Using Finite Element Method to Determine Pad Positions in a Boston Brace for Enhancing Corrective Effect on Scoliotic Spine: A Preliminary Analysis

Transcription

1 Journal of Medcal and Bologcal Engneerng, 3(1): Usng Fnte Element Method to Determne Pad Postons n a Boston Brace for Enhancng Correctve Effect on Scolotc Spne: A Prelmnary Analyss Wen-Ka Chou 1 Chen-Ln Lu Y-Chng Lao 3 Fang-Hsn Cheng 1,4 Zheng-Cheng Zhong 1 Chen-Sheng Chen 1,* 1 Department of Physcal Therapy and Assstve Technology, Natonal Yang Mng Unversty, Tape 11, Tawan, ROC Department of Orthopedc Surgery, Veterans General Hosptal-Tape, Tape 11, Tawan, ROC 3 Department of Rehabltaton, Mackay Memoral Hosptal, Tape 104, Tawan, ROC 4 Department of Physcal Medcne and Rehabltaton, Tape Veterans General Hosptal, Tape 11, Tawan, ROC Receved Mar 010; Accepted 9 Sep 010; do: /jmbe.758 Abstract Scoloss, the three-dmensonal (3D) deformaton of the spnal column, s lkely to worsen wthout early nterventon. The Boston brace has been wdely used to correct abnormal spnal curvature and prevent deformty progresson. However, two-dmensonal (D) X-ray mages and an experenced therapst are requred for a proper Boston brace to be fabrcated. There has been lttle research on how to determne the pad postons of a Boston brace to yeld a better correctve effect on a scolotc spne. Ths study uses the fnte element (FE) method to determne the optmal pad postons for a Boston brace. The software ANSYS 11.0 s employed to establsh an FE model of the trunk and brace from S-shaped scoloss. After the FE model s valdated, ffteen FE models wth pad postons rotated n a range of 0 to 30 degrees and translated n a range of 0 to 30 mm are created to nvestgate the effects on correctng a scolotc spne. A 3D FE model of a scolotc spne s establshed to calculate the correctve effect of a Boston brace. The FE analyss ndcates that the brace pad at the rb of the apex vertebra should be rotated 0 posterorly for the optmal correctve effect. Compared to a tradtonal brace, the modfed brace ncreases the correctve effect on the thoracc and lumbar spne, and lowers the mean contact pressure of the thoracc pad. Addtonally, the comfort of the modfed brace s comparable to that of a tradtonal brace, as measured usng the vsual analogue scale. Keywords: Scoloss, Boston brace, Fnte element method (FEM), Spne 1. Introducton Scoloss, the three-dmensonal (3D) deformaton of the spnal column, ncludes abnormal lateral devaton and a tlt of more than 10 n the frontal plane, dsplacement n the sagttal plane, and rotaton n the transverse plane [1]. If left untreated, the condton cause backaches and functonal mparment n daly actvtes [1-4]. The Boston brace has been proven to slow down the natural progresson of scoloss and reduce the need for surgcal nterventon [5-7]. Compared wth other treatment methods (therapeutc exercse, postonal exercse, and lateral-body electronc stmulaton), the Boston brace yelds a better correctve effect on a scolotc spne [8]. A prevous study noted that the more the Cobb angle (CA) can be lowered, * Correspondng author: Chen-Sheng Chen Tel: ; Fax: E-mal: cschen@ym.edu.tw the less chance there s for aggravaton of the condton durng early brace wearng [9]. Clncally, D posteror-anteror X-ray mages and an experenced therapst are requred for a proper Boston brace to be fabrcated. However, few studes have nvestgated how to poston the pads wthn the brace to produce the optmal correctve effect on a scolotc spne. Because of the dffculty assocated wth human testng and the ethcal problem of repettve radaton exposure for the examnaton of a scolotc spne, prevous studes analysed the bomechancal nteractons between the spne and brace usng fnte element (FE) models. An FE model, ncludng the rbs and spnal column, composed of 3D elastc beam elements, was developed to determne the magntude and drecton of the appled force n a scolotc spne and to predct the effect of wearng a Boston brace before brace fabrcaton [10]. Usng a detaled human trunk model and a parametrc brace model, t was found that scolotc correcton s assocated wth the tensle force of the straps and the brace geometry [11].

2 30 J. Med. Bol. Eng., Vol. 3 No Addtonally, when the sagttal curve of the brace was reduced, both the lordoss and the kyphoss of the patent decreased [1]. To remove redundant materal n a Boston brace, an FE model wth topology optmzaton was mplemented to reduce the brace s weght [13]. Although many studes have examned the relatonshp between the applcaton of a Boston brace and the correcton of scoloss, few studes have consdered the effect of pad placement. The correctve force on the scolotc spne s transferred from the strap force to the scolotc spne va the brace pad. Therefore, the pad poston s the loadng pont for the nteracton between the scolotc spne and the brace strap. However, prevous studes have not addressed how to determne optmal pad postons. Most FE studes have nstead focused on the calculaton of the drectly appled force to the spne and the effect of the brace strap force. For manufacturers, more nformaton s needed for determnng optmal pad poston. Therefore, the present study employs an FE model to analyse the relatonshp between pad postons and the correctve effect on scoloss.. Materals and methods.1 Reconstructon of scolotc trunk and brace model Two subjects provded wrtten nformed consent pror to partcpaton n the study, whch was approved by the Insttutonal Revew Board of Natonal Yang Mng Unversty (#IRB97004). One teenage grl (13 years old, Lenke-type C, 37.4 rght thoracc and 34.3 left lumbar CAs) wth adolescent dopathc scoloss was enrolled n ths study. A tradtonal Boston brace was custom-made for ths grl. The translaton and rotaton of each vertebral body, relatve to the mdpont of the upper endplate of the L5 vertebral body, were measured from an X-ray mage; the results are lsted n Table 1. The rotatonal measurement method of the vertebral body was adopted from a prevous study [14]. The geometry and materal propertes of the vertebral body were adopted from a prevously valdated FE model [15-17]. After acqurng the locaton data, the FE model of a scolotc spne was reconstructed usng the ANSYS parametrc desgn language (APDL) of the FE software package ANSYS 11.0 (ANSYS Inc., Canonsburg, PA, USA), as shown n Fgs. 1 and 1. The vertebral body of the spnal FE model, comprsng cortcal and cancellous bone and posteror elements, was constructed usng 8-node sold hexahedral element. The ntervertebral dsc, comprsng nucleus pulposus, annulus fbrosus, and an endplate, was constructed usng a -node cable and 8-node hexahedral sold elements. The materal propertes of the dsc model were smulated as lnear elastc, homogenous, and sold monophasc behavour. Spnal lgaments, namely the anteror longtudnal lgament, the posteror longtudnal lgament, the nterspnous lgament, the supraspnous lgament, the lgamentum flavum, the transverse lgament, and the facet capsular lgament, were constructed usng -node cable elements. Table 1. Translaton and rotaton of each vertebral body relatve to the L5 vertebral body. Tx (mm) Ty (mm) Tz (mm) Rx (degrees) Ry (degrees) Rz (degrees) C T T T T T T T T T T T T L L L L L Note: Tx: translaton n the medo-lateral drecton; Ty: translaton n the antero-posteror drecton; Tz: translaton n the vertcal drecton. Rx: rotaton n the transverse plane; Ry: rotaton n the sagttal plane; Rz: rotaton n the frontal plane. (c) (e) Fgure 1. FE models of scolotc spne and Boston brace. FE model from C7 to L5 vertebral body, moton segment, (c) measurement of trunk, (d) trunk FE model, (e) measurement of brace shape, and (f) brace FE model. (d) (f)

3 FE Analyss of Boston Brace 31 The geometres of the thoracc cage and abdomnal cavtes were reconstructed accordng to the trunk space coordnates recorded by an optc moton analyss system (PTI Vsualeyez 4000, PhoenX Technologes Incorporated, Canada). 53 markers were attached to the rbs, the xphod process and the seventh cervcal spnous process around the posteror, and the lateral and anteror-lateral regons of the thoracc cavty, as shown n Fg. 1(c). In addton, 1 markers were attached to the abdomnal cavty and pelvs. The FE model of the trunk wth a scolotc spne conssted of elements and 79 nodes, as shown n Fg. 1(d). The FE model of the brace was also reconstructed usng the optc moton analyss system. To obtan an accurate shape of the Boston brace, 05 markers were attached on the brace and nne markers were attached to the thoracc and lumbar pads to measure brace geometry, as shown n Fg. 1(e). The pads and shell of the FE model of the brace were smulated usng four-node sold elements and four-node shell elements, respectvely, and reconstructed usng 1985 elements and 8869 nodes, as shown n Fg. 1(f). The thckness of the brace model was 4 mm, measured from a tradtonal Boston brace. The contact behavour between the brace pads and trunk was smulated usng 8-node surface-to-surface contact elements. The normal penalty stffness and penetraton tolerance factor were set to and 0.1, respectvely. The materal propertes of the spnal components and the brace shell and pads were adopted from prevous studes [15-1].. Loadng and boundary condtons The boundary condtons were set such that the ffth lumbar vertebra was mmoblsed n order to smulate lttle moblty n the ffth lumbar vertebra when the brace s worn. When the actual brace was worn, a dsplacement of mm was measured at the C7 cervcal vertebra from an X-ray mage. A dsplacement of mm was thus appled n the medal-lateral drecton n the FE model. The forces of the three straps of the actual Boston brace were 57, 88, and 93 N, respectvely, as measured usng a tensle meter (Japan Instrument System Co., Ltd, Japan) n 30 seconds; these values were appled to the FE model as the loadng condton. The brace put on the patent as follows: (1) the relatve postons of the brace and pads were confrmed; () a dsplacement was appled at the postons of the straps to open the brace; (3) the dsplacement was removed to make the brace close to the trunk; (4) the strap force measured by a tensle meter was appled (Fg. )..3 Valdaton of the FE model For model valdaton, the calculaton of the FE model was compared to measurements obtaned from an X-ray mage n terms of vertebral body dsplacement, CA, and contact pressure between the torso and brace [19,0]. For each vertebral body dsplacement, the correlaton coeffcent (CC), the mean error, and the maxmum error between the X-ray mage measurement and FE calculaton were compared usng. CC 1 1 {(T _ D T _ D) (FE _ D FE _ D)} (T _ D T _ D) 1 (FE _ D FE _ D) (1) (c) Fgure. Loadng condtons used to smulate the wearng of a brace. Confrmaton of the relatve postons between the brace and trunk. Openng of the brace and movng brace to trunk. (c) Tensle force appled to the strap to nstall the brace. FE _ D _ 1 T D Mean error () T _ D 1 T _ D (3) FE _ D 1 FE _ D (4) Where T_D: vertebral dsplacement measured from X-ray mage; FE_D: vertebral dsplacement calculated from FE smulaton; T _ D : average vertebral dsplacement measured from X-ray mage; FE _ D : average vertebral dsplacement calculated from FE smulaton; : vertebral body n the scolotc spne. Addtonally, an X-sensor pad (XSENSOR Technology Corporaton, Florda, USA) was used to measure the contact pressure at the lumbar and thoracc pads. The mean contact pressures of the X-sensor measurement and FE calculaton were compared for further valdaton..4 Parametrc analyss of pad postons To nvestgate the effect of pad poston, a parametrc analyss of pad movement and posteror rotaton along the nner lnng of the shell was conducted. The dsplacements along the Z-axs (DZ) on the frontal plane were 0, 10, 0, and 30 mm, respectvely, as shown n Fg. 3. A DZ of zero ndcates no change n the pad heght, whch was orgnally set at the rb of the apex vertebra by an experenced therapst, and a DZ of 10 ndcates a 10-mm downward movement of the pad. The rotatons (ROs) along the transverse plane were 0, 10, 0, and 30 posteror to the orgnal pad poston, respectvely, as shown n Fg. 3. A total of sxteen FE models wth varous pad postons were used to analyse the correctve effect on a scolotc spne, measured n terms of the correcton rate (CR). A hgher CR represents a better correctve effect.

4 3 J. Med. Bol. Eng., Vol. 3 No CR={(CA wthout brace-ca wth brace)/(ca wthout brace)}*100% (5) DZ RO Table. Comparson of the vertebral dsplacement between X-ray measurement and FE analyss for a patent wth and wthout a brace. Vertebral dsplacement Vertebral dsplacement Error from measurement(mm) from FE analyss(mm) (mm) C T T T T T T T T T T T T L L L L L *error = measured vertebral dsplacement - calculated vertebral dsplacement Fgure 3. Parameters for pad poston. Dsplacement along Z-axs (DZ) on the frontal plane. Rotatons (RO) along the transverse plane..5 Human test After the optmal pad postons were determned usng FE smulatons, another teenage grl wth a smlar scolotc type (11 years old, Lenke-type C, 37 rght thoracc and 38.9 left lumbar CAs) was recruted to compare the tradtonal and modfed Boston braces. Under a gven set of strap forces, the bomechancal effects of the two braces were compared n terms of CA, contact pressure between the torso and brace, and dscomfort usng a vsual analogue scale (VAS) questonnare. The VAS score ranged from 0 to 10, where 0 ndcates the hghest comfort, and 10 ndcates the hghest dscomfort. 3. Results 3.1 Valdaton of scolotc spne FE model Comparson of vertebral body dsplacement and CA For vertebral body dsplacement, the mean error, maxmum error, and CC were 0.96 ± 0.55 mm, 1.84 mm, and 0.99, respectvely. The FE results were consstent wth the measurements from X-ray mages n terms of vertebral body dsplacement. The maxmum vertebral dsplacement occurred at the L1 vertebral body, as shown n Fg. 4 and Table. For X-ray mage measurement, the CAs of the thoracc and lumbar spne were respectvely reduced to 7.4 (from 37.4 ) and 7.7 (from 34.3 ). However, n the FE analyss, the CAs of the thoracc and lumbar spne only reduced to 30.9 and 31.9, respectvely. Although the FE analyss results and X-ray mage measurements exhbted smlar trends n terms of vertebral body dsplacement, the stffness of the FE model was hgher than that of the real scolotc spne. Fgure 4. Comparson of vertebral body dsplacement between X-ray mage measurement and FE smulaton Comparson of mean pad pressure The mean contact pressure under the rght thoracc pad, measured usng the X-sensor, was 61.6 mmhg; that from the FE model smulaton was mmhg. The mean contact pressure under the left lumbar, measured usng the X-sensor, was mmhg; that from the FE model smulaton was 60.6 mmhg. The contact pressures n the FE smulaton were greater than those from X-sensor measurements by 7 to 10%. 3. FE analyss of pad postons For the thoracc spne, the FE analyss results show that rotatng the pad 0 posterorly yelded the best correctve

5 FE Analyss of Boston Brace 33 effect n terms of the CR, as shown n Fg. 5. For the lumbar spne, rotatng the pad 10 or 0 wth a dsplacement of 30 mm yelded the best correctve effect n terms of the CR, as shown n Fg. 5. Consderng the correctve effect of the thoracc and lumbar spne smultaneously, rotatng the pad 0 posterorly yelded the best correctve effect, as shown n Fgs. 6 and 6. Table 3. Comparson of tradtonal and modfed braces n a human test. Wthout brace Tradtonal brace Modfed brace Thoracc Cobb angle (degrees) (CR, %) (15%) (34%) Lumbar Cobb angle (degrees) (CR, %) (4%) (43%) Thoracc apex rotaton (grade) Lumbar apex rotaton (grade) Mean pressure of thoracc pad (mmhg) Mean pressure of lumbar pad (mmhg) VAS (grade) 6 5 Note: Thoracc and lumbar apex rotatons were graded from 1 to 4 based on a prevous study [14]. Grades 1,, 3, and 4 refer to vertebral body rotatons of 5, 15, 30, and 40, respectvely. (c) Fgure 5. Comparson of CR for FE models wth varous DZs and ROs for thoracc spne and lumbar spne (arrow ndcates the hghest CR value). 3.3 Human test wearng tradtonal and modfed braces The second patent respectvely wore tradtonal and modfed braces. The strap forces were measured to be 35, 40, and 45 N. Under a gven set of strap forces, the CR of the modfed brace was hgher than that of the tradtonal brace n both the thoracc and lumbar spne, as lsted n Table 3. From the X-sensor measurements, the mean contact pressure of the thoracc pad for the modfed brace was about 7% lower than that of the tradtonal brace, as lsted n Table 3 and shown n Fgs. 6(c) and 6(d). However, the mean contact pressure of the lumbar pad was slghtly ncreased n the modfed brace. Addtonally, the VAS score for wearng the modfed brace was reduced from 6 to 5. (d) Fgure 6. Comparson of tradtonal and modfed braces n terms of pad poston and contact pressure. Tradtonal brace, modfed brace (pad rotated 0 posterorly), (c) contact pressure dstrbuton of tradtonal brace, and (d) contact pressure dstrbuton of modfed brace (left crcle for the lumbar pad; rght crcle for the thoracc pad). 4. Dscusson Ths study establshed a scolotc spne FE model to predct the optmal pad locatons for enhancng the correctve effect of the Boston brace. To valdate the FE model, each vertebral body dsplacement from FE analyss and X-ray mage measurements was compared. The results ndcate that the maxmum error s equal to or less than that obtaned n a prevous study [0], as shown n Fg. 7. To further valdate the proposed scolotc spne FE model, the X-sensor devce was employed to measure contact pressure between the brace pad and the torso. Good agreement wth FE calculatons was obtaned, whch can be attrbuted to a detaled constructon of the FE model (dsc and vertebral body sold model was used rather than a smple beam model). As a result, the calculaton of the rotaton of the scolotc spne was more accurate than

6 Dsplacement (mm) 34 J. Med. Bol. Eng., Vol. 3 No that n a prevous FE model [0]. Furthermore, the shape of the FE model of the brace was more accurate than that n a prevous study [11]. However, the mean pad pressures n the proposed FE model were about 10% hgher than those measured usng the X-sensor, whch may be attrbuted to actve muscle contracton durng X-sensor measurement Max. error Present study Case 1 (P'er'e et al._004) Case (P'er'e et al._004) Case 3 (P'er'e et al._004) 0.9 Mean error Fgure 7. Comparson of vertebral body dsplacement between ths study and prevous studes n terms of the mean and maxmum errors. Note: Pere et al s study was performed on three teenage grls (case 1,case and case 3) wth dopathc scoloss ( years old; rght thoracc and 1 40 left lumbar Cobb angles) and treated by a Boston brace. A personalzed bomechancal FE model was bult for each patent wthout brace. The scolotc model contans 1356 nodes and 801 elements representng the osseo-lgamentous structures of the torso. The thoracc and lumbar vertebrae, ntervertebral dscs, rbs, sternum and cartlages were represented by 3D elastc beam elements. The Boston brace offers three-pont bendng correcton for the scolotc spne, as shown n D radographc mages (Fg. 1. Under a gven set of strap forces, ths study showed that the modfed brace could acheve a better correctve effect as well as reduce mean contact pressure on the thoracc pad compared to the tradtonal brace. Rotatng the pad 0 posterorly allowed the modfed Boston brace to generate a de-rotaton effect of the scolotc spne, thus provdng good 3D deformty correcton. Especally n thoracc apex rotaton, the human test results ndcate that the vertebral body rotaton whle wearng a tradtonal brace was about 5, whereas that whle wearng the modfed brace was 0, as lsted n Table 3. Therefore, pad postons can be adjusted wthout ncreasng the brace strap force to generate an axal rotaton effect. Combnng three-pont bendng wth rotaton effects should allow the Boston brace to provde a better correctve effect on a scolotc spne wthout ncreasng the contact pressure between the torso and brace. Ths study employed a detaled scolotc spne FE model to determne the optmal pad postons for correctng scolotc spnes wthout ncreasng contact pressure. However, some assumptons were made n ths study. The cases examned n ths study were thoracc-lumbar S-type moderate dopathc scoloss, but scoloss has many types and degrees of severty. The proposed FE model could accommodate changes n the scolotc type and degree of severty usng parameter control. Brace effectveness for varous types of scoloss can be nvestgated n future studes usng ths FE model. It s notable 1.8 that the FE results are only sutable for the S-type scolotc spne case, rather than for the C-type case. The proposed FE model makes some smplfcatons, such as gnorng actve muscle contracton and smplfyng the artcular surface of the facet jont n cervcal and thoracc vertebrae. As to the materal propertes of the spne, the mechancal behavor of the spne vares wth each scolotc spne case. Addtonally, a scolotc spne s mostly observed n teenagers, whose mmature spnes should be relatvely flexble. However, the materal propertes of the current FE spne model are adopted from an adult spne, makng t more rgd than a real scolotc spne. Each vertebral shape adjusted n ths scolotc spne model referred to the shape of the ffth lumbar vertebral body, so the specfc shapes of the thoracc and cervcal spne and wedged vertebrae and dscs of a scolotc spne are neglected. The rotaton of each vertebral body was measured usng D X-ray mages [14], so the rotaton of each vertebral body may nclude measurement error. In addton, the human test only ncluded one case and evaluated the mmedate correctve effects of wearng tradtonal and modfed braces. However, daly human actvtes have an mpact on the brace treatment effect. Therefore, the long-term correctve effects of the modfed brace must be nvestgated and more cases must be examned n future studes. 5. Conclusons Ths study constructed a parametrc human scoloss FE model ncludng detaled vertebral structures, rbs, and soft tssue of the chest and abdomnal cavtes. A Boston brace FE model wth varous pad postons was also constructed to parametrcally analyse the correcton of S-shaped scoloss. The FE analyss and human test results show that a pad located at the rb of the apex vertebra and rotated 0 posterorly had the best correctve effect on a scolotc spne n terms of the Cobb angle for a Lenke-type C case. 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