1 . a schematic cross sectional view of the artificial hip joint articulation according to current standards . 2 . a schematic cross sectional view of the artificial total hip joint articulation according to the invention , showing a spherical head in an aspherical , fossa cup . 3 . a schematic cross sectional view of the artificial total hip joint articulation according to the invention , showing an aspherical , fovea head in a spherical cup . 4 . a cross sectional view of the artificial total hip joint according to the invention , showing a spherical head in an aspherical , fossa cup , whereby the axis of symmetry of the cup inner shape is offset from the main axis of the cup , so as to place the fossa of the cup into the window of major joint force vectors acting on the cup in actual use . 5 . a cross sectional view of the artificial total hip joint according to the invention , showing an aspherical , fovea head in a spherical cup , whereby the axis of symmetry of the head outer shape is offset from the main axis of the head , so as to place the fovea of the head into the window of major joint force vectors acting on the head in actual use . 6 . a perspective view of a total hip articulation showing contact area under load . 7 . a perspective view of the tibial plateau of a partial , or a total knee prosthesis showing a fossa feature . 8 . a cross sectional view of a spinal disk prosthesis according to the invention . for a simple and clear presentation , a total hip joint articulation has been chosen for this disclosure , but the same technical arguments and design approaches can be used for articulations of other joint prostheses , which , generally , have less conforming surfaces and lesser degree of coverage . fig1 shows a conventional , standardized total hip prosthesis articulation , with a spherical convex component , or head , 2 , seated into a spherical concave component , or cup , 1 . the theoretical contact between them is at a point 9 , provided that the load is oriented along axis 10 . the articulating surface 3 , of the cup 1 is of spherical shape with a radius 4 , centered at point 5 . the surface 6 , of the head 2 , is also spherical , of radius 7 centered at point 8 . the shapes of the two components are axisymmetric , i . e . both are bodies of revolution and can be described in a polar coordinate system , with the origin 8 , the polar axis 10 and the polar angle 12 . the gap width 11 is zero at the polar angle 12 of zero degrees , i . e . at the pole ; it approaches maximum radial clearance equal to the difference between the radii 4 and 7 at the polar angle of 90 degrees . distance 13 between the points 5 and 8 is equal to the difference between the radii 4 and 7 , i . e . 13 is the radial clearance . for uhmwpe cup liners and metal or ceramic heads the usual radial clearance is in excess of 0 . 1 mm ; for metal - metal pairing it is usually less than 0 . 03 mm . diameter 15 of the cup opening is larger than the diameter 14 of the head 2 , so that the head 2 can freely come into its seat within the cup and make the contact at point 9 . under load the point contact will spread out into a surface contact , resulting stresses being known as herzian , after heinrich hertz , who with his 1882 classic publication has provided theoretical basis for calculating contact stresses between bodies of simple geometrical forms ( hertz , h . :“ gesammelte werke ”, vol . i , leipzig , 1895 ). formulas to calculate herzian stresses are given in e . g . “ formulas for stress and strain ”, fifth edition , roark and young , mcgraw - hill , 1982 , chapter 13 . the subject is extensively covered in e . g . “ contact mechanics ”, k . l . johnson , cambridge university press , 1985 . for a sphere in a spherical socket the formulas are valid only if the radius of the socket is larger that that of the sphere ; improved formulas for closely matching radii have also been developed , but if the radii are equal , the contact stress in the herzian sense is eliminated . fig2 shows the head 102 in the cup 101 articulation according to this invention . the head 102 is spherical with its surface 106 having a radius of curvature 107 with the center at the point 108 . the articulating surface 103 of the cup 101 is aspherical — more precisely — only partially spherical , axisymmetric around the axis 110 . over an arc 120 , between the polar angles 113 and 114 , the surface 103 is spherical , congruent to the head surface 106 . in 3d the arc 120 defines a band 121 of theoretical contact , a section of a spherical surface , fig2 a . for polar angles larger than 114 the radius of curvature 104 , of the surface 103 , with the center at 105 , is larger than the radius 107 , opening a gap between the two articulating surfaces 103 and 106 . for polar angles just smaller than 113 , the radius of curvature of the surface 103 is also larger than of the surface 106 , again opening a gap 111 . as the polar angle approaches zero , the radius of curvature of the surface 106 , is decreased to round off the shape of the cup at the pole 109 . the resulting gap at the pole is 118 . the arc of circle 120 of perfect congruency is centered at the polar angle 115 , and its corresponding width angle is 116 . the position , 115 , and the width , 116 , of the band of theoretical surface contact are subject to parametric optimization . first order approximation suggests that the angle 115 should be about 45 degrees ; the width 116 about 30 degrees . theoretical optimizations , coupled with experimental testing , including a cost - function placed on the frictional moments of the articulation , are expected to place the angle 115 into the range between 20 and 50 degrees ; the surface contact width 116 into the range between 10 and 40 degrees . the band of contact 121 , shown in a perspective view on fig2 a , defined by the arc 120 , encloses a volume 130 at the polar aspect between the surfaces 106 and 103 of the head and the cup , respectively . opening 140 of the cup is larger than the diameter of the head 141 , resulting in the clearance 117 , so that the head is free to seat itself into the cup generating a surface contact along the area 121 . the type of cups shown on fig2 will be referred to as fossa type . fossa in general means a cavity , or depression , and in case of the hip acetabulum , it is a centrally located recessed area not covered by cartilage . the scale of the fossa gap is greatly exaggerated on this and on the following figures . in reality , it will depend on the materials used . for an uhmwpe cup of the fossa type the maximum gap size , which conveniently would be 118 at the pole 109 , should be big enough , so as to avoid bottoming out of the head 102 even after maximum anticipated use of the prosthesis , e . g . for 50 years . the wear tests conducted until now suggest the rate of about 4 micrometers per million cycles of loading , which may correspond to 1 to 2 years of in vivo use . to allow for 50 years of wear without bottoming out , the gap 118 should be 0 . 2 to 1 mm ; 2 mm would give a safe margin , but this may call for fairly significant changes of the radius vector 104 for the polar angles between the axis 110 and the first angle of contact 113 . ideally , the changes of the radius of curvature of the surface 103 below and above the angles 113 and 114 , respectively , should be continuous , but for practical reasons one or two steps will suffice , especially if machined in the soft polymeric materials like uhmwpe . it is highly preferable , though , that the transitions are tangential , i . e . that the contour of 103 is smooth , as shown in fig2 b . radius r 1 of the arc 120 centered at c 1 is the nominal radius , equal to that of the head . radius r 2 , corresponding to the arc 122 , is centered at c 2 and is larger than r 1 . as shown , the centers c 1 and c 2 should be placed on the radi - vector defining the transition from 120 to 122 , so as to make the transition smooth , i . e . there is a common tangent to the arcs 120 and 122 at the transition point . radius r 3 with the center c 3 defines the arc 124 ; r 4 with the center at c 4 the arc 123 ; radius r 5 , with the center at c 5 the arc 125 . for metal - metal and ceramic - ceramic articulations the gap 118 should be about 5 to 10 times smaller than for uhmwpe ; i . e . in the range from 50 to 200 micrometers . to minimize the production of wear , international standards ( iso , astm ) have proposed the upper limits on the roughness of the articulating surfaces : ( i ) uhmwpe cup maximum ra of 2 micrometers ( approximately grade n7 ); today , uhmwpe cups are typically machined to surface roughness of n5 to n6 , corresponding to ra of 0 . 4 to 0 . 8 micrometers ; ( ii ) metal or ceramic heads maximum ra of 0 . 05 micrometers ( grade n2 ); ceramic heads are typically finished with ra of less than 0 . 01 micrometers . notwithstanding the value of the standards , in light of the importance of maximizing the efficiency of dynamic lubrication , the surface finish of the inner surface of the cup , and particularly of the uhmwpe cup , should not be uniform over the entire surface . the unloaded , theoretical surface contact over the arc 120 , fig2 b , under load will spread out to a wider band towards the pole 109 by a partial width of the arc 123 and towards the equator by a partial width of the arc 122 . this broader band of contact represents the envelope for major loading vectors across the joint , not only a static , single position / load . all of this surface should be machined to a high degree of smoothness , e . g . n5 . the rest of the cup surface , in order to maximize dynamic resistance to fluid flow out from the pressurized pool 130 , should have a higher degree of roughness , preferably at about grade n12 , corresponding to ra of 50 micrometers . as suggested on fig2 b , the preferred texture is that of grooves running at 90 deg to the direction of flow , which naturally would be the result of machining the cup by turning its inner surface , as is most commonly done . fig3 shows an alternative way of providing similar articulating conditions : the cup 201 is now spherical and the head 202 is aspherical , congruent with the cup along the arc 220 of the surface contact 221 , leaving again a volume 230 enclosed by the surfaces 203 and 206 of the cup and the head , respectively . the radius of curvature 207 of the head 202 for polar angles greater than the angle 213 and lesser than the angle 214 is equal to the radius of curvature 204 of the cup &# 39 ; s inner surface 203 . for polar angles lesser than 213 , the radius of curvature of the head surface first is smaller than 204 to open up a gap 211 . closer to the pole 209 , the radius of curvature is larger to avoid indenting the surface of the head at its polar region . for polar angles larger than 214 the radius of curvature of the head surface is also lesser than 207 , to avoid jamming the head in the cup at equatorial region . the diameter of the head 241 at its equator is smaller than the diameter 240 of the opening of the cup . this type of heads will be referred to as fovea type . fovea also means a pit or cuplike depression and is used to describe the recessed or flattened area of the femoral head where the round ligament inserts . ideally , the changes of the radius of curvature of the surface 206 below and above the angles 213 and 214 , respectively , should be continuous , but for practical reasons one or two steps will suffice . it is highly preferable , necessary in fact , that the transitions are tangential , i . e . that the contour of 206 is smooth . which one of the two solutions is more appropriate depends on the materials and manufacturing technologies employed . for example , if uhmwpe is used for the cup with either a metal or a ceramic head , making the cup aspherical is much easier than making the heads aspherical . this especially so if the cup is compression molded . for metal - metal , and probably for ceramic - ceramic combinations it may well be easier to produce a fovea head than a fossa cup . to get the maximum benefit of either geometry , the axis 110 , respectively 210 , should be directed into the window of functional , physiological force vectors acting on the articulation . fig4 is a schematic representation of the total hip prosthesis , with the cup 101 inserted into pelvic bone 501 , and the head 102 affixed to the femoral stem 502 , which in turn is inserted into the femur 503 . the axis of the femoral neck is 504 . the axis 110 of the fossa geometry of the cup 101 is offset from the main axis 509 of the cup , by an angle 510 . if the angle 510 is approx . 25 degrees , and the cup is inserted at an angle of lateral opening 511 of approx . 45 deg , the arc of contact 120 ( corresponding to the band of contact 121 , fig2 a ) centered on the axis 110 , will meet the requirement to encompass most of the physiological load vectors 512 transmitted from the head to the cup . the cup should also be inserted with an angle of so - called anteversion ( pointing forward ) of about 10 to 15 degrees . such a cup must be clearly labeled for the surgeon to be able to orient it properly at insertion . fig5 shows the preferred position of the fovea depression on the total prosthesis head 202 with respect to the femoral neck , of the femoral stem 502 , as indicated by the angle 510 between the axis 210 of the fovea and the neck axis 504 . the angle 510 should again be approx . 25 degrees . if modular design is used , there must also be a clear indication for the surgeon on which aspect of the head is to be placed superiorly . fig6 shows a perspective view of the contact area 121 , respectively 221 , of the articulation of either fossa or fovea type under loading . due to elasticity of the components , the area of contact will spread out from the original annular surface contact , fig6 a , to a wider area of surface contact fig6 b . the width 53 of the contact area 121 ( 221 ) is load dependent . when the load is high , the fluid from the pool 130 is pushed out , as shown by arrow 51 , through the gap over the area 121 ( 221 ), across , now , the longer distance 53 , fig5 b . as the load is reduced , the elastic recoil of the components will tend to increase the volume of the pool 130 and thus suck the fluid back in , as shown by the arrow 52 , fig5 a . in this phase , the contact area is narrowed down , i . e . 53 is reduced , and thus there is less resistance for the re - filling of the pool 130 . this is important , since the maximum underpressure which can pull the fluid back in is 1 bar , while much higher pressures can be induced during the draining , high load , phase . in case of uhmwpe cup , this non - linearity can be enhanced by provision of a gentle undulation in the shape of the cup over the contact area , i . e . by providing an interrupted area contact 54 , fig6 c . under loading , the gaps in the surface contact will close , increasing the resistance to flow out ; as the load is reduced the gaps will open allowing for reimbibing of the fluid into the pool 130 . if uhmwpe is used for one of the components , articulations as those described above , can demonstrate relevant time dependent behavior ; i . e . deformation of the solid components can only be calculated precisely by solving for the fluid flow as well . while more demanding from the engineering point of view , taking all of these factors into consideration may ultimately reduce the level of wear to an absolutely negligible level . fig7 shows saggital and frontal sectional views of a knee condyle prosthesis with the femoral component 402 making a surface contact 420 against the tibial plateau 401 , produced from uhmwpe , of the fossa type . the area of the tibial component 401 , which normally would be exposed to highest stresses , is now slightly recessed defining the pool 430 , providing for the above - explained means of load distribution and dynamic lubrication . the femoral component being shaped as a torus , the two sectional views differ only in the respective curvatures of the articulating components . fig8 shows a spinal disk prosthesis according to the invention . the central , lens - shaped body 302 , made from either uhmwpe , or a hard material such as ceramic , or metal , articulates on both of its faces against concave components 300 and 301 , along surfaces 320 , so as to leave gap volumes 310 filled with fluid , providing again for the above - explained means of load distribution and dynamic lubrication . there are many ways to approach the practical problem of designing more or less optimized shapes of different articulations . simple analysis , based on known formulas for herzian stresses , can be used to guide the design aiming to minimize the contact stresses . for a ball - and - socket joint , assuming no friction at the gliding surfaces , the result is straightforward , suggesting the optimum solution with the contact area centered at 45 degrees . introducing friction , shifts the optimum angle downwards . and since the invention changes the mode of lubrication , hence the coefficient of friction , the problem of exactly solving for an optimum quickly becomes much more complex . finite element method can be used to solve for solid stresses , and the optimum design can be sought by either parametric approach , or by min - max methods . ultimately , fluid flow analysis could be incorporated into these models as well . to minimize the wear in the actual use , however , another , very serious escalation of complexity would have to be brought in — the mechanism of wear and the presumed regimen of use . an alternative approach would be to start with analysis of the existing articulations , and then , by iteration , remove some material from a chosen side of the articulation , at the areas of maximum stress , aiming to minimize the peaks . for reduction of wear , a cost function should be created penalizing the locations prone to produce more wear in presumed physiological use , i . e . those which experience high relative motion when under load . the inventor has taken a pragmatic approach of using the ready formulas for herzian stress to guide design of the uhmwpe cup for a total hip prosthesis and then performing the actual wear testing in hip simulators against a standard metal head to verify the reduction of wear . there are now internationally accepted standards for wear testing ( iso 14242 - 1 : 2002 - 03 ), which allow for relatively safe comparisons between different laboratories and different test runs . whatever the design process , experimental results are ultimately needed to prove the value of inventions in this area . the uhmwpe cup tested was exposed to conventional gamma sterilization , yet the wear rate ( 3 . 5 mg / mio cycles ) against a 28 mm metal head was at the level of that of highly cross - linked uhmwpe ( 4 mg / mio cycles ). the wear of standard uhmwpe cups has been measured under similar conditions in the range of 35 to 50 mg / mio cycles . this superior outcome of the testing is due to probably all three important aspects of the invention : reduction of stresses in uhmwpe ; improved dynamic lubrication at the contact areas ; and improved stability of the joint under varying load vectors . dispersion of the wear rates was also extremely low compared to conventional designs , suggesting reduced risk in clinical use due to unavoidable specimen variability . regarding terminology used in the disclosure , the crucial concept is that of congruency of the articulating pair over a defined area of contact . the theoretical concept of congruency is simple and unambiguous , but in practice it is a subject to practical limitations of achieving it . the production tolerances set a limitation on what can be achieved in terms of matching the shapes of the two components . as the production methods and the tolerances change rather rapidly , setting the limits of what congruency means for the years of the patent life is not possible . therefore , when the term congruency is used , and unambiguously related to what is meant by equal radii , it defines the intent and the outcome of the intent as materialized in the product , produced by the state of the art technology . the intent to produce congruent components routinely covers the anticipated changes of the dimensions and the shapes due to complete production and ultimate conditions of use , such as influence of sterilization ( e . g ., gamma sterilization results in the shrinkage of uhmwpe ) mounting of the components ( e . g . use of press fit into a metal backing ) and temperature during use in the body . those skilled in art at any particular time period and technology level know what meaning to attach to congruent surfaces — this knowledge is implied in the use of the term in this text . when faced with a possible issue of infringement one could envision a functional test whereby the two components would be brought into articulation and loaded with a tare - load to estimate the extent of contact . tare - load , however , is not of a fixed value , but rater a function of the particular joint in question and would be determined for the particular articulation by using a conventional design as a control . for example , a conventionally designed metal - uhmwpe pair under a load of 100 n ( approx . 5 % of average peak load in walking ) would show a circular contact area at the pole , whereas the pair designed to the specifications presented in this disclosure would show a ring of contact centered at approx . 45 degrees and about 30 deg wide .
the invention reduces wear in total joint articulations by modifications of the shape of either component of the kinematic pair , so as to result in an annular surface contact between the two components . fluid trapped between the two components within the inner contour of the annular contact area is pressurized under load due to elastic deformation of the components and exuded out through inter - articular gap over the surface of contact , aiding in lubrication and reducing the wear . reduced to practice for a total hip joint with uhmwpe - metal pair , the wear rate tested in a hip joint simulator up to five million cycles was reduced by factor seven to fifteen compared to conventionally shaped components .