Transverse tripolar spinal cord stimulation: theoretical performance of a dual channel system

Transcription

1 Trnsducers nd electrodes Trnsverse tripolr spinl cord stimultion: theoreticl performnce of dul chnnel system J. J. Struijk 1"2 J. Holsheimer 1 1 Institute for Biomedicl Technology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlnds 2 currently with Center for Sensory-Motor Interction, Alorg University, Alorg, Denmrk AstrctmA new pproch to spinl cord stimultion is presented, y which severl serious prolems of conventionl methods cn e solved. A trnsverse tripolr electrode with dul-chnnel voltge stimultor is evluted theoreticlly y mens of volume conductor model, comined with nerve fire models. The simultions predict tht high degree of freedom in the control of ctivtion of dorsl spinl pthwys my e otined with the descried system. This implies n esier control of presthesi coverge of skin res nd the possiility to correct undesired presthesi ptterns, cused y led migrtion, tissue growth, or ntomicl symmetries, for exmple, without surgicl intervention. It will lso e possile to preferentilly ctivte either dorsl column or dorsl root fires, which hs some importnt clinicl dvntges. Compred to conventionl stimultion systems, the new system hs reltively high current drin. Keywords--Electricl stimultion, Electrode, Field steering, Finite difference model, Nerve fire model, Presthesi, Potentil field, Spinl cord stimultion Med. & Biol..Eng. & Comput., 1996, 34, Introduction IN SPINAL cord stimultion (SCS), n electrode is usully used, consisting of four-contct rry, oriented rostrocudlly in the dorsl epidurl spce. If ech comintion hs t lest one cthode, the four-contct rry provides 65 possile nodecthode comintions. Together with freely ccessile prmeters such s pulse mplitude, durtion nd rte, nd the medio-lterl nd rostrocudl positions of the electrode, there is some flexiility in directing presthesi coverge nd intensity. However, mjor prolems exist, which re relted to the positioning nd stilistion of the presthesie. With current implntle SCS systems, it is difficult to plce the led in such wy tht optiml presthesi coverge is otined, which is serious drwck ecuse of the widely recognised significnce of complete coverge of the pinful re in SCS for pin mngement (SHEALY et l., 1970; SWEET nd WEPSIG, 1974; NIELSON et l., 1975; BURTON, 1977; KRArNICK et L, 1980; MAIMAN et L, 1985; LAW, 1986; VOGEL et L, 1986; BAROLAT et L, 1991; NORTH et L, 1991). Prolems, such s led migrtion, chnge of the l~in topogrphy, low discomfort thresholds reltive to the perception thresholds, muscle contrctions nd histologicl chnges, such s the growth of connective tissue round the electrode, lso dd to the limittions of SCS (SHARKEY, 1981; LAW, 1983; 1986; Correspondence should e ddressed to Dr. Jn Ho/sheimer. First received 21 July 1994 nd in finl form 26 Octoer IFMBE: 1996 Medicl & Biologicl Engineering & Computing July 1996 BAROLAT et L, 1991). Thus, even if during surgery presthesie cover the pin re totlly, the presthesi pttern often chnges fterwrds. Therefore, it would e highly desirle to e le to refocus presthesie fter surgery. Two pproches hve een dopted to reduce the presthesi coverge prolem. A reltively lrge flt electrode, which requires lminotomy for implnttion, cn e positioned ccurtely during surgery nd, ecuse of its shpe, the electrode hrdly migrtes (BAROLAT et l., 1991). The second pproch is the use of multiple cylindricl electrode rrys in prllel, to increse the numer of possile contct comintions, thus improving the proility of otining proper presthesi coverge nd correcting led migrtion (LAW, 1986). A multi-electrode pproch my lso e needed to reduce the occurrence of motor responses or other uncomfortle segrnentry effects. Both muscle contrctions nd other segrnentry effects re proly cused y direct stimultion of dorsl roots (rdiculr stimultion) (BANTLI et l., 1975; DIMITRIJEVIC et L, 1980; COBURN, 1985; STRUIJK et L, 1993). If fter surgery the presthesi pttern is perfect, the stimultion my still e useless ecuse of the occurrence of motor responses t voltges elow the therpeuticlly effective vlues (BANTLI et l., 1975; BAROLAT et L, 1991). This occurs minly t mid-thorcic levels, cusing so-clled segrnentry nd (BAROLAT et L, 1991), ut sometimes t other levels s well. The prolems of presthesi coverge nd motor responses my e overcome y stimultion method, sed on trnsverse tripolr contct configurtion with two independently controlled voltge stimultion chnnels. In this work we 273

2 illustrte tripolr stimultion method nd its performnce with the help of computer model of the spinl cord nd the most relevnt neurl elements. We show tht the proposed system cretes the possiility of chnging the presthesi pttern from symmetricl to symmetricl, nd vice vers, nd lso of correcting the presthesi pttern in cses of led migrtion, symmetricl spinl cord position nd ntomicl chnges. We lso show tht the ctivtion of dorsl root fires cn e reduced in fvour of dorsl column fires, thus presumly reducing the occurrence of rdiculr effects. 2 Methods 2.1 Dul-chnnel trnsverse tripolr system* Fig. 1 is schemtic drwing of the trnsverse tripolr led with its connections to the pulse genertors, which re voltge sources in ll commercilly ville stimultors ecuse of prcticl dvntges over current sources (see Section 4). The dimensions used in the modelling study re shown in the Figure. The led consists of three metl strips (contcts). The centrl contct (referred to s the cthode, lthough it cn lso e used s n node) is somewht shorter thn the two lterl contcts (nodes). Two voltge sources V1 nd V2 re connected to the led. V1 is connected to one node nd the cthode. V2 is connected to the second node nd the cthode. The lengths nd widths of the three contcts nd the contct spcings re the min led prmeters. In this study these dimensions re fixed. The following design criteri were pplied Contct re." this should e t lest 12 mm 2, ecuse such contct re hs een pproved in commercilly ville leds; ccording to stimultion mplitudes in current SCS prctice (mplitude < 10 V with typicl 1 kf~ lod), verge current densities will thus e less thn 1 ma mm -2 t the electrode surfce Contct length: nodl contcts should e longer thn the centrl cthode to mintin good shielding effect, even if the led is somewht rotted in the coronl plne, which my occur if the electrode hs moved or if it ws not implnted perfectly rostrocudlly Contct spcing: this should e lrger thn the thickness Fig. 1 8"0 1"5 3'0 2'0 1-5 v, 89 Trnsverse tripolr led with two voltge sources; dimensions re in mm * US Ptent numer: 5,501, Fig fl _l] rl chnnel V~ : chnnel V~ i _fln chnnel V2 : chnnel V2 : : i i i i i Timing of the two chnnels in () simultneous operting mode; () lternting operting mode of the dorsl cererospinl fluid (CSF) lyer; otherwise high stimulus mplitudes will e required due to the shunting effect of the highly conductive CSF (HOLSHE1MER nd STRUIJK 1991, HOLSHEIMER et l., 1995). It should e pproximtely the distnce etween the dorsl root entry zone nd the spinl cord mid-line. The thickness of the CSF lyer nd the spinl cord geometry thus ffect the optiml contct spcing for different spinl levels (HOLSHEIMER et L, 1994) Totl led width: this should e s smll s possile to minimise the surgicl procedure Contct width: s consequence of the criteri for contct spcing nd totl led width, contct width should e kept smll. The voltge sources re pulse genertors with independent mplitude control. The system cn e used in two operting modes. (i) Simultneous mode (Fig. 2): in this mode, the system is essentilly tripolr, nd this mode is minly used in this work. (ii) Alternting mode: the pulses of one chnnel re interleved with those of the other (Fig. 2). In this mode, the system cts s two independent ipolr systems. In monopolr stimultion only the centrl contct of the led is used. The second contct is the metl cn of the implntle pulse genertor, which is modelled s distnt ground in the volume conductor model (see Section 2.2). 2.2 Computer models The spinl cord stimultion model consists of two prts. The first prt is 3-D conductor model of the spinl cord nd its surroundings. This model comprises the mjor mcro-ntomicl structures nd the stimulting electrodes. The second prt consists of models of lrge myelinted dorsl root nd dorsl column nerve fires. The dorsl roots nd dorsl columns re the spinl cord structures closest to the electrodes, which re plced in the dorsl epidurl spce, nd will therefore e the primry trgets of the stimultion. These models hve een descried previously (HOLSHEIMER et L, 1991; HOLSHEIMER nd STRUtJK, 1991; STRUIJK et l., 1991; 1992; 1993; 1993). To ssess the direct effects of stimultion on the nerve fires, two-step procedure is followed. First, the potentil field in the volume conductor model is clculted. Secondly, this field is pplied to the nerve fire models to determine which fires re excited y the stimultion. A three-dimensionl conductor model of the mid-cervicl spinl cord (C4-C6) is used s the sic model. In one simultion, model of the mid-thorcic spinl cord (T5-T6) is used. Fig. 3 shows trnsverse sections of these models. The models comprise the spinl cord, which is composed of grey mtter (GM) nd white mtter (WM), cererospinl fluid (CSF), epidurl spce (ES), verterl one (VB), lyer Medicl & Biologicl Engineering & Computing July 1996

3 representing surrounding tissues (SL), contct insultion (IS) nd thin lyer representing the dur mter (DM) t the dorsl side. The smll dorsl root filments, immersed in the highly conductive CSF, re not incorported in the volume conductor model. The model nd the conductivities in the model hve een descried previously (STRUIJK et l., 1993). The electrode contcts in the model re given constnt voltges. In monopo!r stimultion the oundry of the model serves s the distnt node. The thickness of the dorsl CSF lyer ws mesured from MR imges otined from 26 norml sujects (HOLSHEIMER et L, 1994). In the mid-cervicl nd the mid-thorcic models these thicknesses re 2.3 mm nd 5.8 mm, respectively. The volume conductor is discretised using rectngulr grid with vrile grid spcing. The numer of grid points is 57 x 57 x A finite difference method is pplied to discretise the governing Lplce eqution. The resulting set of liner equtions is solved using Red-Blck Guss-Seidel itertion with vrile over-relxtion. Two types of nerve fires were modelled: the dorsl root (DR) fire nd dorsl column (DC) fire. DC fires re longitudinl fires in the dorsl columns tht issue collterls into the grey mtter. The model of DC fire is cle model (MCNEAL, 1976) extended with collterls. Close to the electrode, collterls re ttched to ech second node of Rnvier of the modelled 21- noded fire (STRUIJK et l., 1992). For DR fires cle model with curved trjectory is used, with the proximl end connected to DC fire model (STRuIJK et L, 1993). Tle 1 shows the geometric fire prmeters; the electricl prmeters hve een estlished previously (STRUIJK et l., 1992). In ll simultions monophsic rectngulr pulse with durtion of 210 #s ws used. 2.3 Evlution prmeters To compre the effects of different stimulus prmeters in vrious settings, severl evlution prmeters were defined. In these prmeter definitions, the threshold stimulus is defined s the lowest stimulus mplitude t which the (10 #m dimeter) fire under concern is excited when pulse of 210 #s durtion is used. Aprt from these prmeters, plots of the recruited res for DC fires show how symmetricl or how selective the stimultion is. In trnsverse section the recruited re is ordered y the spinl cord's dorsl oundry nd y recruitment contour line more ventrlly in the dorsl columns. The recruited re is then the re in which 10 #m DC fires re excited t given stimulus mplitude. In generl, recruitment contour lines do not hve the sme shpe s isopotentil lines, nd thus the isopotentil lines do not lwys reflect the delinetion of the recruited re. Tle 1 Fire prmeters DC fire DR fire dimeter of min fire 10 #n. I 0 #m dimeter of collterls 3.33 #m inner fire dimeter 0.6 x fire dimeter 0.6 x fire dimeter length of node of Rnvier 1.5 #m 1-5 #m numer of nodes of min fire numer of nodes per collterl 8 -- numer of collterls 7 internodl length 100 x fire dimeter I00 x fire dimeter collterl spcing 2 x intemodl length -- Fig. 3 SL 8_ ES L_ CSF ~--~-~.fl 5"0 mm I V~ V2 Trnsverse section of() mid-cervicl spinl cord mode# () mid-thorcic model," the connections of the contcts to the voltge sources re drwn schemticlly The following evlution prmeters were defined. Voc = threshold stimulus of DC fire t the dorsomedil oundry of the spinl cord. VoR = threshold stimulus of DR fire entering the cord t the rostrocudl level corresponding to the centre of the cthode; if the simultion is symmetricl, then the fire with the lowest threshold (either the left or right DR fire) is tken. Pr=fire type preference; Pr is defined s Pr= VDc/VDR; therefore, Pr > 1 (Pr < 1) mens tht DR fires (DC fires) re more likely to e excited. AsDc=left-right symmetry coefficient for dorsl column fires; ASDc= VDC, left/vdc.right. VDC, left (VDc, right) is the threshold of DC fire t the dorsl order of the dorsl columns, t 2.5 mm left (right) of mid-line. If AsDc>l (Asoc < I), the stimultion is symmetricl nd thresholds re lower t the right (left) side. AsDR = left-right symmetry coefficient for dorsl root fires; ASDR= VDR,left/VDR,right. VDR.Ief t (VDR,right) is the threshold of the left (right) DR fire. If ASDR> 1 (AsoR< 1), then the stimultion is symmetricl nd thresholds re lower t the right (left) side. W= the width of the recruited dorsl column re. To clculte W we choose the stimulus mplitude such tht DC fire t midline nd 1.0 mm from the dorsl oundry in the dorsl columns is just excited. This mplitude is then used to otin the recruitment contour. W is defined s the distnce etween the two intersection points of the recruitment contour line nd the dorsl oundry of the spinl cord. I (ma) = stimulus current needed to excite the dorsomedil DC fire. 3 Results 3.1 Monopolr compred with tripolr stimultion The mrked difference etween the potentil fields of monopolr nd tripolr configurtion (simultneous mode, symmetricl stimultion) is illustrted for the mid-cervicl model in Figs. 4 nd. These Figures show isopotentil lines in trnsverse section t the level of the centre of the contcts. The monopolr nd tripolr electrodes re positioned symmetriclly with respect to the spinl cord mid-line. Figs. 4c nd d show the recruited res (D = 1.0 mm). Figs. 4-d show tht, with tripolr stimultion, the potentil field nd the recruited re re more restricted to the medil prt of the dorsl columns thn with monopolr stimultion. Figs. 4e nd f show the recruited res in monopolr nd tripolr stimultion of the mid-thorcic model. The min difference etween the mid-cervicl nd the mid-thorcic i Medicl & Biologicl Engineering & Computing July

4 for DR fires in the monopolr cse nd, in contrst, preference for DC fires in the tripolr configurtion. Consequently, in trnsverse tripolr stimultion it is less likely tht motor reflex loops will e ctivted ecuse the stimultion is more confined to the dorsl columns. In oth monopolr nd tripolr stimultion, DR fire preference is higher in the midthorcic model thn in the mid-cervicl model. W reflects the phenomenon tht in trnsverse tripolr stimultion the width of the recruited re is smller thn in monopolr stimultion. This is lso shown in Fig. 4. Therefore, DC fire thresholds in the lterl prts of the dorsl columns re incresed, s compred with thresholds in the medil prts. For the sme reson, it is unlikely tht fires in the dorsolterl columns will e ctivted in trnsverse tripolr stimultion. In mid-cervicl tripolr stimultion, the current drin I is out 40% higher thn in monopolr stimultion. In the midthorcic model the increse is out 150%. If the monopole is replced y ny rostrocudl (longitudinl) multipolr electrode configurtion, the trnsverse shpe of the field nd the vlue of W would hrdly chnge (HOLSHEIMER et l., 1991). Fig. 4 c I I I..... i e Potentil fields in the mid-cervicl model; () monopolr; Co) trnsverse tripolr stimultion; solid lines = negtive; dshed lines =positive; dotted line = zero potentil," recruited res = shded; (c) mid-cervicl monopolr; (d) mid-cervicl trnsverse re'polr; (e) mid-thorcic monopolr; (f) midthorcic trnsverse tripolr stimultion models is the difference in the thickness of the dorsl CSF lyer, nd therefore the difference in distnce etween contcts nd the spinl cord, resulting in higher threshold stimuli in the mid-thorcic model (HOLSHEIMER et L, 1991; STRUIJK et l., 1993). A quntittive comprison of monopolr nd trnsverse tripolr stimultion is given in Tle 2. From this Tle the following conclusions my e drwn. In tripolr stimultion, oth VDc nd VDR re higher thn in monopolr stimultion. In prticulr, the tripolr VDR is high. This is reflected in the prmeter Pr, which shows preference d f 3.2 Asymmetricl sources In the preceding Section oth the volume conductor model nd the two voltge sources were symmetricl, nd consequently the potentil fields nd the recruited res were symmetricl s well (AsoR=AsDc= 1.00). With multipolr longitudinl configurtion it is impossile to chnge symmetricl into n symmetricl stimultion in controllle wy, without chnging the led's position. As shown in Fig. 5, symmetricl stimultion is esily otined using unlnced sources in the trnsverse tripolr configurtion, even if the electrode position is perfectly symmetricl. In this simultion V2 = 0-0 V, where V2 is the voltge etween the node on the right nd the centrl cthode (Fig. 3). Tle 3 (left columns) shows the evlution prmeters of the trnsverse tripolr led with lnced sources nd with unlnced sources. The Tle shows mrked drop in VoR in the cse of unlnced sources nd thus high preference for DR fires. The symmetry coefficients lso chnge drmticlly, especilly for the DC fires. If the led is not t the mid-line (due to led migrtion or to lterl positioning during surgery), it is still possile to otin n lmost symmetricl stimultion. Fig. 6 shows the potentil fields nd the recruited res, where the centre of the led is 1.0 mm from the mid-line. In Figs. 6 nd the voltge sources hve equl mplitudes (V1 = V2) nd the stimultion is clerly symmetricl. Figs. 6c nd d show the sme geometricl configurtion with unlnced sources: V2 = 2VI. Although the potentil field in Tle 2 Evlution prmeters in monopolr nd symmetricl trnsverse tripolr stimultion mid-cervicl model mid-thorcic model monopolr tripolr monopolr Wipolr VDc 2-01 V~ = V2 = V1 = V2 = 22.9 VDR 1.47 V1 = V2 = VI = V2 = 20.3 Pr W, mm /, ma Fig. 5 Symmetricl electrode position nd unlnced sources (1/2 = O) in the mid-cervicl model: () potentil field; () recruited re 276 Medicl & Biologicl Engineering & Computing July 1996

5 Tle 3 Trnsverse tripole with lnced nd unlnced sources symmetricl electrode position lnced sources unlnced sources symmetricl electrode position lnced sources unlnced sources Voc Vx = Vz =3-36 V~ =6-73; Vz = 0.0 V~ = II2=3.85 V~ =2.33; V/=4-65 VDI~ V1 = 1/2=5-43 Vl =2.51; I"2=0"0 V~ = V2= 2.92 V 1 = 2.26; Vz =4'52 Pr ASDC AsoR J Tle 4 Trnsverse tripole with lnced nd unlnced sources nd n symmetricl lod lnced sources unlnced sources VDc, V V~ = V2 = 3.37 V1 =3.06; V2 =4.08 VDR, V V~ = 112=3.98 VI =4-78; I"2=6.37 Pr Asoc AsoR Fig. 6, /] c J Trnsverse tripolr led 1.0 mm lterlly in the mid-cervicl model; () potentil field, 9 () recruited re with lnced sources (VI = Vz); (c) potentil field, (d) recruited re with unlnced sources (V: = 21Ii) Fig. 6c is much more symmetricl thn in Fig. 6, the recruited re in Fig. 6d is lmost symmetricl. The results in Tle 3 (right columns) show tht symmetry is lmost completely restored (symmetry coefficients Asoc nd AsDR re close to 1), wheres fire type preference Pr is only slightly ffected. 3.3 Asymmetricl spinl cord If the spinl cord nd not the led is symmetriclly positioned in the spinl cnl, the stimultion will lso e symmetricl. An symmetricl spinl cord position of 1-2 mm will occur in t lest 40% of the ptients (HOLSHEIMER et L, 1994). Cliniclly, this my cuse unexpected symmetricl presthesie if the led is t the rdiologicl mid-line (BAROLAT et l., 1991). The modelling results re similr to those in the cse of lterl led, ecuse the geometricl reltion etween electrode rid spinl cord is the sme in oth cses. A slightly symmetricl recruited re is otined when the voltge sources re lnced. Restortion of symmetry is relised y unlncing the voltge sources (VI =0.75 V2), resulting in symmetricl recruited re. The evlution prmeters in Tle 4 show tht oth the symmetry coefficients nd the fire type preference Pr with unlnced sources re lmost the sme s in the symmetricl lnced sitution (Tle 3). 3.5 Simultneous compred with lternting mode So fr we hve illustrted only the possiilities of the tripolr configurtion in the simultneous operting mode. However, the lternting mode my lso e useful, especilly when lrger prts of the ody should e covered with presthesie, ut only if no prolems occur due to motor responses. Fig. 7 shows the recruited res otined with the simultneous nd the ltemting operting modes (Fig. 7 is identicl to Fig. 4d). The recruited re in the simultneous mode is clerly smller thn tht relised with the lternting mode. In the simultneous mode the tripolr potentil field is the result of superposition of two ipolr fields (oth ipolr fields re present t the sme time). The resulting potentil field is nrrow nd so is the recruited re. This superposition of the potentil field occurs only if oth ipolr fields re present t the sme time, s hppens with the stimulus sequence of Fig. 2, ut not in the lternting mode (Fig. 2). In the lternting mode the recruited re consists of the union of two (overlpping) recruited res, s shown in Fig. 7. Fires in re 1 re recruited when chnnel Vt (Fig. 3) is ctive, [rr'r~ rn-r~l J % J 3.4 Asymmetricl lod After surgery connective tissue will grow round the led nd other histologicl chnges my occur, possily yielding n symmetricl electricl lod of the contcts. An symmetricl lod is modelled y decresing y fctor 2 the conductivity of the dur mter in contct with the right node (0.015 insted of S m-l). Medicl & Biologicl Engineering & Computing July 1996 Fig. 7 Recruited res for () simultneous mode nd () lternting mode; in () the recruited re is the union of two different res 277

6 wheres fires in re 2 re excited when chnnel Vz is ctive. This implies tht the fires in the overlp of res 1 nd 2 re ctivted t twice the frequency of ech chnnel. In oth operting modes the symmetry of the recruited re nd the symmetry coefficients Asz~c nd As~R cn e influenced y chnge of the rtio V1/Vz. 4 Discussion nd conclusions In this pper we hve proposed nd theoreticlly evluted new method for epidurl spinl cord stimultion. This method is sed on trnsverse tripolr electrode configurtion, together with dul-chnnel pulse genertor. According to the simultions, stimultion with such system is very flexile nd hs some importnt dvntges over the usul monopolr or rostrocudlly rrnged multipolr systems. The use of voltge sources insted of current sources hs prcticl dvntge with respect to the field steering. For exmple, to chieve the symmetry of Fig. 5, the current in genertor V2 (Fig. 3) is negtive, lthough the voltge Vz is zero. If V2 is current source, this genertor hs to e idirectionl to otin the sme symmetricl field. The primry gol of the simultions is to illustrte the chnges of nerve fire ctivtion ptterns tht result from chnges in stimulus prmeters, such s the voltge lnce of the chnnels, monopolr versus tripolr stimultion nd simultneous versus lternting stimulus mode; however, we do not predict exct thresholds of DC nd DR fires. We ssume equl DC nd DR fire dimeters nd uniform fire dimeter distriution in the entire trnsverse section of the dorsl columns, even though the rel dimeter distriution is not tht simple (HOLSHEIMER et L, 1991; STRUIJK et l., 1992, 1993). Therefore, the vlues of severl evlution prmeters should not e invested with solute significnce. The dul-chnnel set-up of the system provides the opportunity of two distinct operting modes: simultneous nd lternting. If the centrl contct of the trnsverse tripole is cthode nd oth outer contcts re nodes, the simultneous mode yields recruited re tht is restricted to the medil prt of the dorsl columns; wheres in the lternting mode the recruited re lso includes the lterl prts nd, possily, prts of the dorsolterl columns. If the centrl contct is used s cthode nd the outer contcts s nodes in the simultneous mode, the thresholds of DR fires re reltively high compred to stimultion with monopole nd most rostrocudl configurtions. Therefore, the thresholds of rdiculr responses will e incresed significntly, which is desirle especilly when stimulting t midthorcic levels (BAROLAT et l., 1991). If the centrl contct is used s n node nd the outer contcts s cthodes, the thresholds of DR fires will e reltively low. This my e useful if only smll prt of the ody, corresponding to the dorsl roots t the segmentl level of the contcts, should e covered with presthesie, lthough the proility of motor responses will lso e higher. In oth operting modes i,t is possile to move the recruited re in lterl direction, nd consequently to ffect the symmetry coefficients for DR nd DC fires. Therefore, it is possile to chnge the presthesi coverge y chnging the mplitude rtio of the two chnnels to llow for difference etween rdiologicl nd physiologicl mid-line, histologicl chnges, led migrtion etc. Led positioning during surgery is less criticl ecuse corrections ofpresthesi coverge cn e mde fter implnttion. The voltges required to excite DC nd DR fires re higher in trnsverse tripolr stimultion thn in monopolr or rostrocudl multipolr stimultion. In prticulr, voltges re 278 reltively high if the thickness of the dorsl CSF lyer is lrge. Owing to the higher voltges, the current drin is lso reltively high in trnsverse tripolr stimultion, nd therefore ttery longevity will e less thn in monopolr or rostrocudl multipolr stimultion with conventionl leds. The geometry of the led used in this study is chosen ccording to the criteri given in Section 2.1. This geometry cn e optimised y further modelling. The optimum design of the led my e different t vrious spinl levels, due to differences in spinl cord geometry nd thickness of the dorsl CSF lyer (HOLSHEIMER et l., 1994). Acknowledgment--This work ws supported in prt y grnt from Medtronic, Inc., Minnepolis, USA. References BANTLI, H., BLOEDEL, J. R., LONG, D. M., nd THIENPRASIT, P. (1975): 'Distriution of ctivity in spinl pthwys evoked y experimentl dorsl column stimultion', J.. Neurosurg., 42, pp BURTON, C. V. (1977): 'Session on spinl cord stimultion: sfety nd clinicl efficcy', Neurosurg., 1, pp BAROLAT, G., ZEME, S., nd KETCIK, B. (1991): 'Multifctoril nlysis of epidurl spinl cord stimultion', Stereotct. Funct. Neurosurg., 56, pp COBURN, B. (1985): 'A theoreticl study of epidurl electricl stimultion of the spinl cord--prt II: Effect on long myelinted fiers', IEEE Trns., BME-32, pp DIMITRIJEVIC, M. R., FAGANEL, J., SHARKEY, P. C., nd SHERWOOD, A. M. (1980): 'Study of senstion nd muscle twitch responses to spinl cord stimultion', Int. Reh. Med., 2, pp HOLSHEIMER, J., STRUIJK, J. J., nd RIJKHOFF, N. J. M. (1991): 'Contct comintions in epidurl spinl cord stimultion. A comprison y computer modelling', Stereotct. Funct. Neurosurg., 56, pp HOLSHEIMER, J., nd STRUIJK, J. J. (1991): 'How do geometric fctors influence epidurl spinl cord stimultion? A quntittive nlysis y computer modelling', Stereotct. Funct. Neurosurg., 56, pp HOLSHEIMER, J., DEN BOER, J. A., STRUIJK, J. J., nd ROZEBOOM, A. R. (I 994): 'MR ssessment of the norml position of the spinl cord in the spinl cnl', Am. J NeurordioL, 15, pp HOLSHEIMER, J., STRUIJK, J. J., nd TAS, N. R. (1995): 'Effects of electrode geometry nd comintion on nerve fire selectivity in spinl cord stimultion', Med. Biol. Eng. Comp., 33, (5), pp KRArNICK, J., THODEN, U., nd RIECHERT, T. (1980): 'Pin reduction in mputees y long-term spinl cord stimultion', J Neurosurg., 52, pp LAW, J. D. (1983): 'Spinl stimultion: sttisticl superiority of monophsic stimultion of nrrowly seprted longitudinl ipoles hving rostrl cthodes', AppL Neurophysiol., 46, pp LAW, J. D. (1986): 'The 'filed ck syndrome' treted y percutneous spinl stimultion'. Proc. 2nd Ann. Meeting Americn Assocition of Neurosurgery nd College of Neurol. Surg. Sn Diego, Cliforni MAIMAN, D. J., LARSON, S. J., nd SANCES, Jr. A. (1985): 'Spinl cord stimultion for pin' in 'Neurl stimultion 1' (CRC-Press, Florid) pp MCNEAL, D. R. (1976): 'Anlysis of model for excittion of myelinted nerve', IEEE Trns., BME-23, pp NIELSON, K. D., ADAMS, J. E., nd HOSOBUCHI, Y. (1975): 'Experience with dorsl column stimultion for relief of chronic intrctle pin: ', Surg. Neurol., 4, pp NORTH, R. B., EWEND, M. G., LAWTON, M. T., nd P]ANTADOSI, S. (1991): 'Spinl cord stimultion for chronic, intrctle pin: superiority of "multi-chnnel" devices', Pin, 44, pp SHAggY, P. C. (1981): 'Technologicl prolems of spinl cord stimultion systems: clinicl perspective', Appl. Neurophysiol., 44, pp SHEALY, C. N., MORTIMER, J. T., nd HAGFORS, N. R. (1970): 'Dorsl column electronlgesi', J Neurosurg., 32, pp Medicl & Biologicl Engineering & Computing July 1996

7 SWEET, W. H., nd WEPSIG, J. G. (1974): 'Stimultion of the posterior columns of the spinl cord for pin control: indictions, technique nd results,' Clin. Neurosurg., 21, pp STRUIJK, J. J., HOLSHEIMER, J., VAN VEEN, B. K., nd BOOM, H. B. K. (1991): 'Epidurl spinl cord stimultion: clcultion of field potentils with specil reference to dorsl column nerve fiers', IEEE Trns., BME-38, pp STRUIJK, J. J., HOLSHEIMER, J., VAN DER HEIDE, G. G., nd BOOM, H. B. K. (1992): 'Recruitment of dorsl column fiers in spinl cord stimultion: influence of collterl rnching', 1EEE Trns., BME- 39, pp STRUIJK, J. J., HOLSHEIMER, J., nd BOOM, H. B. K. (1993): 'Excittion of dorsl root fiers in spinl cord stimultion: theoreticl study', IEEE Trns., BME--40, pp STRUIJK, J. J., HOLSHEIMER, J., BAROLAT, G., HE, J., nd BOOM, H. B. K. (1993): 'Presthesi thresholds in spinl cord stimultion: comprison of theoreticl results with clinicl dt', 1EEE Trns., RE-l, pp VOGEL, H. P., HEPPNER, B., HOMBS, N., SCHRAMM, J., nd WAGNER, C. (1986): 'Long-term effects of spinl cord stimultion in chronic pin syndromes', J. Neurol., 233, pp Author's iogrphy Johnnes J. Struijk ws orn in Rijssen, The Netherlnds, in He received his MSc in Electricl nd Biomedicl Engineering in 1988, nd his PhD in Electricl Engineering in 1992, from the Biomedicl Engineering Division t the University of Twente, Enschede, The Netherlnds, respectively. After two yers s postdoctorl fellow t the University of Twente he joined the Centre of Sensory-Motor-Interction t Alorg University, Denmrk, where he is currently n ssistnt professor, His reserch interests re in electricl stimultion neuroprostheses, volume conduction nd ioelectricity. Medicl & Biologicl Engineering & Computing July