JRRD Volume 42, Number 2, Pges 167 174 Mrch/April 2005 Journl of Rehbilittion Reserch & Development Bending stiffness of the lumbr spine subjected to posteronterior mnipultive force Rymond Y. W. Lee, PhD; 1* Bonnie Y. S. Tsung, MPhil; 1 Pin Tong, PhD; 2 John Evns, PhD 3 1 Deprtment of Rehbilittion Sciences, The Hong Kong Polytechnic University, Hong Kong; 2 Deprtment of Mechnicl Engineering, The Hong Kong University of Science nd Technology, Hong Kong; 3 Centre for Rehbilittion Science nd Engineering, Queenslnd University of Technology, Queenslnd, Austrli Abstrct This study mesured the bending stiffness of the spine when it is subjected to posteronterior mobiliztion force. The lumbr spine ws modeled s n initilly curved bem column supported over the rib cge nd the pelvis. Posteronterior mobiliztion ws ssumed to be three-point bending of the bem. The mobiliztion force ws mesured by the mounting of force plte onto the mnipultion couch, where electromgnetic sensors mesured the chnge in spinl curvture. The bending stiffness of the spine ws derived from the force nd curvture dt. The technique developed in this study provided highly repetble dt. The theoreticl nlysis suggests tht the pelvic rottion produced by mobiliztion my be used cliniclly to indicte the mgnitude of the mobiliztion force. Future reserch my employ the present method to determine how bck pin my ffect the bending stiffness of the spine. The bending stiffness vlues reported in this study will be vluble to future modeling work. Key words: bck pin, bem nlysis, biomechnics, mnipultion, physiotherpy, posteronterior mobiliztion, rehbilittion, spine, stiffness, three-point bending. studies exmined the mechnicl chrcteristics of posteronterior mobiliztion [3 11]. In some of these studies, posteronterior forces were delivered by mechnicl mechnism nd mesured by lod cell [6 8]. Other reserchers mesured the forces by ttching strin guges to specilly constructed couch on which the subject ly [3 4]. The intervertebrl movements produced by mobiliztion hve lso been quntified by video nd rdiogrphic techniques [5 6,9 10]. For full understnding of the mechnicl response of the spine to mobiliztion force, mesuring the forces nd the movements produced simultneously is essentil. Lee nd Evns successfully developed technique for such mesurements [6 8]. They found tht the loddisplcement chrcteristics of mobiliztion were nonliner. The spine ws shown to exhibit time-dependent properties such s creep nd preconditioning [6 7]. The rdiogrphic study of Lee nd Evns showed tht under the ppliction of mobiliztion lods, the lumbr motion segments tended to extend [9]. They lso showed tht the INTRODUCTION Mnipultive techniques re commonly employed in the clinicl ssessment nd tretment of low bck pin [1]. Posteronterior mobiliztion, highly populr technique, generlly involves the ppliction of verticl forces over the spinous process of given vertebr while the subject is lying prone (Figure 1) [2]. Severl reserch Abbrevitions: ASIS = nterior superior ilic spine, ICC = intrclss correltion coefficient. This mteril ws bsed on work supported by the Hong Kong Reserch Grnt Council, grnt PolyU 5195/01E. * Address ll correspondence to Rymond Y. W. Lee, PhD; Deprtment of Rehbilittion Sciences, The Hong Kong Polytechnic University, Yuk Choi Rod, Hunghom, Hong Kong; 852-2766-4889; 852-2330-8656. Emil: rymond.lee@polyu.edu.hk DOI: 10.1682/JRRD.2004.01.0002 167
168 JRRD, Volume 42, Number 2, 2005 upper lumbr segments (L1/2 L3/4) trnslted posteriorly nd the L5/S1 segment nteriorly. The L4/5 segment did not exhibit trnsltion in consistent direction nd ppered to be trnsitionl segment. The movement pttern observed in this study strongly suggests tht the spine is subjected to three-point bending under the ppliction of mobiliztion lods. Cliniclly, spinl stiffness is simply determined ccording to the mgnitude of the movement detected or perceived by clinicins. This pproch is unstisfctory becuse it does not tke into ccount the lods exerted on the spine. Previous reserch ttempted to quntify posteronterior stiffness by determining the bsolute verticl displcement of the mobilized vertebr in spce [11]. Such mesurement ws subject to lrge error becuse the vertebrl displcement could be ffected by fctors such s the stiffness of plinth pdding rther thn the intrinsic stiffness of the spine [12]. Becuse previous definitions of spinl stiffness re rther imprecise, the effects of symptoms on spinl stiffness remin uncler. These issues must be ddressed, becuse they will provide fundmentl informtion on the mechnisms of ction underlying therpy. Posteronterior stiffness should not be defined simply by the verticl displcement of the spine without considertion of the geometry of the spine nd the mechnicl effects on the djcent ntomicl structures. One should interpret it s the bending stiffness of the spine tht my be modeled s n initilly curved bem under three-point bending. Previous studies mesured the bending stiffness of the vertebrl column during flexion, extension, lterl bending, nd twisting of the trunk [13 14]. These reserchers found tht wering belt, holding the breth, nd receiving nesthesi would significntly chnge spinl stiffness. Quntifying the bending stiffness of the spine when subjected to mobiliztion would be cliniclly useful, but no previous reserch hs ttempted to do this. Posteronterior mobiliztion ws found to induce extension moment nd sher on the lumbr spine [6,8 10]. The loding conditions re rther complex, nd the stiffness property of the spine under these conditions my be different from tht during simple physiologicl loding. Therefore, with this study, we developed method for mesuring the bending stiffness of the spine when subjected to posteronterior mobiliztion. METHODS Theoreticl Model We used two-dimensionl bem-column model to study the mechnicl response of the whole lumbr spine under the influence of posteronterior mobiliztion lods. The lumbr spine ws modeled s n initilly curved bem column supported over the rib cge nd the pelvis (Figure 2) [6,8,10]. The model ssumed tht no significnt compressive forces existed long the spine. Yoon Figure 1. Appliction of posteronterior mobiliztion over L4 spinous process of subject lying prone. Figure 2. Biomechnicl model of posteronterior mobiliztion. Lumbr spine is shown s initilly curved bem supported over T8/9 nd nterior superior ilic spine (ASIS). Distnces nd L represent distnces of point of ppliction of mobiliztion force (P) nd ASIS from T8/9. Solid blck squres represent plcement of electromgnetic sensors. M(x) refers to moment cting on bem t point x (represented by gry circle).
169 LEE et l. Biomechnics of posteronterior mobiliztion nd Mnsour showed tht the pssive hip moment ws negligible in the neutrl position nd with smll ngle of rottion [15]. The pelvic support ws considered to be pin joint locted effectively over the nterior superior ilic spine (ASIS). A force plte study ws crried out tht estblished the boundry condition t the thorcic end of the bem [6]. No significnt chnge in moment ws observed t the thorcic cge during the ppliction of mobiliztion force. The thorcic end ws therefore ssumed to be pin boundry. The effective point of support ws found to be t T7/8 level. According to the theory for n elstic bem with bending stiffness b [16], the chnge in curvture of the bem κ is given by where M(x) is the bending moment cting on the bem. The bending moment cting t point x on the right side of the force P (for x ) (Figure 2) is given by where L is the distnce between the two ends of the bem (T8/9 nd ASIS), is the horizontl distnce between the ASIS nd the point of ppliction of the force P, nd x is the horizontl distnce from the ASIS. The bending moment cting on the bem on the left side of the force P (for x ) is given by At the point of mobiliztion (x = ), both Equtions (2) nd (3) become Combining Equtions (1) nd (4), Mx ( ) κ = ------------, ( 1) b x Mx ( ) right = P 1 --, ( 2) Mx ( ) left = Px 1 --. ( 3) Mx ( ) ( x= ) = P 1 --. ( 4) P b = ---------------------κ. ( 5) 1 -- The vribles P nd κ my be mesured experimentlly with the use of force trnsducers nd ngulr displcement sensors ttched to the spine. The distnces L nd my lso be determined by recording of the positions of the two ends of the bem nd the point of force ppliction. The bending stiffness of the spine when subjected to mobiliztion cn then be determined. According to Eqution (2), the differentil eqution for the right side of the bem (for x ) is given by b d2 ------- y dx 2 right x = P 1 --, ( 6) where y is the verticl distnce from the ASIS. Integrtion of Eqution (6) yields b dy ----- dx right Px 2 = Px ----------- + C 2L 1, ( 7) where C 1 is constnt. Integrtion of Eqution (7) gives Px 2 by right ----------- Px 3 = ----------- + C 2 6L 1 x+ C 2, ( 8) where C 2 is constnt. The differentil eqution for the left side of the bem (for x ) is given by b d2 y ------- dx 2 left = Px 1 --. ( 9) First integrtion of Eqution (9) yields b dy ----- dx left Px 2 -------- 2 1 = -- + C 3, ( 10) where C 3 is constnt. Further integrtion gives Px 3 by -------- left 6 1 = -- + C 3 x + C 4, ( 11) where C 4 is constnt. To solve the unknown coefficients C 1, C 2, C 3, nd C 4, one must estblish four boundry conditions: y left( x = 0) = 0, ( 12)
170 JRRD, Volume 42, Number 2, 2005 y right x= L ( ) = 0, ( 13) y left( x= ) y right( x= ), dy ----- dx left( x= ) = ( 14) dy = -----. ( 15) dx right( x= ) Solving Equtions (7), (8), (10), nd (11) with the boundry conditions in Equtions (12) to (15) results in C 1 L = P -- -----, ( 16) 3 6L At the pelvic (left) end of the bem (x = 0), ccording to Eqution (10), Substituting Eqution (18) into Eqution (21), Eqution (22) defines the mthemticl reltionship between the bending stiffness of the spine, the mgnitude of mobiliztion force, the geometry of the spine, nd the mgnitude of pelvic rottion. Therefore, the bending stiffness of the spine is shown to be proportionl to the mgnitude of the mobiliztion force but inversely proportionl to the mgnitude of pelvic rottion. 2 P 3 C 2 = --------, ( 17) 6 C 3 2 L P -- = + -- -----,nd ( 18) 3 2 6L C 4 = 0. ( 19) b dy ----- dx left( x = 0) = C 3. ( 20) Hence, for smll rottion of the pelvis ( θ θ 0 ) withθ 0 the initil position of the pelvis, b b C 3 s = ( ------------------- θ θ 0 ). ( 21) L P -- + -- ----- 3 2 6L = -------------------------------------------. ( 22) θ θ 0 2 Experimentl Study Twenty subjects (12 men nd 8 women, men ge = 20 ± 2 yr, men height = 1.59 ± 0.09 m, men weight = 67.5 ± 4.9 kg) greed to prticipte in this study. They were in good helth, with no history of bck pin or leg pin tht could be ttributed to the bck within the lst 12 months. They were excluded if they hd undergone previous bck surgery, or hd frcture, disloction, or ny structurl defects of vertebrl structures. A nonconductive force plte (4060-NC Bertec Corportion, Columbus, OH) ws mounted underneth the mnipultion couch. Subjects were requested to lie on the couch fce down. The forces experienced by the force plte represented the forces exerted onto the lumbr spine. An electromgnetic trcking system (FASTRAK, Polhemus Nvigtion, Colchester, VT) ws used to mesure the chnge in curvture of the spine. Such system could be dversely ffected by the presence of metls or other conductive mterils, nd thus the force plte used in this study ws nonconductive. Our erlier reserch showed tht the system ws highly relible in recording spinl motion [17 18]. A physiotherpist with specilized trining in mnipultion nd with more thn 5 yers clinicl experience pplied posteronterior mobiliztion force to the L4 spinous process. The clinicl technique (Grde III, which ws cliniclly defined s lrge mplitude of oscilltions t the end of the rnge), described by Mitlnd et l. [2], involved cyclic pplictions of verticl forces over the spinous process while the subject ws lying prone, s shown in Figure 1. The physiotherpist ws instructed to perform the technique tht ws deemed pproprite for Grde III. No instructions were given to control the rte of mobiliztion nd the mgnitude of force so tht the technique would resemble how it would be crried out in norml clinicl sitution. Two electromgnetic sensors were ttched with double dhesives to the skin overlying the T7/8 vertebrl junction nd the position of the spine tht corresponded to the level of the ASIS. These sensors llowed for determintion of the chnge in curvture of the spine. The orienttions of the sensors were initilly recorded when no mobiliztion force ws pplied. These orienttions defined the initil curvture of the spine. After mobiliztion hd been performed for 30 s, dt were recorded for three oscilltory cycles of mobiliztion. A computer progrm ws developed to cquire the force nd motion sensor dt. The force signl ws low-pss filtered digitlly with the use of second-order Butterworth
171 LEE et l. Biomechnics of posteronterior mobiliztion filter with cutoff frequency of 6 Hz in both the forwrd nd reverse directions so there would be zero phse distortion. Dt were converted nlog to digitl (DT3001, Dt Trnsltion Inc., Mrlboro, MA) nd cquired by personl computer t smpling rte of 30 Hz. The motion sensor dt were cquired vi the seril port t 115.2 kb with the sme smpling rte s the force dt (tht is, 30 Hz per sensor). The force nd motion sensor dt were synchronized with the use of n externl pulse to trigger dt collection of both signls t the sme instnt. The positions of T7/8 junction, the ASIS, nd the L4 spinous process (where the mobiliztion lod ws pplied) were recorded by stylus ttched to n electromgnetic sensor. The distnces nd L cn be determined from these digitized points. All mesurements were repeted three times so tht the relibility of the dt obtined could be ssessed. Anlysis of Experimentl Dt The mobiliztion force (P) ws plotted ginst the chnge in curvture of the spine. Dt were fitted with liner regression eqution with the use of the lest squres method. According to Eqution (5), the bending stiffness of the spine (b) could be derived from the slope of the regression line: An intrclss correltion coefficient (ICC) ws used for the exmintion of the repetbility of the bending stiffness dt obtined in the three mesurement trils. RESULTS b = slope 1 --. ( 23) The results of this experiment re presented in the Tble. Three cycles of mobiliztion force nd the chnge in spinl curvture of one of the subjects (subject 20, 19 yr old, mle, weight = 65.6 kg, height = 1.55 m) is shown in Figure 3. The force nd movement dt generlly follow sinusoidl pttern, nd this ws observed in ll subjects. The men mximum posteronterior force of ll subjects ws found to be 178 ± 30 N (rnge = 141 273 N), nd the men frequency of mobiliztion ws 1.2 ± 0.6 Hz (rnge = 0.3 2.5 Hz). Figure 4 shows typicl plot of the mobiliztion force ginst the chnge in curvture (subject 20). The reltionship ws lmost liner, s predicted by Eqution (5). The line of best fit, s obtined by liner regression, nd the bending stiffness vlue, which ws derived from the slope of the line, re lso shown in Figure 4. The force-curvture plot ws found to follow liner reltionship in ll subjects. The Tble shows the slopes nd bending stiffness of ll subjects, together with their summry sttistics. The men bending stiffness of the spine ws found to be 15.1 ± 4.3 Nm 2 (rnge = 8.7 25.9 Nm 2 ). The men ICC ws found to be 0.98 ± 0.01 (rnge = 0.97 0.99) (Tble), showing tht the stiffness vlues derived in the three mesurements were highly similr. The mesurement method ws highly relible. DISCUSSION This pper reports new method of mesuring the bending stiffness of the lumbr spine when subjected to posteronterior mobiliztion. The method, found to provide highly repetble dt in ll the subjects s demonstrted by the high ICCs, could therefore be recommended, with confidence, for clinicl uses nd future reserch studies. The Tble shows tht the experimentl observtions were highly consistent mong ll the subjects exmined. This would enble reserchers to drw conclusions on the mechnicl properties of the spine in group of young helthy subjects. The bending stiffness dt reported my be used s reference vlues for comprison with those of n older popultion nd subjects with low bck pin. The bending stiffness vlues obtined in this study were similr to those reported in previous work [13 14]. However, we should note tht previous work exmined the stiffness of the spine when subjected to physiologicl lodings (flexion/extension, lterl bending nd twisting) rther thn posteronterior mobiliztion. Our study lso reveled lrge vrition in the bending stiffness vlues mong the subjects. This observtion ws lso consistent with the results of previous studies [13 14]. The physiotherpist ws sked to perform the mobiliztion in mnner tht would be pproprite ccording to his clinicl experience. Lrge mplitudes of sinusoidl oscilltions of force nd movement signls were observed, reflecting the clinicl definition of Grde III mobiliztion proposed by Mitlnd et l [2]. Similr force nd movement ptterns were reported in previous work [7,17]. The mgnitude of the force nd the frequency of mobiliztion were not controlled in this study
172 JRRD, Volume 42, Number 2, 2005 Tble. Results of experimentl study. Personl chrcteristics of subjects (ge, weight, nd height), geometric dt of trunk ( nd L), slope of line of best fit, bending stiffness, mximum mobiliztion force, frequency of mobiliztion, nd intrclss correltion coefficients (R) re shown for ech subject. Summry sttistics of vribles re provided in lst four rows of tble. Subject No. Age Weight (kg) Height (m) (m) L (m) Slope (Nrd 1 ) Bending Stiffness (Nm 2 ) Mximum Mobiliztion Force (N) Mobiliztion Frequency 1 20 67.1 1.6 0.072 0.257 390.5 20.2 154.6 1.9 0.99 2 18 61.2 1.4 0.068 0.237 378.3 18.3 159.8 2.0 0.97 3 21 62.5 1.55 0.067 0.241 232.2 11.2 167.9 0.9 0.98 4 18 78.2 1.78 0.074 0.266 311.4 16.6 187.7 1.0 0.99 5 22 69.9 1.62 0.068 0.239 199.5 9.7 169.5 1.9 0.99 6 24 72.4 1.64 0.076 0.264 334.5 18.1 188.8 0.7 0.98 7 21 69.2 1.52 0.069 0.250 335.5 16.8 157.1 1.2 0.98 8 19 63.2 1.54 0.071 0.251 171.2 8.7 155.0 2.5 0.97 9 20 68.3 1.65 0.066 0.240 327.1 15.7 273.2 1.7 0.97 10 19 65.7 1.66 0.069 0.244 266.7 13.2 148.3 1.5 0.99 11 19 73.3 1.72 0.073 0.263 275.6 14.5 229.1 0.9 0.98 12 21 73.9 1.74 0.053 0.247 333.5 13.9 194.4 2.0 0.97 13 23 65.2 1.52 0.062 0.223 245.5 11.0 178.4 1.3 0.97 14 20 62.1 1.55 0.062 0.227 353.0 15.9 187.0 0.3 0.98 15 19 65.9 1.52 0.064 0.226 221.7 10.2 172.5 1.2 0.97 16 22 63.4 1.59 0.070 0.249 345.6 17.4 176.1 0.8 0.99 17 24 75.4 1.67 0.069 0.246 211.2 10.5 141.1 0.4 0.98 18 21 64.1 1.57 0.070 0.245 389.6 19.5 150.3 0.5 0.98 19 18 62.7 1.5 0.067 0.235 304.2 14.6 190.5 0.8 0.99 20 19 65.6 1.55 0.095 0.267 423.4 25.9 187.1 1.2 0.98 Men ± SD 20 ± 2 67.5 ± 4.9 1.59 ± 0.09 0.069 ± 0.008 0.246 ± 0.013 302.5 ± 71.4 15.1 ± 4.3 178.4 ± 30.4 1.2 ± 0.6 0.98 ± 0.01 Min 18 61.2 1.40 0.053 0.223 423.4 25.9 141.1 0.3 0.97 Mx 24 78.2 1.78 0.095 0.267 171.2 8.7 273.2 2.5 0.99 = horizontl distnce between nterior superior ilic spine (ASIS) nd point of ppliction by mobiliztion force. L = horizontl distnce between two ends of bem (T8/9 nd ASIS). SD = stndrd devition. R so tht they could reflect the loding conditions in clinicl sitution. The vlues obtined in this study were similr to those reported elsewhere [7 8]. Posteronterior mobiliztion should not be interpreted s posteronterior trnsltion of one vertebr upon the other. Previous reserch ttempted to define the bending stiffness of the spine using the verticl displcement of the spine t the point of force ppliction [11 12]. This definition ws unstisfctory becuse this could be ffected by the geometry of the spine nd the stiffness of the plinth pdding [12]. The method reported in this study employed bem model tht took into ccount the geometry of the spine ( nd L). The bending stiffness of the spine ws derived from the reltionship between the mobiliztion force nd the chnge in spinl curvture. An interesting finding of the theoreticl nlysis is tht, ccording to Eqution (22), if the bending stiffness of the spine remins constnt, the mgnitude of the mobiliztion force is proportionl to the mgnitude of pelvic rottion. Cliniclly, quntifying the forces pplied to the spine so tht tretment cn be implemented ccurtely is importnt. However, lod cells or force plte my not be
173 LEE et l. Biomechnics of posteronterior mobiliztion the mgnitude of pelvic rottion. In the clinicl environment, ll these vribles cn be esily mesured with inexpensive devices. The mobiliztion force my be determined with the therpist stnding on bthroom scle. The distnces nd L my be mesured with ruler nd the pelvic rottion with n inclinometer s described previously. Future reserch should further explore this pproch. CONCLUSION Figure 3. Typicl pttern of three cycles of mobiliztion force nd chnges in curvture of spine in subject 20. The method described in this pper is recommended for the mesurement of the bending stiffness of the spine when subjected to posteronterior mobiliztion. Bending stiffness should be derived from the reltionship between the mobiliztion force nd the chnge in spinl curvture. Cliniclly, medicl stff my mesure pelvic rottion to indicte the bending stiffness of the spine. In future studies, reserchers my employ the present method to study vrious fctors tht my ffect the bending stiffness of the spine for instnce, brething nd musculr contrction. The effect of bck pin on the bending stiffness should lso be investigted. The bending stiffness vlues reported in this study will be vluble to future modeling work. ACKNOWLEDGMENT We wish to thnk Rchel Boyd for her ssistnce with dt collection. Figure 4. Typicl plot of mobiliztion force ginst chnge in curvture in subject 20. Line of best fit is lso shown. vilble in the clinicl environment. In this cse, simple tilt sensor or n inclinometer ttched to the scrum my be employed for mesurement of pelvic rottion, indicting the force pplied. Such simple device my lso be used s visul id in the trining of student therpists. However, we should note tht the these rguments re bsed on the theoreticl nlysis only, nd future reserch should exmine the fesibility of using the scrl inclinometer in nlyzing mobiliztion lods. Eqution (22) my lso be used to determine the bending stiffness of the spine with knowledge of the geometry of the spine ( nd L), the mobiliztion force pplied, nd REFERENCES 1. Foster NE, Thompson KA, Bxter GD, Allen JM. Mngement of nonspecific low bck pin by physiotherpists in Britin nd Irelnd. A descriptive questionnire of current clinicl prctice. Spine. 1999;24:1332 42. 2. Mitlnd GD, Hengeveld E, Bnks K, English K. Vertebrl mnipultion. 6th ed. London: Butterworth-Heinemn; 2000. 3. Hrms MC, Milton AM, Cusick G, Bder DL. Instrumenttion of mobiliztion couch for dynmic lod mesurement. J Med Eng Technol. 1995;19:119 22. 4. Trino J, Schultz AB. Lods trnsmitted during lumboscrl spinl mnipultive therpy. Spine. 1997;22:1955 64. 5. Gl J, Herzog W, Kwchuk G, Conwy PJ, Zhng YT. Movements of vertebre during mnipultive thrusts to unemblmed humn cdvers. J Mnip Physiol Therpeut. 1997;20:30 40.
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