Y E 0 ε Y ε elastc plastc

22 Fgure 5 Magntude of 3D forces at each screw calculated from mplant rod deformaton Tadano Fgure 5 Forces actng at each screw of Patent 1 F (N) Patent 1 θ (Degrees) T5 T5 182 T5 13 T6 43 T6 133 T7 66 T7 159 T8 T8 T9 T9 T T T11 84 T T12 65 T z L2 L1 35 L1 167 Patent 2 x y L2 L Patent 3 F (N) θ (Degrees) F (N) θ (Degrees) T5 T5 T5 T5 T6 59 T6 62 T6 375 T6 20 T7 55 T7 82 T7 260 T7 162 T8 T8 T8 T8 T9 T9 T9 T9 T10 T10 T10 T10 T T T T T12 T T T L1 L1 L1 L L2 L2 L2 L

23 Fgure 6 von Mses stress dstrbuton of deformed rod after the surgcal treatment Patent 1 Patent 2 Patent 3 MPa T5 T6 T7 T6 T7 T6 T y z cross- secton z x T10 T11 T12 L1 L2 y z cross- secton z x T11 T12 y z cross- secton z T11 T12 L1 x Maxmum Stress at T10 Maxmum Stress at T11 Maxmum Stress at T11

24 Fgure 7 Rod geometres n the concave and convex sde before and after the surgcal treatment of Patent 1 Concave Rod Convex Rod T5 T6 T7 Before Surgery T5 T6 T7 T8 T9 z x T10 T11 T12 L1 L2 After Surgery z x T10 T11 T12 L1 L2

25 Table 1 Clncal data of the three scolotc patents Scoloss Gender Age Cobb angle before surgery Cobb angle after surgery Screw locatons at vertebra Length of Rod (mm) Patent 1 Female T5, T6, T7, T10, T11, T12, L1, L2 226 (T5 to L2) Patent 2 Female T6, T7, T11, T (T6 to T12) Patent 3 Female T6, T7, T11, T12, L1 177 (T6 to L1)