Mechanical compatibility of noncemented hip prostheses with the human femur

The Journal of Arthroplasty Vol. 8 No. 1 1993

Mechanical Compatibility of N o n c e m e n t e d Hip Prostheses With t h e H u m a n Femur A. R. Dujovne, Ing, MSc,* J. D. Bobyn, PhD,* J. J. Krygier, CET,* J. E. M i l l e r , MD,-[-:[: a n d C. E. B r o o k s , MD-[-

Abstract: It is generally accepted that more flexible implants are needed to reduce stress shielding and postoperative thigh pain. However, there is no detailed information on the stiffness of currently used implants relative to the human femur. The purpose of this study was to determine the stiffness characteristics (bending, torsional, and axial) of human femora relative to commercially available prostheses as a first step in assessing the mechanical compatibility of the implants. This was achieved by computerized torn'ography scanning of a collection of human femora from proximal to distal at 10 mm intervals, digitizing the cross-sectional contours, and calculating the stiffness characteristics of each section using standard beam theory. The results show that significant stiffness mismatches exist, especially for larger stem sizes and for stems fabricated from cobalt-chrome alloy. Interestingly, certain implant stiffness values are lower than those of the femur for stems up to 15 mm in diameter, substantially so if the implant is made from titanium alloy and incorporates design features that reduce area and moments of inertia. The data suggest that only larger implant sizes need to be adjusted for increased flexibility compared with current stands. K e y words: femur, stiffness, stem, mechanical properties, hip prosthesis, arthroplasw.

The clinical success of porous-coated n o n cemented hip stems depends partly on good fit and fill of the implant within host bone. This has b e e n s h o w n to increase the likelihood of bone ingrowth and provide m o r e even stress distribution. To achieve tit and fill, n o n c e m e n t e d hip stems are typically larger than cemented stems. From a mechanical perspective, increased stem size results in increased stiffness and this has raised concerns regarding the pot e n t i a l for greater stress shielding. 2~ Resorptive femoral b o n e remodeling c o m m o n l y occurs after n o n c e m e n t e d total hip arthroplasW (THA) and is reported to increase in severity with larger and stiffer From the *OrthopaedicResearch Laboratory and tDepartment of Orthopaedic Surgery, Afontreal General ttospitaL McGill University, Montreal Canada.

:I:Deceased. Supported by the Medical Research Council of Canada. Reprint requests: A. R. Dujovne, Ing, MSc, Bioengineer Coordinator, Jo Miller Orthopaedic Research Laboratory, Montreal General Hospital Research Institute, Room L5I 409, Livingston Hall, 1650 Cedar Avenue, Montreal, Quebec, H3G IA4 Canada.

A n o t h e r clinical p r o b l e m often associated with n o n c e m e n t e d hip prostheses is thigh pain, with incidences of up to 30% being reported for a variety of porous-coated implants. 14 It has been suggested that distal m o d u l u s m i s m a t c h between the implant and f e m u r is one of the causes of end-of-stem pain. 4 It is widely believed that m o r e flexible, or isoelastic, implants are needed to reduce stress shielding and postoperative thigh pain. 304A3"~4"2~ There h a v e been several attempts to design hip stems that are more mechanically compatible with the h u m a n femur, either by changing the material properties or including design features to reduce cross-sectional areas and m o m e n t s of inertia (structural p a r a m eters). 6A2,I7AS"24.26 However, past efforts to design more mechanically compatible stems h a v e b e e n quite arbitrary because they have not accounted for the actual stiffness characteristics of the h u m a n femur. F e m u r stiffness is the key p a r a m e t e r that m u s t be k n o w n prior to judicious design or assessment of s t e m s . 2"3"8"9"14"19"20"23"26

8 -The Journal of Arthroplasty Vol. 8 No. 1 February 1993

implant stiffness. Yet, no detailed information exists on the relative stiffnesses of the human femur and noncemented hip prostheses. The purpose of this study was to determine the stiffness characteristics of the human femur. These were compared with the stiffness characteristics Of two noncemented hip prostheses to provide an indication of their mechanical compatibility.

Materials and Methods Cadaveric Femora and Noncemented Implants A collection of 65 normal embalmed human femora, consisting of 24 pairs and 17 singles, were analyzed. The age range of the subjects was 60-89 years (25 men, 16 women). Two noncemented femoral hip prostheses were analyzed: the AML (DePuy, Warsaw, IN) and the HG MultiLock (Zimmer, Warsaw, IN). These were chosen as representativ~ examples of straight-stem designs, manufactured from different alloys. The AML prosthesis is a cob.alt-chrome alloy implant (Young's modulus = 210 GPa), with a sintered porous coating (structural modulus = 105 GPa) on the proximal 40% of its length, and a solid cylindrical stem. The MuhiLock prosthesis is machined from Ti6A1-4V alloy (Young's modulus = 117 GPa), and possesses chemically pure titanium fiber-metal coating (structural modulus = 39 GPa) that is diffusionbonded to the proximal stem. The distal cylindrical portion of the MultiLock stem is fluted to reduce stiffness; the flutes increase in depth with increasing stem size.

Determination of Cross-sectional Geometry A method based on simple engineering beam theory was used to calculate the stiffness parameters. This required knowledge of the geometry of the serial cross-sections of the femora and implants, as well as knowledge of the moduli of the various constituent materials. The computerized tomography (CT) scanning technique, with a beam width of 1 mm, was used to obtain cross-sectional images of the femora. A plexiglass box was custom built for positioning the specimens under water. The water bath was required by the scanning technique to avoid scatter that obscures the definition of the cortical contours. Each specimen was mounted so that the geometrical longitudinal axis of the femoral shaft, defined as the line between the subtrochanteric center and the mid-point of the

.z";'-.,/ ~ "

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Fig. 1. Custom-built plexiglass box to obtain CT sections perpendicular to the geometric longitudinal (femoral shaft) axis of the femur. The position of each specimen is corrected by a distal wedge at an angle with respect to the femoral shaft axis equal to the transcondylar angle plus the hip center-femoral shaft angle.

trans-epicondylar segment, lay parallel to the bottom and lateral sides of the box (Fig. 1).27 An orthogonal coordinate system was defined for each specimen with the x axis on the lateromedio direction, the y axis on the posteroanterior direction, and the z axis on the proximal to distal direction, coincident with the longitudinal axis of the femoral shaft (Fig. 2). Seventeen serial cross-sections (perpendicular to the longitudinal axis) were obtained of each femur by CT scanning at 10 mm intervals starting at the femoral neck (Fig. 3). The first section (considered level 0) was defined as the resection level, 20 m m above the lesser trochanter. The geometry of each CT section was manually digitized and processed using computer software to ascertain bone geometric factors: areas and moments of inertia (rectangular and polar). Bones were grouped in 1.5 mm intervals accordTng to the mediolateral diameter of the intramedullary canal at the isthmus, as determined from the CT sections. Based on data from the literature, values for the moduli of elasticity (compression) and rigidity (shear) of n ~ m a l bones were assigned to cortical and cancellous bone areas, assuming bone as an isotropic material (Table 1). x,5,~o,~1,~ Serial implant cross-sections at 10 mm intervals were obtained from design blue prints starting at the level of the collar (Fig. 4). Values for the elastic and shear moduli of the alloys and the structural moduli

Mechanical Compatibility of Noncemented Hip Prostheses

9

Dujovne et al.

9

Table 1. Materials Moduli

Material Cobalt-chrome solid Ti 6AI 4V solid Cobalt-chrome beads Ti fiber metal Conical bone Cancellous bone

Z (+)

X (+)

Elastic Modulus (GPa)

Shear Modulus (GPa)

210 117 105 39 12 0.31

8l 44 40.5 15 4.5 0.12

y of the porous coatings were obtained from published data (Table 1).22

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Stiffness Calculations The theoretical m e t h o d for calculating the stiffness of a cross-section is based on the simple formula:

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Fig. 2. A global orthogonal coordinate system was defined for each specimen: the x axis on the lateromedio direction, the y axis. on the posteroanterior direction, and tile x axis on the proximal to distal direction, coincident with the longitudinal axis of the femoral shaft. For each cross-section, instantaneous systems--parallel to the global syst e m - w e r e defined. The moments of inertia of each section were calculated with respect to the corresponding instantaneous system.

Stiffness = Geometric Factor • Material Modulus For axial stiffness, the geometric factor was the cross-sectional area (A) and the modulus was the modulus of elasticity (E). For bending stiffness in the lateromedio direction (in the frontal plane) the geometric factor was the rectangular m o m e n t of inertia about the y axis (Iy), and the material m o d u l u s was the modulus of elasticity. Bending stiffness in the anteroposterior direction (out of the frontal plane) was the product of the rectangular m o m e n t of inertia about the x axis (Ix), and the modulus of elasticity. Finally, for torsional stiffness the geometric factor was the polar m o m e n t of inertia (J) and the modulus was the shear modulus (G) (Appendix) 9 Beam theories for composite materials were used to account for the contribution of the various material constituents of each cross-section (cortical and cancellous in bone sections, and solid and porous coating in implant sections). Calculations were per- , formed by computer software (Beams Sections, Kern International, Inc., Duxbury, MA) on a MS-DOS based system. For femur sections, only two material properties were assigned to corresponding regions of cortical and cancellous bone. The hydraulic stiffening effect of the bone m a r r o w was neglected, as was the variation in modulus of elasticity at different locations in the proximal femur. As a condition of the applied theory, the ratio of modulus of elasticity to modulus of rigidO.y was the same for all materials in the sections (E = 2.6 x G). This assumption is generally true for engineering materials but not necessarily true for biological anisotropic materials 9 For impl~int sections, both solid base metal and porous coating were accounted for in the calculations. Femoral and implant stiffness data were compared

10 _ The Journal of Arthroplasty Vol. 8 No. 1 February 1993

Fig. 3. Computerized tomography sections of the human femora obtained at 10 rnm intervals were digitized and the geometric parameters calculated.

for each stem size at corresponding intervals and matched intramedullary canal size. A discrete matching criterion b e t w e e n f e m u r and implant was chosen assuming some reaming of endosteal cortical b o n e to achieve a press fit. Since the AML series increases from 10.5 m m to 19.5 rnm in 1.5 m m steps, a n d the MultiLock series ranges from 11 m m to 18 m m in 1 m m steps, for each size group the MultiLock stem size was chosen with the same stem diameter as the AML or the next size up (Table 2). For example, all femora with a canal diameter b e t w e e n 12 m m and 13 m m inclusive (which belong to group 3 in Table 2), were matched with a 13.5 m m AML prosthesis and a 14 m m MultiLock prosthesis. It is important to note that in a clinical situation, the b o n e - i m p l a n t stiffness relationships w o u l d be slightly modified by

the removal of b o n e to create the implant site. H o w ever, this modification is negligible because the b o n e removed proximally is low stiffness cancellous bone, and the cortical b o n e r e a m e d distally has the least influence o n the overall stiffness due to its position with ~respect to the neutral axis of each section.

Results Femora The 65 femora presented a frequency distribution of the canal size similar to the distribution of sizes observed on a normal population of patients receiving n 0 n c e m e n t e d TttAs. Thirty-six specimens (55%) were within the canal diameter range of 1 2 - 1 5 m m ,

Mechanical Compatibility of Noncemented Hip Prostheses

9

Dujovne et al.

11

I -

-

-

X (H-L)

X (H-L)

,11

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Y (A-P)

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Fig. 4. Cross-sections of the implants were obtained from original blue prints at matching bone levels. (A) The AML hip prosthesis, a cobalt-chrome alloy, proximal oval cross-section, proximally coated with beads, and solid distal stem. (B) The HG MultiLock hip prosthesis, a Ti-6AI-4V alloy, proximal trapezoidal cross-section, and proximally coated with fiber metal and distal flutes.

and 56 specimens (86%) were within the range of 10.5-16.5 mm. Comparing average values for each femur size, the axial stiffness was found to be quite constant along the femur length with a m a x i m u m 1.5-fold variation over the entire size range (Fig. 5A). No obvious relationship between intramedullary canal size and axial stiffness was observed. Femora with larger canals did

Table 2. Femoral Canal Size Distribution and Stems Matching Criterion

Group GI G2 G3 G4 G5 G6

M-L Diameter (ram) 9 10.5 12 13.5 15 16,5

--< dp < < ~b < ~ ~b < --< d~ < < ~b < -< d~ <

10.5 12 13.5 15 16.5 18

No. of Specimens

HG MultiLock (mm)

AML (mm)

3 10 16 20 10 6

11 12 14 15 17 18

10.5 12 13.5 15 16.5 18

not necessarily have more cortical bone than femora with smaller canals. Some of the largest axial stiffness values were obtained from femora with 1 0 - 1 2 m m canals. In contrast, bending (within and out of the frontal plane) and torsional stiffnesses increased exponentially with increasing proximal cross-section (Fig. 5B-D). There was a m a x i m u m 2-fold variation in the distal region and less than a 1.5-fold variation in the most proximal region for the entire femur size range. In the metaphysis, the femora were about two times stiffer in bending within the frontal plane compared to bending out of the frontal plane. In the diaphysis, bending stiffness was approximately equal in each direct'ion.

Implants For. both stem designs, axial, bending, and torsional stiffness increased exponentially, proximally with each stem, and with increasing stem size (Figs.

12

The Journal of Arthroplasty Vol. 8 No. 1 February 1993

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Mechanical Compatibility of Noncemented Hip Prostheses

9

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6, 7). As for the femora, the relationships between stiffness and stem size or cross-sectional level were also nonlinear. There was a 2-4-fold variation in axial stiffness and a 3-10-fold variation in bending and torsional stiffnesses over the entire stem size range. These variations w,ere more accentuated distally than proximally, and were larger for the AML than for the MultiLock design. In the proximal region, both stems were stiffer in bending in the frontal plane than in bending out of the frontal plane by as much as 5 and 10 times for the MultiLock and tlle AML prostheses, respectively. In the distal region, because of the geometrical symmetry that existed in both designs, bending stiffness in both directions was equal. When the overall stiffness data for the two implants were correlated, the MultiLock stem was about 2-3 times less stiff than the AML prosthesis, for all corresponding stem sizes. The majority of this difference was derived from the simple 2-fold difference in the elastic modulus between cobalt-chrome and titanium alloys. Additional difference was gained for the larger stem sizes because of the distal flutes on the MultiLock prosthesis. Implants versus Femora To illustrate the mechanical compatibility of the implants with the femora, the data for axial and bending stiffness of the 12 nun, 15 mm, and 18 nun sizes are presented. Only the data for bending stiffness within the frontal plane are illustrated because they were representative of the implant-femur relationships for torsional stiffness and bending stiffness out of the frontal plane. The stems were ahvays stiffer axially than the corresponding femur, more proximally than distally, and by as much as 10-30-fold

for all sizes (Figs. 8A, 9A, 10A). For bending, the largest stiffness mismatch between stems and femur was proximally for both stem designs; distally, there were different relationships according to the size group and stem characteristics (Figs. 8B, 9B, 10B). In the distal portion of the small 12 mm diameter AML prosthesis (Fig. 8B), maximum values for bending and torsional stiffness were up to two times smaller than the average corresponding femur into which they would be implanted. An inverse situation was found proximally where the 12 mm AML implant was up to four times stiffer than the corresponding bone. At 15 mm and larger, the AML stem was increasingly stiffer than the corresponding sized femur along its full length in bending and torsion (Fig. 9B). By contrast, the 15 mm MuhiLock prosthesis was less stiff in bending than the femur along most of its length and was three times stiffer proximally. The stiffness characteristics ofthe 18 mm MultiLock prosthesis were equal to those of the corresponding femur in the most distal region and w,Sre approximately five times stiffer proximally (Fig.

lOB). Discussion There has been a long-standing recognition of the fact that rigid metallic implants can deprive bone of physiologic stresses and cause resorptive bone remodeling. With femoral hip prostheses, this problem has become accentuated with the use of larger and stiffer noncemented stems. The solution to this problem has often been discussed in terms of more flexible implants, although no quantitative definition of flexibility has been proposed. Developmental approaches towards increased stem flexibility include conven-

14

The Journal of Arthroplasty Vol. 8 No. 1 February 1993 8O

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Mechanical C o m p a t i b i l i t y of N o n c e m e n t e d Hip Prostheses

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tional metal implants with flutes or slots, and more complicated designs such as carbon composites or polymer-coated implantL Surprisingly, these approaches have largely ignored the stiffness characteristics of the human femur Without femoral stiffness data, adjustments in stem flexibility are made without the requisite physiologic basis of comparison. This study was conducted to generate fundamental data on the stiffness characteristics of the human femur. The theoretical method of calculating the stiffness of cross-sections was adopted over the more experimental methods of mechanical testing because of simplicity and the need to evaluate a relatively large number of femora. The theoretical approach is dependent on two major factors: determination of cross-sectional geometry and assignment of material properties to the appropriate fractions of cortical and cancellous bone. The geometric factor was determined by manual digitization of the periosteal and endosteal cortical envelope of transverse CT sections. This procedure was found to be reproducible for any given section within 10%. A larger source of error existed for assigning the appropriate moduli to the area fractions of cortical and cancellous bone. A wide range of elastic and shear moduli for both materials have been published and the final stiffness parameters directly depend on the assigned property values. The dominant factor in this consideration is the choice of property values for cortical bone since it so much stiffer than cancellous bone and is located furthest from the femoral neutral axis. A cortical bone elastic modulus of 12 GPa was selected because it represents approximately the middle range of published values and, more importantly, is approximately the value found to exist for femoral cortical bone..The cancellous bone elastic modulus

of 0.31 GPa was chosen from data on h u m a n femoral cancellous bone. In fact, because of the much lower modulus of cancellous bone and its location relative to the neutral axis, the assigned value was not very critical. A cancellous bone modulus an order 0f magnitude higher or lower than 0.31 GPa did not significantly alter the cross-sectional stiffness calculations. While the method of determining femoral stiffness parameters was associated with sources of error and was not correlated with data from actual mechanical testing of femoral stiffness, it was based on sound engineering principles of beam theory and provided a reasonable estimate of bone properties. The important information to glean or rely on from this study is not the small differences in absolute stiffness values from one femur to another, but the overall pattern of femoral stiffness and the general range of stiffness values for the femora with different intramedullary canal sizes. The collection of cadaveric femora was derived from an elderly population with an average age of 73.6 years. This is older than and thus not representative of the population that would generally be selected for noncemented THA. Cortical and cancellous bone from elderly patients would be expected to be less dense and thus possess lower mechanical properties than bone from younger patients. As discussed above, however, the method of calculating stiffness from cross-sections depends on assigning bone moduli to a bone geometry. While the bone geometries were generated from femora of an elderly population, the bone moduli were more representative of a patient population in the 5th decade, thus compensating somewhat for the age discrepancy. The 65 femora that were analyzed were derived from 24 matched pairs and 17 single bones. The

16- The Journal of Arthroplasty Vol. 8 No. 1 February 1993 160 --I--~MI.l~ ff~11

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Mechanical Compatibility of Noncemented Hip Prostheses

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-18 The Journal of Arthroplasty Vol. 8 No. 1 February 1993

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B

study protocol was initially designed to average the data from each matched pair of femora and consider them as a single specimen. However, u p o n measurement of the intramedullary canal diameters of the femora and calculation of the stiffness parameters, 7 of the 17 pairs possessed canal diameters that differed by one increment and stiffness parameters that differed by as m u c h as 40% for some cross-sections. It was thus decided to treat each femur as an individual specimen and average the data accordingly. Overall, the n u m b e r of specimens in each canal size was sufficient to provide an impression of the various stiffness characteristics. Statistical comparisons of the averaged stiffness data for the different canal sizes was not performed, primarily because of the inherent sources of error in the stiffness calculations as described above, but also in order to simplify the very large volume of data generated. Should it be neces-

sary, for some future study, to determine w h e t h e r statistically significant differences in stiffness parameters exist from one femur size to another, it would probably be necessary to increase the n u m b e r of specimens studied. It was interesting to note that there was no obvious c o , e l a t i o n between canal size and femoral stiffness. The stiffness value of any given cross-section strongly depends on the a m o u n t of cortical bone, and femora with small canals often possess relatively thick cortices. Accordingly, some of the highest stiffness values were derived from femora with 10 n u n or 11 m m canal diameters. Of significant note was the relatively close grouping of all femoral stiffness parame t e r s - a x i a l , bending, and torsional. The greatest variation between femora, regardless of canal diameter, was only about 2-fold. This was quite surprising given the wide range of shapes and sizes that existed

Mechanical Compatibility of Noncemented Hip Prostheses

9

Dujovne et al.

19

O.8

E o)

,,+, 0.6 E. I=

28 x 0.4

o

--,--c

~

-2(X)

c. o

~

-

-150

o

~

~

__

-100

-50

-50

0

LEVF-.LBELOWCOLLAR[ram] A 1.5

12

E Z x

1C

m

t 0.5

--"

-

-~, A

lOx

A

2.5 x 4

2 0

,

-200

-150

k_j~

Fig. 10. Stiffness relationship curves between human femora and the 18 man stems. (A) Axial stiffness (A • E). (B) Bending stiffness in the lateromedio direction (Iy • E).

0

=

-100

1_

-50

LEVELBELOWCOLLAR[mm ] B

in our collection of femora. Also of interest was the generally constant axial stiffness of the femora over the entire length that would be occupied by a prosthesis. In bending and torsion, the stiffness values increased exponentially with increasing proximal location. This is a function of the power relationships that govern the rectangular and polar moments of inertia and, again, of the strong influence of the peripheral distribution of the conical wall. These power relationships mean that slight changes in the geometry of the section can cause relatively large changes in femur stiffness. The CT sections revealed that cortical thickness tended to be thinner anteriorly and posteriorly than medially and laterally, in agreement with prior studies on the effect of age on conical thinning. 23 The stiffness data for the femoral prostheses were more precise because of the increased accuracy of the

cross-sectional geometry and the materials moduli. The cross-sections had well-defined edges and were digitized with a reproducibility of 5%. Bulk material properties for cobalt and titanium-based alloys, as well as the structural properties of the respective porous coatings are well established. On a comparative basis, the differences in stiffness parameters between the AML and the MultiLock prostheses were not surprising. The simple difference in bulk material moduli between cobalt and titanium based alloys accounted for a 2-fold stiffness difference. The MultiLock prosthesis possesses a trapezoidal proximal geometry that is larger for corresponding implant sizes than the oval geometry of the AML prosthesis. The increased stiffness caused by the larger trapezoidal shape was offset by the fact that the fiber-metal coating on the MultiLock prosthesis is thicker and lower in structural stiffness than the beaded coating

20

The Journal of Arthroplasty Vol. 8 No. 1 February 1993

on the AML prosthesis. The net effect of these geometric differences was for the proximal body of the MuhiLock prosthesis to possess lower stiffness parameters compared with the AML prosthesis. In the larger stem sizes, this a m o u n t e d to a total difference of up to 3-fold, including the 2-fold factor from the difference in materials. In the distal cylindrical region of*the stems, the fluted geometry of the MultiLock prosthesis.reduced the cross-sectional area and the moments of inertia compared with the solid stem of the AML prosthesis. The stiffness-reducing effect of the flutes increased as the stem size increased, reaching about 25% for the 18 m m stem. For each prosthesis, the range of bending and torsional stiffness values between the smallest and largest stem diameter was between 3 and 10-fold, a marked contrast from the 2-fold range found between the various sized femora. This is a clear indication of a mismatch in stiffness properties between implants and femora. The stiffness data for the 12 ram, 15 nun, and 18 m m implants and femora that are illustrated in Figures 8, 9, and 10 provided some interesting comparisons. First, the 12 m m diameter implants were less stiff distally than the femora of the corresponding intramedullary canal size. This is not a c o m m o n l y recognized relationship and probably helps explain w h y resorptive bone remodeling with small diameter n o n c e m e n t e d stems is rarely pronounced. 2"8 The 15 m m size represented a transition wherein the AML prosthesis was stiffer than the femur distally and the MultiLock prosthesis was less stiff. With both prostheses, the proximal stiffness was greater than the femur. At 18 mm, the MultiLock prosthesis was almost isoelastic with the femur distally while the AML prosthesis was far stiffer. Once again, the greatest stiffness mismatches occurred proximally, a relationship that may explain the proximal bone resorption that is reported to occur so often after noncemented THA. 2.3,s,9 It should be realized that a stem having equal stiffness as the femur (isoelastic), w h e n implanted, results in a composite structure that is twice as stiff as the nonimplanted femur and can still cause significant stress shielding. The value of this study lies in its ability to provide some fundamental insight into the mechanical relationships between noncemented hip prostheses and the h u m a n femur. Resorptive bone remodeling has often been discussed solely in terms of implant stiffness. With the femoral stiffness data, comparisons of implant-femur stiffness and a better understanding of stress shielding p h e n o m e n a are n o w possible. The term "mechanical compatibility" does not have a strict definition but implies some acceptable mechanical relationship between implant and femur in terms

of stiffness parameters. While the details are b e y o n d the scope of this study, it is pertinent to m e n t i o n that studies of bone remodeling with the AML prosthesis have indicated that the long-term ( > 10 years) resorptive remodeling response to small-diameter prostheses ( 10.5 m m and 12 ram) is quite acceptable, even with porous coating and roentgenographic signs of bone ingrowth along the full implant length. 8 In this study, these prostheses were found to be about two to four times less stiffthan the femur, in bending and torsion, over the distal two thirds of the implant length. These relative stiffness relationships provide a reasonable working definition of mechanical compatibility. From this arises the tempting hypothesis that acceptable bone remodeling might result with all stem sizes if similar conditions of mechanical compatibility were respected. As the data for the larger stem sizes indicated, this would require modifications in implant stiffness parameters, less so if titanium alloy is used instead of cobalt-chrome. The femoral stiffness data provide the requisite physiologic bases for such modifications.

Acknowledgments The authors thank Sara Aravena, CT scanning technician, and Mr. Nell D e n b o w for their collaboration.

References 1. Ashman RB, Rho JY: Elastic modulus of trabecular bone material. J Biomech 21:177, 1988 2. Bobyn JD, Mortimer ES, Glassman AH et al: Producing and avoiding stress shielding: laboratory and clinical observations. Ciin Orthop 274:79, 1992 3. Bobyn JD, Glassman AH, Goto H et al: The effect of stem stiffness on femoral bone resorption after canine porous coated total hip arthroplasty. Clin Orthop 261: 196, 1990 4. Cameron HU, Trick L, Shepard B et al: An international multi-centre study on thigh pain in total hip replacements. Scientific experiment. Annual Meeting of the American Academy of Orthopaedic Surgeons, New Orleans, LA, 1990 5. Carter DR, Hayes WC: The compressive behavior of bone as a~vo-face porous structure. J Bone Joint Surg 59A:954, 1977 6. DeMane M, Beals NB, McDowell DL et al: Porous polysulfone-coated femoral stems, p. 315. In Lemons JE (ed): Quantitative characterization and performance of porous implants for hard tissue applications. ASTM, Philadelphia, 1987 7. Engelhardt JA, Tomaszewski PR: Hip fixation and tip

Mechanical Compatibility of Noncemented Hip Prostheses

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

geometry: a theoretical model for thigh pain. Presented at the 35th Open Scientific Meeting of the Hip Society, Anaheim, CA, 1991 Engh CA, Bobyn JD: The influence of stem size and extent of porous coating on femoral bone resorption after primary cementless hip arthroplasty. Clin Orthop 231"7, 1988 ~alante JO: Determinants of stress shielding design vs. materials vs. interface. Presented at the 19th Open Scientific-Meeting of the Hip Society, Anaheim, CA, 1991 Goldstein SA: The mechanical properties oftrabecular bone: dependence on anatomic location and function. J Biomech 20:1055, 1987 Halawa M, Lee AJC, Ling RSM, Vangala SS: The shear strength of trabecular bone from the femur. Arch Orthop Traum Surg 92:19, 1978 Huttner W, Huttinger KJ: The use of carbon as an implant material, p. 81. In Morscher E (ed): The cementless fixation of hip endoprostheses. Springer-Verlog, New York, 1984 Jalim I, Barlin C, Sweet MBE: Isoelastic total hip arthroplasty: a review of 34 cases. J Arthroplasty 3: 191, 1988 James CM: The problem of thigh pain: current concepts in implant fixation program. Presented at the 5th Annual Meeting of Current Concepts in Implant Fixation, Orlando, FL, 1989 Keller TS, Mao Z, Spengler DM: Elastic modulus, bending strength, and tissue physical properties of human compact bone. J Orthop Res 8:592, 1990 Koeneman JB: Fundamental aspects of load transfer and load sharing, p. 241. In Lemons JE (ed): Quantitative characterization and performance of porous implants for hard tissue applications. ASTM, Philadelphia, 1987 Magee FP, Weinstein AM, Longo JA et al: A canine composite stem: an in vivostudy. Clin Orthop 235:237, 1988

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18. Morsher EW: Nine years' experience with isoelastic hip endoprostheses made of plastic material, p. 184. In Morscher E (ed): The cementless fixation of hip endoprostheses. Springer-Verlag, New York, 1984 19. Morsher EW, Mathys R, Henche HR: Iso-elastic endoprosthesis: a new concept in artificial joint replacement. p. 403. In Schaldach M, Hohmann D (eds): Advances in artificial hip and knee joint technology. Springer-Verlag, New York, 1976 20. Natarajan RN, Freeman P, Summer DR et al: A relationship between stress shielding and stem stiffness in the proximal femur after total hip replacement. Advances in Bioengineering, 17:307, 1990 21. Otani T, Whiteside LA, White SE: Strain distribution changes in the proximal femur caused by metallic and flexible composite femoral components under torsional load. Presented at the Open Scientific Meeting of Hip Society, Anaheim, CA, 1991 22. Pilliar RM, Camerson HU, McNab I: Porous surface layered prosthetic devices. J of Biomed Eng 10:126, 1975 23. Poss R: Natural changes in femoral bone mass and shape with age. Presented at the 19th Open Scientific Meeting of the Hip Society, Anaheim, CA, 1991 24. Skinner HB: Composite technology for total hip arthroplasty. Clin Orthop 235:224, 1988 25. Spector M: Low modulus porous system, p. 227. In Fitzgerald R Jr (ed): Noncemented total hip arthroplasty. Raven Press, New York, 1988 26. Summer DR, Tumes TM: The effects of femoral components design features on femoral remodeling, p. 143. In Fitzgerald R Jr (ed): Noncemented total hip arthroplasty. Raven Press, New York, 1988 27. Yoshioka Y, Siu D, Cooke TDV: The anatomy and functional axes of the femur. J Bone Joint Surg 69A: 873, 1987 28. Young WC: Roark's formulas for stress and strain. 6th ed. McGraw-Hill, New York, 1989

Appendix In this study, it was assumed that the femur behaved as an elastic straight cantilever beam (rigidly fixed at one end and free at the other end) u n d e r axial loads, bending m o m e n t s in two orthogonal directions, and torsional moments. These bending directions correspond to the lateromedio (frontal plane) and anteroposterior (coronal plane or out of the frontal plane) directions. The stiffness characteristics of a section are defined by two factors: the geometry of the section (or properties of the plane area) and the material properties (modulus of elasticity and rigidity). By definition, the geometric factors are: In axial stiffness [A x El, the total area (A) of a composite section i s e q u a l to the sum of the areas of its. c o m p o n e n t parts. Voids are taken

into account by subtracting the corresponding areas. In bending stiffness out of the frontal plane [Ix • El, the rectangular m o m e n t of inertia of the section area (or second m o m e n t of a n area) w~th respect to the x axis in the plane of the section (I• is the sum of the products obtained by multiplying each element of the area dA by the square of its distance from the x axis, that is. Ix

=

dA

y2

For example, the m o m e n t of inertia of a solid rectangle of dimensions b • d is Ix = bd3/12, which varies with the 4th p o w e r of dimension.

22

The Journal of Arthroplasty Vol. 8 No. 1 February 1993

In bending stiffness within the frontal plane [Ix x E], the rectangular m o m e n t of inertia of the section area with respect to the y axis the plane of the section (Iy) is the sum of the products obtained by multiplying each element of the area dA by the square of its distance from the y axis, that is, Iy = dA x 2 For the previous example, its m o m e n t of inertia with respect to the vertical axis is n o w Iy = b3d/12, which, as for I,,, varies with the 4th power of dimension. In torsional stiffness [J • G], tile polar m o m e n t of inertia of the section area with respect to the zaxis normal to the plane of the section (J) is the sum of the products obtained by multiplying each element of the area dA by the square of its radial distance from the axis r, that is:

J = dA r 2 and the polar m o m e n t of inertia of a solid rectangle given as an example is J = r4/12, which also varies with the 4th p o w e r of dimension. The material property used to calculate the axial and bending stiffness was modulus of elasticity (Young's modulus, E), which is the rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain for the condition of uniaxial stress within the proportional limit. For torsional stiffness, tlle modulus of rigidity (modulus of elasticity in shear, shear modulus, G) was used. The shear modulus is defined as the rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit.