RIGID BODY MODEL OF THE HYBRID III DUMMY LOWER LIMB INCLUDING MUSCLE TENSION UNDER CAR CRASH CONDITIONS

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1 RIGID BODY MODEL OF THE HYBRID III DUMMY LOWER LIMB INCLUDING MUSCLE TENSION UNDER CAR CRASH CONDITIONS Philipps PETIT, Laurent PORTIER ", Xavier TROSSEILLE "' * CEESAR 132, rue des Suisses, Nanterre - FRANCE. ** TEUCHOS 6 avenue du General De Gaulle, Versailles - FRANCE. *** Biomedial Researh Department - RENAULT S.A 132, rue des Suisses, Nanterre - FRANCE. ABSTRACT As of today, neither human surrogates suh as rash test dummies and adavers, nor mathematial models an take lower limb braing into aount. lt is however reported that more than 50% of ar drivers have time to antiipate an impending rash. Based on an in-depth literature review, a mathematial representation of musle tension was adapted from gait onditions to ar rash onditions using available animal experiment results. This mathematial representation uses 3 generi funtions assoiated with 3 speifi parameters to desribe musle mehanial responses. Meanwhile, the human musle/skeleton geometry of lower extremities was saled to orrespond to the thigh and leg lengths of the 50th perentile Hybrid III dummy model available in Pamsafe software. For the model development, musle paths were imposed using origins, insertions and a variable number of pulleys, in order to obtain proper musle moment arms relative to the different joints whatever the position of the dummy. A partiular attention was paid to the knee extensors and to the patella. The entire lower limb musulature was modeled using 18 equivalent musles per limb, inluding both agonist and antagonist musles responsible for the appliation of a load on a brake pedal or a foot-rest. Dynami adaver experiments and volunteer tests were used both to determine the musle ativation oeffiient set and to validate the ontributions of passive and ative musle fores of the model. Simulations show that musle tension an signifiantly modify the dummy kinematis during a rash. JRCOBJ Conferene - Göteborg, September

2 AS OF TODAY, NEITHER HUMAN surrogates suh as rash test dummies and adavers, nor mathematial models an take lower limb braing into aount. lt is, however, reported that more than 50% of ar drivers have time to antiipate an impending rash [ 26]. lt means that the driver's hip, knee and foot extensors are fully ativated when the rash ours. Moreover, Portier [ 23] reported that during a dynami dorsiflexion imposed to the foot of a adaver, the tensile fore in the Ahilles tendon ould reah 1.9 kn due to the passive influene of plantarflexion musles. An ative fore of 5.3 kn measured in the Ahilles tendon was reported by Grafe [ 12] during arobati jumps. Keeping in mind that the foot over range of motion dorsiflexion was learly identified as one of the ankle injury mehanism, both ative and passive musle tensions ould have a protetive effet on the ankle joint. Sine it is not possible to perform volunteer tests under severity onditions omparable to real world aidents, a new method was developed to set up a simplified lower extremity musulature on a mathematial artiulated rigid body model of the 50th perentile Hybrid III. The atual objetive is to study the influene of musle tension on both the oupant kinematis and the loads passing through the lower limbs. The entire work was based on geometrial and physial data available in the literature for either human being or animals. EQUIVALENT MUSCLES In the literature, methods suh as the «quik release» or the «ontrolled release», initially used in isolated animal musular preparations were adapted to measure human in-vivo musular harateristis [ 11 ]. Other authors assessed the viso-elasti properties of systems omposed of musles surrounding a single joint, using either the natural frequeny of the free osillations [ 9], or the frequeny response of either stohasti [ 16] [ 17] or harmoni [ 1] [ 2] applied osillations. All the in-vivo methods are based on the 4 following assumptions the different segments are onsidered as artiulated rigid bodies, the joint enters of rotation are fixed (hinge, spherial and universal joints), the problem of distinguishing between individual musles is avoided by assuming that a single equivalent musle ats to flex or extend a partiular joint. the latter impliitly assumes first that the ation of the antagonists is either negligible or modeled separately, seond that the ratio between the moment produed by a partiular musle of the group and the total moment produed by the group is onstant all over the range of motion. When listing the main musles involved in lower limb braing and their antagonists, they orrespond to the musles involved in gait. This remark provides many musuloskeletal results available in the literature from the physiologial gait investigation studies. One regroupment that satisfies the assumptions above and ontains the musles of our interest is proposed by Hoy [ 15]. Table 4 gives the equivalent musles and their ations relative to the lower limb joints. 174 IRCOB/ C01tfere1le - <iöteborg, September 1998

3 MUSCULOSKELETAL G EOMETRY THE DATA CONC ERNING MUSCLE ORIG I NS AND I NSERTIONS are mainly based on the study performed by White [ 27]. In that study, the authors have identified and loated the origins and insertions of 40 lower limb musles from dry bones of a human adaver. White reported a l l the oordinates in loal frames. The thigh, alf and pelvis dimensions of the adaver did not orrespond to the distanes between the enters of rotation of the 50th perentile Hybrid I I I dummy. That is the reason why some geometrial transformations were applied to the adaver data. The pelvis was transversally saled using the distane between the two hip sokets. Femur and tibia/fibula salings were also performed using the distanes between the hip, knee and ankle joint enters of rotation. Table 1 reports the saling ratios. Distanes CR left hip right hip CR hip knee CR knee ankte Cadav. White (m) HIII Pamsafe (m) Table Hip 1 Saling ratio CR to CR distanes and saling ratios Left hip Knee 0==-=====r=.--0 Right knee Right hip Right ankle (side view) Ankle (top view) Figure 1 Lower limb position of the Pamsafe 50th perenti!e Hiif rigid body dummy model. One the origins and insertions of the 40 musles were alulated in a global oordinate system for a dummy positioned as desribed in Figure 1, musles were grouped. In ase of spread origin or insertion, W h ite reported the enter of gravity of the origin or insertion area. The origin or insertion points of an equivalent musle was defined as the enter of gravity of the different origins or insertions the weightings of whih were the musle ative ross setion areas. The musle ative ross setion areas used (Table 2) were those reported by Brand for a male speimen (37 years old, 1.83 m, 9 1 kg) and defined as the ratio between the musle volume (measu red by water displaement) and the average musle fiber length. Note no ative ross setion area value was available for the bieps femoris long head and no geometrial information was reported for the origin and insertion of the peroneus tertius musle. As a onsequene, those two musles were not taken into aount to alulate the equivalent musl e origins and insertions although their mehanial ontribution were inluded into the equivalent musle total tensions. IRCOBI Conferene - Gäteborg, September

4 Musle Ative ross Muse Je Ative ross setion areas setion areas (m2) (m2) Addutor brevis (Sho11 head*) l l.52 Superior gemellus 2.13 Addutor brevis (Long head*) 5.34 B ieps femoris Addutor longus Grailis 3.74 Addutor magnus (Anterior*) Retus femoris Addutor magnus (Middle*) Sartorius 2.9 Addutor magnus (Posterior*) Semimembranosus Gluteus maximus (Anterior*) 20.2 Semitendinosus Gluteus maximus (Middle*) Tensor fasia latae 8 Gluteus maximus (Posterior*) 20 Gastronemius (Medial*) 50.6 Gluteus medius (Anterior*) 25 Gastronemius (Lateral*) 14.3 Gluteus medius (Middle*) Bieps femoris (Short head*) 8.14 Gluteus medius (Posterior*) Vastus intermedius 82 Gluteus minimus (Anterior*) 6.76 Vastus lateralis Gluteus minimus (Middle*) 8.2 Vastus medialis Gluteus minimus (Posterior*) Tibialis anteriosus Iliaus Extensor digit omm 7.46 Psoas 25.7 Extensor hatluis longus 6.49 Inferior gemellus 4.33 Flexor dig 6.4 Obturator externus Flexor hall long Obturator internus 9.07 Peroneus brevis Petineus 9.03 Peroneus longus Piriformis Peroneus tertius 4.14 Quadrieps femoris 21 Tibialis posterior Soleus Table 2 Ative ross setion areas reported by Brand [ 8] for a male (37 years old, 1.83 m, 91 kg) and defined as the ratio between the musle volume (measured by water displaement) and the average musle fiber length (taking the fiber pennation angle into aount). Note the * indiates that the omplete word was guessed from Brand's indiations MUSCLE MOMENT ARMS relative to the joints they ross greatly depend on the oupant position and the musle path. A variable number of pulleys were used for eah musle in order to ensure orret musular moment arms relative to the hip, knee and ankle joints. The loations of the pulleys were determined from both anatomy papers and minute in-vivo examinations. A partiular attention was paid to the knee extension. Knee extensors insert on the patella, and the patella slides on the 2 femur ondyles. A tendon onnets the patella to the tibial anterior tuberosity. A solution involving an artiulated rigid body was determined to model the patella. The positions of the musle and tendon insertions and the loation of the hinge joint onneting the patella and the femur were optimized in order to obtain a musular moment arm (Figure 2) in agreement with the data reported from adaver tests in the literature [ 25) [ 5) [ 20) [ 13). Note the knee extensor moment arm was defined as the ratio between the musular tensile fore and the moment reated at the joint. 176 IRCOJJI Conferene - (;iiteborg, September J 998

5 r femur/ kn xlns A_ E pallla / B 0 / / " tndon ' D g J E 0 "' "' g \'( "' Model *""- Smidt et al Figure Knee Joint llxlon(') - -Bandi et al Lindahl et al ?(-- Grood et al.1983 sketh of the artiulated rigid body solution used to model the patella and omparison of the moment arm obtained in that ase and on adaver versus knee angle. The angular position of the patella relative to the femur is given by Equation 1. lt is a polynomial approximation of the solutions determined in the resolution of the positions suh that the distane C D (Figure 2) is onstant all over the knee range of motion. The theoretial error due to the approximation is less than 1. 1 for a total range of motion of 1 65 for the knee, and less than 0.2 for a knee flexion ranging from 60 to pate11a = 6E-08 8 \nee + 2E knee knee knee Equation 1 angular position of the patella relative to the femur where 8knee is the angle between the urrent knee flexion and the referene pamsafe position (Figure 1). 8pate11a is the rotation angle to be applied to the patella from the referene position in order to have the proper length for the tendon inserted on the tibia. Note angles are in radians. The use of a pul ley to impose the diretion of the Ahilles tendon at its insertion on the alaneus provided a moment arm for the trieps surae in agreement w ith the data reported by Rugg [ 24] over the full ankle range of motion in flexion whatever the knee angle ( Figure 3 ). IRCOBJ Conferene - Göteborg, September

6 g "' 31 = g 0.04 " " 0.02 E E 0 E -- Augg et al ; --Model (! a. "' u Figure Dorsttlexlon angle ( ) Moment arm of the soleus and gastronemius musles relative to the ankte joint versus the dorsiflexion angle for both our model and the adaver [ 24]. Musles Musles Origin pelvis Pulley 1 femur inf. Insertion tibia sup. Addutor longus and brevis Origin pelvis Insertion femur sup. Grailis Addutor magnus Origin pelvis Insertion femur sup. Sartorius Retus femoris Origin pelvis Pulley 1 femur inf. Insertion patella Origin pelvis Inse11ion femur sup. Origin pelvis Inse11ion femur sup. «Harnstrings Origin pelvis Insertion tibia sup. Bieps femoris (short head) V asti Origin femur sup. Insertion tibia sup. Origin femur sup. Pulley 1 femur inf. I nsertion patella lliopsoas Gluteus maximus Gluteus medius Origin pelvis Insertion femur sup Origin pel vis P ulley 1 femur sup. Pulley 2 femur inf. Insertion tibia sup. Origin femur inf. Pulley 1 tibia sup. Pulley 2 tibia in f. Insertion foot Gastronemius. Gluteus minimus Origin pelvis Insertion femur sup. Soleus Petineus Origin pelvis Insertion femur sup. Other plantarflexors Tensor fasia latae Origin pelvis Pulley 1 femur sup. Insertion tibia sup. Dorsiflexors Origin tibia sup. Pulley 1 tibia inf. Insertion foot Origin middle tibia Pulley 1 tibia inf. Insertion foot Origin middle tibia Pulley 1 tibia inf. Insertion foot Table 3 Desription of the musle paths. Note on the Hybrid III dummy, a load ell is p/aed in the diaphysis, it defines the proximal and distal parts respetively. ««femur sup. Tibia sup», «and «femur inf. middle tibia and portions as the «tibia inf» were defined similarly IRCOBJ Confere11e - Giitehorg, September 1 998

7 MUSCOLOTEN DON ACTUATOR MODEL Based on many works reported in the literature and more speially on Hoy [ 1 5) and Zajak [ 3 1 ] studies, the 1 8 equivalent musles of eah lower limb were modeled using 3 generi dimensionless funtions and 3 speifi parameters. The 3 generi dimensionless funtions were the isometri ative and passive fores vs musle fiber length, and the fore vs. shortening/strengthen i ng veloity funtions. They were normalized by the optimal musle fiber length, the maximal isometri fore and the maximal musle fiber shortening veloity i n order to obtain dimensionless relations. The 3 speifi parameters were therefore the musle optimal fiber length L0M defined as the fiber length at whih the maximal isometri fore an be generated, the maximal isometri fore F0M, the maximal musle fiber shortening veloity V m STATIC PROPERTI ES - W hen musles were fully ativated, we assumed that the isometri fores of any musle ould be determined using Equation 2. This impliitly assumed that the passive fore starts for a musle fiber length equal to the optimal fiber length. Ative (0.5 $ x $ 1.5) Passive ( 1 $ x $ 15) Equation 2 F Fo M F -- F0 M -- = = -xs x4-7 l.75x x x l.l 46x4 - l 9 l.03x x2-263.l 6x Generi dimension/ess funtions giving the isometri ative (for fully ativated mus/es) and passive fores where x represents the musle fiber length normalized by the optimal fiber /ength L 0M_ lt is weil established i n the literature that the isometri ative effort generated by a partially ativated musle equals the produt of the ative effort generated when fully ativated by the ativation oeffiient a, i. e. F( a<1 )=a F(a=1 ). DYNAMIC PROPERTIES - Myers [ 21 ] arried out dynami experiments on isolated rabbit tibialis anterior. The results showed that the peak dynami strething effort did not depend on musle ativation and was approximately 1.9 * F0M. Several authors laimed that the i ntersetion of the urve with the absissa axis remained unhanged whatever the ativation. Moreover, sine the intersetion between the ordinate axis and the u rve orresponds to an isometri fore, we assumed that the fore vs. shortening/lengthening veloity ould simply be dedued from the fully ativated musle properties. Equation 3 finally gives the musle isotoni dynami properties as a funtion of normalized veloity and ativation. IRCOBI Conferene - Göteborg, September

8 l+x F. Shorte11 111g x s; 0 - = a. ( --) x Fo 1_ Lengthening x?. 0 _! = Fo Equation 3 1), ß r; a + x'.- l + µ -a µ musular fore - veloity generi dimensionless properties. a is the ativation oeffiient (ranging from O to ri is the ratio between the peak dynami strething fore and the maximal isometri fore, ß and µ are 2 urve shape parameters hosen equal to 0.3 and respetively in our study. x positive is the strething veloity normalized by the maximal mus/e fiber shortening veloity. In agreement with many results reported i n the literature, tendons were assumed to behave l i ke l i near springs, and to have a Young modulus equal to Pa. Several authors [ 1 4] [ 1 8] [ 7] [ 3] showed that tendon harateristis were not sensitive to the lengthening veloity within the range of veloity aused by gait. We assumed this remained true under rash test onditions. Tendon Contratile Component fore vs. veloity properties fore vs. length properties Figure 4 Musle model. As presented in Figure 4, musles were finally modeled using a linear spring (tendon) in series with a ontratile omponent omposed of a non linear damper (dynami musular properties - Equation 3) in paral lel with a non linear spring (stati passive and ative musular properties - Equation 2). In agreement with literature results [ 6], we onsidered that the rash had suh a short duration that the ontratile omponent was unable to reat. The musular ative effort versus time was thus assumed onstant and equal to the initial ative isometri fore assoiat ed with the initial position of the dummy. In the model we used (Figure 4) the initial musular ative fore was represented by a pre-stressing of the elasti omponent (offset added to the fore 1 80 IRCOJJJ Conferene - (;;Heborr. September 1998

9 vs. length urve). Before a rash si mulation, the dummy was positioned in the vehile. For this partiular position, the length of eah musle path was alulated using the ori g i n, insertion a n d pulley oordinates. The length of the ontratile omponent was then equal to the musle path minus the length of the tendon (note the latter did not depend on the position). From the length of the ontratile omponent and the generi fore vs. length musular properties, an i nitial isometri ative fore was alulated, and the strain shift to be applied on the passive fore vs. length urve was determined. The first ms of simulation were used to reah a n equilibrium position prior to the rash inluding ative musle tension. M USCULOTENDON PARAMETERS The musulotendon parameters used were based on those reported by Hoy and determined by Wiekiewiz [ 28], and Brand [ 8]. To alul ate eah tendon length, we assumed that the peak moment generated at a joint was reahed for a ontratile omponent length equal to L0M. The joint angular positions orresponding to the maxima were determi ned from the moment u rves reported by Hoy. Musle Ation Fmax N 0.75 Vm m/s Lt m Kt N/m M Lo m hip ext., hip flex. 838 Addutor magnus hip ext Retus femoris hip flex, knee ext 926 l Iliopsoas hip flex Gluteus maximus Gluteus medius Gluteus minimus hip ext hip ext, hip flex 1794 l hip ext, hip flex hip flex hip flex, knee flex hip flex, knee flex Grailis Sartorius hip flex, knee flex hip ext, knee flex l Addutor longus and brevis Petineus Tensor fasia latae «Harnstrings» B ieps femoris (short knee flex head) Vasti knee ext Gastronemi us knee flex, plantarflexion Soleus plantarflex. Other plantarflexors Dorsiflexors Tab/e 4 ation " Ativ. (<I ) 3837 plantarflexion 3507 dorsiflexion l l Usting of the equivalent musles used in our study, their parameters and their relative Hamstrings» to the joints. Note aording to " Gray 's Anatomy p» 432, is used for bieps femoris, semitendinosus and semimembranosus. Aording to Hoy, " other plantarflexors» means tibialis posterior, f/exor halluis!ongus, flexor digitorum longus, peroneus brevis and peroneus /ongus. " Dorsif/exors means tibialis anterior, extensor hal/uis /ongus, extensor digitorum /ongus and peroneus tertius. The mus/e ativation set orresponds to a braing situation. IRCOBJ Co11fere11e - Göteborg, September

10 Figure 5 /ower limb musulature model. RESULTS Simulations were run to ompare the results obtained by the model and those obtained on volunteers by Armstrong [ 4). Armstrong performed sied tests where the sied was equipped with a seat, a belt and an instrumented foot rest. One of the sied experimental deeleration pulse is reported i n Figure 6. N'.s Cl) -- Q) ü CU 'O Q) (.) U Figure time (s) Sied dee/eration in one of the test run by Armstrong. The model longitudinal fore ating at the foot and toe-pan ontat was approximately 800 N higher than the experiment results whatever the musular ativation. This was due to a fore offset at the pre-rash equilibrium. The sketh presented in Figure 7 shows a omparison of the standard Hybrid I I I dummy (with no musulature) and the ful ly braed model. In ase of a moderate severity deeleration pulse (peak = 1 4 G reahed at t=0.04 s), the simulation results showed that the oupant kinematis was greatly modified by musle tension. l ndeed, the standard dummy translated until the seat-belt was tensed (t=0.064 s), then the pelvis rotated around -Y and penetrated the seat ushion. Prior to the rash (t < s), the braed model moved rearward due to musle tension, and during the rash, the knees remained extended and prevented the pelvis from translating. The seat-belt slak was then entirely taken up by the thorax forward movement IRCOJJJ Conferene - (iiitehorg, September 1998

11 Hili at t=0.064 s Hili at t=0.096 s BRACED at t=0.120 s Figure 7 Kinemati omparison of the standard HI// dummy (no musulature) and the braed model. The initial positions were the same for both. Note the deeleration pulse is presented in Figure 6, for the braed simulation the pulse was de/ayed of s in order to /et the model reah an equilibrium prior to the rash. The model validation was also onduted using adaver tests performed by Portier [ 23 ]. The adavers were plaed as presented in Figure 10 and a brake pedal, initially in ontat with the head of the metatarsals, imposed a dynami dorsiflexion of the foot. The fore ating at the ontat between the pedal and the sole of the foot was used to adjust the parameter µ in Equation 3. A omparison between the simulation and test results is presented in Figure 8 and Figure 9. Simulation results for a fully ativated volunteer are also plotted. IRCOBJ Conferene - Göteborg, September

12 , 1 Simulation volunteer 0%... ', - oo \ \ \ \.,._...,_......,. w. ' l! ' - - _,.;- -. ' "-,_ I Cadaver test -uoo., _ ! Simulation volunteer 1 00% -lloo '--- o L O.Ol., - 0. O l u L...J... J Figure 8 Longitudinal fore ating a t the ontat between the foot and the pedal. Comparison of the results obtained from a adaver test and from simulations of 0% and 100% ativated volunteers tl.. Simulation volunteer 1 00% Simulation volunteer 0% Cadaver test Positioning prior to the rash JIOO Figure 9 Tensile fore ating in the Ahilles tendon. Comparison of the results obtained from a adaver test and from slmulations of 0% and 1 00% ativated volunteers. 184 IRCOBI Confere11e - Giiteborg, September 1998

13 Figure 1 O simulation of the adaver tests performed by Portier. Aording to the simulations performed for the 100% ativated volunteer (Figure 8 and Figure 9), the peak fores ating respetively in the Ahilles tendon and under the metatarsals are approximately 6500 N and 3700 N. The resultant ompressive fore ating in the tibia is then approximately N. From the literature review, suh fores are supposed to result neither in Ahilles tendon, nor in tibial injuries. lndeed, [ 1 O] [ 19] and [ 29] reported maximal allowed stress in the Ahilles tendon ranging from Pa to Pa. lf we assume that the Ahilles tendon ross setion area is m 2 [ 12], the maximal fore to be sustained by the tendon is then ranging from 7371 to N. [ 22] reported a maximal ompressive fore of N in the tibia. DISCUSSION At this stage, the model should be onsidered as a researh tool. lndeed, before aurate preditions ould be provided for higher severity, some additional validations and fittings should be performed. All the simplifiation assumptions of the study were exposed as learly as possible. Some of them may be disussed. For example, the isometri passive fore was assumed to start for a fiber length equal to the optimal fiber length. Data provided by [ 30] who investigated several trog musles do not onfirm our assumption (see Figure 11 ). lndeed, a parameter should be added to desribe the fiber length where the passive isometri fore starts. However, suh data is not available for the 18 equivalent musles that ompose the lower limb musulature. Reasonable simplifiations were hosen in order to overome the lak of biomehanial data. IRCOBJ Conferene - Göteborg, September

14 Gastron emius 0 "(/) <ll..., Sartorius.Q (J) (J.)..., Semitendinosus.Q (J) (J.)..., total length Figure 1 1 length length Example of isometri passive and ative fore of trog mus/es. I n the musulotendon model, the optimal fiber length normalized all the lengths i nvolved i n the representation. A sensitiveness study showed this physial parameter had a major influene on the simulation results. An i n-depth literature review showed!arge disrepanies on that point. The lak of onsistent biomehanial data is thus of primary importane for further model development. Moreover, sine the skeletal geometry was determined from one adaver and saled to orrespond to the dummy size, the musle ross setion areas were measured on a seond adaver, the physial properties suh as the optimal fiber length were obtained on a third adaver and finally the musle paths were determined from anatomy papers and minute in-vivo examinations of a fou rth person, the different parameters despite they were i ndividually aurately i nvestigated remain i nonsistent. lt is then very diffiult to assess the global auray of the musle length estimation. Thus, the isometri passive and ative fores alulation inlude this lak of onsisteny. This paper is based on an i n-depth literature review of lower l i mb musle tension modeling. The authors attempted to adapt the i nformation of both musuloskeletal geometry, and musulotendon property modeling, to develop an Hybrid I I I dummy artiulated rigid body model plaed i n rash-test onditions. lt provides a list of assumptions to be made i n order to overome the enormous lak of preise knowledge of the lower limb musle harateristis. lt seems, however, that no model provid i ng aurate preditions an be developed as long as biomehanial data is not available. CONCLUSIONS Same priorities learly appear for the next adaver i nvestigation studies. Among those priorities, the neessity of onsistent musuloskeletal geometry and musulotendon physial properties is widely emphasized.. Aording to Hoy, the Ahilles tension i"s responsible for approximately 90% of the peak ankle moment. Results reported in the literature shows that during a dynami dorsiflexion of a adaver foot [ 23], the Ahilles load an reah 36% of 1 86 IRCOBI Confere11e - Göteborg, September 1998

15 the tension generated by a trained volunteer during arobati jumping [ 1 2]. The dynami strengthening of the trieps surae ould thus reate a passive musle tension that ould reah approximately half of the ative fore ating in the Ahilles tendon of an athlete during an arobati jump. The results of the fi rst version model suggests that in a moderate severity rash, musle tension may signifiantly modify the oupant kinematis. The researh efforts should keep on evaluating the importane of the l ak of musle tension on the Hybrid I I I dummy sine it is urrently used for ar regulation. REFERENCES [ 1] ABBOTT B. C., and WILKIE D. R., " The relation between ve/oity of shortening and the tension-length urve of skeletal mus/e '" J Physiol (London), 120, 214, { 2] AGARWAL, C. G., et GOTTL/EB, G. L., (1977 a) " Osillation of the human ankte joint in [ 3} ALEXANDER, R., MN, MALOIY G. M. 0., KER R. F., JA YES A. S., WARUI C. N., " The rote of tendon elastiity in the loomotion of the amel (Camelus dromedarius), J. Zoo/. (London), 198, 293, response to applied sinusoidal torque at the foot», J. Physiol., London, 268, [ 4] ARMSTRONG., R. W., WATERS, H. P., and S TAPP, J. P. (1968), " Human musular restraint sied deeleration '" Soiety of Automotive Engineers, SAE No , in Pro. of the Stapp Conf. { 5] BAND/ W., " Chondroma/aia patellae und femoro-patelre arthrose. Ä tiologie, Klinik und therapie ", He/vetia Chir. Ata, Suppl. 1 1, [ 6} BEGEMAN Paul C., KING A.I., LEVINE R.S., VIANO D.C., "Biodynami response of the musuloskeletal system to impat aeleration", 24th Stapp Conferene Proeedings, pp , [ 7] BENNETT, M. B., KER, R. F., DIMERY, N. J., and ALEXANDER, R. MN (1986), " Mehanial properties of various mammalian tendons J. Zoo/., Lond. 209, », { 8] BRAND R., PEDERSEN D., FR/EDER/CH J., " The sensitivity of musle fore preditions to J. Biomeh., Vol. 19, No 8, pp , hanges in physiologi ross-setional area», { 9] CA VAGNA, G. A., (1970) " Elasti boune of the body, J. Appl. Physiol., 29, [ 10] CRONKITE, A. E. (1936) Anat. Re. 64, { 1 1} GOUBEL, F., (1971) " Relation entre l'emg integre et le travail meanique dans Je as de mouvements effetues a inertie onstante, ave ou sans harge ", J. Physiol. (Paris) 63, 224. { 12} GRAFE, H. (1969), " Aspekte zur Ä tiologie der subutanen Ahillessehnenruptur " Zentralblatt f. Chirurgie 94, 33, [ [ 13} GROOD E. S., SUNTA Y W. J., NOYES F. R., BUTLER D. L., " Biomehanis of the knee extension exerise '" The J. of Bone and Joint Srgery, vol. 66-A, no 5, June } HERRICK W. C., KINGSBURY H. B., and LOU D. Y. S., " A study of the normal range of strain, strain rate, and stiffness of tendon ", J. Biomed. Mater. Res., 12, 877, [ 15} HOY, M. G., ZAJAC, F. E., and GORDON, M. E., (1990) " A musu/oskeletal model of the human lower extremity the effet of musle, tendon, and moment arm on the moment-angle relationship of musulotendon atuator at the hip, knee, and ankte ", J. Biomehanis 23, 2, { 16] HUNTER, /. W., and KEARNEY, R. E., (1982) " Dynamis of human ankte stiffness variation with mean ankte torque ", J. Biomehanis, 15, 1 0, IRCOBI Conferene - Göteborg, September

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