the prosthesis 10 includes a socket member or assembly 11 that is only schematically illustrated because its details do not form a part of the present invention . suffice it to say , the socket member 11 can be formed in accordance with known practices in the art . the femoral member 12 , which provides the ball 14 of the hip joint prosthesis is secured to the femur 15 by cement 16 filling the medullary cavity 18 and fixing a femoral fixation stem 20 in place within the medullary cavity . a collar 21 defines the upper end of the stem 20 and resides at the upper end of the femur and its medullary cavity to locate the stem 20 at the desired depth in the cement - filled cavity . a neck section 22 of the femoral member 12 extends superiorally and medially from the collar to locate the ball 14 relative to the femur 15 and secure the ball to the stem 20 . at the tip 24 or distal end portion of the stem 20 is a surface 25 that slopes downwardly and medially and helps guide the tip 24 towards the medial side of the cavity 18 as the stem 20 is inserted through the still - to - set cement 16 . the tendency , then , is for the stem 20 to locate , during insertion , closer to the medial side of the cavity , as desired . the cross - section of the stem 20 at all locations along its length between the section lines 2 -- 2 and 3 -- 3 ( namely , the portion of the stem that is referred to herein as the intermediate portion ) is circular about a major part of its periphery 27 and truncated by a flat 28 . the stem becomes gradually thinner moving down from section 3 -- 3 . just above the location of the cross - section 3 -- 3 the stem becomes essentially round , except for anterior and posterior flats 29 . the flats 29 extend to a greater or lesser extent along the length of the stem and enhance fixation against rotation about the femoral axis . in fig1 the neutral axis of bending of the composite structure ( the intact bone , hardened cement , and stem ) has been drawn in as the line n ; the axis n is located near the central axis x of the composite structure . for purposes of the next section of this specification , several parameters of the design are shown in fig3 : the radius of r 0 of the femur at a given cross - section ; radius r m of the medullary cavity ; the radius r p of the arcuate part of the stem cross - section ; the offset distance h from the flat 28 to the center of the circle that forms the arcuate portion of the periphery of the cross - section . the cross - sectional parameters to be determined for a given bone geometry are r p and h . the objective in fashioning the best prosthesis is to choose , for each bone diameter , the values of r p and h that best satisfy the three design criteria , i . e ., minimum stem stress in the intact composite structure , minimum stem stress absent proximal support , and minimum decrease in bone stress when the composite structure is intact . stresses due to a bending moment m applied to the composite structure were computed for the case where the circular portion 27 of the prosthesis stem cross - section and the inner and outer surfaces of the bone are concentric . the design stresses were determined using composite beam theory as follows . for the stem as part of the composite , the stress in the prosthesis as part of the composite , σ p . sbsb . composite is : ## equ1 ## for the stem alone , the stress in the prosthesis , as it would be supporting the load alone , σ p . sbsb . alone , is : ## equ2 ## for the bone as part of the composite : ## equ3 ## and for bone alone : ## equ4 ## the location of the neutral axis of bending of the composite with respect to the centroid of the bone is determined by : ## equ5 ## i b , i c , i p are the area moments of inertia of the bone , cement , and prosthesis , respectively ; e b , e c , e p are the moduli of elasticity of the bone , cement , and prosthesis , respectively ; a b , a c , a p are the respective areas of the bone , cement , and prosthesis ; y p and y c are the location of centroids of the prosthesis and cement with respect to the centroid of the bone ; and t b and t p are the distances from the neutral axis to the point of maximum stress in the bone and prosthesis , respectively . the three - criteria design problem can be reformulated as a problem with a single objective and two constraints as follows : ## equ6 ## where : s p . sbsb . f is the fatigue strength of the prosthesis ; and r min is the minimum allowable ratio of bone stress as part of the composite to bone stress when it alone carries the load . the value of s p . sbsb . f depends upon the material used and the value of r min can be chosen based upon clinical experience and judgment . the design criteria stresses , σ p . sbsb . composite , σ p . sbsb . alone , σ b . sbsb . composite , and σ b . sbsb . alone , were computed for a wide range of prosthesis and bone geometries . the procedure for choosing optimum design parameters , r p and h , is demonstrated here for bone geometry that represents a typical large femur . the resulting composite structure is described as follows . bone : e b = 17 . 2 × 10 3 mn / m 2 ( 2 . 5 × 10 6 psi ) cement : e c = 3 . 45 × 10 3 mn / m 2 ( 0 . 5 × 10 6 psi ) ti 6al 4v stem : e p = 117 × 10 3 mn / m 2 ( 17 × 10 6 psi ) co cr mo stem : e p = 248 × 10 3 mn / m 2 ( 36 × 10 6 psi ) yield strength of ti6al 4v stem : s y = 800 mn / m 2 ( 115 , 000 psi ) estimated conservatively to be 0 . 50 sy : s p . sbsb . f = 400 mn / m 2 ( 57 , 600 psi ). in addition to the above , the minimum allowable ratio , ## equ7 ## must be chosen . r values for existing designs were determined using the procedures outlined . it was found that these values consistently fell in the range 0 . 7 to 0 . 8 . although the bone is loaded less , no particular long - term problems have been observed to date . consequently , these stress levels are assumed to be safe , and the minimum value of r was chosen to be : in order to satisfy the second design criterion , a large stem is required . the maximum size must allow a cement layer of sufficient thickness for consistent implantation and good load transfer from the stem to the bone . structural analyses suggest that cement thickness should be minimized ; therefore limitations are based on surgical considerations . cement thickness will be adequate if the prosthesis radius r p is no greater than approximately 80 % of the cavity radius r m . therefore , the following values of r p were used in the design curves presented here . the choice of stem material was between ti 6al 4v ( curve t in fig4 and 5 ) and co cr mo ( curve c in fig4 and 5 ). bone stresses , σ b . sbsb . composite , are always greater ( r larger in fig4 a and 5a ) for ti 6al 4v stems . prosthesis stem stresses , σ p . sbsb . composite , are always less for the titanium alloy stems than for the cobalt chrome stems . see fig4 c and 5c . therefore , the first and third of the foregoing design criteria are satisfied best by ti 6al 4v stems . material choice does not affect satisfaction of the second design criterion , since σ p . sbsb . alone is independent of material . see fig4 b and 5b . it is convenient to determine h as a fraction of r p . therefore , fig2 and 3 have been plotted as functions of for h = 0 , the cross - sectional shape of the stem is semicircle ; for h = 1 a circle . is only satisfied for values of h greater than approximately 0 . 5 ( fig4 b and 5b ). the design constraint that ## equ8 ## is satisfied for all values of h for r p = 9 . 94 mm ( r p = 0 . 7 r m , fig4 a ) and for values of h less than approximately 0 . 7 for r p = 11 . 4 mm ( r p = 0 . 8 r m , fig5 a ). therefore , all design criteria are satisfied for values of h between 0 . 3 and 0 . 7 . over the range σ p . sbsb . alone decreases about 20 percent ( fig4 b and 5b ), and σ p . sbsb . composite increases about 20 percent ( fig4 c ) or 13 percent ( fig5 c ). since stem stresses , σ p . sbsb . composite , are well below the fatigue strength of ti 6al 4v , the greatest benefit is obtained by taking larger values of h in the acceptable range . based on this , a value of h = 0 . 65 was chosen . although particular characteristics of a preferred embodiment are described above for a typical femur , other hip joint prostheses with stems conforming to both the spirit and the scope of the invention will be readily apparent to those skilled in the art . accordingly , the foregoing description of a preferred embodiment should not be understood to limit the scope of the invention , which scope is set forth in the appended claims .
a total hip joint prosthesis has a ball , replacing the ball of the hip joint ball and socket , affixed to the femur by a stem . stem stress is reduced by providing a rounded cross - section of the stem truncated along the lateral side in the critical section subject to greatest cyclic loading . the stem is of controlled low flexibility so that when the bone cement and stem composite structure is in place , the bone is subject to a maximum percent of normal stress from bending moments . by virtue of the truncated shape and its size relative to the bone cavity , stress in the stem is minimized when the stem alone carries the load .