WEAR PREDICTION OF A TOTAL KNEE PROSTHESIS TIBIAL TRAY

Transcription

1 APPLIED PHYSICS MEDICAL WEAR PREDICTION OF A TOTAL KNEE PROSTHESIS TIBIAL TRAY L. CÃPITANU, A. IAROVICI, J. ONIªORU Institte of Solid Mechanics, Romanian Academy, Constantin Mille 5, Bcharest Received September 6, 006 By replacing the natral joint, a knee prosthesis mst allow complex movements flexion extension (FE), antero-posterior translation (APT) and inner oter rotation (IOR) all of them defining a cyclic loading regime. The paper is devoted to the experimental determination of the wear of a UHMWPE prosthetic tibial tray, sing stdies of a ball/flat cople nder constant compressive loading. The reslts obtained lead to the conclsion that many clinically reported failres of the tibial tray are cased by the mechanisms of adhesive and fatige wear. Key words: total knee prosthesis, wear, experimental methods, simlator.. THE HERTZIAN CONTACT MECHANISM Two bodies that are in contact in a point become deformed when pressed against each other, ths creating a small contact srface. Hertz has calclated the deformations and stresses in the case of homogenos, isotropic, frictionless, linear elastic bodies. For two different materials, having the elasticity modls E and E, and the Poisson ratios ν and ν, the eqivalent elasticity modls E is defined, throgh the relation []: EE E = () ν E + ν E ( ) ( ) For a ball/flat type cople, where the ball is made ot of CoCr alloy, with the elasticity modls E = dan/mm and Poisson s coefficient ν = 0.3 and the plane sample made ot of UHMWPE (ν =0.36 and E = 06 dan/mm ), the eqivalent elasticity modls is E = dan/mm. Considering two revoltion bodies having bondary srfaces with / R and / R crvatres, one introdces the relative crvatre given by: Paper presented at the National Conference on Applied Physics, Jne 9 0, 006, Galaþi, Romania Rom. Jorn. Phys., Vol. 53, Nos., P , Bcharest, 008

2 50 L. Cãpitan, A. Iarovici, J. Oniºor = + R R R If one of the srfaces is concave, the crvatre of that srface will be considered negative. For the particlar case of the contact between a sphere of radis r and a plane, we have. = and R r R 0 Applying an F compression load between the two parts leads to the appearance of a contact area, de to srfaces deformation. The F compression force cases an h movement of the center of the sphere, throgh its penetration in the flat body, according to relation: h = 9F (3) 6rE The relation between the circle diameter l (of the spherical contact spot) and the penetration h is []: 4 /3 l = r h Using (3) it reslt the diameter of the contact spot: 6F r ( ) 3 () l = (4) E. DETERMINATION OF WEAR PARAMETERS An experimental device was created for the simlation of the wear process of total knee prosthesis components. For this prpose, a ball/flat type cople was sed. It consists of a ball made of CoCr alloy, simlating a condyle of the femoral component, and a polyethylene disk of high density (UHMWPE) placed nderneath representing the tibia component. The thickness of UHMWPE disk was 5 or 0 mm and was monted on a CoCr alloy plate. The movements made and the applied loadings were based on biomechanical stdies. The complex movement consisted in: flexion extension (FE), anteroposterior translation (APT) and inner oter rotation (IOR). The FE movement is applied to the ball and the APT and IOR to the disk (Fig. ). These movements were made by intermediate of a rod-handle mechanism. The movements variation in time was almost sinsoidal, a movement cycle period being of s. The experimental nit made is very similar to that sed by V. Saikko, T. Ahlroos and O. Calonis at the Helsinky University of Technology [].

3 3 Wear prediction of a total knee prosthesis 5 Fig. The friction cople kinematics. The amplitde of the flexion extension movement was of 40. For FE movement only, the sliding distance between the extreme positions wold be of 0 mm, for a 54 mm diameter ball. Anyway, the APT movement, with the amplitde of 0 mm, was synchronized with the FE movement so that the maximm flexion wold coincide with the maximm posterior translation of the disk, and the maximm extension with the corresponding maximm anterior translation. This has shortened the sliding distance between the extreme positions. De to both movements, the contact spot moved relatively cyclic on the disk srface. The rod-handle mechanism was created so that the phase angle between the IOR and the APT sinsoids is π/. As a conseqence, the locs of the point where the force is applied on the disk (meaning the geometrical path of a theoretical contact point) was an antisymmetrical narrow figre, in the shape of an eight (see Fig. ). Fig. The trajectories of the contact point between the ball and the plane.

4 5 L. Cãpitan, A. Iarovici, J. Oniºor 4 The parametrical eqations of the crve (C ) are: x = d k cos ( ϕ0 k ), ( 0 where: k is the adimensionalized time; d is the relative translation between the srfaces; ϕ 0 is the maximm IOR angle. Similar, the eqations of the crve (C ) are: y = d k sin ϕ k ); k [0,] (5) x = d cosϕ d k cos ( ϕ k) 0 0 y = d sinϕ d k sin ( ϕ k), k [0,] 0 0 The crves (C 3 ) and (C 4 ) are antisymmetrically defined: (6) x 3 = x, y 3 = y, k [0, ] (7) x 4 = x, y 4 = y, k [0, ] (8) The length of one of the crves is: From (5) it reslt: 0 ( ) L = ( x ) + ( y ) dk (9) 0 L = d + k dk (0) The area of the circlar segment defining the vertical profile of the wear imprint is: S r ( arcsin l l ( r) r) = () where l is the width of the imprint. The volme of the theoretical imprint can be calclated as: V = S L () The APT movement was realized so that lever fixed on the FE shaft led to a low-friction movement of a straight, horizontal beam, copled to a force transdcer. The transdcer signal was proportional to the friction force between the ball and the disk. This method allow for the determination of the friction coefficient μ. The first experiments carried ot, sing only FE and APT movements, led to a very small wear rate. By adding the IOR movement, the wear rate increased, the wear phenomenon becoming more complex.

5 5 Wear prediction of a total knee prosthesis 53 The vertical loading of.5 kn loading was constant, corresponding to the maximm load indced in the knee by the rotine activities. De to translations, the stresses in the disk modify in a cyclic manner, even for a constant compression force. The disk samples (having a diameter of 40 mm) were made ot of high density polyethylene, type GUR 050. The tests were made on five different disks. Oxidation was simlated throgh the ageing of the polyethylene after the gamma irradiation. The lower part of the disk was placed on a level spport of CoCr alloy. The lbricant sed was sterilized, filtered 0. μm physiological serm with a low content of proteins and endotoxines. The tests were carried ot at the room temperatre. Dring the tests, the vale of the friction force was also achieved. The dration of the tests was of cycles, at a freqency of Hz. The tests were stopped every 500,000 cycles in order to change the lbricant. The elastic deformation of the polyethylene nder pressre, has as conseqence an increase of its radis in the contact area. By noting r the radis of the ndeformed contact area and r m the radis of the area deformed by the contact, it can be seen in Fig. 3b that r m > r. Fig. 3 Elastic deformation of the flat part in the contact area [3]. a theoretical case; b practical case. The eqivalent crvatre radis in the point where the l m impression width was measred, noted by r m, can be calclate from (4): 3 E lm rm = (3) 6F The volme of material for the flat element, removed throgh wear, will be:

6 54 L. Cãpitan, A. Iarovici, J. Oniºor 6 L = m r m l arcsin m l V m r r where L m is the measred length of the imprint. Solving nmerically one obtains the soltion: r m = 7,3 mm,0r (4) Practically, the microscopic measrement of the imprints width in five established points, allow comptation of the medim width of the imprint. Based on this vale, the volme of worn material of the flate polyethylene element V is determined as well as the medim depth of the layer removed throgh wear h m. 3. RESULTS The reslts obtained from the experimental trials, for a constant force of 50 dan, having an FE of ± 0 and an APT of ± 5 mm, are presented in Table. Table Wear of polyethylene disks and average coefficient of friction Test Wear Wear factor Wear pit dimensions μ (0 3 mm 3 ) (0 mm 3 /Nm) Length (mm) Width (mm) Depth (0 3 mm) 7,58 8,559 7,3 0,399,475 0,935,697 0,94,54,48 0,3 0, 0,4 0,6 0,5,3,6,3,55,5 0,6,3 0,5 0,9,0 0,036 0,053 0,035 0,034 0,047 The tests and were performed on polyethylene disks having a 5 mm width, and tests 3, 4 and 5 on disks having 0 mm width. The theoretical length of the frictional distance covered by the contact spot, on each movement cycle, was 0 mm. The measrements carried ot with the microscope have shown an effective increase of these vales, probably cased by the shear stresses occrred on the edges of the contact area. For tests and 3, the UHMWPE samples were sterilized throgh γ irradiation and aged throgh air convection. Tests and 4 were carried ot on samples that were not irradiated and test 5 on samples that were irradiated bt not aged. The wear factor was determined based on Archard s relation [4]: V = F k v t (5)

7 7 Wear prediction of a total knee prosthesis 55 where: V volme of material removed throgh wear (cm 3 ); F working load (dan); v relative sliding velocity (cm/s); t test dration (hors); k wear factor (cm 3 s/ dan m h). Relation (5) expresses a general law for the dependency of the wear as fnction of the compressive force between the bodies in contact and the space covered by friction. Therefore we can write: k = V /( F v t) = V /( F L ) (6) f where L f = v t is the space covered by friction. Table also shows the medim vales of the friction coefficient, determined based on the measrements carried ot by intermediate of the force transdcer copled on the bearing with low linear friction, part of the generator of the APT movement. 4. CONCLUSIONS Appreciating the wear of the tibial tray of total knee prosthesis is very difficlt. Measring the wear becomes more challenging de to polyethylene s considerable yield. It is also difficlt to establish the vale of the wear factor becase measring the volme of material removed is also complicated to do. At the moment, appreciating the wear of the tibial tray throgh simlation is generally done sing qalitative methods, based on the microscopical investigation of the wear impressions. The initial polishing of the polyethylene s contact srface is a sign certifying the adhesive natre of wear. The tests carried ot for a different nmber of cycles prove that the wear rate of the γ irradiated and air convection aged disks was greater in the beginning, decreasing afterwards and getting stabilized arond the vales of the wear rates for not irradiated specimens. The wear rate of the γ irradiated and aged 0 mm thick disks is abot twice as for those that were not irradiated. The wear rate for 5 mm, aged disks is greater than that of similar disks, with a 0 mm thickness. REFERENCES. K. L. Johnson,, Contact Mechanics, Cambridge University Press, Cambridge, V. Saikko, T. Ahlroos, O. Calonios, A three-axis Wear Simlator with ball-on-flat Contact, Wear, 49, pp , L. Capitan, Drabilitatea endoprotezelor ortopedice, Ed. Bren, Bcharest, J. F. Archard, Contact and Rbbing of flat Srfaces, J. Appl. Phys., 4, pp , 953.